THE IMPACTS OF THE FEDERAL AID HIGHWAY PROGRAM ON STATE AND LOCAL HIGHWAY EXPENDITURES by LEONARD SHERMAN S.B., Massachusetts Institute of Technology (1971) S.M., Massachusetts Institute of Technology (1971) Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology February, 1975 A Signature of Author. . . . . . . Department of Civil Engineepng, January 22, 1975 Certified by . . . . . . . . . . . . . . . Th9sis Supervisor Accepted byI..I...... Chairman, Departmental Committwon Graduate Students of the Department of Civil Engineering A P F 17 2ABSTRACT THE IMPACTS OF THE FEDERAL AID HIGHWAY PROGRAM ON STATE AND LOCAL HIGHWAY EXPENDITURES by LEONARD SHERMAN Submitted to the Department of Civil Engineering on January 22, 1975 in partial fulfillment of the requirements for the degree of Doctor of Philosophy This thesis investigates the impacts of the Federal Aid Highway Program on State and local highway expenditures. Our concern throughout the conduct of the research is to focus on this issue from a national policy perspective. Several recent events have led to an increasing interest in restructuring the Federal role in highway finance, most notably the controversy surrounding the passage of the 1973 Federal Aid Highway Act and the debate over post-Interstate System highway policy. Accordingly, the motivation of this research is a consideration of the design of and response to Federal Aid highway financing. The starting point is a review of the mechanics of State and Federal highway finance. Special attention is given to the unique aspects of the Federal Aid Highway Program (FAHP) and the attendant implications for empirical modelling. The thesis then proceeds to develop a theory of State highway expenditure behavior. Our purpose here is to draw atten- tion to the premise that State highway expenditure behavior depends not only on the level of available Federal grants-in-aid, but on the struc- tural characteristics of the grant program as well. The theoretical models suggest that for the Interstate program, Federal grants have stimulated State expenditures that would most likely have not been made in the absence of the grant program. This behavior is contrasted with the experience on the non-Interstate Federal Aid programs where the theoretical models suggest that Federal grants have had a relatively insignificant impact on States' expenditure levels. The theoretical hypotheses of State expenditure behavior are then validated with econometric models designed to explore the factors influencing States' total highway expenditure levels and the alloca- tion of States' highway budgets amongst alternative expenditure cate- gories. The models are estimated using a pooled data sample compris- ing the forty eight mainland States over a fourteen year analysis period. 3Evaluation of the empirical results from the expenditure models suggest several basic policy recommendations for future Federal highway policy. Most notably, it is recommended that the U.S. Department of Transporta- tion undertake a grant consolidation program, eliminate existing grant matching provisions, and restructure current apportionment factors and Interstate Highway Trust Fund revenue mechanisms. Thesis Supervisor: Marvin Lee Manheim Professor of Civil EngineeringTitle: 4 ACKNOWLEDGEMENTS Throughout the course of this research, I have benfitted from the advice, encouragement and assistance from many individuals. The contri- butions of Professor Marvin L. Manheim, my thesis advisor to the devel- opment of this study extend far beyond his valuable suggestions on par- ticular phases of the research. In a larger sense, he has been singlu- larly influential in stimulating my interest in the anlysis of trans- portation policy issues. Professors Paul Roberts, Wayne Pecknold, and Moshe Ben-Akiva, as members of my doctoral committee provided several valuable ideas and suggestions that aided in both the develop- ment of the theoretical analyses and in the writing of the final manu- script. I would also like to express particular appreciation to Pro- fessor Richard Tresch of Boston College. I have benfitted greatly from reading his own research in this field. And as a member of my doctoral committee, Professor Tresch's advice and encouragement have contributed greatly to the development and presentation of the ideas in this dissertation. Several individuals in the U.S.Department of Transportation also deserve special mention for their role in assisting in the conduct of this research. Ira Dye of the Office of Transportation Planning Analysis is gratefully acknowledged for his constant encouragement and for arranging the financial support by DOT that allowed this study to be undertaken. Arrigo Mongini and George Wiggers, also in the Office of Transportation Planning Analysis have been extremely helpful in contributing numerous keen insights throughout the conduct of this research. In addition I would like to express my appreciation to Ed Gladstone and Bill McCallum of the Federal Highway Administration for freely giving of their time, advice and encouragement during the for- mative stages of this research. To my friends and colleagues at M.I.T., in particular Frank Kop- pelman, Uzi Landau and Steve Lerman, I would like to express my thanks for their constant help alon the way. Bronwyn Hall of the Harvard Bureau of Economic Research must also be acknowledged for jer assis- tance in ironing out problems encountered in using the computer for the econometric analysis phases of this research. And finally, my thanks go to the numerous people who contributed greatly to the preparation of the final document: Carol Walb, Charna Garber, Charlotte Goldberg, Rebecca Lord and Shulamit Kahn. 5TABLE OF CONTENTS Page TITLE PAGE........................... ABSTRACT............................. ACKNOWLEDGEMENTS..................... TABLE OF CONTENTS.................... LIST OF FIGURES... .............. LIST OF TABLES................. CHAPTER I: Introduction and Summary.. I.1 Motivation for Research 1.2 Summary of Previous Studies 1.3 Modelling Strategy 1.4 Theoretical Models of State 1.5 The Empirical Study 1.6 Summary and Conclusions 1.7 Organization of the Thesis Expenditure Behavior CHAPTER II: The Mechanics of Highway Finance: A Factual Settin ........................ II.1 Introduction 11.2 Historical Development of the Federal Aid Highway Program i. The Early Federal Aid Highway Acts ii. The Federal Aid Primary System iii. The Federal Aid Secondary System iv. Urban Extensions of the Primary and Secondary Systems v. The Federal Aid Urban System 1 2 4 5 11 15 18 18 22 28 33 36 45 47 50 50 52 52 64 65 66 66 6Page vi. Traffic Operations Projects to Increase Capacity and Safety 69 vii. The Federal-Aid Interstate System 69 viii. Structural Revisions to the FAHP Incor- porated in the 1973 Federal-Aid Highway Act 71 11.3 The Mechanics of the Interstate Highway Trust Fund 74 i. Program Structure 74 Source of Federal Funds 74 Total Expenditure Levels 74 Expenditure Restrictions 77 Local Recipients of Federal Funds 79 Authorization Cycle 79 Apportionment Method 79 Matching Provisions 80 Sources of Local Matching Funds 80 ii. Time Lag Structure 87 iii. Aspects of Trust Fund Taxation 97 Definitions of the Revenue Terms 98 Income Redistributive Properties of the IHTF 100 Equity Considerations in Admini- stering the IHTF 112 II.4 Comparison of the Federal-Aid Highway Program With the Federal Public Transportation Assistance Program 119 Sources of Federal Funds 119 Total Expenditure Levels 119 Authorization Cycle 120 Apportionment Method 120 Matching Provisions 121 Expenditure Restrictions 121 7Page Local Recipients of Federal Funds 122 Sources of Local Matching Funds 122 11.5 Summary and Conclusions 124 CHAPTER III: The Federal-Aid Highway Program: The Ana- lytics of Design and Response................ 129 III.1 Introduction 129 111.2 Fiscal Federalism - The Normative Aspects of Federal Highway Grant Program Design 133 i. The Theory of Intergovernmental Grants 134 ii. Functional Grants as Solutions 138 iii. Practical Limitations of the External Benefit Criterion 142 iv. Additional Goals of the Federal Aid Highway Program 146 v. Theoretical Aspects of Policy Evaluation 150 111.3 The Analytics of State Responses to Federal Grants 153 i. The Basic Model 154 ii. Addition of a Conditional Matching Open- Ended Grant 156 iii. Analysis of Conditional Matching Close- Ended Grants 162 iv. Evaluation of Other Grant Program Structures 169 v. Summary of the Responses to Alternative Grant Structures 174 vi. Qualifications of the Theoretical Analyses 181 111.4 The Analytics of State Responses to Federal Grants: The Benefit/Cost Investment Model 186 i. A Hypothetical Example 186 ii. A liagrammatic Description 193 8Page iii. Conclusions from the Benefit/Cost Investment Model 195 111.5 Observed Expenditure Patterns: The Impact of the ABC and Interstate Programs 198 i. Data Analysis of the ABC Highway Program 199 ii. Data Analysis of the Interstate Highway Program 203 111.6 Summary and Conclusions 208 CHAPTER IV: Development of the Total Expenditure Model.... 211 IV.1 Introduction 211 IV.2 Derivation of the Model 213 IV.3 Estimation Techniques for the Total Expen- diture Model 218 Error Component Analysis 222 IV.4 The Data Set and Modelling Considerations 229 i. The Socio-Economic Descriptors 231 ii. The Measurement of Highway Capital Stocks 239 iii. Descriptors of Financing Conventions and Instiutional Characteristics 247 iv. The Highway Grant Terms 248 v. The Price Deflators 251 IV.5 Research Strategy and Conseiderations for Model Interpretation 253 i. The Total Expenditure Model: Consider- ations for Model Interpretation 253 ii. Data Set Stratification 256 IV.6 Empirical Results 258 i. The Federal Grant Terms 263 ii. Differences in Grant Term Coefficients Between the Two Data Subsets 271 9Page iii. Interpretation of the Coefficient Estimates of the Socio-Economic and Institutional Descirptor Variables State Size Variables The Income Measures Institutional Characteristics The Existing Inventory Measure iv. The Deflated Data SEt v. Tests of Equality Between Coefficients in the Two Data Subsets IV.7 Summary and Conclusions CHAPTER V: Development of the Short Run Allocation Model.. V.1 Introduction V.2 Derivation of the Short Run Allocation Model V.3 Statistical Properties and Estimation Procedures V.4 Modelling Considerations and Data Requirements Equation 1 - The Interstate Construc- tion Share Equation 2 - The Primary System Con- struction Share Equation 3 - The Secondary System Con- struction Share Equation 4 - The Non-Federal-Aid Sys- stem Construction Share Equation 5 - The Maintenance Expendi- ture Share Equation 6 - The "Other" Expenditures Share V.5 Empirical Results - Parameter Estimates of the SRAM V.6 Evaluation of the Elasticities and Derivatives From the Short Run Allocation Model 272 272 275 275 277 277 280 285 289 289 292 307 313 318 320 321 323 324 326 327 339 - 10 Page V.7 Integration of the Results From the Total Total Expenditure Model and the Short Run Allocation Model: Long Run Responses 351 i. Socio-Economic Charactersistics 362 ii. Highway System Charactersistics 363 V.8 Summary 366 CHAPTER VI: Summary and Conclusions...................... 368 VI.1 Summary of the Thesis 368 VI.2 Policy Implications of the Empirical Findings 373 VI.3 Limitations of the Empirical Approach and Directions for Further Research 380 Bibliography............................................ 383 Biographical Summary ................................ 390 Appendix A: Estimated Parameter Values of the Long Run Revenue Policy Model...................... 391 Appendix B: Derivation of Derivatives and Elasticities from the Expenditure Models................427 Appendix C: Derivatives and Elasticities from the Two Expenditure Models....................440 11 LIST OF FIGURES Figure Title Page 1.3.1 State Highway Investment Behavior........... 29 1.4.1 The Total Expenditure Model ..................... 37 1.4.2 The Short Run Allocation Model................. .. 39 1.4.3 Elasticities of the Categorical Expenditures.... 42 11.2.1 State Expenditures on the Federal Aid Systems......................................... 62 11.3.1 States Having Anti-Diversion Consti- tutional Amendments............................. 86 11.3.2 Frequency Distribution of Interstate Obligations..................................... 90 11.3.3 Frequency Distribution of ABC Obligations ....... 91 11.3.4 Federal Aid Highway Program Lag Structure ....... 94 11.3.5 Interstate Highway Trust Fund Expenditures and Receipts.................................... 96 111.2.1 Internal and External Highway Benefits and Costs.................................... 136 111.3.1 Highway Investment Indifference Curves.......... 155 111.3.2 Analysis of Conditional Matching Open- Ended Grants............... .............. 157 111.3.3 Grant Responses for Alternative Price Subsidies....................................... 160 111.3.4 Analysis of Conditional Matching Close- Ended Grants.................................... 163 111.3.5 Affect of Grant Ceilings and Price Subsidy Levels................................ 168 12 LIST OF FIGURES (Continued) Figure Title Page III.3.6 Analysis of Conditional, Non-Matching Close-Ended Grants.............................. 170 III.3.7 Analysis of Responses to Grants for Functions Not Previously Undertaken by State Governments................................... 173 111.3.8 Summary of State Responses to Alternative Federal Grant Structures........................ 175 111.4.1 Illustrative Example of the Benefit/Cost Investment Model.............................. 188 111.4.2 Diagrammatic Illustration of the Benefit/ Cost Investment Model.......................... 194 IV.4.1 The Total Expenditure Model..................... 230 IV.4.2 Lorenz Curves................................... 237 IV.4.3 Depreciation Functions.......................... 246 IV.6.1 Estimation Results, Total Expenditure Model Number SUl............................... 259 IV.6.2 Estimation Results, Total Expenditure Model Number SU12............................... 260 IV.6.3 Estimation Results, Total Expenditure Model Number SU6............................... 261 IV.6.4 Estimation Results, Total Expenditure Model Number TUl2............................... 262 IV.6.5 Estimation Results, Total Expenditure Model Number SU21.............................. 264 IV.6.6 Estimation Results, Total Expenditure Model Number SU31............................. 265 LIST OF FIGURES (Continued) Figure IV.6.7 IV.6.8 IV.6.9 V.2.1 V.2.2 V.4.1 V.5.1 V.5.2 V.5.3 V.5.4 V.5.5 V.5.6 V.5.7 V.5.8 Title Estimation Results, Total Expenditure Model NumberS ......................... Estimation Results, Total Expenditure Model Number 5D21.. ...................... Estimation Results, Total Expenditure Model Number SD3l ......................... Constrained Estimation Form for the Short Run Allocation Model................ Corner Solutions in the SRAM............... The Short Run Allocation Model............. 48 State Sample, OLS SRAM Product Form Estimation Results......................... 48 State Sample, GLS SRAM Product Form Estimation Results............................. 7 State Sample, OLS SRAM Product Form EstimationResults..................... 7 State Sample, GLS SRAM Product Form EstimationResults ....................... 41 State Sample, OLS SRAM Product Form Estimation Results.................. 41 State Sample, GLS SRAM Prodcut Form Estimation Results..........................0 48 State Sample OLS SRAM LExponential Form Estimation Results.....,................... 48 State Sample. GLS SRAM Exponential Form EstimationResults ........................ Page 256 267 268 300 304 316 329 330 331 332 333 334 335 336 14 LIST OF FIGURES (Continued) Figure Title Paje V.6.1 48 State Sample Short Run Model Derivatives..... 343 V.7.1 48 State Sample Long Run Model Derivatives...... 356 V.7.2 48 State Sample Long Run Model Elasticities.... 359 15 LIST OF TABLES Table Title Page 11.2.1 Year in Which First State-Aid Law Passed and Highway Department Created.............. 54 11.2.2 Date of Authorization or Creation of State Highway Systems........................... 58 11.2.3 Factors Employed in Apportioning Federal Aid System Funds (Prior to Federal Aid Highway Act of 1973) ....................... 67 11.2.4 Current Factors Employed in Apportioning Federal Aid System Funds...................68 11.3.1 Trust Fund Revenue Sources............ ...... 75 11.3.2 Interstate Highway Trust Fund Revenue By Source - Calendar Year 1970............... 76 11.3.3 Interstate Highway Trust Fund Receipts and Authorizations................. .......... 78 11.3.4 Variable Matching Percentage for States With More Than Five Percent of Public Lands.......... 81 11.3.5 State Highway Finance: Highway Bond Sales, 1961-1971...................................... 83 11.3.6 Distribution of Person Miles by Income and Type of Transport....................... 102 11.3.7 Distribution of Auto Travel Patterns by Household Income Levels.........................104 11.3.8 Relationship of Mode Choice and Household Income for Home-to-Work Trips................... 105 11.3.9 Relationship of Average Commute Time for Home- to-Work Trips by Household Income............... 106 16 LIST OF TABLES (Continued) Table Title Page 11.3.10 Comparison of Estimated State Payments to the Highway Trust Fund with State Receipts from the Highway Trust Fund and Federal Aid Apportionments; Fiscal Years 1957-1970............................... 108 11.3.11 Distribution of 1968 Mileage of Travel On and Off Federal Aid Systems by Functional System in Urban Areas by Population Group.............................. 114 11.3.12 Incremental Costs of Rush Hour Travel by Various Modes.............................. 116 11.3.13 Total Federal Trust Fund Expenditure Allocation versus Tax Payments.................. 118 111.3.1 Summary of Equilibrium Expenditure Patterns..... 158 11.3.2 Comparison of Equilibrium Points for Alternative Grant Structures Shown in Figure 111.3.4................................ 165 11.3.3 Summary of Grant Responses.................... 180 111.5.1 State Expenditures Over and Above Minimal Matching Requirements Expressed as a Fraction of Total Expenditures on "ABC" Systems................................. 200 111.5.2 ABC System Expenditures/Grants: New York, 1963........................................ 204 111.5.3 State Expenditures Over and Above Minimal Matching Requirements Expressed as a Fraction of Total Expenditures on the Interstate System.......................... 206 IV.4.1 Percent of Population Residing in Urban Places With More Than 5000 Residents.................... 234 17 LIST OF TABLES (Continued) Table Title Page IV.4.2 Measures of Income Inequality, 1963............. .240 IV.4.3 Consumer Price Index........................... 252 IV.6.1 Direction of the Influence of the Explanatory Variables on Total State Highway Expenditures...........................278 IV.6.2 Tests of Selected Subset Coefficient Equalities.................................... 284 18 CHAPTER I INTRODUCTION AND SUMMARY I.1 Motivation for Research This study is concerned with the impact of Federal aid financing on the highway expenditures of State and local governments. Tne moti- vations for this research are numerous. First, it is aimed at provi- ding useful input to the ongoing debate over structural changes in the Federal aid highway program. Although Federal responsibility for the financing of highway facilities has been increasing in recent years, both in terms of the extent of activity and the amounts of money involved, the basic principles upon which the Federal aid highway program operates was established over 50 years ago in the Federal-Aid Act of 1916. For the first time proposals have been advanced which, in one case will allow Federal monies to be used for non-highway urban mass transit systems,I and in another, would establish non-modally aligned block funding for a broad spectrum of transportation activities (including non-capital expenditures).2 In order to evaluate the con- sequences of these, and other program variants, it is first necessary to assess the impacts of the existing Federal grant-in-aid program. By any measure, the Federal aid highway program represents a large expenditure of funds. Its magnitude, combined with its singular status as a restricted trust fund, provide a second motivation for As embodied in the Federal-Aid Highway Act of 1973. 2As embodied in S.1693: the Special Transportation Revenue Sharing Act of 1969. 19 focusing this analysis on the Federal aid highway program. Federal expenditures for highways in 1970 amounted to $4.84 billion,I second only to Federal welfare payments ($6.47 billion2). Moreover, Federal highway outlays account for a large percentage of total (by all units of government) highway expenditures,, averaging 27% nationwide, and over 60% in some States (1970).3 Consequently, changes in the struc- ture of the Federal aid highway program (e.g., amounts of Federal money available, changes in the matching provisions, etc.) may cause significant changes in State and local governmental highway invest- ment behavior. Viewed in this perspective, the structure of the Federal aid highway program is a significant policy tool with which the U.S. Department of Transportation can influence the pattern of highway investments. 4 To exploit this potential, an understanding of the dynamics of State and local transportation investment be- havior is essential. A third motivation for focusing this investigation on the Federal aid highway program as opposed to the broader question of IFederal Highway Administration, HIGHWAY STATISTICS, 1970. 2Advisory Commission on Intergovernmental Relations, STATE-LOCAL FINANCES: SIGNIFICANT FEATURES AND SUGGESTED LEGISLATION, 1972 ed. 3ibid. 4In this regard, the federal aid highway program has been used as a tool to counteract cyclical fluctuations in the Nation's economy. During the recession of the late 1950's, Congress appropriated $600 million (the so-called "D" funds) in addition to the appropri- ations for the Interstate and "ABC" programs, for the purpose of stimulating governmental expenditures. For a description of the State response to the D fund program, see Friedlaender, A.F., "The Highway Program as a Public Works Tool," pp. 93-101, in Ando, A., 1 20 intergovernmental fiscal relations (in all functional areas ), is that it allows for a more detailed analysis of the complexities involved in State and local investment decision-making behavior. There exists ample evidence to suggest that States' expenditure responses to Federal functional grants (e.g. highways, welfare, education, etc.) exhibit more significant trade-offs amongst expenditures within a particular function than between different functions. Federal grants for public assistance provide one example. Since their inception in 1935, these grants have been restricted to specific categories of needy people,2 leaving general welfare payments as the sole responsibility of States and metropolitan areas. The experience has been that the States were liberal in expanding the welfare programs in the Federally eligible categories, and parsimonious in spending for general (non-aided) relief.3 et al., STUDIES IN ECONOMIC STABILIZATION, The Brookings Institution, 1968. In this thesis, we will be more concerned with the allocative impacts of the Federal aid highway program than with the use of Federal funds in conjunction with a stabilization policy. We will raise the issue of whether Federal aid stimulates State expenditures (i.e. over and above the amounts required to simply match Federal funds). IFor a general discussion on the characteristics of the various functional Federal aid programs, see: Break, G.F., INTERGOVERNMENTAL FISCAL RELATIONS IN THE UNITED STATES, The Brookings Institution, 1967; Maxwell, J.A.,, FINANCING STATE AND LOCAL GOVERNMENTS, The Brookings Institution, Revised Edition, 1969. 2There are currently five major Federal aid welfare programs: Old Age Assistance, Aid to the Blind, Aid to the Permanently and Temporarily Disabled, Aid for Dependent Children, and Medicaid. 3Maxwell, J.A.,"Federal Grant Elasticity and Distortion," National Tax Journal, Vol XXII , No. 4, pp. 550-552 Highways present perhaps an even more striking example where 21 State/local responses to Federal grants are more manifest in expen- diture adjustments between particular highway categories, than in overall adjustments to the State budget. Here too, Federal grants are directed at designated types of highways,I leaving expenditures on other highway-related activities to the discretion of the States. Moreover, State restrictions on the use of their own trust fund monies2 indicate that there is minimal interaction between investment decisions in the highway "sector" and other sectors (e.g. welfare, health, education, etc.) of the State budget. In short a basic premise of this research is that investigation of the impacts of the functional Federal grants in aid must explicitly consider State/local expenditure responses within the aided function. Thus, we will be more concerned with the magnitude of State highway expenditures and the allocation of these expenditures amongst various highway programs, than in attempting to trace the overall State/local budget responses to Federal grants in terms of broadly defined functions. IFor example, Federal aid highway programs include capital grants for Interstate, Primary ("A"), Secondary ("B"), Urban Extension Roads ("C"). 2Twenty eight States have "anti-diversion" (State) constitutional amendments. In all but four of the 50 states, gas tax and motor vehicle revenues are earmarked exclusively for highway related expenditures. 1.2 Summary of Previous Studies 22 Whether we approach the subject from a normative or a postive stance, the central issue is an analysis of the consequences of al- ternative congressional actions. From a normative perspective, we must know how the marketI reacts to various program structures so that we can choose a policy which in some sense optimizes public sector decision making. From a positive analysis stance, we must establish a framework for predicting how the market will react to specific policies (in particular, the existing program structure), so that we can determine directions for incremental changes in program structure. Thus, the central issue is a consideration of the design of, and the response to Federal aid highway financing. These questions have not gone totally unanswered in the lit- erature, (although few researchers have chosen to focus their efforts specifically on the highway sector). And yet, despite the formidable array of recent statistical articles which purport to measure the affects of federal grants on State/local spending, we do not as yet have conclusive answers to such questions as: Have increasing levels of Federal highway aid stimulated additional State/local spending, or have Federal grants served mainly as a substitute for State expen- ditures? How will the recently increased Federal share of "ABC"2 In this context, we make use of the term "market" to signify the investment pattern of State and local transportation decision-making units. 2The Federal-Aid Highway Act of 1970 stipulated that as of fiscal year 1974, the Federal share of Primary, Secondary, and Urban Extension ("ABC") expenditures would increase from 50% of project cost to 70% of project cost. 23 road expenditures affect the allocation of highway investments in Wisconsin? Will this behavior differ significantly from that of West Virginia (or any other State for that matter)? If so, what factors -- social, economic, demographic, and political will temper their separate reactions? Our task would be relatively simple if we can address these questions by simply adapting existing empirical studies to an investi- gation of highway investment behavior. This is not the case however, because neither of the two general approaches to estimating State/local expenditure models advanced to date are appropriate for our purposes. The first, and most common approach found in the literature has been advanced by Sacks and Harris, Osman, and researchers.I The basic method here is to estimate a model of State and Local expenditures in a variety of functional categories, as a function of Federal grants and socio-economic indicators. The National Tax Journal, which has served as a forum for these articles since 1957, has published each new study on the basis of the: 1) introduction of a new variable which apparently increases the explanatory power of the models Sacks, Seymour, and Richard Harris, "The Determinants of State and Local Government Expenditures and Interfovernmental Flow of Funds," National Tax Journal, Vol. XVII, No. 1 Osman, J.W., "The Dual Impact of Federal Aid on State and Local Government Expenditure," National Tax Journal, Vol XIX, No. 4 Gabler, L.R., and J.I. Brest, "Interstate Variations in Per Capita Highway Expenditures," National Tax Journal, Vol. XX, No. 1 Fisher, Glenn W., "Interstate Variations in State and Local Government Expenditures," National Tax Journal, Vol. XIV, No. 2 24 2) incorporation of different structural model forms -- e.g. log-linear as opposed to linear 3) discussion of a new technique for including grants-in- aid as explanatory variables. The basic problem with these studies is that they proceed with- out an underlying model of individual State preferenczs. No account is taken of the States' budget constraint, and as such, the essential interdependence between functional activities (i.e. that a decision to increase expenditures on one function must simultaneously by compensated by reduced expenditure on others, or an increase in taxes) is ignored. A second weakness with these approaches is their failure to distinguish between long and short run State responses. In all but O'Brien's study,1 a single year cross section of State expenditures is regressed against explanatory variables (including Federal grants) of the same year. This raises two immediate questions, both related to inferring time series information from cross section data. First we must question the validity of assuming (as the previously cited studies implicity do) that States and localities react fully and Kurnow, Ernst, "Determinants of State and Local Expenditures Reexamined", National Tax Journal, Vol. XVI, No. 3 Fisher, Glenn W., "Determinants of State and Local Government Expen- ditures: A Preliminary Analysis," National Tax Journal Vol.XIX , No.3 Bishop, George A., "Stimulative Versus Substitutive Effects of State School Aid in New England," National Tax Journal, Vol.XVII , No.2 Pogue, Thomas F., and L.G. Sgontz, "The Effect of Grants-in-Aid on State-Local Spending," National Tax Journal, Vol.XVIII, No. 1 O'Brien, T., "Grants-in-Aid: Some Further Answers," National Tax Jour- nal, Vol. XXIV, No. 1 Sharkansky, Ira, "Some More Thoughts About the Determinants of Govern- ment Expenditures," National Tax Journal, Vol.XXII , No. 4 1op cit 25 immediately to changes in the explanatory variables. And second, we must question the value of "one-shot" cross section models in light of the likelihood of inter-temporal instability of the cross section estimates. These questions will be considered in greater detail in Chapter V. We raise these issues here in order to stress the inadequate treatment of the impact of Federal grants-in-aid on State and local highway expenditures advanced to date. In summary, our basic objec- tion to these studies (and at the same time, a starting point for the methodology to be advanced by this study) are: 1) they fail to distinguish intra-(highway) function allocation tradeoffs from the less significant inter- function State allocation decision-making process 2) they fail to account explicitly for the influence of a constrained budget on allocation choices 3) no distinction is made between short and long run ex- penditure responses 4) a limited data set - usually a single year cross section is employed in the estimation of models. Some of these objections are overcome in the second general approach that has been taken in estimating the affects of Federal grants-in-aid on State and local expenditures. The common theme of the studies advanced by Henderson1, Gramlich2, and Tresch3 , is that IHenderson, James M., LOCAL GOVERNMENT EXPENDITURES: A SOCIAL WELFARE ANALYSIS, Unpublished Ph.D. Thesis, University of Minnesota, 1967. 2Gramlich, Edward M., "Alternative Federal Policies for Stimulating State and Local Expenditures: A Comparison of Their Effects," National Tax Journal, Vol. XXI, No. 2. 3Tresch, Richard W., ESTIMATION OF STATE EXPENDITURE FUNCTION, 1954- 1969, Unpublished Ph.D. Thesis, M.I.T., 1973. States' expenditure decisions can be described in a manner analogous 26 to the (individual) consumer utility maximization framework. Thus, the starting point of these analyses is the specification of the States' utility function (in terms of the variety of functional activ- ities, i.e. expenditure categories) and a budget constraint. The actual demand relations for public good consumption which are empirically estimated are derived from first order utility maximization conditions. Our criticism here is not so much with the theoretical under- pinnings of these models1, as with their treatment of the highway expenditure question. Neither the Henderson2 or Gramlich3 study dis- aggregate State and local expenditures by functional (in particular, highway) category. As such, their results are not germane to the questions which motivate the present study. The Tresch thesis was the first study to employ both cross It is important, however, to recognize that adoption of the State- as-utility-maximizer framework implies rather heroic assumptions on the political and administrative realities of State expenditure behavior. In particular, the use of social indifference maps imply the existence of a well defined, consistent set of preferences for publically provided goods. If we choose to regard these preferences as belonging to a governmental body, then we must assume that the legislature accurately expresses societal preferences. Furthermore, we must assume that the often conflicting preference orderings of different governmental agencies can be subsumed into one -- in some sense "final" -- utility mapping. See chapter III. 2Henderson's model is directed towards explaining the factors in- fluencing inter-county differences in per-capita total county govern- ment spending. His data set is a single year 3080 county cross section. 3Gramlich uses a time series formulation on quarterly national account (all State aggregate) data. As such, his results explain neither inter-function, nor inter-State expenditure behavior. section and time series data in estimating State expenditures in a 27 variety of functional areas (including highways) within a utility maximizing model framework. He correctly addresses the second and fourth weaknesses (cited on page 25 ) of the previous studies by ex- plicitly accounting for the influence of the States' budget constraint on the provision of publically provided goods, and testing for the stability of his cross section estimates over time. But he fails to distinguish between intra and inter-function expenditure tradeoffs, and ignores possible time lagged expenditure responses. These omis- sions are particularly serious for the highway sector.I The structure of Tresch's model "explicitly recognizes the ,2 simultaneous nature of State expenditure decisions, whereas we have argued that the States' highway budgeting and decision making insti- tutions operate quite apart from other State functional expenditure decisions. Because the underlying structure of his model assumes an expenditure interaction which is not relevant, it is not surprising for Tresch to conclude that "the transportation equation is most notable for what is missing, rather than the single variable (per- centage of State population living in urban areas) that entered significantly."3 1Tresch focuses his research on State welfare expenditure behavior. Since these expenditures are financed from States' general tax revenues (as are other non-highway expenditures), and Federal grants are provided on a year-to-year basis (i.e. there is no "grace period" for grant obligation analogous to the highway program), his assumed structure seems reasonable. The problem is that he applies this structure to the estimation of highway expenditure response. 2Tresch, op cit, page 21 3ibid, page 374. Variables that proved insignificant include: driving age population, Federal Highway grants, population growth rates, all income variables, and ratio of debt to total revenues. 28 1.3 Modelling Strategy The basic premise of this research is that States' highway invest- ment behavior can be separated from the overall State budgetary process. In this context, it is useful to distinguish between State highway revenue (or total expenditure) policy -- i.e. long range fiscal planning, and allocation policy -- i.e. short range project programing. In the simplest sense, we can say that policy decisions in the first category determine the level of State highway expenditures over several years, while the second policy determines the allocation of a (predetermined) budget amongst alternative geographical areas and highway projects within the State on a year-to-year basis. Figure I.1 summarizes the hypothesized structure of highway investment behavior that will be adopted in this study. The depicted structure is recursive in nature, wherein the determination of highway revenue is non-project specific, and allocation policy reflects project selection given a fixed budget. The fiscal planning policy model is based on the States' widespread use of Needs Studies.I Perceived needs (expenditures), K are deter- mined by design standards (d), traffic and socio-economic indicators (A), institutional characteristics and financing conventions (I), and the age and mix of the existing highway stock (K). Given the gap Needs Studies develop a State's perceived highway expenditure level necessary to provide road service at a level consistent with current standards. All States have conducted Needs Studies, both for fiscal planning purposes, and in conjunction with the FHWA's National Highway Needs Study. 29 STATE HIGHWAY INVESTMENT BEHAVIOR {I} + REVENUE/FISCAL {d} + {G}PLANNING POLICY F]+ {A} + KI {T},B3 + [R] +[ET] {A} {GF [{E}] ALLOCATION POLICY {K} {I} {A} NOTATION * + {dJ E {A} E {I} {K} B K* GFGF {T} B B [R) (E9E {GF} {E} B vector of values of bracketed term decision stage desired value of variable design criteria (standards) socio-economic descriptors institutional characteristics mix and age of existing highway stock desired highway plant ("needs") total amount of Federal highway grants highway-related State tax rates amount of bond obligation assumed highway-related revenue total highway expenditures program components of Federal aid highway expenditures on each of several categories Figure 1.3.1 30 between perceived (desired) highway stock K , and available revenues -- determined by existing tax rates CT), tax base, (A), approved bond issues B, and Federal grants, GF -- the State exercises its adopted revenue policy by adjusting tax rates, seeking new bond issues, and possibly effecting transfers to or from State general tax revenues. These policy decisions ultamiately determine available highway revenues R, and total State highway expenditures ET' While the administrative and political realities of altering tax rates and debt obligation inhibit quick adjustments to changes in costs and demand 1, the project selection (programming) process operates on a relatively short cycle time.2 In figure I.1, allocation policy is reflected by the choices of expenditure levels (E), i.e. the component categories (Interstate, Primary, Secondary, and maintenance, etc.) of highway expenditure. These choices are influenced by the categorical provisions of Federal aid (GF), the fixed State highway budget R (as determined by revenue policy), and the traffic and socio-economic, and institutional characteristics of the State. The specification of the empirical models of total expenditure and allocation policy that are empirically estimated in this thesis follow the block recursive structure shown in figure I.1. In its simplest form, the total expenditure model asserts that: IBond approval is usually issued over a two to five year period. The average duration between tax rate adjustments is even longer -- some- what over ten year during the 15 year period 1951-1965. 2We refer here to the time required to obligate funds for particular projects (in response to changes in Federal aid, travel demand, etc.), not the construction time to complete individual projects. 31 (1) TOTAL STATE HIGHWAY GAP BETWEEN EXISTING AMOUNTS OF EXPENDITURES FROM = f AND DESIRED HIGHWAY , FEDERAL H/W OWN RESOURCES STOCK GRANTS REC'D. The allocation model builds on the study of Treschl where the States' highway investment demands for each expenditure category are derived as first order conditions2 from a utility function and budget constraint (where the budget constraint is determined in the revenue policy model) specification. We argue in chapter III that adoption of the utility maximization framework does not necessarily impose an un- realistic assumption on the motivations of State highway investment behavior. In fact, the fundamental premise of our model specification is simply that States allocate their fixed highway budget so as to maximize their derived benefits (utility)3 . To state the allocational process formally, let Ei represent State expenditure on category i; ET represent total expenditures from the State's own resources; GF represent total Federal aid received by the State. The model asserts that States allocate their budget so as to maximize their utility, U: lop cit 2We refer to the optimization conditions that requires marginal utility to equal marginal cost for each investment alternative. 31t should be noted here that this study is largely limited to allocational problems, and questions of economic efficiency. We will not dwell on the distributional implications of specific highway tax systems or investment decisions. Nor will we raise the issue of whether the States' investment behavior truly represent the preferences of a voting polity, or simply repre- sent a set of decisions made by an isolated bureaucratic agency. 32 (2) max U = U(EI , E2,..., En) subject to Ei = ET + GF We are not directly concerned with the utility function itself but with first order maximization conditions which provide the investment relations:1 (3)EXPENDITURES STATE SOCIO- TRANSPOR- FEDERAL TOTAL DEVOTED TO = g ECONOMIC AND TATION AID FOR HIGHWAY CATEGORY i INSTITUTIONAL CHARAC- CATE- REVENUE CHARACTERISTICS, TERISTICS, GORY i, The essential structure of the revenue policy model and the allocation policy model have been presented in this chapter in their simplest form. We have ignored for the moment, specification of appropriate dynamic structures, the distinction between the price and income effects of Federal grants, and the specification of a capital stock adjustment process. These details are left for later chapters. Our purpose in briefly outlining the model structure here is to indi- cate the differences in the approach that will be followed in this thesis from the previous studies in this area. IThe derivation of these first order condition relations requires an assumption on the fom of the utility function. The derivation is discussed fully in chapter V. 33 1.4 Theoretical Models of State Expenditure Behavior One of the major findings of this research is that both the level and structure of Federal grant programs influence State expend- iture behavior. It is useful to characterize a grant structure according to the following provisions: --categorical vs. non-categorical --matching vs. block funding --open-ended vs. close-ended The first distinction relates to whether the grant is restricted to expenditure on specific activities. The second classification dis- tinguishes grants requiring specified matching funds from grants with no matching provision. Finally, the open vs. close-ended classifica- tion distinguishes grant programs with predetermined authorization ceilings from those programs placing no limit on available Federal Aid. The current Federal Aid Highway Program (FAHP) is an example of categorical, matching close-ended grants. A transportation reve- nue sharing program would exemplify non-categorical, close-ended block funding. While the empirical models employed in this research are perfectly general (in the sense that they may be used to assess the expenditure impacts of any grant structure) , the fact is that the structure of the FAHP did not change over our analysis period (1957- 1970). For this reason, it is important to develop theoretical models that enable the formulation of hypotheses describing the expected State expenditure responses to various structural variants of the FAHP. Two theoretical models of State expenditure behavior are 34 advanced in this thesis -- one based on an application of consumer allocation theory and the other based on a simple benefit/cost investment criterion. Although these theoretical analyses apparently differ with respect to their underlying assumptions, in fact the con- clusions drawn from both approaches are quite similar. Both the models draw attention to the rice and income effects introduced by Federal grants, and proceed to demonstrate how State responses will differ according to the presence of one or both of these grant charac- teristics. In simplest terms, a price effect refers to the allocational responses to grants which effectively reduce the perceived price (or benefit/cost ratio) of a particular aided function. An income effect describes changes in expenditure patterns resulting from grants which increase States' available resources, but do not alter the prices of alternative highway facilities. The importance of the theoretical models is to demonstrate the relationship between the structural characteristics of a grant (e.g. matching vs. non-matching) and the corresponding price and income effects of the grant in State expendi- ture behavior. The major findings here are twofold. First, grants providing price subsidies on specific highway categories will induce a more significant reallocation of State highway expenditures (both in terms of concentrating expenditures on the aided function and increasing total expenditure levels) than grants (of like amount) that serve solely as income subsidies. Second, it was shown that grants which are ostensibly characterized by matching provisions may in fact be (allocationally) equivalent to income subsidies. That is, 35 the notion of marginality was introduced to distinguish between non- binding matching grants and grants which effectivel serve as price subsidies. The latter finding is particularly germane to the evaluation of the Federal Aid Highway Program. It is shown that although both the ABC and Interstate programs are characterized by matching provisions, ABC grants are not of sufficient magnitude to serve as price subsidies at the States' investment margin. Accordingly, the theoretical models indicate (and the emperical models validate) that changes in the level of Interstate grants will have a greater allocational impact on the States' highway investments than changes in the level of ABC grant funding. A complete typology of alternative Federal highway grant struc- tures and the theoretical modelling framework to assess their relative impacts is presented in chapter III. 1.5 The Empirical Study 36 The empirical models developed in this research attempt to explain the factors influencing States' total highway expenditures (the total expenditure model - TEM) and allocation decisions (the short run allocation model - SRAM ), amongst alternative highway expenditure categories. The data set employed in the estimation of the empirical models consists of a fourteen year time series (1957- 1970) of a 48 State cross section.Thus the pooled time series/cross- section data set yields 672 (14 years x 48 States) observations of State highway expenditures, Federal grant availability, and socio- economic, institutional and highway inventory descriptors. While it would have been desirable to estimate separate expen- diture models for each State (i.e. as forty eight separate time series), lack of sufficient time series data precluded this approach. Accordingly, both the total expenditure model and the allocation model were estimated using the pooled (time series plus cross-section) data set. In addition to the use of the full pooled data set, sev- eral estimations were performed on selected subsets of the data -- for example singling out those States with conspicuously low Inter- state expenditures over and above minimal matching requirements. Several alternative specifications of the total expenditure model were estimated using both price deflated and undeflated data. The basic form of the TEM is presented in figure 1.2. The first eight explanatory variables in the model correspond to the set of socio- economic and institutional characteristics which influence a States' perception of "desired" highway capacity (c.f. equation 1). The 37 THE TOTAL EXPENDITURE MODEL RU= a0 + a 2*SPOP + a2*UFAC + a 3*PCY + a4*GINI + a 5*RLTOT + a6*TOLPCT + a7*BIPTCX + a 8*KSTK + ag*AVNIGP + a10*AVIGP + u ere: Ru = State expenditures on highways exclusive of Federal per capita grants a 0= constant terms a = estimated coefficients SPOP = State population UFAC = percent of population residing in urban areas PCY = per capita State income GINI = index of income inequality KSTK = present discounted value of highway capital stock per capita RLTOT = percent of total expenditures (all units of government) contributed by local (i.e. county and municipal) governments BIPTCX = percent of total capital expenditures provided for by debt financing AVNIGP = apportioned "ABC" grants (three year moving average) per capita AVIGP = apportioned Interstate grants (three year moving average) per capita u = error term Figure 1.5.1 wh 38 variable KSTK serves as a proxy for existing highway inventories. Finally, the availability of Federal highway aid is represented by AVNIGP and AVIGP -- a three year moving average of non-Interstate and Interstate grants respectively.1 The short run allocation model actually consists of six dis- tinct structural equations -- one for each expenditure category -- although the estimation technique employed explicitly accounts for the joint interaction between shares.2 The estimated form of the SRAM is reproduced in Figure 1.3. As indicated, the six shares con- sidered in this analysis consist of expenditures on the Interstate System, Primary System, Secondary System, non-Federal Aid System construction, maintenance and a miscellaneous expenditure category. The dependent variable in each of the equations of the SRAM represents the share of total expenditures devoted to a particular highway expenditure type. Similar to the total expenditure model, the explanatory variables fall into three categories; socio-ecunumic and highway system characteristics (SPOP, UFAC, GINI, PCY, KSTK, PCCRMT, PCMF, KSTK), institutional characteristics (TOLPCT, RLTOT) and the highway grant terms (AVIG, AVNIG, AVPG, AVSG and AVTG). IThe use of three year moving averages was employed to account for two factors. First, since Federal aid highway grants are actually avail- able for obligation over a three to three and one-half year period, inclusion of just a single years' grant would not accurately reflect the multi-year grant availability. Second, the use of moving aver- ages partly accounts for the fact that States may not fully and im- mediately adjust to changes in Federal grant availability. 21n effect, the six equations are not independent. Since the sum of the shares must equal 1.0, an increase in expenditures on one cate- gory must be accompanied by a decrease in expenditures in one or more of the remaining share categories ( in conformance with the budget constraint). THE SHORT RUN ALLOCATION MODEL ESoal 1 a. 2 a1 T a14 a15 a 16SHARE 1: E= a SPP UFAC 2 KSTK %OLPCTaAVIGa5AVNIG ET 1 SHARE 2: E aaSPOPa21UFAC 22KSTKa23AVPGa24AVIGa26 SHARE 3: SOa30P 31UFAC 32GINI33TSPMR 34PCCRMT 35AVSG 36AVIG 37 T SHARE 4: EN 40UFAC 41 PCCRMT 42 RLTOT 43AVIG 4 4 SHARE 5: EM a a51 KSTKa52PCMFa 53RLTOT a54AVTGa55rE=Ta50 SHARE 6: E5 = a6 SPa61PCY a62KSTKa62RLTOT a63AvrGa64 Tir 5 Figure I.5.1 w4 40 EI = total State Interstate expenditures (State and Federal) EP = total. Primary System expenditures ES = total Secondary System expenditures EN = non-Federal-Aid System construction expenditures EM = maintenance expenditures E= "other" expenditures (administration, grants to local govts., miscellneous expendi Lures) ET = total expenditures: sum of the above expenditures SPOP = State population UFAC = percent of population residing in urban areas KSTK = present discounted value of highway capital stock TOLPCT = percent of total State revenues raised on State-administered toll roads AVIG = apportioned Interstate grants (three year moving average) AVNIG = apportioned "ABC" grants (three year moving average) AVPG = apportioned Primary System grants (three year moving average) AVSG = apportioned Secondary System grants (three year moving average AVTG = apportioned total grants (three year moving average) GINI = index of income inequality TSPMR = State rural primary system mileage PCCRMT = percent of rural primary system mileage carrying more than 10,000 ADT PCMF percent of total primary system mileage carrying more than 5,000 AD RLTOT = percent of total expenditures (all units of govt.) contributed by local governments PCY = State per capita income aij = estimated coefficients Figure 1.5.1 (contd.) It should be clear that the total expenditure model and the 41 short run allocation model may be evaluated in a complementary fashion. The TEM serves to predict the effect of Federal grants (among other factors) on total State highway expenditures while the SRAM predicts how the total budget will be allocated amongst alternative expenditure categories. It is not our purpose here to provide a detailed descrip- tion of the estimation results. However, a convenient means to sum- marize the most important emperical findings is contained in figure 1.4. The entries in this figure represent the elasticities of the expendi- tures in each of the six highway categories with respect to each of the variables in our analysis.' Perhaps the most striking finding in light of our research objective to assess the expenditure impacts of the Federal Aid Highway Program (FAHP) is that States have viewed the Federal "ABC" grant program as a substitute for their own expen- ditures as contrasted with Interstate grants which has served to stimulate States' own highway expenditures. This is evident from 1Chapter VI derives the simple result that TEjfXk = ET/Xk + rSj/Xk where "Ej/Xk = elasticity of category j expenditures w.r.t. variable Xk nET/Xk = elasticity of total expenditures w.r.t. variable Xk (derived as a function of the estimated parameters of the TEM) lSj/Xk = elasticity of the share of ex- penditures devoted to category j w.r.t. variable Xk (derived as a function of the estimated parameters of the SRAM) ELASTICITIES OF THE CATEGORICAL EXPENDITURES Forty Eight State Sample LONG RUN MODEL ELASTICITIES INTERSTATEVARIABLE SPOP UFAC PCY GINI KSTK TSPMR PCCRMT PCMF TOLPCT RLTOT AVIG AVPG AVSG SHARE PRIMARY 0.943 -0.198 0.623 -0.029 0.214 -0.031 -0.011 -0.001 0.023 0.028 -0.057 0.534 -0.045 SECONDARY 1.117 -0.287 0.623 0.302 0.127 0.277 0.026 -0.001 0.023 0.028 -0.074 -0.176 0.261 Figure 1.5.3 42 0.330 0.396 0.623 -0.029 -0.067 -0.031 -0.011 -0.001 -0.059 0.028 1.232 -0.070 -0.002 43 LONG RUN MODEL ELASTICITIES VARIABLE SPOP UFAC PCY GINI KSTK TSPMR PCCRMT PCMF TOLPCT RLTOT AVIG AVPG AVSG SHARE MAINT 0.497 -0.042 0.623 -0.029. 0.387 0.031 -0.011 0.007 0.923 -0.043 0.440 u 062 t001 NONFASYST. 1.662-- -0.890 0.623 -0.029 0.127 -0.031 0.183 -0.001 0.023 -0.489 0.198 -0.130 -0.026 Figure 1.5.3 (contd.) OTHER 1. 987 -0.042 1.440 -0.029 0.034 -0.031 -0.011 -0.001 0.023 0.026 -0.146 -0.226 -0.066 the elasticities in figure 1.4 which indicate that a 1% increase in 44 Primary or Secondary grants leads to less than a 1% increase (.53% and .26% respectively) in total expenditures on these systems while each dollar increase in Interstate grants have tended to increase total Interstate expenditures by more than the amount of the grant (elas- ticity = 1.23). A more complete discussion of the impacts of the FAHP (as well as other explanatory factors) in both total highway expenditure and expenditure allocation is developed in Chapters IV through VI. Suffice it to say here that the true value of the econo- metric models is to allow us to isolate the effects of Federal grants on State highway expenditures. Clearly there are factors other then Federal grants -- socio-economic, demographic and institutional char- acteristics -- that influence State highway expenditure behavior. The total expenditure model arid the short run allocation model dev- eloped in this thesis evaluate the influence of each of these factors in States' highway expenditures. 45 1.6 Summary and Conclusions This study develops a methodology for assessing the impacts of the Federal Aid Highway Program on State expenditure behavior. Unlike several previous studies in this area, the empirical work conducted in this thesis builds upon a behavioral representation of State highway investment decision making. As such, it has been possible to develop several hypotheses, based on theoretical models, of the expected State responses to numerous structural variants to the Federal Aid Highway Program. Most importantly, it was shown that not only the level, but the structure of a grant program influence State expendi- ture behavior. In general, the findings from the empirical research corrob- orate the theoretical hypotheses. Interstate grants have been shown to have a more significant impact on both the total expenditures and allocation of States' highway budgets than the non-Interstate grant programs. These results were reported in terms of the stimulatory impact of the grants on States' own expenditure levels. The empir- ical models clearly demonstrate that ABC grants have been viewed as a substitute for expenditures the States would have undertaken in the absence of grants. Contrastingly, the Interstate program has been characterized by expenditure stimulation. These results have important policy implications for the US Department of Transportation. This research has shown that (for the ABC program)) whereas the Federal government provides categorical grants, presumably in those types of activities for which it per- 46 ceives a national interest in stimulating expenditures (i.e. inducing construction that may not have been undertaken in the absence of grants), the net result may be the expansion of expenditures (or con- traction through tax relief) in other (non-aided) areas in which the Federal government has no officially stated interest. The major pol- icy implications of this finding are twofold. First, if essentially the same expenditure pattern as currently exists can be achieved with grants devoid of categorical restrictions and specific matching pro- visions, the administrative requirements of the FAHP are ineffective and wasteful. Secondly, to the extent that the Federal Aid Highway Program (and specifically the ABC component of that program) has not achieved a significant reallocation of States' resources, it raises the fundamental question of the objectives accomplished by the Federal role in highway finance. While it may be argued that the chief rat- ionale for the FAHP is to accelerate the construction of highway systems that serve the national interest, the evidence developed in this research indicates that at least some components of the FAHP singularly fail to meet this objective. 1.7 Organization of the Thesis 47 This thesis has attempted to develop a series of econometric models derived from an explicit representation of highway investment decision making behavior. Accordingly, the elements of State highway planning and programming procedures are presented in chapter II. The intent here is to provide a factual setting for development of empir- ical models. In this vein, the mechanics of Federal highway financing, and a comparison of the highway program to the Federal role in other modal areas are also discussed. Chapter III sets forth a series of theoretical models which address the question of the impacts of Federal grants-in-aid on State and local transportation investments. We begin with models drawn from consumer theory and applied to State highway investment behavior. We choose to present these models for several reasons. First, as men- tioned above, our State highway allocation models are based on con- sumer theory. Second, this theory provides the basis for normative statements on the design of Federal highway grant programs. And third, consumer theory provides a convenient framework with which to evaluate a wide variety of questions concerning State responses to Federal grant availability. Thus, accepting the assumptions which the con- sumer theory imposesl, we can investigate the differences in the "idealized State" response to matching as opposed to block grants. IThese assumptions will be itemized in full, and discussed in view of the description of actual State highway planning and program- ming procedures presented in chapter II. 48 Similarly the analysis can be applied to the questions of "distortion" (i.e. whether Federal matching grants cause unsubsidized highway serv- ices to be neglected relative to subsidized activities), and the effects of the grant program specificity (i.e. the allocational con- sequences of restricting Federal grants to narrowly defined highway categories). Next, a modelling framework based on a simple benefit/ cost investment criterion is presented to further clarify the dis- tinction between the price and income effects characterizing Federal highway grants. Chapter III concludes with an application of the benefit/cost investment model to the Interstate and ABC grant programs. Needless to say, we would like to assess the expenditure im- pacts of the Federal Aid Highway Program with empirical analyses as well. This is the purpose of chapters IV - VI. Chapter IV develops an econometric model designed to explain the States' total expenditure responses to the Federal Aid Highway Program. Because we are using a pooled data set of time series and cross sectional observations, careful attention must be given to the correct specification of error variance - covariance matrix. A recent technique developed by Theil and Goldberger is applied to our estimation problem to develop generalized least squares estimates of the total expenditure model. Chapter V develops an econometric model of the second dimension of States' highway expenditure behavior, namely budget allocation. A six category share model is estimated using data covering the forty eight Mainland States over a fourteen year analysis period. Here too special attention must be given to the proper econometric treatment of the model structure. A generalized least squares technique is 49 advanced to account for the joint interaction between expenditure shares. Chapter V also attempts to unite the empirical findings of the SRAM with TEM developed in the previous chapter. In particular, the analysis shows how to derive the elasticities'and derivatives of highway expenditures as a function of the estimated parameters of the total expenditure and short run allocation models. These emprirical measures of the impacts of the Federal Aid Highway Program are compared to the theoretical hypotheses of State highway expenditure behavior advanced in chapter III. Finally, chapter VI presents a summary of-the major findings developed in this thesis. The policy implications of the theoretical and empirical models are discussed and related to directions for future fruitful research. 50 CHAPTER II THE MECHANICS OF HIGHWAY FINANCE: A FACTUAL SETTING II.1 Introduction Any attempt to model the highway investment behavior of State governments must take careful account of the institutional, political, and administrative realities of the Federal-Aid Highway Program (FAHP). The purpose of this chapter is to summaraize the major features of the FAHP, and draw attention to the issues that will be addressed in the theoretical and empirical analyses that follow. Although not all of the material described in Chapter II is directly required for the development of the empirical models of State highway investment behavior, the presentation of a detailed description of the FAHP provides a useful perspective for the evaluation of the Federal highway programs in following chapters. The Federal-Aid Highway Program has evolved in an incremental fashion. Although the recently enacted Federal-Aid Highway Act of 1973 established several new Federal policies, the fundemental prin- ciples upon which the FAHP operates were established in the germinal highway legislation of 1916. Section 2 of this chapter traces the historical development of the Federal-Aid Highway Program with partic- ular emphasis on landmark legislation in the years 1916, 1921, 1944, 1956, and 1973. In each of these years, new Federal-Aid Systems were incorporated into the FAHP starting with the Primary System in the earliest acts, through the Interstate System of the 1956 act, to the mass transit-inclusive Urban System of the 1973 act. Each Federal Aid System is described in detail with respect to categorical restric- tions, Federal matching provisions and authorization levels. Section 3 focuses on the mechanics of the Interstate Highway Trust Fund (IHTF). Particular attention is paid to tracing out the flow of Federal funds from the point of initial Congressional authori- zation to the actual receipt of funds by State Highway Departments. In addition, this section includes a discussion of highway taxation to show the various aspects of regressiveness and inequities inherent in the IHTF revenue measures. Section 4 presents a comparison of the FAHP to the Federal mass transit assistance program in order to highlight the singular aspects of the Interstate Highway Trust Fund. The IHTF is unique not only by virtue of its magnitude of expenditures, but becuase of the mech- anics of its operation as well. The comparison between the Federal aid programs in these two modal areas is presented in terms of the sources of Federal funds, total expenditure levels, authorization cycles, apportionment methods, matching provisions, expenditure restrictions, local recipients of Federal funds, and the sources of local matching funds. Chapter It concludes with a summary of findings, with particu- lar emphasis on the major considerations for empirical models of State expenditure response to the Federal-Aid Highway Program. 52 11.2 Historical Development of the Federal-Aid Highway Program The Federal interest in transportation has its origin in the Constitution, which enpowers the United States Government to regulate interstate commerce, to provide for the general welfare and the common defense, and to establish post roads. Obviously, the evolution of the national transportation policy has undergone innumerable changes since the original mandate of 1787, most notably in the area of Federal highway policy. Road development in the United States began slowly, with the first major Federal highway capital investment program coming in 1916. At that time, Congress established the fundamental princi- ples upon which the Federal-Aid Highway Program (FAHP) still oper- ates today. These principles - namely that the States would act as financial intermediaries in the planning, construction and main- tenance of roads, receiving Federal aid in the form of matching grants - have been refined in land-mark legislation in the years 1921, 1944, 1956, 1970, and 1973. i. The Early Federal-Aid Highway Acts The provision of roads in the United States was almost entirely under local jurisdictional control before the turn of the century. Although several States began organizing State Highway Departments (SHD) in the early 1900's in response to a growing aware- ness of the inadequacy of existing road networks in light of the rising popularity of the automobile, a major stimulus for creation 53 of SHD's came with the passage of the Federal-Aid Road Act of 1916. This act - the first Federal-aid highway legislation, stipu- lated that each State seeking a grant was required to establish a State Highway Department as well as meet Federal standards of road construction and management. Although Federal aid under this Act was minimal,1 the States responded immediately in establishing SHD's. As shown in table 11.2.1 all States had legislated the creation of State Highway Departments by 1917. Four fundamental principles were established by the Federal- Aid Road Act of 1916 which still dictate the operation of the FAHP: 1) The conditional, matching 2grant in aid would be the sole instrument of Federal financial assistance for the provision of highways. 2) Federal funds would be restricted to expenditure on construction. 1. The total 1917 appropriation under this Act was only $5 million. By the time this appropriation was apportioned to the States, Delaware received scarcely more than $8000. Moreover, this aid was restricted to the improvement of rural post roads. A State could receive no Federal funds for bridges greater than 20 feet in length, and were limited to a maximum of 10,000 Federal dollars per road mile. 2. Conditional grants-in-aid refer to the requirement that funds are restricted to particular categories of expenditure (e.g. rural post roads). Matching grants require States to furnish funds from their own sources (in some fixed matching ratio) in order to qualify for Federal funds. A complete taxonomy of grant charac- teristics will be presented in chapter III. 54 YEAR IN WHICH FIRST STATE-AID LAW PASSED AND HIGHWAY DEPARTMENT CREATED YEAR DATE OF ESTABLISHMENT OF FIRST STATE FIRST HIGHWAY DEPARTMENTSTATE STATE-AID LAW YEAR REMARKS J-_PASSED Al abama Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri 1911 1909 1913 1895 1909 1895 1903 1915 1908 1905 1905 1917 1904 1911 1912 1910 1901 1893 1892 1905 1905 1915 1907 1911 1909 1913 1907 1909 1895 1903 1915 1916 1913 1905 1917 1904 1917 1912 1910 1907 1898 1892 1901 1905 1916 1907 State Department of Engineering, Highway Commission created in 1911. Originally to administer aid to coun- ties only. Commission of 3 members; single com- missioner provided for in 1897. Organization to administer State-aid; present organization created in 1917. First commission provided for road study; State Highway Department created in 1913. Held unconstitutional same year; present organization created in 1919. Iowa State College designated as commission; in 1913 a 3-man commission provided. State department with limited powers for administration of Federal-aid. Commissioner with advisory powers only; State Highway Department created in 1920. Present highway board created in 1921. Commissioner to supervise State-aid roads; law of 1913 established commission. Highway Division of geological survey; commission established 1908. Preliminary commission for studies; in 1893 new commission established. Highway committee appointed; State Reward Law in 1905. Commission authorized in 1898; enacted into law in 1905. Engineer advisory to county officials; Hiqhway Commission created in 1913. Table 11.2.1 55 YEAR IN WHICH FIRST STATE-AID LAW PASSED AND HIGHWAY DEPARTMENT CREATED YEAR DATE OF ESTABLISHMENT OF FIRST STATE FIRST RIGHWAY DEPARTMENT STATE-AID STATE LAW YEAR REMARKS PASSED Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina aorth Dakota Ohio Okiahoma Oregon Pennsyl vania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West 'irninia Wisconsin Wyoming 1913 1911 1911 1903 1891 1909 1893 1901 1909 1904 1911 1913 1903 1902 1917 1911 1915 1917 1909 1892 1898 1905 1909 1911 1911 1913 1911 1917 1903 1894 1909 1898 1915 1909 1904 1911 1913 1903 1895 1917 1913 1915 1917 1909 1898 1906 1905 1909 1907 1917 Commissioner appointed in 1905 after study by engineer conission. Aid to counties in 1891 under ackninistration of board of agri- cul ture. Territorial road commission; State Highway Conmission created in 1912. Appropriation for State-aid approved by state engineer and surveyor. "Good roads experiment station"; State Highway Commission created in 1913. Advisory until 1910. Report of Board of Public Roads approved by legislature, and a commissioner appointed. Present department created in 1917. Board provided for. Commissioner; a bureau provided in 1913. Work by geoloqical survey; commission created in 1911 Source: U.S. Bureau of Public Roads -e-"HIGHWAY STATISTICS, Summary Table 11.2.1 to 1945 (contd.) 56 3) The States would act as financial intermediaries in the expenditure of Federal highway funds. 4) The States would be legal owners of Federal aid roads, in that the responsibility for planning, constructing and maintaining these roads would be "the duty of the States, or their civil subdivisions, according to the laws of the several States."' The second major piece of Federal-aid Highway legislation was passed in 1921, with the purposes of increasing the minimal existing Federal authorizations, designating a primary system on which all Federal aid would be spent, and establishing a floor on minimal State appropriations. With passage of the Federal Road Act of 1921, Congress established two more fundamental principles (in addition to the four principles of the 1916 Act) which still guide the FAHP: 5) Federal-aid would be accorded to specific road categories on designated Federal-Aid Systems. Each Federal-Aid System would be defined according to operating and design criteria established by the Bureau of Public Roads. 6) Apportionment of national highway authorizations to the States would be made according to a formula which weights the 1. Section 7, 39 Stat. 355 57 States' population, land area, and existing road mileage. No State would receive less than .5% of the total yearly authorization. States were quick in responding to the Federal requirement of designating a primary road system. As shown in Table 11.2.2 all States had designated their primary systems by 1924. Al though the expenditure of Federal funds on secondary and urban roads was permitted on a limited scale during the depression, the official creation of the Federal-Aid Secondary and Federal-Aid Urban systems was first stipulated in the Federal-Aid Road Act of 1944. The Federal-Aid Secondary (FAS) program provided matching grants for "principal secondary and feeder roads, including farm-to- market roads, rural free delivery mail, and public school bus routes."1 Federal-aid urban extension funds were provided for portions of primary roads which passed through urban areas. The 1944 Act served to establish what has since become known as the "ABC"program. 2 The total Federal aid ABC authorization was (and still is) divided in the ratio of 45 percent FAP, 30 percent FAS, and 25 percent urban extension. Only minor modifications have been made to the provisions of the ABC program as stipulated in 1944. 1. Federal-Aid Road Act of 1944. 2. "A" refers to the Federal Aid Primary (FAP) system, "B" the FAS system, and "C", urban extensions of FAP and FAS. 58 DATE OF AUTHORIZATION OR CREATION OF STATE HIGHWAY SYSTEMS STATE [YEAR REMARKS Alabama Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska 1915 1910 1923 1902 1917 1913 1917 1915 1919 1915 1913 1917 1913 1918 1912 1921 1913 1908 1893 1913 1921 1924 1917 1913 1921 Tentative State system laid out in 1910 by State Highway Department. Legislative enactment. Constitutional amendment empowered legis- lature to establish State system; system laid out in 1910. System of State routes for present and future improvement approved by legislature. Map of trunk lines prepared in 1901 but not approved by legislature until 1913. System designated as a result of planning to expend Federal-aid funds. State Highway Department authorized to designate system; revised system adopted by legislative enactment, 1923. Legislative enactment. Legislature directed commission to desig- nate trunk highway system. Law provided for the systematic laying out of 16,000 miles of State-aid roads. System of main market highways provided by legislative enactment. Inter-county road system designated. System designated as a result of planning to expend Federal-aid funds. Primary system established by legislature as "Inter-county seat system." Complete system, including trunk lines, State- aid, and "3rd Class", roads designated. State system established to be improved with state bond issue. Roads classified about 1899. Trunk-line system established limiting state road mileage in each county. Trunk-line plan presented to legislature in 1919; in effect May 1, 1921. System designated as a result of planning to expend Federal-aid funds. Table 11.2.2 59 DATE OF AUTHORIZATION OR CREATION OF STATE HIGHWAY SYSTEMS STATE YEAR REMARKS Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming 1917 1905 1917 1912 1907 1915 1917 1911 1913 1917 1911 1903 1917 1919 1915 1917 1912 1917 1918 1905 1917 1917 1919 I I Certain roads designated "inter-county", later called "State highway." State engineer's map adopted by legislature. Map of State system included in of commissioner. Authority granted dommission to State routes annual report designate System designated as a result of planning to expend Federal-aid funds. Trunk road system provided for. Commission provided to plan system. System designated as a result of planning to expend Federal-aid funds. Selected by commission. System designated as a result of planning to expend Federal-aid funds. System designated as a result of planning to expend Federal-aid funds. System in isolated units. Primary highway designated by legislature in 1913. Trunk highway system selected. Source: U.S. Bureau of Public Roads HIGHWAY STATISTICS, Summary to 1945 Table 11.2.2 (contd.) 60 "C" funds are now accorded to extensions of the secondary as well as the primary system (1954 Federal-Aid Road Act). Further- more, States now are allowed to transfer up to 201 percent of their appropriation in any one Federal-Aid System to any other System (1956 Federal-Aid Highway Act). In historical perspective the 1944 Federal-Aid Road Act was perhaps even more significant for its germinal role in establishing the Interstate Highway System. Culminating six years of cooperative study by the Bureau of Public Roads (BPR) and individual SHD's, the 1944 Act directed the BPR to designate a "National System of Inter- state Highways." Although no special funds were appropriated at this time, the Interstate network did become an established compo- nent of the Federal-Aid System. The Federal-Aid Highway Act of 1956 carried with it the most sweeping reforms in the history of the Federal-Aid Highway Program. Building on the six fundamental principles of FAHP operation estab- lished in previous legislation, two final principles were added by this landmark Act: 7) The National System of Interstate and Defense Highways would be established as a distinct Federal Aid system with separate authorizations, apportionment formulas, and matching ratios. 1. Changed to 40% by the Federal-Aid Highway Act of 1973. 61 8) The Interstate system as well as other Federal Aid systems would be financed from the Interstate Highway Trust Fund (IHTF). This Fund would be composed of excise taxes on motor fuel, auto-related parts and oil, and truck use. Fur- thermore, the IHTF would be restricted solely for the dis- bursements of grants to States for the construction of roads on the Federal-Aid System. Since its inception in 1956, the Interstate program has domina- ted the Federal-Aid Highway Program, with over $43 billion of Federal funds obligated as of the end of calendar year 1972 (approximately 73% of the total Federal highway aid over this period). Although the States' share of the Interstate program is at most 10 percent, State funds devoted to Interstate construction represent a sizeable fraction of total yearly SHD budgets as shown in figure 11.2.1. In fact, in the mid-1960's, State expenditures on the Interstate system exceeded expenditures on the ABC system. More recently, Federal-aid legislation has given increased emphasis (i.e. funding) to urban road systems. Without changing the structure of the FAHP, new functional classes have been added to the already existing ABC and Interstate programs. In particular, the Federal Aid Highway Act of 1968 initiated the Traffic Operation Pro- gram to Increase Capacity and Safety (TOPICS) funded at $100 million per year. In the next highway bill (1970) Congress authorized funding for the Urban (arterial) system which provided $100 million in addition STATE EXPENDITURES ON THE FEDERAL AID SYSTEMS 375C- CI, 14 - r27NV - I20 0 c o Iso '75C> I 560 -- 4 ft 5 ll 'Ns 51 '60 'Vi '62 '65 'C4IC 68 '6 '61 'O '6 '70 YEAR 4 oce55 0 0 -4 -15 6 '~ 6 '5 '4 '6f '~ '6 6 61 '0 YA' /5 -4 F5I Figure 11.2.1 62 63 to the extant urban extensions (of FAP and FAS) program. With passage of the 1968 and 1970 Federal Aid Highway Acts, the over- all level of funding for urban road systems increased from 25 percent to 33 percent of non-Interstate authorizations.1 The current Federal Aid Highway Program is administratively structured in terms of several distinct Federal Aid Systems. Each System is characterized by a separate biyearly authorization, and a distinct set of factors employed in apportionment formulas. The design and operating characteristics of each Federal Aid System are broadly defined in various pieces of enabling legislation described previously in this section.2 However, the legislative definitions of the Federal Aid Systems are intended to provide only general guidance as to the Congressional intent in stimulating the construc- tion of particular class of roads. Ultimately the States, in coop- eration with the Federal Highway Administration are responsible for 1. Prior to the 1968 Act, urban road funding (exclusive of Inter- state) was limited to the "C" program, where ABC authorizations were divided on a 45/30/25% basis. For FY 1972 urban road system authorizations included $275 million for urban extensions, and $100 million for each TOPICS and urban arterial comprising 33% of the total $950 million non-interstate authorization. 2. Sections II.2.i through II.2.vii inmediately following will trace out the characteristics of the FAHP as of the end of calendar year 1972, and thus are relevant for the empirical analyses found in chapters III, IV and V (the empirical analyses cover the period 1954-1970). Section II.2.viii outlines the changes in the FAHP introduced by the Federal-Aid Highway Act of 1973. 64 the specific assignment of roads to a particular Federal Aid System. ii. The Federal Aid PrimarySystem (the "A" System) The Federal Aid Primary (FAP), first established in 1921, is the oldest of the Federal Aid Systems. The FAP is defined as "an adequate system of connected main highways" not to "exceed 7 per centum of the total highway mileage of each ... State."1 Although the ultimate size of each State's FAP appears to have been limited by law, this is not the case. Provision has been made to increase the relative size of the FAP whenever the 7 percent ceiling is approached. As a matter of practice, no State has had to forfeit FAP grants because of the mileage restriction. FAP authorizations are normally made from the Interstate Highway Trust Fund every two years by two means: as a fixed percen- tage of total ABC authorizations, and (possibly) as a supplemental authorization. Forty five percent of the total ABC funds are dedi- cated to the Primary System. In addition, Congress may authorize funds over and above the ABC percentage Primary share.2 Apportionment of FAP authorizations to the States is derived from the following formula: 1. 103(b), Subpart A, Title 23, U.S.C. 2. For example, in the Federal Aid Highway Act of 1970, Congress authorized $1.1 billion for the ABC System (yielding $495 million for the FAP), as well as a supplemental $75 million FAP (rural) grant for each of fiscal years 1971 and 1972. 65 1) one third of the total apportioned on the basis of a State's land area relative to the total U.S. land area 2) one third of the total apportioned on the basis of a State's population relative to total U.S. population 3) one third of the total apportioned on the basis of a State's rural postal route mileage relative to the U.S. total of such mileage 4) no State to receive less than 0.5% of the total appor- tionment iii. The Federal Aid Secondary System (the "B" System) The Federal Aid Secondary System includes farm-to-market roads, rural mail routes, public school bus routes, local rural roads, county roads, and township roads. As the legislative guidelines indicate, the FAS consists of projects on a smaller scale than the FAP. There is no mention of connectivity (as in the legislative guidelines for FAP). The secondary system is intended to provide a series of routes of secondary Statewide significance linking markets to urban centers or to other FAS or FAP highways. The method of authorization and apportionment for FAS is very similar to the FAP System. Thirty percent of the total ABC authorization from the IHTF is dedicated to the Secondary System. 66 Additional funds for rural sections of the FAS may be authorized.1 The apportionment formula is identical to the provisions of the FAP formula, except that rural rather than total population is used as an apportionment factor (see summary Tables 11.2.3, and 11.2.4). iv. Urban Extensions of the Primary and Secondary Systems (the "C" System" This system consists of projects on approved extensions of the Federal Aid Secondary and Federal Aid Primary Systems in urban areas. In practice, this System is merely an administrative classi- fication, since urban roads can be Federally financed from "A," "B," or "C" funds. Federal funds for FAP/FAS urban extensions are set at 25 percent of the total ABC authorization. Apportionment to States is based on each State's relative population living in urban places with population over 5000. v. The Federal Aid Urban System (FAU) The FAU program was established by the Federal Aid Highway Act of 1970 as a distinct system of urban roads. That is the FAU and "C" systems conform to different project selection criteria, authori- zations, and apportionment factors. The FAU system is intended to be "so located as to serve the major centers of activity, and designed taking into consideration the highest traffic volume corridors, and 1. For example, the Federal Aid Highway Act of 1970 authorized $50 million for this purpose. 67 FACTORS EMPLOYED IN APPORTIONING FEDERAL AID SYSTEM FUNDS (as of December 31, 1972) 1. FEDERAL AID PRIMARY ("A" FUNDS)* One third on land area One third on total State population One third on rural postal route mileage 2. FEDERAL AID SECONDARY ("B" FUNDS)* One third on land area One third on rural State population One third on rural postal route mileage 3. PRIMARY AND SECONDARY URBAN EXTENSIONS ("C" FUNDS)* Population in urban places over 5000 4. FEDERAL AID URBAN SYSTEM Population in urbanized areas over 50,000 5. TOPICS Population in urban places over 5000 6. FEDERAL AID INTERSTATE Federal share of the estimated cost of completing the the Interstate System in each State * No State to receive less than one half of one percent of the total ABC apportionment Table 11.2.3 68 CURRENT FACTORS EMPLOYED IN APPORTIONING FEDERAL-AID SYSTEM FUNDS1 Pursuant to the Federal-Aid Highway Act of 1973 1. FEDERAL AID PRIMARY ("A" FUNDS)* One third on land ** One third on population of rural areas One third on the mileage of intercity mail*;outes where service is performed by motor vehicles 2. FEDERAL AID SECONDARY"B"FUNDS* ** Same as primary apportionment formula * 3. PRIMARY AND SECONDARY URBAN EXTENSIONS ("C" FUNDS) Population in urban places over 5000 4. FEDERAL AID URBAN SYSTEM ** Population in urban places over 5000 5. FEDERAL AID INTERSTATE Federal share of the estimated cost of completing the Interstate System in each State * No State to receive less than one half of one percent of the total ABC apportionment ** Apportionment formula has changed from previous legislation Table 11.2.4 69 the longest trips within such (urban) area."I Authorizations from the IHTF are made every two years.2 Apportionment to States is on the basis of each State's relative population living in urbanized areas (population over 50,000) vi. Traffic Operations Projects to Increase Capacity and Safety (TOPICS))3 The TOPICS program is intended to stimulate the construction of projects "designed to reduce traffic congestion and to facilitate the flow of traffic in the urban areas.4 Of all the Federal Aid Systems, TOPICS projects are generally of the smallest scale. Exam- ples of TOPICS improvements include grade separation of intersections, widening of lanes, channelization of traffic, traffic control systems, and loading and unloading ramps. Authorization from the IHTF for TOPICS are made every two years. Apportionments are made in the same basis as for the FAU system (see Table 11.2.3). vii. The Federal Aid Interstate System The Interstate System (FAI) is different in several important 1. 103 (d), Subpart A, Title 23, United States Code. 2. For example, the 1970 Highway Act authorized $100 million for each fiscal years 1972 and 1973 3. The TOPICS program was discontinued as of the beginning of fiscal year 1974 4. 135 (a) Subpart A, Title 23, U.S.C. TOPICS was established by the Federal Aid Highway Act of 1970 70 respects from the other components of the Federal Aid System. First, the FAI is the only System that is close-ended in terms of both total System mileage and required completion date. Current legislation limits the mileage of the Interstate System to 41,200 miles,l and stipulates completion of the FAI by the end of fiscal year 1979.2 Secondly, unlike the other Federal Aid Systems, the Bureau of Public Roads played a major role in the selection of corridors for future Interstate development. As early as 1944, a 41,000 mile Interstate network (excluding urban sections) was established. Thus, the major policy option exercised by the States was simply the pro- gramming3 of Interstate investments on the approved network. A third innovation of the Interstate System is in its method of financing. The Federal/State matching ratio on the Interstate is 90/10, compared with the 50/50 matching ratio on other Federal Aid Systems. Interstate authorizations are established for the entire 1. As of December 31, 1972, total expenditures on completed Interstate projects amounted to $49.3 billion, 65% of the 1972 estimated cost of $76.3 billion for the entire Interstate system. 2. Future Federal Aid Highway Acts may extend this completion deadline. 3. In this context, programming refers to the scale of the projects (i.e. number of lanes), and the timing of Interstate investments. 4. The Federal Aid Highway Act of 1970 increased the Federal share payable on non-Interstate projects to 70% beginning with fiscal year 1974. The new matching ratio also applies to funds unobli- gated from previous apportionments. duraction of the FAI program. Thus unlike the biannual cycle for 71 other Federal Aid Systems, new Interstate Authorization levels are set only when the duration of the Interstate program is extended.I Finally, the method of Interstate apportionment differs from other Federal Aid System apportionment in that it is based on the estimated Federal share of the total cost to complete the FAI in each State, rather than on State socio-economic characteristics (see table 11.2.3). viii. Structural Revisions to the FAHP Incorporated in the 1973 Federal Aid Highway Act2 The Federal-Aid Highway Act of 1973, signed into law on August 13 of that year introduced perhaps the most sweeping policy revisions since the inception of the Federal-Aid Highway Program in 1916. The revisions reflected the increasing awareness on the part of Congress and various interest groups of the shortcomings of the FAHP (see Section III.2.iii). In fact, Congressional debate on the proposed measures carried past the end of the 1972 legislative session representing the first time in more than two decades that a highway bill was not signed on a biennial basis. The majority policy revisions incorporated into the Act are: - diversion of gracts from the Interstate Highway Trust Fund to urban mass transit facilities are allowed for the first 1. For example, the 1973 Highway Act established FAI authorizations for 6 years covering 1974 through 1979. 2. Public Law 93-87. An excellent description of the specifics of the 1973 Act is contained in the pamphlet HIGHWAYS, SAFETY AND TRANSIT: AN ANALYSIS OF THE -FEDERAL AID HIGHWAY ACT OF 1973,. published by the Highway Users Federation for Safety and Mobility, Washington, D.C. 72 time beginning in fiscal year 1975 - greater emphasis is placed on the upgrading of non-Inter- state systems - significant expansion of the Federal-Aid Urban System is called for - for the first time States are directed to channel Federal urban planning monies directly to authorized metropolitan area planning agencies - grants designated for construction on the Interstate System may, under certain conditions be used instead as mass transit aid - a major realignment of the Federal-Aid highway systems is called for. In addition, three new systems are established: Priority Primary Routes, the Special Urban High Density jraffic Program, and Economic Growth Center Development Highways The most significant message imparted by the Federal-Aid Highway Act of 1973 is the increased flexibility incorporated into the Federal-Aid Highway Program. Although the Act did not go to the extreme of dropping all categorical restrictions on the use of Federal aid (as embodied in S. 1693 - the Special Transportation Revenue Sharing Act of 1969), several features of the 1973 legislation allow 1. The major thrust of the Federal-Aid highway system realignment is to redesignate routes eligible for Federal assistance on the basis of anticipated future functional usage. The greatest change effected by the Act will be on the Federal Aid Secondary System where the 636,000 miles of the 1972 System is expected to be reduced to 275,000 miles (as reported in the Federal Highway Administration's Report on Functional Classification, 1972). The intent here is to concentrate Federal aid on those segments of the nation's road network with the greatest regional significance. For a concise description of the characteristics of the three new Federal-Aid systems, see the Highway Users Federation pamphlet (oo. cit.) 73 the States greater latitude in tailoring the use of Federal highway aid to neet the particular needs of their highway and transit investment program. The diversion provisions on the use of FAHP grants for mass transit, the increase in the allowed fund transfer between non-Interstate systems from 20% to 40% (see Section II.2.i), and the recent increase (stipulated by the 1970 Act) in the Federal share payable in all non-Interstate systems from 50% to 70% of total project cost, all signal a relaxation in the specificity of the categorical restrictions which characterized previous FAP legislation. Despite the numerous innovations introduced in the 1973 Federal- Aid Hinhway Act, the Interstate !irghway Trust Fund (tt!TF) continues to serve as the primary vehicle of Federal highway finance. The IHTF is a unique Federal finance program, not only by virtue of its magnitude of expenditures, but because of the mechanics of its operation as well. The next section will detail the operation of the Trust Fund. 74 11.3. The Mechanics of the Interstate Iliqhway Trust Fund i. Program Structure It is convenient to summarize the program structure of the Interstate Highway Trust Fund in terms of the following major characteristics: source of Federal funds, total expenditure levels, authorization cycle, apportionnent method, matching provisions, expenditure restrictions, local recipients of Federal funds, and 3ources of local matching funds. )ource of Federal Funds Since the 1956 Highway Act, all Federal disbursements for expenditures on the Federal-Aid Systems have been made from the Interstate Highway Trust Fund (ITF). The IHTF is an institutional iechanisrn designed to serve as the respository for all earmarked Federal user charges associated with road use. The major sources of IHTF revenue are shown in table 11.3.1. 3y far the greatest contribution to the Trust Fund comes from the ex- cise tax on gasoline. In calendar year 1970, for example, highway- related consumption yielded over $3.67 billion, or 70% of the total IHTF revenues (see table 11.3.2). IHTF revenues have been growing at an average rate of 9.2% through the late 1960's (fiscal years 1966-1971), currently yielding )ver $5.5 billion dollars. Total Expenditure Levels The Federal-Aid Highway Program represents by far the largest 75 TRUST FUND REVENUE SOURCES SOURCES Motor Fuel Trucks, buses, and trailers Inner tubes Tread rubber Truck and bus parts Lubricating oil Vehicle use TAX RATE 4 per gallon 10% of manufacturers wholesale price 10 per pound 5 per pound 8% of the manufacturers wholesale price 6 per gallon $3.00 per 1,000 lbs. (gross vehicle weight) for trucks weighing more than 26,000 lbs. Source: page 56, HIGHWAY STATISTICS 1970, Federal Highway Administration Table 11.3.1 76 INTERSTATE HIGHWAY TRUST FUND REVENUE BY SOURCE CALENDAR YEAR 1970 Source Inount (billions of dollars) Motor Fuel Trucks, buses and trailers Inner Tubes :lotor Vehicle Use Parts and Accessories Lubricating Oil Tread Rubber $3.673 .655 .585 .141 .085 .065 *028 5.232 Percent of Total 70.1 12.4 11.2 2.89. 1 .69. 1 .39. 0.69. 1.00% Source: Tables FE-205, FE-206 HIGHWAY STATISTICS 1970, Federal Hiqhway Administration Table 11.3.2 77 Federal public works grant program. In fact, of the more than 500 categorical grant programs administered by the Federal government, the FAHP ranks second (to the welfare program) in expenditure of funds. The latest FAHP authorization allows for a total expenditure o01 $16.7 billion dollars (over the three year period 1974-1976) divided among the Federal Aid Systems as follows: $8.75 million FAI, $3.42 billion FAU, Urban High Density Routes and urban extensions of FP/FAS, $1.19 billion FAS, and $2.127 billion FAP. Authorization levels over the 10 year period 1961-1971 are shown in Table 11.3.3. Expenditure Restrictions Federal-Aid Highway Program funds are restricted to expendi- ture on preliminary engineering,I right-of-way acquisition, and construction of Federal-Aid Systen roads. Federal disbursements on each Federal-Aid System are limited to the amounts specifically appor- tioned with the exception that States may reapportion up to 40% of their funds for any one System to any other System. 2 1. Preliminary engineering includes surveys and other elements of a location study, and detailed designs and other plans, specifica- tions and estimates covering the construction on a selected location. 2. It's interesting to note that as of 1972, only 11 isolated cases of reapportionment have been exercised by the States. The reluc- tance to transfer funds among systems is partly explained by the flexibility in employing FAHP grants. For example, "C" projects may be funded from "A", "B", or "C" funds, without the need for formal reapportionment. 78 INTERSTATE HIGHWAY TRUST FUND RECEIPTS AND AUTHORIZATIONS 1961-1971 REVENUES (in billions of dollars) 2.799 2.956 3.293 3.539 3.670 3.924 4.455 4.428 4.690 5.469 5.725 AUTHORIZATIONS 1 (in billions of dollars) 2.725 3.125 3.325 3.550 3.675 3.800 4.000 4.400 4.800 5.425 5.425 FISCAL CONTROL TOTALS {tin billions of dollars) 4.769 5.000 4.600 Sources: (1) pp. 11-153, FEDERAL LAWS, REGULATIONS MATERIAL RELATING TO THE FEDERAL HIGHWAY ADMINISTRATION, FHWA, 1971. (2) TABLE 1, PROGRNI PROGRESS, FHWA memo dated 1/19/73 Table 11.3.3 Funds administered by the Bureau of Public Roads YEAR 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 79 Local Recipients of Federal Funds The States are the sole recipients of Federal Highway capital grants. No money is directly channeled to lower units of government, although States are free to enter into agreement with their subdivi- sions to financially cooperate on particular Federal-Aid projects. In any event, the States maintain sole responsibility relative to plans, specifications and estimates (PS & E), surveys, contract awards, design, inspection, and construction of all projects on the Federal -Aid Systems. Authorization Cycle FAHP funds for all Federal-Aid Systems except the FAI are normally authorized every two years.1 These authorizations are included in a biennial Highway Act enacted at least one-half year before the States are allowed to use Federal funds. For example, the Federal-Aid Highway Act of 1970, passed December 31, 1970, authorized I11TF expenditures for fiscal years 1972 (beginninr July 1, 1971) and 1973. Interstate authorizations are determined for the duration of the FAI program. The Federal-Aid Highway Act of 1973 authorized FAI funding through FY 1979. Apportionment Method Apportionment refers to the amount of Federal Aid made avail- able to each State for each of the Federal-Aid Systems. As shown in 1. The Federal-Aid Highway Act of 1973 departed from the biennial pattern of highway legislation. This Act authorized funds for three fiscal years. 80 Tables 11.2.3 and 11.2.4, each Federal-Aid System is associated with a specific apportionment formula, expressed in terms of State demographic and geographic characteristics. Ordinarily, the apportionment of IHTF funds among States would be derived directly from the approved authorization levels. However, between 1969 and 1973, the Office of Management and Budget (0MB) imposed restrictions on Federal highway expenditure levels, in an effort to curb govern- ment expenditures. Consequently, the amounts apportioned to the States in these years were actually derived from the 0MB-imposed Federal highway fiscal control totals. (see Table 11.3.3) Matching Provisions The Federal-Aid Interstate Systems is characterized by a 90/10 Federal/State matching ratio, All other Federal-Aid Systems are subject to a 50/50 matching ratio. States Hith a large piblic land holding are entitled to a larger Federal share of highway funds, as determined by a "sliding scale" formula which increases the Federal share in proportion to the amount of State land in the national public domain. Thirteen States qualify for an increased Federal highway share as shown in Table 11.3.4. Sources of Local Matching Funds Although all levels of government assume some responsibility for collecting and disbursing funds for highway-related activities, the States are by far the largest contributor in the FAIP. For example, in calendar year 1970, the States' highway expenditures 81 VARIABLE MATCHING PERCENTAGE FOR STATES WITH MORE THAN FIVE PERCENT OF PUBLIC LAND Federal Share Federal Share on other State on Interstate Federal-Aid Systems ,laska -------- 95.00 (max) Arizona 94.39 71.96 California 91.62 58.09 Colorado 91.31 56.57 Idaho 92.30 61.50 lontana 91.31 56.54 :evada 95.00 (ceiling 83.74.0level)837 :lew Mexico 92.58 62.91 Oregon 92.38 61.90 South Dakota 91.71 55.83 Utah 94.88 74.42 Uashington 90.71 53.54 Vyoning 92.87 64.36 Source: flurch, P.1., HIGHWAY REVENUE AND EXPENDITURE POLICY IN THE UNITED STATES Table 11.3.4 1. Other States subject to 90/10 Interstate share, and 50/50 share on other Federal-Aid Systems. 82 (10.55 billion), were greater than the combined highway expenditures of the Federal government (4.96 billion), county governments (1.43 billion), and municipal governments (2.39 billion). 3esides the sheer magnitude of their financial commitment to the FAHP, the States play a central role in highway finance for two more reasons. First, Federal grants-in-aid for highways are received, programmed, and expended by States. In this context, Federal highway "expenditures" can be considered as State highway revenue. Second, all States have estab. ;hed some form of shared tax or grant-in-aid mechanism with their civil subdivisions. As such, the State influ- ences the expenditure pattern of the counties and municipalities. State highway revenue derive from four major sources: Federal highway grants, State taxes on motor fuel and motor vehicles, pro- ceeds from bond sales, and appropriations from State general tax re revenues.1 Motor fuel/vehicle tax revenue is the largest component of State highway revenue, yielding about 60% (nationwide average) of total SHD revenue in 1970. Highway bond sales represent varying degrees of importance in different States. At one extreme are the 11 States that have not resorted to bond financing of either toll or free roads (see Table 11.3.5) over the ten year period 1961-1970. At the other extreme are 5 States which have established debt financing 1. In addition, several States derive revenue from the collection of tolls. For the purposes of this thesis, activities concerning toll facility construction and operation will not be discussed. 83 STATE HIGHWAY FINANCE: HIGHWAY BOND SALES, 1961-1971 Category I: States which have not issued bonds for toll or free roads Arkansas Colorado Idaho Iowa Kansas Category II: States which have California Illinois Mi ssouri iontana levada South Dakota Utah Wyoming issued bonds solely for toll road constructi on Indiana Texas Louisiana Virginia Category III: States which have issued (free and toll) hiqhway bonds at irreqular intervals Kentucky Nai ne Maryl and Michigan Minnesota Oregon Pennsylvania South Carolina Mitsissippi Nebraska New Hampshire New Jersey New riexi co Washington West Virgina Wisconsin Table 11.3.5 New York North Carolina North Dakota Ohio Oklahoma Tennessee Vermont Alaska Arizona Florida Georgia Hawaii 84 STATE HIGHWAY FINANCE: HIGHWAY BOND SALES, 1961-1971 (contd.) Category IV: States which have issued free road bonds every year Alabama Connecticut Del aware Massachusetts Rhode Island Table 11.3.5 (contd.) 85 as a regular component of their highway finance program. These States (see Table 11.3.5) have issued free road bonds in each of the ten years 1961-1970. The remainder of the States have resorted to bond financing on an irregular basis, presumably to meet perceived short-term highway "needs" that could not be financed out of current revenue sources. Appropriations to State Highway Department programs from State general tax revenues do not represent significant amounts of money, nor are these transfers performed on a regular basis for the great majority of the States. The notable exceptions to this rule are the so-called general fund States: Delaware, New Jersey, New York and Rhode Island. In these four States, all highway user tax revenues are deposited in the State General Treasury, and thus technically all appropriations for highway activities come from a non-earmarked general fund. In practice, even in these States, yearly highway appro- priations tend to nearly equal highway user tax revenues. For the remainino States, all highway user revenues are set aside in State Trust Funds, earmarked exclusively for highway-related expenditures. Of the 46 "Trust Fund States" 28 States are subject to anti-diversion Constitutional Amendments (see Figure 11.3.1). The remaininn States have either established expenditure restrictions by State Statute or simply through historical practice. STATES HAVING ANTI-DIVERSION CONSTITUTIONAL AMENDMENTS "*Fly -States having anti-diversion constitutional amendments - 28 Figure 11.3.1 wat I 1 Irv ar --f I F-4 I -1I LA I F- I F--l I -L r771 If[_- T *. I t:!J f EfTEI rim H I FH r-H+r4' IF-4 I RI L V"lr L wis 644mlj4 -1 1 go -THI %Ora- PA I P41.1a -Um I F-i I ILL U-A T I F- wall= w DC L 7-L COL4 -T V- IHI i =: I -i I I I MH 1 -41 1 1 J 1-i I H.11 NCI -T L- 0 k X A121C sc LA t -07mH 87 ii. TimeLag Structure From the time that highway-related revenue is deposited in the Federal Treasury account for the IHTF, to the time States receive Federal reimbursements for completed work on Federal-Aid Systems, Trust Fund monies pass through a series of stages at the Federal and State level. These stages can be defined as: authorization - the Congressional allotment of Federal funds to each of the Federal-Aid Systems apportionment - the division of Federal funds on each of the Federal-Aid Systems among each of the 50 states obligation - a contracted agreement between a State and the Federal governnent to commit funds to a particular Federal-Aid System project reimbursement - the actual transfer of Federal funds to a State based upon a State's current billing of contracted highway construction In practice, there is a contracted stream of funds passing between the IITF and the States. However, the actual reimbursement from a given annual authorization nay take as long as 15 years.I In order to trace the dynamics of the intergovernmental transfer of highway funds, we represent the lag structure in five distinct steps. 1. That is, a State may receive a reimbursement from funds authorized 15 years prior to the fund transfer. 88 Lag 1:Authorization-to-Aportionment As previously noted, Congressional authorization of highway funds precedes apportionment by at least six months. Lai 2:_Apportionment-to-Programming This lag relates to the time required by States to develop highway programs for submittal to BPR review. The duration of this lag is somewhat uncertain, varying for different project types, and from State-to-State (for a given project type). Since the level of Federal highway aid has been nrowing at a fairly steady rate since the inception of the IHTF, States are well aware of the amounts of rrants they can expect to receive. Accordingly, the States have tried to "keep one step ahead" of the apportionment process by developing programs containing enough projects to fully obligate their apportion- ment levels. In practice however, States have encountered varying degrees of corrunity opposition to proposed projects. The result has been a lag between the initial availability of Federal-Aid apportionments, and subnittal of an approved program of Federal-Aid System projects. Friedlaender has estimated that the apportionment-to-programming lag was usually on the order of four to six weeks in the late 1950's. In recent years, the increasing difficulty in negotiating community 1. Friedlaender, Ann, F., "The Federal Highway Program as a Public Works Tool," in Ando, A. et al, STUDIES IN ECONOMIC STABILIZATION, The Brookings Institute, 1968. 89 acceptance of highway projects has led to a significant increase in the duration of the apportionment-to-programming lag. In fact, there has been one case where a State,1 was unable to program its highway apportionment before the deadline for obligating Federal funds was reached. Each State is given two years beyond the year for which funds are authorized to obligate its highway apportionment. Figures 11.3.2 and II.3.3 show that most States are, in recent years programming projects from previous years' apportionments. Figure 11.3.2 presents the frequency distribution of State obligations for Interstate appor- tionments. Midway through fiscal year 1973, four States were still obligating 1971 funds, nine States were obligating 1972 funds, and the remaining thirty eight States had obligated some portion of their current apportionment.2 Taking the nation as a whole, only 17% of the then current Interstate apportionment had been obligated by December 31, 1972. Figure 11.3.3 shows the frequency distribution of ABC apportion- ments obligated as of December 31, 1972. Relative to the Interstate program, a higher percentage of current ABC apportionments have been obligated. Only one State was still obligating 1971 funds, twelve 1. Actually, the "State" was ashington, D.C., which for the purposes of highway apportionments receives Federal funds in the same manner as States. 2. States always obligate their "oldest" apportionments first. Thus, any State obligating current apportionments has already completely obligated its previous apportionments. Frequency Distribution of Interstate Obligations Number of States Obligating Various Percentages of Their Interstate Annortionments 10 10 20 30 40 percent 50 60 70 obligated 80 90100 10 20 30 40 50 60 70 80 90100 10 20 30 40 50 60 70 80 90 100 percent obligated percent obligated 1971 Apportionments 1972 Apportionments 1973 Apportionments Figure 11.3.2 U.S.Average 9 8 7 6 5 4 3 2 Frequency Distribution of ABC Obligations Number of States Obligating Various Percentages of Their ABC Apportionments U.S. Average 3 ------------- 2A 8 1_________ 27 _______________ NN 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 percent obligated percent obligated 1971 Apportionments 1972 Apportionments 90 100.10 20 30 40 50 60 70 80 90 100 percent obligated 1973 Apportionments Figure 11.3.3 ko 92 States were obligating 1972 funds, and the remaining thirty nine States were obligating current ABC apportionments. The U.S. average of ABC apportionments obligated by mid-fiscal year 1973 was 32%. It may be concluded from these two figures that the appor- tionment-to-programming lag is greater for the FAI program than for the ABC program. Moreover, it is apparent that this lag has lengthened significantly since Friedlaender's estinate in the late 1950's. Several States have been unable to program potentially funded Federal- Aid System projects for 2 1/2 years or loncier. The nationwide average lag between apportionment and programming appears to he on the otder of ten months. Lag 3: Pronramming-to-Approval Following a State's submission of a highway project to the BPR, the District Engineer reviews the plans, specifications End estimates detailed in the State aprlication. The review process can take anywhere from one month to more than a year, depending on the complexity and scale of the project. For example, a simple rural resurfacing project may be approved within one or two morths, while a large Interstate section with several complex drainage and [ridge structure requirements would take several months to review. The culmination of the BPR review is an approved project agree- ment, allowinr States to obligate the use of Federal funds. Lag 4: Obliiation-to-Contract Lag An obligation does not involve an actual flow of funds. At this point, a State has merely obtained the approval of the BPR to 93 seek bids on an approved project. The State now proceeds to enter the project into its ongoing construction program. The State's decision as to when to advertise a contract for construction is in- fluenced by its capital budgeting status. Assuming a State advertises a contract immediately upon signing a project agreement with the BPR, there is usually a minimum of a three to four week period before sealed Lids are opened. After the low bidder is determined, the State must obtain the BPR's final approval on the contractor's quali- fications. Thus, the minimum lag between initial BPR approval, and the finel signing of a construction is typically on the order of one month. Lag 5: Contracts-to-Federal Reimbursement ITF monies are disbursed to States on a reimbursement basis. Thus, the final lag in this process involves the time required for the contractors to mobilize their work force and submit the first month's expense voucher, and for the State to verify that the work has been done, and submit a record of expenses to the BPR office in Washington. The lag here could be anywhere from one to two months. Summary: La9 Structure on the Federal-Aid Highway Program Figure 11.3.4 traces the FAHP lags from initial Congressional authorization to the time that Federal funds actually enter the income stream as construction expenditures. Two alternatives sequences are shown, one with a total lag of one year, and the other with a two year total lag. The major source of variation between these two lag FEDERAL AID HIGHWAY PROGRAM LAG STRUCTURE 1- ~pzproximatJy -A yr 6 moa. II rI Figure 11.3.4 I l. yrs I I I I I z yrs Leoend rnl AtlorisnrioM W[ A Inii'oV oj conract A Eim1( ieam rsrnenf frm I HT H Fh3rammir1 O f cc4-.F id &prem consfructoN ®...G Lae vou rae ,A )Fi flpoual oj AnS r 95 sequences is in the apportionment-to-programming lag, which may take anywhere from one month to several years. It should be noted that the total authorization-to-reimbursement lag for those States who are still programming prior years' FAHP funds, will generally be longer than the lag for States who are pro- gramming current apportionments. In other words, States with a relatively large unobligated portion of FAHP funds will not react fully and immediately to changes in present FAHP apportionment levels. Taking the nation as a whole, total highway obligations have been running fairly close to the OMB-imposed fiscal control limitation on IHF expenditure levels, as shown in figure 11.3.5. The total lag between project approval (obligation), and Federal reimbursement is represented by a horizontal line connecting the obligation and expen- diture lines on figure 11.3.5. For example, at the point marked A, this lag appears to be approximately 18 months. 96 FEDERAL-AID HIGHWAY PROGRAM INTERSTATE HIGHWAY TRUST FUND EXPENDITURES AND RECEIPTS Di 26 24 22 20 18 16 4 2 *IS71/65 FY 1q7o 7/1/70 FY --197-1 7/-1/71 F)Y -197Z 7/1/72 FY -Iq73 7/1/73 0=43, 847.1 Source: FHWA Memo Dated 1/19/73, "Progress of the Federal Aid Highway Program" Figure 11.3.5 Allars (millions) .01elol --0 - /.11 0 97 iii. Aspects of Trust Fund Taxation The previous sections have detailed the mechanics of the Feleral-Aid Highway Program as it has evolved since the early 1900's. While the focus of this chapter - in fact of the entire thesis - is an investigation of how States react to the availability of Federal highway grants, an underlying issue that deserves some attention is the tz.xation conventions associated with the Interstate Highway Trust Fund. It is somewhat paradoxical that while the IHTF has come under serious scholarly and Congressional scrutiny in recent years, the use of Trusts Funds as a mechanism to finance transport facilities has been introduced to other modal areas. In particular, the Airport andi Airway Developnent Act of 19702 established tickeL tax-based trist funds to finance the development of aviation facilities, and sinilar proposals have been raised in regard to the inland waterway system. Perhaps the strongest argument in favor of a trust fund finan- cing approach is in facilitating the orderly long-range planning and implementation of public facilities by guaranteeing a stable level of Federal financial assistance. Nonetheless, the practice of establish- ing a set of earmarked user charges in the use of transport facilities 1. As manifest by the prolonged debate over passage of the 1973 Federal-Aid Highway Act. 2. Public Law 91-258, Titles I and II, enacted May 21, 1970. 98 represents an intervention into the private market sector, and carries with it impacts on equity, efficiency and redistribution of income. This section will attempt to evaluate the economic consequen- ces of the IHIF with particular attention paid to the aspects of trust fund taxation. Depending on one's viewpoint, the revenues raised for the Interstate Highway Trust Fund are variously referred to as indirect excise taxes, user charges, or prices for the use of the publically provided road system. Some unambiguous definitions of these and related key terms are essential if this analysis is to proceed on a conmon ground. 1 De'initions of the Revenue Terms Prices - a cost-based charge for the consumption of a scarce resource User Charges - a revenue-raising levy, not necessarily based on the real economic cost incurred in producing a (public) good Taxes - a pure revenue measure which bears no explicit relation to the cost of providing public goods.2 In general, a tax is associated with a pure revenue objective, an I evaluated in terms of its regressiveness/progressiveness (the relative burdci of the levy on various income classes). User charges 1. The definitions presented here are drawn from "The Public Finance Aspects of the Transportation Sector," A Staff Paper prepared by the Office of Policy and Plans Development, U.S. Department of Transportation. 2. In fact, the inherent nature of a pure public good (e.g. national defense) renders an explicit pricing system infeasible. 99 are cornonly associated with an equity goal - the concept that users should pay a fair share for their consumption of a service and prices are normally related to the concept of economic efficiency. The importance of these distinctions between taxes, prices and user charges is more than a mere semantic issue. The fundamental question relates to goals of the Interstate Highway Trust Fund revenue measures. For if the IHTF is to be viewed as a price system, then those prices must be justified on the basis of Vie real costs incurred by an individual user (driver) of the Federal-Aid Syteras. Conversely, if the IHTF revenue measures are to serve as user charges, then a valid concern is whether those charges meet an equity criterion. Finally, to view the IHTF as a pure revenue mechanism raises the question of the relative regressiveness of the revenue measures. It would be difficult to argue the case for the IHTF as a mechanism to foster efficient use of scarce highway resources. No claim was originally made that the Trust Fund was to be financed through a price (as previously defined) system.1 The revenue sources (see Table 11.3.1) simply represented a pragmatic means to provide an assured stream of revenues for highway construction. Because the IHTF revenue sources have the properties of (excise) 1. Referring to Table 11.3.1, it is clear that the revenue sources of the IHTF do not fit our definition of prices. The levies on tires, tread rubber, oil, new trucks, buses and trailers, parts and accessories, gasoline, diesel and special fuels may be con- sidered as either user charges or (excise) taxes. 100 taxes and user charges, it is important to assess the impacts of the program in terms of income redistribution and equity. Income Redistributive Properties of the IHTF The income redistributive properties of the IHTF can be viewed in terms of either an individual driver, or in terms of the fifty States. In the former case, we are concerned with the burden of the IHTF revenue measures on an individual driver relative to his income. In the latter case, the focus is on the amounts of FAHP aid received by each State relative to their per capita income. In either case the IHTF revenue measures may be defined as: progressive - a wealthier individual (State) pays more (receives less) in both absolute and proportional terms than a poorer individual (State) proportional - a wealthier individual (State) pays more (receives less) in only absolute terms than a poorer indivi- dual (State) regressive - a wealthier individual (State) pays less than or an equal amount (receives more than or an equal amount) as a poorer individual (State). In general, excise taxes tend to be proportional, or in some casesI even regressive. This is true as long as consumption of an item by individuals tends to grow less than proportionately with 1. Excise taxes will be regressive if the taxed item is an inferior good - i.e. an individual's consumption of the item decreases with increasing income. For a general note on the regressivity of excise taxes see Due, J.F. and A.F. Friedlaender, GOVERNMENT FINANCE, Richard D. Irwin, Inc., Fifth Edition, 1973, page 384. 101 increases in personal income. Thus, for an evaluation of the rergressivity of the IHTF revenue measures, in terms of the burden on the individual driver, the issue is to determine the relative case of the automobile (and thus the relative amount of the IHTF levy) by individuals with differing income levels. Ta!le 111.3.6 displays the distribution of person miles by income class anr' type of transport based on a 1967 nationwide survey. The survey was restricted to trips involving overnight stops away from home and/or journeys in excess of 100 miles each way. Thus, we may infer that the data is indicative of travel patterns for vacation ani business travel rather than journey-to-work travel. The most striking finding indicated by the table is that the percent of households in each income class using auto for vacation or business travel tends to decrease with increasing household income. Thus for example, while auto accounted for 06% of the total person miles of travel by house- holds with income $6000 - 7499, the corresponding figure for the highest income group ($15,000 and over) is only 51.7%. The difference in the intensity of auto usage between income groups for trips in excess of 100 miles derives primarily from the marked increase in the patronage of commercial air service by higher income households. The choice of the air mode varies from a low of 8.5% of total person miles of travel by the lowest household income category to a high of over 41% commercial air patronage1 by the highest income households. 1. The percentages reported here do not indicate the frequency with which one mode or another is chosen, but only the percent of total miles traveled on each mode. Thus one transcontinental car trip may account for more mileage than dozensFf auto trips of a shorter distance. 102 Distribution of Person-Miles by Income and Type of Transport (For Overnioht Journeys and/or Trips in Excess of 100 Miles One Way) Percent of Households in Each Income Class Choosing Each Mode Source: Bureau of the Census, 1967 CENSUS OF TRANSPORTATION, Volume 1, July, 1970, pp. 35-36 (Table 12) Table 11.3.6 Annual Household Primary Node of ravel Income Auto Bus rain Coimercial Air Combinations and Other Under $4000 79.0 6.1 4.4 8.5 2.0 $4000-5999 84.8 2.8 2.6 9.0 0.8 $6000-7499 86.0 1.0 1.9 9.4 1.7 $7500-9999 82.9 1.2 1.4 13.3 1.2 $l0,000-14,999 74.8 0.7 1.1 21.1 2.3 $15,000 and over 51.7 0.6 1.6 41.1 5.0 Income not reported 74.0 1.7 j25 18.6 3.2 All income groups 77.3 1.9 2.0 16.8 2.3 103 The data is indicative, if not conclusive of the phenomenon that consumption of auto travel for relatively long trips may be considered an inferior good. Further insight into this question is provided by Table 11.3.7 which combines the modal split information of Table 11.3.6 with data describing total person miles of travel across all modes by income class. Tie last column of this table lists the auto person-miles per household as a function of household income. The pattern that emerges is that auto travel per household increases yith income, but less than proportionately, except for the highest income level where auto travel decreases sharply. Note that travel by all modes increases uniformly with (column 4, Table 11.3.7) income, indicative that vacation/business trips per se are superior economic goods. Nonetheless, auto travel exhibits the characteristics of decreasing patronage with increasing income. Since the IHTF is (partly) financed through an excise tax on the sale of casoline, the tax burden on an individual household is directly re"ated to the intensity of auto usage. Given the above findings on the pattern of auto usage for relatively long trips, it is clear that IHTF taxation is regressive. A similar pattern emerges for home-to-work auto trips. Data supporting the contention that IHTF taxation is regressive with respect to commuting is found in Tables 11.3.8 and 11.3.9. The first table displays the modal split of home-to-work trips as a Distribution of Auto Travel Patterns by Household Income Level (For Overnight Journeys and/or Trips in Excess of 100 Miles One Way) Source: Bureau of the Census, 1967 CENSUS OF TRANSPORTATION, Volume 1, July, 1970, pp. 17, 35-46 Table 11.3.7 Annual Household Number of Number of Person-Miles Percentage of Auto Person Income Households Person-Miles Per Household Person-Miles Miles Per (Millions) (Billions) Per Year by Auto Household Under $4000 7.3 35.0 4790 79.0 3790 $4000-5999 6.8 46.0 6770 84.8 5740 $6000-7499 5.2 42.9 8270 36.0 7110 $7500-8999 6.5 58.6 9020 82.9 7490 $l0,000-14,999 5.7 65.9 11570 74.8 8660 $15,000 and over 2.6 34.8 13400 51.7 6920 Income not reported 4.0 28.6 7170 74.0 5300 All income groups 38.1 311.8 8180 77.0 6300 __ Relationship of Mode Choice and Household Income for home-to-Work Trips _,utombi_____Mode of Transportation Automobil e ___ Annual Househol d Driver Passenrer Total Public Walking Other In comQ Transportation Under $3000 25.5 20.1 45.7 12.8 11.9 29.6 $3000-3999 29.7 18.8 48.5 12.5 12.7 26.3 $4000-4999 34.7 21.4 56.1 11.6 7.0 25.3 $5000-5999 45.2 13.5 63.7 9.4 5.5 21.4 $6000-7499 46.4 20.3 67.2 6.9 5.3 20.6 $7500-9999 49.8 20.5 70.3 5.9 4.5 19.3 $10,000-14,999 54.9 19.2 74.1 5.1 2.9 17.9 $15,000 and over 58.8 16.4 75.2 6.5 3.3 15.0 All 48.4 19.1 67.5 7.2 5.0 20.3 Percent of employedjpersons in each household income group by mode of home-to-work transportation (1%69) Source: U.S. Department of Transportation, Federal Highway Administration, NATIONWIDE PERSONAL TRANSPORTATION STUDY, HOME-TO-WORK TRIPS AND TRAVEL, Report No. 8, August, 1973. Table 11.3.8 0m- 106 Relationship of Average Commute Time for Hone-to-Work Auto Trips and Household Income Annual Household Income Average Commute Time (in minutes) Figures represent 1970 data Source: U.S. Department of Transportation, Federal Highway Administration, NATIONWIDE PERSONAL TRANSPORTATION SURVEY, HOnE-TO-WORK TRIPS AND TRAVEL, Report No. 8, August, 1972 Table 11.3.9 Under $3000 18 $3000-3999 18 t4000-4999 20 $5000-5999 22 $0000-7499 19 $7500 -9999 20 $10,000-14,999 20 $15,000 and over 21 Pll income groups 20 107 function of income, based on a 1969-1970 nationwide survey.1 As might be expected, the choice of auto for the journey-to-work tends to increase as household income increases. However, it should be noted that this increase is less than proportional: the range in household income varies by a factor of more than five to one, while auto patronage increase by only slightly more than two to one. Sore indication of the average trip distance for journeys-to- work by income groups is given by Table 11.3.9. The Nationwide Personal Transportation Survey did not directly report on the varia- tion in trip distance by income group. However, it is apparent from the striking uniformity of corruting travel time across different income groups, that travel distance for journeys-to-work cannot vary appreciably across income classes. The conclusion from these data is that the total auto mileage devoted to journey-to-work trips (and thus the corresponding burden imposed by the IHTF tax levies) increases less than proportionately to increases in household income. Accordingly, with respect to this trip purpose, the IHTF represents proportional tax system. In addition to the income redistributive consequences of the IHTF revenue measures on individual drivers, the FHAP effects on explicit redistribution of income among States. We refer to the fact 1. The Uationwide Personal Transportation Survey conducted by the Bureau of the Census. Comparison of Estimated State Payments to the Highway Trust Fund with State Receipts from the Highway Trust Fund and Federal-Aid Apportionments, Fiscal Years 1957-1970 Estimated Pa ents tothe H wa rust und(Millions of Dollars) Federal Aid Apportionments For Each Dollar the State Paidiito the Higwa Trust Trust fnd 75pto7/70, State was Apportioned State Per Capita In- come 1963 Al abaa Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska 833 451 539 4,766 561 624 143 1.500 1 ,152 224 2,358 1,372 780 674 744 800 258 768 1,083 2,089 938 555 1,258 235 448 1,006 682 539 4,102 647 692 180 1,032 1,008 361 2,508 1,188 747 613 930 1,124 291 799 1,073 1,778 1,157 638 1,279 627 463 $1.21 1.51 1.00 .86 1.15 1.11 1 .26 .69 .88 1.61 .1.06 .87 .96 .91 1.25 1.40 1.13 1.04 .99 .85 1.23 1.15 1.02 2.67 1.03 1669 2220 1625** 2993 2479* 3113 2994* 2141 ** 1878** 2045 2911* 2467 2299 2398 1840 1839 1957 2678* 2774** 2581 2365* 1434 2360* 2263 2273 Source: Federal Highway Administration, 1972 National Highway Needs Study Project C-i. Table 11.3.10 C) State Comparison of Estimated State Payments to the Highway Trust Fund with State Receipts from the Highway Trust Fund and Federal-Aid Apportionments, Fiscal Years 197-1970 (Continued) Estimated Payments Federal Aid For Each Dollar the State State Per to the Highway Apportionments Paid into the Highwa Trust Capjgjncome Trust Fund Fund 7/S to 7/7, State 1963 (Millions of Dollars) was Aportioned Nevada 155 352 $2.27 3235* New Hampshire 169 246 1.46 2343* New Jersey 1,514 1,238 .82 2960 New Mexico 340 583 1.71 2048 New York 2,897 2,718 .94 3009 North Carolina 1,234 719 .58 1801** North Dakota 176 349 1.98 1999 Ohio 2,442 2,689 1.10 2508* Oklahoma 776 668 .86 1990** Oregon 593 820 1.38 2471* Pennsylvania 2,424 2,311 .95 2437 Rhode Island 185 251 1.36 2510* South Carolina 606 494 .82 1576** South Dakota 207 428 2.07 1908 Tennessee 939 1,156 1.23 1772 Texas 3,192 2,579 .81 2102** Utah 276 601 2.18 2210 Vermont 110 320 2.91 2013 Virginia 1,056 1,369 1.30 2093 Washington 804 995 1.24 2618* West Virginia 394 804 2.04 1778 Wisconsin 963 706 .73 2375 Wyoming 147 469 3.19 2412* * States with higher than average per capita income who are apportioned more than they contribute to the Trust Fund ** States with lower than average per capita income who are apportioned less than they contribute to the Trust Fund Table HI.3.10 (contd.) a '0 110 that the various apportionment formulas described in section 11.2, determining the relative amounts of Federal-Aid System grants to be given to the States result in several States contributing more to the IHTF than they receive in the form of grants (and vice versa). Table 11.3.10 indicates the extent of income redistribution resulting from the Federal-Aid Highway Program apportionment formulas. Of the thirty-one States which were apportioned more than they con- tributed to the Trust Fund (over the period 1957-1970), fourteen had higher than average per capita income.1 Conversely, the same amount as they contributed to the IHTF, eight had a lower than average per capita income. Both of these instances are examples of perverse income distribution. It is not surprising to find that the formulas used to apportion FAHP grants result in several cases (22 out of the 48' mainland States) of States with higher than average per capita incomes receiving proportionately higher income transfers in the form of highway grants (and vice versa), since the enabling legislation did no consider income distribution as an espoused goal of the Federal-Aid Highway Program.2 None of the apportionment formulas described in Tables 11.2.3 and 11.2.4 take account of per capita income, fiscal capacity tax effort, or similar measures of State Wealth. Nonetheless, as has been shown, the fact that a Federal grant program does not l.The average per capita income in 1963 was $2287. Income data is shown for 1963 because this represents the meddle of the 1957-1970 sample period for which apportionment data is presented. 2. For a good discussion of the debate over the selection of factors to be incorporated into apportionment formulas, see Burch, P. op.cit. 111 address an explicit income redistribution goal, does not imply that the program will be distributionally neutral.I In summary, two aspects of the income redistributive impacts of the Interstate Highway Trust Fund have been explored. First, the excise taxes used to finance the IHTF tend to be regressive or proportional, depending on individual drivers' trip purposes. Secondly, the formulas employed in apportioning IHTF revenues among States result in a mildly progressive redistribution of income. One more point should be stressed with regard to the latter conclusion. The low value of the correlation coefficient between per capita income and apportionments (see footnote 1 below) reflects the fact that there are nearly as many States exhibiting perverse income distribu- tion with respect to the FAHP grants, as there are States emblematic of the "commonly accepted" goals of income distribution. 2 1 Taken as a whole, the FAHP appears to be mildly progressive. The correlation coefficient between apportionments and per capita income in 1970 was -0.1965. However, it is still the case that for more than 20 States, the FAHP results in perverse income distribution. 2 It should be noted that the Federal government does administer several grant programs -- most notably the general revenue sharing program, and the welfare grant program -- which are structured to accomplish explicit income distribution goals. Pursuant to the State and Local Fiscal Assistance Act of 1972 (general revenue sharing), States with lower per capita income and/or higher tax effort receive proportionately higher Federal aid. And in the welfare grant programs, States with relatively large numbers of welfare recipients (and thus presumably those States with relatively low per capita income), receive proportionately higher amounts of Federal welfare assistance. 112 Equity Considerations in Administering the IHTF The issue of equity deserves some attention if for no other rea- sen than that it has been the primary argument espoused by proponents of continuing the trust fund approach to financing roads. This justi- fication follows the general principle that those who use roads often should ppy more than those who use them little. The obvious extension of this principle -- often referred to as the benefit principle -- is that those who do not use the road system (e.g. transit patrons) should neither pay for, nor receive aid fron a highway trust fund. Although the concept of equity inevitably involves the vagaries inherent in deciding on what constitutes a "fair" distribution of the tax burden, some general conclusions on the equity characteristics of the Interstate Highway Trust Fund can nonetheless be established. On an elementary level, it is indisputably true that the excise tax on gasoline sales guarantees a rough measure of equity in that those who drive more pay more. But the more sophisticated treatment of equity examines both aspects of IHTF taxation: the distribution of the tax burden and the distribution of benefits derived from the IHTF. It is not s-fficient to conclude that the IHTF assures equity based only on examination of the revenue side of the IHTF. Since Federal highway grants are restricted to expenditure on roads comprising the Federal Aid System, a more rigorous test of equity would require that the tax burden assessed on individual users be distributed according to the intensity of their use of the Federal-Aid System. If all people drove in exactly the same proportion on the different Federal-Aid highways as well as on roads off the Federal-Aid System, 113 (FAS), then the policy of spreading the costs of the FAS over all drivers would be justified. But as long as all drivers do not use the various highway systems equally, inequities are bound to result. More succintly, the driver who never uses the Federal-Aid System will effec- tively subsidize a person who predominately does. Table 11.3.11 provides evidence that drivers in different size cities tend to make disproportionate use of roads on and off the Federal- Aid Systems. The pattern that emerges is that the percent of travel on all Federal-Aid Systems classified as principal and minor arterials tends to decrease monotonically with increasing city size. For example, while drivers in cities in the smallest population group devote 95.6% and 86.1% of their vehicle miles to principal arterials and minor arterials respectively on the Federal Aid System, the corresponding figures for cities in the highest population group are only 80.7% and 66.7%. Thus for each mile driven (and thus for each Federal excise tax dollar collected per vehicle mile), the population in smaller cities get greater use from Federally financed roads than their coun- terparts in larger cities. In addition, there exists an equity issue with respect to the relative use of roads within-the Federal-Aid System. In particular, the Interstate System carries only 27.2% 1 of the total vehicle miles on all Federal-Aid Systems in 1968, while accounting for 72% of the total Federal apportionments in the same year. Accordingly, users 1 As reported in the 1972 National Highway Needs Report (op cit) Distribution of 1968 Mileage on Travel on and Off Federal"Aid Systems by'Functional System in Urban Areas by Population Groups 114 Percent of Travel on Federal Aid Systems Population Group 5,000 10,000 25,000 50,000 100,000 250,000 500,000 1,000,000 Principal Arterial Systems - 9,999 - 24,999 49,999 - 99,999 - 249,999 - 499,999 - 999,999 and over 95.6 94.2 93.3 91.0 86.4 87.9 83.8 80.7 Minor Arterial Systems 86.1 82.2 78.1 76.5 72.8 74.2 70.2 66.8 Source: Part II of the 1972 National Highway Needs Report, House Document No. 92-266 (Table 111-2, page 111-8) Table 11.3.11 115 of the Interstate System are heavily subsidized by drivers on the other Federal-Aid Systems. Two other examples of inequitable financing within the Federal Aid Highway Program may be cited. Again, the rigorous test of equitable- ness employed here relates the use of specific classes of highways relative to the tax burden faced by specific types of highway users. Along these lines, it has often been cited th&t peak-hour highway users in urban areas are heavily subsidized by off-peak drivers. The point was made as early as 1959 by Professor William Vickrey in testi- fying before the Jiont Committee on Washington Metropolitan Problems. Table 111.3.12 is condensed from Exhibit 51 of these hearings. The data attempt to separate out the capital cost required in implementing alternative transportation plans solely due to peak hour traffic. The major finding here is that single occupant peak-hour arivers require an incremental investment of $63 per round trip per year (i.e., over and abive the investment required to provide adequate capacity for off-peak auto use). While the exact figures reported by Professor Vickrey might be subject to question, it is nonetheless true that the IHTF revenue measures average costs over peak and off- peak users alike, while peak users are responsible for the greater share of the costs.I This is clearly an inequitable distribution of the costs for the provision of urban highway facilities. This issue also involves efficiency considerations, since the gasoline taxes do not serve as cost-based prices. In fact it may be argued that the result has been as an overexpansion of urban high- ways, since it is not at all clear that peak-hour drivers would be willing to pay the true social costs of their auto use. Incremental Costs of Rush Hour Travel by Various Modes Investment Costs Per Round Trip Per Person Investment Per Round Trip per Year ($) Mode Rate of Capital Charge (percent) Cost Per Round Trip Operating Costs Per Round Trip Per Person ($) Totai Costs Per Round Trip Per Person ($) Express Bus Rail Private Automobile: 1 Person Roads and Vehicles Out of Pocket Operating Cost Parking Total Auto I Person Total Auto 2 Persons Source: Transportation Plan for Washington Metropolitan p. 478. the National Capitol Region, Hearing Before the Joint Problems, Congress of the United States, Eighty-Sixth Committee on Congress, 1959, Table 11.3.12 2.70 4.20 15 10 63.00 0.40 0.42 0.35 0.19 5 3.15 10.00 73.00 36.50 8 0.75 0.61 3.15 0.30 1.00 4.45 2.23 0.80 3.95 1.98 0.30 0.20 0.50 0.25 117 One final example of inequities inherent in the IHTF is provided by the Federal Highway Administration's 1969 study on the Allocation of Highway Cost Responsibility and Tax Payments. The major findings from this tudy are summarized in Table 11.3.13. These data estimate the total IHTF tax payments assessed on various highway users (automobiles, buses, and trucks) as compared to the costs of providing the Federal Aid Highway Systems attributable to each of these users. The apparent conclusion from these data is that buses andmedium-sized trucks are subsidizing automobile and heavy truck users of Federal-Aid roads. Whether the subsidies (inequities) cited in this section are desirable or not ultimately depends on value judgments as to the rela- tive merits of different types of travel. Inevitably, the choice of a financing mechanism for the provision of highways calls for compro- mises and political_judgment. Thus for example, the explicit subsidy of the Interstate System by drivers on the other FAS might be justified on the basis of the particular importance of the Interstate System for the national defense, and interstate commerce. While the other instances of inequities inherent in the IHTF -- rural vis-a-vis urban, peak user vis-a-vis off peak user and auto vis-a-vis turck users -- might be harder to justify, the complexity involved in administering a "perfectly equitable" user charge mechanism must be weighed in deciding upon any changes that would reduce these inequities. I The allocation of cost responsibility was based on the traffic volume, vehicular weight and vehicle size of each of the highway user classes. Heavier and/or larger vehicles require Ipecial structural considerations in the design of highway facilities (thicker pavements, taller overhead structures, etc.). 118 Total Federal Trust Fund Expenditure Allocation vs. Tax Payments 1969 Type of Vehicle Total Costs Allocated (Millions $) Total Tax Payments (Millions $) Ratio of Payments to Costs Automobiles Buses 2 Axle-4 Tire Trucks Other Single Unit Trucks Heavy Truck Combinations Other Total 2914 39 329 267 922 7 2742 59 546 480 702 11 4540 .94 1.51 1.66 1.80 0.76 1 .57 4540 Source: Allocation of Highway Cost Responsibility and Tax Payments 1969, U.S. Department of Transportation, Federal Highway Administration, Bureau of Public Roads, p. 74, Table 25. Table 11.3.13 119 11.4 Comparison of the Federal Aid Highway Program with the Federal Public Transportation Assistance Program In order to provide further insight into some of the unique aspects of the Federal-Aid Highway Program (FAHP) it is interesting to compare its operation with the Federal Public Transportation Assistance Program (FPTAP). The FPTAP differs in several important respects from the FAHP. A convenient framework for comparing the Federal roles in these two nodal areas is to summarize the FPTAP in terms of the same program descriptions used to characterize the FAHP (see Section I1.3.i). Sources of Federal Funds There is no FPTAP trust fund analogous to the previously described Interstate Highway Trust Fund. Federal funds for transit assistance derive from United States Treasury general tax revenues. /n important consequence of this characteristic is that Federal authori- zation levels are subject to Congress general budgetary review. Au- thorizations in years of "tight money" may be limited. This is in contrast to the IHTF whose financing is relatively automatic and "painless", determined primarily by the total revenues accruing to the Trust Fund. Total Expenditure Levels The magnitude of Federal financial effort in highway transpor- tation dwarfs the FPTAP. Since the first Urban lass Transportation Assistance Act (1964), Federal Transit grants have totaled $1.215 hillion (FY 1965-1971), only 3.85% of the total FAHP funds over the 120 same period. The most recent FPTAP bill, the Urban Mass Transpor- tation Assistance Act of 1970 (as amended by Title III of the Federal-Aid Highway Act of 1973) authorizes $6.1 billion through fiscal year 1976. uthorization Cycle There is apparently no fixed authorization cycle in the FPTAP analogous to the 2-year Federal highway authorization process. The first significant Federal financial commitment to public transpor- tation began with the Urban Mass Transportation Act of 1964 which authorized funds for the three fiscal years 1965-1967. Public Law 0-562 provided additional grants for the two fiscal years 1968-1969. Funds for the single FY 1970 were authorized by 701 of Public Law 90-448. Current authorizations derive from Public Law 91-152 which provides funding for at least five years (FY 1972-1976). Apportionment2ethod Unlike the FAHP, Federal transit funds are not apportioned anong States or local areas on a formula or other prespecified basis. Federal grants are awarded on a project by project basis. A metro- politan area or public transportation agency may apply for as many Federal grants as it chooses. The only apportioning limitation is that no State (i.e., the aggregate of all grant-receiving agencies or municipalities in a State) may receive more than 12 1/2% of the cumulative national level of grants obligated since the beginning of 121 FY 1971.1 An interesting consequence of this apportionment restric- tion is that a State which embarks on an ambitious transit capital improvement program may have to wait until other cities "catch up" before qualifying for additional funding. ' tch i nProvisions Grants for any type of qualifying public transportation project are provided at a single matching rate -- a Federal share payable of 00% of the net project cost.2 UNet project cost is defined as the estimated portion of the cost of a project which cannot be reasonably financed from farebox revenues. It is clear that the stated matching provisions give transit agencies the incentive to build relatively high capital cost projects. Expenditure Restrictions Similar to the FAHP, the FPTAP is based upon Federal conditional, matchin grants. In both programs, the conditional grants are 1. An exception is that any State which has received more than two- thirds of its grant limit may qualify for additional funding from a discretionary account which amounts to 15% of the total cumula- tive EPTAP authorization. 2. The initial determination of net project cost is made on the basis of estimates of total project cost and anticipated revenues derived from engineering studies, studies of economic feasibility, and data showing the nature and extent of the expected utilization of the project facilities and equipment. The actual amount of the Federal grant is determined at the completion of the project on the basis of the actual net project cost. Further information on the mechanics of Federal transit aid may be found in CAPITAL GRANTS FOR URBAN MASS TRANSPORTATION: INFORMATION FOR APPLICANTS, distribu- ted by the Urban Mass Transportation Administration (June, 1972). 122 restricted to financing capital expenditures. Grant-eligible public transit projects include land acquisition, (re)-construction of transit-related facilities, and the purchase of buses, rail rolling stock, and related equipnent. Local Recipients of Federal Funds A fundamental difference between the FAHP and the FPTAP is tat the latter deals with municipalities and transit line agencies. The only State involvement with the acdiinistration of transit grants is in a general advisory capacity. Applications by local governments or transit agencies for Federal transit grants must be preceeded by a State and local review process as stipulated 1by 0MB circular A-95 and other Federal proceedural requirements. In comparison, the FAHP is administered exclusively through the States, with netropolitan areas acting solely in an advisory/review capacity. Sources of Local 1atching Funds The definition of transit net project cost implies that local agencies must provide some external (i.e. beyond operating revenues) means of financing their share of Federally-aided public transportation systems. Just as there is no established Trust Fund at the Federal level, very few cities have chosen to enact Trust Funds at the local level.1 The traditional means of local financing is through a two 1. An exception is found in Minnesota where the Twin Cities Metropoli- tan Transit Commission is empowered to set aside a levy of $1.00 on all automobiles registered in Minneapolis-St. Paul for develop- ment and operation of mass transit systems. 123 layer bond issue: local property tax-supported bond issues for fixed plant, and revenue bonds for the purchase of rolling stock. However, there are several structural varients in the method of transit financing in different metropolitan areas. It is interesting to note that the necessity to obtain bond issues to finance transit construction gives the local electorate (where referenda are required to ratify bond issues) or State legislatures virtual financial veto power. Several cases have arisen where transit bondin9 referenda have been defeated (e.g. Seattle (1969), Atlanta (1970), and New York (1972)), resulting in at least a temporary delay in project construction. In contrast, t:he FAHP is not characterized by an analogous veto process at the State level. Although several States have provided for local veto power over proposed highway projects, this control is not exercised through restrictions on the use of public funds. 124 11.5 Summary and Conclusions This chapter has provided a factual setting necessary for the development of empirical models designed to assess the impacts of the FAHP on State highway expenditure behavior. Of particular im- portance is the finding that highway finance employs a trust fund approach at both the Federal and State levels. The modelling im- plication here is that the evaluation of alternative Federal highway grant policies can proceed without a complete analysis of State budgetary processes across functional areas outside the transport- ation environment. In other words, since nearly all States finance highway construction and maintenance from earmarked excise taxes, we can restrict our modelling attention to how the FAHP affects long range highway revenue policy, and short run highway programing (allocation). The highway financing environment stands in contrast to financing conventions employed in the provision of other types of State services (e.g. welfare assistance, health facilities, education facilities) wherein all expenditures are made from a common budget. In these areas, changes in Federal grants (e.g. for education) would be expected to influence expenditure decisions on all functions other than highways due to the effect of a State's budget constraint.1 1. For an empirical analysis of the interaction between expenditure behavior on various State functional areas, see Tresch, R., op cit. 125 The interaction between highway expenditure behavior and the perform- ance of other State functions is minimal, and thus this research will restrict the analysis to the highway sector. 1 A second major finding with regard to the development of empirical models of expenditure behavior relates to the dynamics of the Federal-Aid Highway Program. As discussed in Section 11.3, Federal highway grants are available for abligation by States over a period of up to three and one half years. This raises the issue of a time lagged response to the FAHP -- i.e., States may not react fully and immediately to the availability of any one year's highway authorization. In fact, the amount of Federal highway grants available to a State in one year is not simply that years' apportion- ment. The empirical models presented later will employ a three year moving average on Federal grants to account for this character- istic of the FAHP. A third major characteristic of highway finance which must be accounted for in empirical models concerns the organization of the FAHP into several distinct Federal-Aid Systems. The implication here is that an important aspect of the highway expenditure behavior is the decisions on the aliocation of a State's highway budget be- tween alternative Federal Aid Systems (as well as expenditures on 1. Some interaction between highway and other functional area expenditure behavior may exist in those States with legis- lation limiting debt ceilings. In these cases, the decision to sell binds for construction of a State University (for example) might limit the debt service available for highway construction. Since debt financing does not constitute a major source of highway revenue for most States this type of interaction will be ignored. other highway categories). Several previous studiesI have simply 127 attempted to model the effect of total Federal highway grant avail- ability on total State highway expenditures. The problem with this approach is that it fails to distinguish between the separate expend- iture effects of Federal grants for each of the Federal-Aid Systems (each characterized by distinct authorization levels, matching pro- visions, etc.). The research strategy adopted in this thesis explicitly accounts for the possibility of distinctly different State expenditure responses to each of the major Federal-Aid System grants. Finally, the discussion of highway finance presented in this chapter serves to illustrate the two fundamental dimensions of State highway investment behavior: revenue policy and allocation policy. The former issue deals with the question of which factors influence a State to raise a greater or lesser amount of (earmarked) highway revenue. The second issue concerns the analysis of the factors that determine how a State allocates its highway budget amongst candidate expenditure categories. In this research the major focus is on the effects of Federal grants on these two dimensions of State highway expenditure behavior. Accordingly the empirical models presented 1. For example, O'Brien, T., op.cit., Gabler, L.R. and J.I.Brest, op cit. 128 in this research will explicitly deal with the behavioral bases for long run re venue policy formulation and short run allocation policy determination.I 1. The distinction between revenue policy as a "long run" phenomenon and allocation policy as a "short run" phenomenon derives from the fact that changes in the determinants of State highway revenue (e.g. tax rates, bond sales, etc.) tend to be infrequent relative to the expression of a State's allocation policy (e.g., year-to-year capital budget- ing decisions.) 129 Chapter III THE FEDERAL AID HIGHWAY PROGRAM: THE ANALYTICS OF DESIGN AND RESPTNSE III.1 Introduction Economists have developed an extensive set of theoretical and analytical tools that have been applied with some measure of success in analyzing the operation and performance of the private sector. Attempts to extend these economic tools to the analysis of the public sector cannot boast of similar success. This is particularly true of recent research into the nature of the impacts of Federal grants - in-aid on State and local governments. This chapter will set forth a series of theoretical models that serve to illustrate the expected consequences of a variety of Federal aid program structures. It should be stressed at the outset that there are several obstacles to a fruitful theoretical analysis of the impacts of the Federal aid highway program. An inmediate issue is whether to approach the analysis from a normative (prescriptive) or positive (descriptive) per- spective. Indeed, in studies of the private sector, the norma- tive analysis of, for example an optimal pricing policy, is often facilitated by rather simple assumptions on the objectives of the economic agents in the system (for example, profit 130 maximization by a firm). Section 2 of this chapter discusses the difficulty of inferring a set of goals guiding the Federal government's role in highway finance. Despite the fact that the Federal objectives in administering the highway grant program are neither easily identifiable, non-conflicting or static, Section two does attempt to develop a series of possible ra- tionales for Federal participation in the provision of the national highway system. For each rationale, the appropriate design of the Federal aid highway program is presented. Section three adopts a descriptive analytic framework. A basic allocation model is presented based on the economic theory of the consumer (i.e. the State is viewed as a consumer of highway facilities), to develop the expected expenditure responses of States to a variety of Federal-aid program struc- tures. Needless to say, the results reported here are relevant only to the extent that the assumptions underlying the alloca- tion model accurately describe the decision-making calculus employed by the States. Here too, an obstacle to fruitful theoretical analysis is the lack of an easily identifiable set of objectives defining the criteria by which States determine the level and allocation of their transportation budget. Nonetheless, section three proceeds on the basis of a somewhat simplistic decsion rule: a State will allocate its transporta- tion budget so as to maximize its perceived benefits (utility). 131 Qualifications to the analyses of State responses to a variety of grant types (open and close ended, categorical and non-cate- gorical, and matching and block type grants) are discussed in subsection vi of section three. Section four presents a different approach to analyzing State responses to Federal grants. The concept of the benefit/ cost ratio of candidate highway projects is introduced as the basic investment criterion used by States. Although the theo- retical analyses of sections three and four apparently differ with respect to their underlying assumptions, in fact the con- clusions drawn from both approaches are quite similar. Both sections draw attention to the price and income effects intro- duced by Federal grants, and proceed to demonstrate how State responses will differ according to the presence of one or both of these grant characteristics. Section five extends the analysis of the preceding section with an investigation of historical grant and expendi- ture levels of the Interstate and ABC highway programs. It is shown that for the Interstate program, Federal grants have stimulated State expenditures that would most likely have not been made in the absence of the grant program. This result is contrasted with the experience in the ABC program, where it is shown that Federal grants have had a relatively insignificant impact in determining total expenditure levels on an allocation 132 within the ABC system. Section six summarizes the theoretical findings of chapter three. The relationship between the response to Federal grants, and the structural characteristics of the grants is discussed. The similarity of findings between the consumer allo- cation model (Section 3) and the benefit/cost investment model (Section 4) are drawn, and related to the empirical evidence presented in Section 5. Finally, the importance of validating the theoretical findings in this chapter with econometric models of succeeding chapters is stressed. 133 111.2 Fiscal Federalism -- The Normative Aspects of Federal Highway Grant Program Design A logical starting point for an evaluation of the consequences of the Federal Aid Highway Program (FAHP) is to consider the Federal role in highway financing in the broader context of Fiscal Federalism.1 Viewed in this perspective, the immediate questions to be addressed relate not so much to a detailed examination of the merits of one or another apportionment formula or matching ratio, as to an ex ante discussion of the justification for any Federal involvement in highway finance. The distinction we wish to draw is simply this: proposed changes to the existing structure of the FAMP may be called for because the initial justification for the Federal role in highway finance is no longer (or has never been) valid, or because the structure of the FAHP is not compatible with the accepted goals of the Federal role in high- way finance. The former issue is clearly normative. Although Congress- ional debate over highway policy is not normally conducted at an abstract level, it may be inferred that current Federal highway legislation does recognize a need for Federal involvement in highway finance, and is in- tended to, inter alia,-stimulate State expenditures on the Interstate Highway System. 1. Fiscal Federalism is a generic title for the study of the dis- tribution of fiscal responsibilities in a decentralized- system of governmental units. See Musgrave and Musgrave, PUBLIC FINANCE IN THEORY AND PRACTICE, McGraw-Hill Boook Company, 1973, chapters 26,27, and Due and Friedlaender, GOVERNMENT FINANCE, Richard D. Irwin, Inc., 1973 (5th Edition), Chapter 19. 134 Accepting this policy statement for the moment, the often ex- pressed criticisms that the current FAHP has stimulated State ex- penditures on the Inter-State system beyond economically justifiable levelsi is directed not so much against the provisions of the FAHP as against the implicit national goals from which the FAHP is derived. On the other hand, if the provisions of the FAHP did not stimu- late Interstate Highway expenditures2 (again accepting this policy for the moment), then there may be ample justification for realigning the provisions of the FAHP. Thus the argument comes full circle. there is a clear distinction between stated (or implicit) national highway policy, and the characteristics of a particular highway program designed to implement that policy. In the broadest sense, the normative issue is to gain consensus on both of these aspects of the Federal Aid Highway Program. i. The Theory of Intergovernmental Grants Theoretical considerations can give some indication of the ap- propriate policy goals to be served by a program of intergovernmental grants. In general, there are three factors inherent in a decentral- ized system governmental jurisdictions that call for Federal fiscal 1. For example, see Testimony of Robert E. Gallamore, Director of Policy Development, Common Cause, Before the Subcommittee on Roads of the Senate Public Works Committee, February 15, 1973. 2. This would be the case if the States' Interstate Highway ex- penditures would have been at the same level in the absence of Federal grants. In this instance, it may be argued that Federal funds are primarily diverted to other expenditure categories in- cluding tax relief in which the Federal government has no officially stated interest. 135 intervention. The first factor relates to the existence of signifi- cant benefit spillovers, i.e., the incidence of benefits (or disbene- fits) beyond the boundaries of the jurisdictions responsible for financing public projects. In the case of highway investment, it is clear that at least part of the benefits derived from the provision of road services in any one State are enjoyed by residents of other states. To the extent that one state provides an adequate system of highways, adjoining states benefit from reduced over-the-road inter- state transport costs, and increased personal mobility for vacation and business travel. The problem here is when some of the benefits are external, the level of highway activity provided by any one state is likely to be too small relative to the interests of the country as a whole, if highways are financed locally, and decisions about the quantity to produce are left solely in local hands. Formally, this problem can be stated as follows. Consider a level of highway production Qi in State i and the associated costs C%, and benefits B (internal bene- fits) and Be (external benefits).1 In abstract terms, we represent highway costs and benefits as continuous functions of the level of highway production as shown in Figure 111.2.1. Borrowing the calculus of economic production theory, the optimal scale of highway production 1. This example is solely for illustrative purposes. It is not necessary at this time to distinguish between direct and in- direct benefits, nor between benefit incidence on subgroups within the population of a given state. The main thrust here is simply to investigate the allocative consequences of fragmented jurisdictional highway investment ecision-making. 136 INTERNAL AND EXTERNAL HIGHWAY BENEFITS AND COSTS ,00 000A .0 a-~ / / - / / - A -S - Figure 111.2.1 137 in the absence of external incentives. Qi is determined as that point where the marginal cost of highway production is equal to marginal highway benefits. In particular, if each jurisdiction bases its in- vestment decisions solely on the basis of benefits accruing to residents within its boundaries, we have the optimal production scale condition: 1 1 (1) aQi aQi Graphically, the optimal level of highway production is indicated by the point Q. where the slope of the cost curve and benefit curve are equal. Note that in this solution, no account has been taken of the benefits accruing outside of State i. If the residents of each jurisdiction were to base expenditure decisions upon benefits to the entire country rather than to their own areas alone, the optimal scale for provision of highways would be guided by the condition: aBT aBe 9BB aCi (2) where BT = total highway benefits (BT = B + Be) In this case, the optimal level of production is Q resulting in net benefits, Bi(QI) - C(Qi) indicated by line segment cd (see figure 111.2.1). This latter solution results in an expansion of highway 138 production in State i from Qi to Q7 and more importantly, an increase in net benefits from ab to cd. Simply stated, the issue is this: in the absence of external financial incentives, it is unrealistic to assume that individual jurisdictions (e.g. states) will pursue a highway investment policy that systematically accounts for benefits accruing beyond their boundaries. In cases where significant benefit spillovers occur, the consequences of this atomistic behavior is an underinvestment in highway facilities. ii. Functional Grants As Solutions The above comments serve not only to outline a valid concern for Federal intervention in highway finance, but serve to indicate the appropriate structure for remedial Federal action. Short of an out- right transfer of all highway investment activi es to the Federal government,1 the Federal objective is to prov de a set of financial incentives that will encourage lower level j isdictions to account for benefit spillouts in their investmen -decisions. 2 To illustrate the mechanics of the appropriate program structure to meet this objective, assume the federal government assumes a 1. By definition, a nationalized highway investment program would internalize benefit spillouts effects. 2. Clearly, counteracting the adverse effects of benefit spillouts on state investment behavior is not the only objective of a Federal Aid Highway Program. In fact, there exist other, con- flicting federal objectives. These will be discussed in the following sections. 139 (matching) share of the cost of the ith state's highway program as determined by the ratio of external to total benefits accruing from the provision of highways in State i. Returning to our initial model of optimal highway production scale where State i considers only in- ternal benefits in its investment calculus, we get the optimality condition: ,C C C ) Q 1BT (3) where C' = State i's share of the cost of highway production.1 1 Assume for the moment that the external benefits Be are some fixed proportion of internal benefits Bij, i.e.: Bi = f(Qi) (4) Be = af(Q.) then condition (3) reduces to 6T 'Bi jB Be B aci (5) B i Qi BQi Bi Qg Qi 1. C1 represents the total cost of highway construction in State i. Ifthe federal government assumes a share of highway cost equal Beto the ratio of external to total benefits, i.e., , the States' highway cost is just -C (see figure 11I.2.1.). 140 But assumption (4) also implies: B dB. "BB (6) Bi Q Q Thus, optimality condition (3) takes the form: - B1 Be SDBT Ci --- + - (7) DQi 3Qi DQi qQi The important conclusion that can be drawn from the above derivation is that the consequences of a federal highway matching grant program in situations where individual states consider only internal benefits in their investment calculus is allocationally equivalent to the highway production scale implied by states' ex- penditure decisions (in the absence of grants) based upon benefits accruing to the nation as a whole. Moreover, the production scale implied by optimality condition (2) or (3) represents the most ef- ficient level of highway production.1 Thus, to the extent that the provision of highways results in significant benefit spillovers which are not accounted for in in- dividual states' investment decisions, economic theory suggests a justifiable federal policy role in highway finance intended to in- crease the allocational-efficiency of highway investments. Moreover, 1. In the terms of figure 111.2.1, conditions (2) or (3) imply a production scale Q*. The net benefits associated with Q*, BT(Q*) - C(Q*) > BT(Q) - C(Q) V Q / 141 the economic theory dictates the appropriate program structure of financial incentives designed to implement this policy. In parti- cular, solely on the grounds of allocational efficiency,1 the federal government should administer grants with the following program characteristics. conditional The grants should be restricted to those classes of highways that are characterized by significant external (interstate) benefits. matching ratios The grants should be offered on a matching ratio basis. The matching provisions are determined by the nationwide signifi- cance of a particular highway class. Thus, for example, the federal government should assume a larger share of the cost of routes of major interstate importance than the share assumed for highways of primarily local or regional significance. open-ended The grants should not be limited by a fixed grant ceiling. In light of the theoretical considerations discussed above, open- grants do not imply that States will expand their highway 1. It is again stressed that there are other criteria dictating the appropriate structure of the federal highway program. Some of these criteria will be discussed in the following sections. 142 investments arbitrarily. On the contrary the theory suggests that open-ended grants with the appropriate] matching provisions will encourage states to expand their highway investment pro- gram only to the point where net (nationwide) benefits are maximized. iii. Practical Limitations of the External Benefit Criterion. Although theoretical considerations point to the use of condi- tional, open-ended, matching grants as a means to internalize benefit spillouts,2 there are several limitations to the practicality of this approach. Needless to say, the investment criteria discussed in the previous section were somewhat simplistic. And cavalier re- ferences to "benefits" quantified as a continuous function of "the quantity of highways" ignores the facts that: a) highway benefits cannot be quantified by a single measure; b) nor can we make a neat distinction between benefits which are internal or external to a given state; c) the benefits derived from the provision of highways is not de- finable over a continuum of the scale of highway investment; d) The determination of internal and total highway benefits-- however measured--is exceedingly difficult; for any one state, 1. We refer here to an adjustment of the matching ratio to reflect the ratio of external to total highway benefits. 2. These grants are often called "optimizing grants." 143 these measures are conditioned on the level of highway invest- ment undertaken in adjoining states. Taken together, these facts suggest that any practical applica- tion of optimizing grants will of necessity involve compromises and deviations from a rigid adherence to economic theory. The Federal Aid Highway Program described in Chapter 2 may be viewed as one such compromise. In light of the numerous criticisms that have been levied against this program, it is necessary to question whether the complaints constitute a general indictment of grants as an inter- governmental fiscal device, or merely identify inherent structural defects which must be balanced against the benefits of the FAHP. It has been charged thatl there are too many separate highway programs imposing excessively complex eligibility requirements and using unduly complicated apportionment formulas. Others claim that the FAHP has misdirected state and local expenditure allocation, rigidified state budgetary processes, and curtailed local autonomy. All of these charges are, to varying degrees, true. Take for example the alleged distortion of the allocation of local funds among different highway programs. Poorly designed grant programs will have this effect--i.e., to the extent that the matching pro- visions of the existing FAHP do not reflect the actual distribution I See for example, Break, George F., INTERGOVERNMENTAL FISCAL RELATIONS IN THE UNITED STATES, Brookings Institution, 1967, Chapter 3, for a good summary of arguments against federal categorical grants. 143 these measures are conditioned on the level of highway invest- ment undertaken in adjoining states. Taken together, these facts suggest that any practical applica- tion of optimizing grants will of necessity involve compromises and deviations from a rigid adherence to economic theory. The Federal Aid Highway Program described in Chapter 2 may be viewed as one such compromise. In light of the numerous criticisms that have been levied against this program, it is necessary to question whether the complaints constitute a general indictment of grants as an inter- governmental fiscal device, or merely identify inherent structural defects which must be balanced against the benefits of the FAHP. It has been charged thatl there are too many separate highway programs imposing excessively complex eligibility requirements and using unduly complicated apportionment formulas. Others claim that the FAHP has misdirected state and local expenditure allocation, rigidified state budgetary processes, and curtailed local autonomy. All of these charges are, to varying degrees, true. Take for example the alleged distortion of the allocation of local funds among different highway programs. Poorly designed grant programs will have this effect--i.e., to the extent that the matching pro- visions of the existing FAHP do not reflect the actual distribution 1 See for example, Break, George F., INTERGOVERNMENTAL FISCAL RELATIONS IN THE UNITED STATES, Brookings Institution, 1967, Chapter 3, for a good summary of arguments against federal categorical grants. 144 of internal and external highway benefits, allocational inefficiencies are bound to occur. However, properly designed grant programs will have the opposite effect: these grants will simply serve to finance a level of highway construction activity commensurate with the bene- fits accruing to the notion as a whole. Related to this question is the criticism that the FAHP has curtailed local autonomy. Here.too, while this charge may be perfectly valid for the existing FAHP pro- gram structure, an appropriately designed optimizing grant program2 will not shift state policy responsibilities to Washington, but rather will remove the burden of state taxation for the financing of benefits the states do not directly receive. It is true of course that the present system of highway grants does complicate the planning and administration of state highway in- vestment programs. Grants are made available for some highway activities (e.g., Interstate Highway construction) but not others (e.g., road maintenance). Each grant comes with restrictions on road 1. This criticism stems partly from the assertion that federal highway funds far exceed transit grant availability. Conse- quently, the local incentives for transit system improvements are curtailed. This criticism does not indict federal grants per se, but serves to underline the need for a realignment of the existing FAHP/transit grant program. If grants for both of these modes were made available on an open-ended basis, such that each recipient could choose the extent of its own partici- pation in highway and transit programs, these criticisms would no longer be valid. 2. Implicit in this discussion is an equity issue. Since the intent of the optimizing grants is to finance the provision of external highway benefits, these grants should be derived from taxes on states as determined by the net spill-in highway bene- fits they enjoy. V 145 design standards, labor hiring practices, and planning and admini- stration process guidelines. While economic theory may provide the rationale for a federal highway grant program in simplistic terms, it is undoubtedly true that in the inherently complex political and social environment in which they operate, rjgid grant procedures, carried out in isolation, no longer yield acceptable solutions. In a tightly integrated society, where the consequences of one functional grant program directly effect states' performance of other functional activities and where actions taken in one locality or state have widespread impact, a premium is placed on effective fiscal cooperation among all levels of government. In light of the issues raised in the preceeding pages, it is clear that while func- tional grants are an important instrument for effecting highway in- vestment allocational efficiency, there are numerous ancillary consequences of a Federal grant program that must be considered as well. Ultimately the normative issues of grant program design must explicitly account for the political and institutional consequences of a system of intergovernmental grants. Although the allocative impacts of specific highway grant programs will be the central focus of this thesis, we will address the institutional questions in a later chapter. 146 iv. Additional Goals of the Federal Aid Highway Program In section III.2.ii, it was shown that a system of conditional, open-ended, matching grants were the appropriate fiscal policy tool to address the problem of benefit spillovers. There are other reasons why the Federal government may desire to influence the investment behavior of lower level governments. One example is the case of merit goods1 -- that is those services deemed to be sufficiently meritorious as to encourage the Federal government to offer incentives for their provision. Implicit in the notion of merit goods is an element of coercion. A Federal program of merit good incentives is intended to redirect states' consumption oatterns in those instances where it is considered that states systematically underestimate the value of the services to themselves. 2 Putting it differently, merit goods may be considered as a special case of Federal fiscal intervention to ensure a certain mini- mum standard for the provision of public goods. 3 Arguments for merit good subsidies have been frequently aired for non-transportation ser- vices, particularly for health and old age care services (e.g., 1. Musgrave and Musgrave, op.cit., page 612. 2. This stands in contrast to benefit spillover situations where states are assumed to systematically underestimate the value of highway services to the nation as a whole. 3. To be more specific, of a national consensus on the minimally acceptable quality of a public service is achieved, Federal merit good subsidies play the role of protecting the interests of the minority in a particular locality where majority decision pro- vides for a substandard level of public services. 147 Medicare, Medicaid, and Old Age Assistance programs). However, to extend these arguments to the provision of highways is hardly defen- sible as it would imply that over-the-road transport is an especially meritorious means of travel relative to the service offered by com- peting modes. While this rationale for Federal fiscal intervention is not par- ticularly relevant to the transportation sector,1 it should be noted that conditional, close-ended, matching or block grants are best suited to serve as merit good subsidies. This program structure as- sures that the grants are selective (i.e., limited to specifically identifiable merit goods) and supportife of only the minimum accept- able level of merit good provision. In addition to the fiscal objectives of correcting for benefit spillovers, and subsidizing the provision of merit goods--both pri- marily allocative objectives--the Federal government may wish to pursue a grant program to meet explicit distributive goals. To be sure, grant programs designed to meet reallocative goals are also characterized by distributive consequences, and vice versa. However, there is a clear distinction between grant programs whose rationale is primarily allocative, and those whose rationale is primarily dis- tributive. 1. On a limited scale one could present a case for highway grants in the guise of merit good subsidies on the grounds that: -- safety considerations demand aicertain minimal level of highway design standards --new modal technologies appear particularly promising, but local authorities are adverse to experimenting with untried techniques. 148 In the latter case, the Federal government would pursue measures which tend to equalize interstate fiscal strength without interfering with their preferences among alternative public (e.g., highway) ser- vices. 1 As in our previous discussion, the important point here is that the design of a particular grant program is strongly related to the adopted set of Federal objectives. In the instance where the Federal goal is strictly distributive, the appropriate federal action is the institution of unconditional, non-matching grants apportioned on the basis of the differences between fiscal need and fiscal capa- city among the states.2 Grants under the general heading of "revenue sharing" have these program characteristics. The advisability of these grants ultimately rests on the existence of significant interstate differences in fiscal capacity and fiscal needs. The highway sector presents a special case where the interstate variations in fiscal strength are minimal, since both fiscal need and fiscal capacity correlate positively to the level of automobile travel. Given the existing method of gasoline taxation, states with relatively 1. That is, grants designed to meet distributional goals would not alter the perceived prices of specific public goods. This is in contrast to the previously discussed matching grants which play the role of price subsidies for specific public goods. 2. This program calls for a measure of fiscal need--i.e., the cost of providing a given level of (highway) services, and of fiscal capacity--i.e., the tax rate required to raise a given level of revenue. The intent of this type of grant would simply be to equalize the tax rates required in various states to render a given level of highway services. 149 high levels of automobile use (and presumably with correspondingly high capital and maintenance investment requirements) will also enjoy relatively high levels of available taxable income. This relationship stands in contrast to government activities where the level of fiscal need is inversely related to fiscal capacity.1 While it is simplistic to presume that redistributive-oriented grant programs play no allo- cative role (and vice versa2 ), there is little justification of the need to structure the highway grant program to meet explicit fis- cal equilization objectives. 1. Welfare assistance programs are one example. In this case the fiscal requirements of welfare programs are highest in those states and localities with the lowest fiscal capacities. To some extent this relationship holds for the provision of transit services as well, in the sense that transit ridership (and the associate of transit investment requirements) are inversely re- lated to income (see Wells, J.D. et al., ECONOMIC CHARACTERISTICS OF THE URBAN PUBLIC TRANSPORTATION INDUSTRY, Institute for De- fense Analyses, February, 1972, Chapter 4). 2. For example, federal aid highway apportionments in fiscal year 1970 were mildly redistributive. The coefficient of correla- tion between apportionments and state per capita income was -0.1965. 150 v. Theoretical Aspects of Policy Evaluation As is evident from the previous discussion, attempts to address the normative issues of Federalhighway grant program design along the lines of the underlying economic and institutional structure of the national highway system are not particularly fruitful. We have argued that the traditional rationales for Federal fiscal intervention -- correction for benefit spillover, merit good provision, and fiscal equalization -- are not demonstrably applica- ble to the existing highway investment environment. What is clear is that highway policy has developed as an evolutionary process. The highway environment of the early 1900's, when the initial federal-aid highway legislation was passed, was characterized by significant benefit spillover and to some extent merit good and fiscal equalization problems.I The policies that have evolved since the Federal Road Act of 1916 (see Chapter 2) have consisted primarily of additions to extant policy (e.g., new Federal- Aid Systems, new institutional and planning requirements). The end result has been an ever increasingly complex system of detailed provisions governing the conduct of numerous federal aid grant programs. 1. See Burch, op.cit., for a good discussion of the evolution of highway investment policy. 151 Against this setting, it is extremely difficult to extract an identifiable set of national highway investment goals. From a normative standpoint, the design of the Federal Aid Highway Program must confront two basic issues: - can we achieve a consensus on the objectives of the Federal government's role in the provision of highways? - if these objectives can be achieved by the imple- mentation of a Federal grant-in-aid program, what program design would Lest serve the Federal goals? Political realities preclude a meaningful and conclusive response to the first question. Policy formulation at the Federal level is not a static process. Perceptions and priori- ties change over time. Moreover, in any given year, Congressional declarations of policy1 are expressed in vague terms, rather than the operational statement of objectives required to pursue a normative analysis of grant program design. In short, the inherent complexity of the intergovernmental finance framework discourages meaningful normative analysis. Accordingly, the primary focus of this research is in the framework of positive analysis -- a detailed investigation of the consequences of the existing program structure, and an evaluation 1. As inferred from Federal highway legislation 152 of selected (incremental) changes to the existing structure. A theoretical model of grant program design is presented in the following section. 111.3 The Analytics of State Responses to Federal Grants 153 This section presents a basic model for use in analyzing how a variety of highway grant programs could be expected to influence the short run expenditure patterns of recipient governments. The analy- sis framework focuses on the highway investment decision-making body -- be it a State Highway Department (SHD), legislature, governor, or a combination of these institutions. In any case, the decision-making body is considered to represent a behavioral unit (BU) in the sense that it exhibits a consistent set of preferences among alternative transportation goods. The preference structure of the BU can be re- presented by an indifference map among any combination of the trans- portation goods.I Furthermore, we assume that the BU seeks to maxi- mize the utilities inherent in that set of preferences, subject to given prices and the resources available to it. The resources consist of the sum total of all revenue earmarked for transportation expendi- ture, plus the funds the BU receives from external sources in the form of federal grants. Without loss of generality, resources may represent funds dedicated solely to highway expenditure (i.e., a BU Highway Trust Fund) or a multimodal trust fund. The analysis does presume however that the budgetary and investment functions of the BU operate 1. The analysis is analogous to the consumer theory of an individual's resource allocation. Thus we assume that our indifference maps are convex to the origin and non-intersecting. These maps are not necessarily assumed to represent the true preferences of the voting polity, and thus do not derive from a "social welfare func- tion." Throughout the discussion, references to maximizing utility are in the context of the utility of the. BU, whether or not this utility truly reflects societal welfare. 154 independently of the BU's decision-making activities for non-transpor- tation functions. i. The Basic Model Formally, the investment model takes the form: max U = U(E , E2, ... E) (8) n subject to E. < R i =1~ where U is the utility derived by the BU for a given allocation of expenditures amongst transportation goods E1, FE2, ... EnI and R is the total resource availability. For clarity, we focus the analysis on the level of expenditure devoted to one specific hiphway category, X, relative to the resources available for all non-X transportation expenditures. Thus in figure 111.3.1, we display the indifference map of the BU, with the units of X on one axis (e.g. lane miles), and resources for all other transportation uses, Y (in dollar terms) on the other. Each indifference curve represents a distinct set of combinations of X and Y for a given level of utility, i.e., U = U = U(X, Y) (9) where Ui = i th level of utility. 1. These expenditure categories may represent distinct classes of highways, for example the various Federal Aid Systems. 155 HIGHWAY INVESTMENT INDIFFERENCE CURVES Y4 - 0' 44 a ~ ;z;1 Cz9x3 4 Figure 111.3.1 156 Figure 111.3.1 depicts an indifference map at four distinct levels of utility (U1 - UQ). Given an initial resource level Y. , and the price of highway commodity X, we can define a budget line B (in the absence of any grants) as: Y = Y. - pX (10) Taken together, the indifference map and the budget lines define an expansion (income-consumption) path of equilibrium resource allocation (00' on figure 111.3.1). Each equilibrium point e = (x , y) satisfies the condition of tangency between the budget line and indifference curve: 9U = P ii. Addition of a Conditional Matching Open-Ended (CMO) Grant. Figure 111.3.2 reproduces the original, pre-grant equilibrium point e2 = (x2, Y2). In this case, the RU is devoting y2Y2 dollars to highway type X, and Oy2 dollars to all other highway expenditure cate- gories. Assume now that the federal government has agreed to bear a fixed percentage g bf the--costs of the local program for highway commodity X. In terms of our initial expenditure model, a grant of this type reduces the BU's perceived price of highway commodity X to the 157 ANALYSIS OF CONDITIONAL MATCHING OPEN-ENDED GRANTS / ej t O0 K1 K j3 K Figure 111.3.2 6z 158 level (1-g)p . This is shown in figure 111.3.2 by a shift in the bud- get line from Y2J to Y2K. Note that the new budget line has pivoted around 0oint Y2, reflecting the fact that a CMO grant does not in- crease the resources available to the BU if no expenditures on high- way commodity X are undertaken. Furthermore, it is easy to show that the federal matching share g is represented on the figure by the ratio L. The equilibrium expenditure pattern along the post-grant budget line B' is indicated by point e = (x, yb). More units of X have been purchased, but at lower cost to the BU out of its own funds. In particular, the post-grant expenditure pattern takes the form sum- marized in Table 111.3.1 Table 111.3.1 Line Expenditure Descriptor Units of X Expenditure on X out of own funds Expenditure on Y out of own funds Grant money received Total expenditure on X Toti expenditure on Y Pre-Grant Post-Grant 0x2x,Ox2 O2x Y2y 2 Y2 y -- y5Y2 y2 2 2 2 O 0y2 Oy2 Charge: Post-Grant minus Pre-Grant x2x2 (+ y Y 2 2 2 y2y2 (+ 0Y2 OYf 1. The post-grant price of X is = (1-g)p =(1-g) . 03 -OK x03-03 Thus g= 1 OJ OK - wOJJKK OK OTK' 1 2 3 4 5 6 159 From the last two lines in this table, it is clear that the CMO grant has resulted in increases in total expenditures on both X and Y. But reference to lines 2 and 3 of Table 111.3.1 indicates that in terms of the allocation of the BU's own resources, expenditures on X have decreased relative to the expenditure on non-aided highway commodities (Y). In other words, the net result of the conditional (on X) matching open-ended grant has been a shift of y2y' dollars (formerly devoted to expenditure on highway commodity X) to expendi- ture on non-X highway activities. This is not necessarily the case however. The response of the recipient government to the CMO grant will depend in general upon the BU's expressed demand for highway goods, and in particular upon its demand for the grant subsidized activity. More specifically, the response will be a function of the B's price elasticity of demand for the aided activity. The generalized grant response is shown in figure 111.3.3 where we have again indicated the initial pre-grant equilibrium point e2"(x2, Y2), as well as the equilibria corresponding to CMO grants with two different matching ratios.I These alternative- equilibria trace out a price-consumption curve Y2Q describing expenditures on X and Y for given grant matching ratios.2 In the declining portion 1. For clarity, the indifference curves have been omitted from the figure. Budget line B2 in figure 111.3.3 is identical to B5 in figure 111.3.2. 2. Each point on the price-consumption curve represents apoint of tangency between a specific budget line and indifference curve. 160 GRANT RESPONSES FOR ALTERNATIVE PRICE SUBSIDIES y -PECR~eASIQ PICE AS PEPCEIJE> OY~Z ..0Q- Y TH E J ERICE ELASTICITY oF "HI6'HWAY CeflOPfTY X Figure 111.3.3 161 of the price consumption curve, the demand for highway commodity X is price elastic: a decrease in price by g% (i.e., the federal share of a grant for X) will result in a greater than g% increase in con- sumption of X. In other words, federal grants in this region will stimulate greater levels of expenditures on X from the BU's own resources. This is clear from the comparison of the pre-grant equilibrium point e2= 2y2) and the equilibrium point e'(x', y') resulting from a CMO grant with matching ratio L (figure 111.3.3). In the latter case, the BU's own expenditures on X have increased from y2Y2 to yj'Y2-- the precise amount that expenditures on non-aided highway activities have decreased. In fact, the equilibrium e' corresponds to the unit-elastic point on the price consumption curve (see lower portion of figure III.e.3). CMO grants with federal shares greater than )L -- as represented by budget line B" -- will result in a sub-Of stitution nf expenditures on X for Y. In this region of the price- consump io: cui ve,the demand for highway commodity X is inelastic with respect to post-grant price. Summarily, the theoretical analysis indicates that conditional, matching open-ended grants may result in a stimulation of the BU's own allocation of resources to the aided highway function, or sub- stitution of expenditures from the aided to non-aided functions de- pending on the price elasticity of the subsidized commodity. 162 iii. Analysis of Conditional , Matching Close-Ended (CMC) Grants The analysis of expenditure response to conditional, matching, close-ended grants proceeds in a manner analogous to the previous section. In this instance, we assume that the federal government agrees to bear g% of the costs to provide highway commodity X up to a fixed grant ceiling level. The graphical representation of this grant structure is shown in figure 111.3.4, where the pre-grant equilibrium point is indicated by e2=(x2 , y2 and the CMC grant has a matching ratio of JK Suppose for example the federal government has agreed to share in the cost of OxDI units of X--or equivalently has invoked a grant ceiling of Y2Z1 dollars.1 The budget line facing 1. This equivalence can be demonstrated in terms of figure 111.3.4 as follows: The total cost of OxDI units of X is given by line segment Z0ZI If Y2Z = federal share of this total cost, then 2Z 1 Tg Z0 1 z0Y2 _ Qy2 z0z 1 -OzI But Z% OK , and Z % Oi Y2z1 O 1 Oz01 2 1D12 0K Thus -- Z =Z Kz 0z1 Z1 1Oil<0 Z10OK O Q.E.D. 163 ANALYSIS OF CONDITIONAL MATCHING CLOSE-ENDED GRANTS z5 0AO z2 Z2 2, I \ 4 Xt X2 I \?\\\ 3 Figure 111.3.4 164 the BU is given by Y2D1J1, with consumption of highway commodity X beyond OXDl units costing the full market price 2 . Under these con- ditions equilibrium resource allocation is indicated by point D0 where the income consumption line intersects the budget line. Note that in this case, where the break or "deflection"' point in the budget line falls to the left of the income consumption path, the CMC grant, and an unconditional non-matching, close-ended (UNC) grant of equivalent magnitude (as indicated by budget line Z1DJ1 ) are allocationally equivalent. Thus, in terms of figure 111.3.4, CMC grants with sta- tutory ceilings up to Y2z2 dollars yield the same expenditures on highway commodity X as equivalent dollar amount UNC grants. Beyond this grant ceiling, CMC grants result in greater X expenditures than an equal amount UNC grant, but less than an open- ended matching grant with the same matching ratio as the CMC grant. For example a CMC grant withceiling Y2Z3 yields the equilibrium point D3, which involves a greater expenditure on highway commodity X than the equilibrium point D' associated with the equivalent amount UNC grant but less X expenditure than the equilibrium point D4 associated with an equivalent matching ratio CMO grant (see Table 111.3.2). For a given matchinq ratio, the grant ceiling ultimately reaches a level at which it is no longer binding on resource allocation. In particular, beyond the grant ceiling Y2Z4 where the CMC budget line 1. See Wilde, James A., "The Expenditure Effects of Grant-in-Aid Programs," NATIONAL TAX JOURNAL, VOL. XXI, Number 3. TABLE 111.3.2 COMPARISON OF EQUILIBRIUM POINTS FOR ALTERNATIVE GRANT STRUCTURES SHOWN IN FIGURE 111.3.4 [1] [2] Equilibrium with Grant CMC Grant , Ceiling (Matching Ratio O) [3] Equilibrium with UNC Grant [4] Equilibrium with CMO Grant (Matching Ratio !) [5] Change in Expenditure on X([3]-[2]) [6] Change in Expenditure on X([4]-[2]) Y2Z1 ODOD (+)y2zI D0 D90D40 Y2Z2 D2 D2 D 0 (+) Y2Z3 D3 D3 04 (-) y9294 D4D D4 (-) 0 Y2Z5 D4 D5 D4 () 0 atj CF) 166 intersects the price-consumption curve (point D4), CMC grants are al- locationally equivalent to CMO grants. Thus increases in the grant ceiling beyond the level Y2Z4 will in no way alter the highway expen- diture pattern of recipient governments. In general, the greater the federal matching share of expendi- tures on highway commodity X, the greater is the upper limit on the binding grant ceiling level. This relationship is shown schematically by curve OP' in figure 111.3.5. The shaded area A. above OP' repre- sents the region in which increases in the statutory grant ceiling for a given matching ratio (for example moving from point III to point IV ) will not alter the BU's allocation of resources between X and y. Conversely, the area in B to the right of curve OP' re- presents the region over which increases in the federal matching share for a given grant ceiling (for example, movement from point III to IV ) will not effect changes in the BU's consumption of X and Y. Finally, the area C between curves OP' and OP' describes the region over which changes in either the matching provisions, or the statutory ceiling of a CMC grant will result in a reallocation of the BU's re- sources amongst highway commodities X and Y. I The actual allocation 1. In terms of our schematic representation of the allocative impacts of CMC grants in figure 111.3.4, regions A , B , and C are defined as follows: region A --break point in the budget line lies to the right of the price-consumption curve Y 0 region B --break point in the budget ling lies to the left of the income-consumption curve 00' region C --break point in the budget line lies between the price- consumption and income-consumption curves. 167 of the BU's resources between X and Y in this region is uniquely de- fined by the deflection point in the post-CMC grant budget line. The preceding analysis has served to demonstrate three distinct response patterns to conditional, matching, close-ended grants. In one pattern of CMC grant response, what is nominally conditional matching aid, may in fact have only the influence of an unconditional block grant. This behavior is manifest in region B of figure 111.3.5, and is readily observable ex post facto in cases where the recipient govern- ment devotes more than enough of its own resources to highway commodity X than the amount required simply to match the federal highway grant. The allocative impact of grants of this type is to induce a shift in the resources the BU would have devoted to highway commodity X in the absence of the CMC grant, to non-aided highway activities. In those instances where the BU is observed to provide for expen- ditures on X enabling them to qualify for only part of the total avail- able federal grant, the CMC grant is allocationally equivalent to a conditional, matching, open-ended arant. This behavior is represented in figure 111.3.5 by region A , and may result in a greater or lesser expenditure of theBU's own resources on highway commodity X, depending on the price elasticity of the aided function at the pre-grant price level. Finally, the behavior response manifest in region C results in a greater total expenditure on hiohway commodity X than equal amount non-matching grants, but less than an open-ended grant with the same 168 AFFECT OF GRANT CEILINGS AND PRICE SUBSIDY LEVELS OPPER LiuiTS oP 8O1PWOM GRANT CEiLiAJ&. ... I / 1~ Lit- FFPEVL rAThflMiA)& 5 HeIRE OF EMENtJiTARSS OJ Hi1HLJAy COMoPtT X. Figure 111.3.5 / P/ 169 matching ratio. Allocation of the BU's own resources between X and Y in this situation again depends on the price elasticity of the BU's demand for highway commodity X. This response pattern is readily recognizable ex post facto where the BU just matches the full federal CMC grant. iv. Evaluation of Other Grant Program Structures It should be evident that the analysis framework presented in the three previous sections may be used to evaluate a wide range of alternative grant program structures. For completeness, this section will briefly evaluate the allocative consequences of two additional cases: conditional, non-matching, close-ended (CNC) grants, and CMC grants applied to situations where the BU has not previously allocated any resources to the aided function. The former case is illustrated in figure 111.3.6, with the pre- grant equilibrium a point e2 (x2, Y2). Assume now that the federal government introduces a non-matching grant of y3y4 dollars which is restricted to expenditure on hgihway commodity X. This grant is re- presented by budget line y3dJ, indicating that the CNC grant will wholly finance up to OK1 units of X. Equilibrium in this case is at point e =(x, y') (where the income-consumption curve 00' intersects the budget line y3dJ), the allocational equivalent of an unconditional non-matching grant of the same (y3y4) dollar amount. It follows that the specificity characteristic of this CNC grant is not allocationally significant: expenditures on X and Y are the same whether or not the 170 ANALYSIS OF CONDITIONAL NON-MATCHING CLOSE-ENDED GRANTS C X ' Figure 111.3.6 171 grant is restricted to expenditure on X. This situation occurs wherever the post-grant consumption of highway commodity X exceeds the statutory grant ceiling--i.e., expenditures on X include the~BU's own resources. Moreover, it is clear that this grant has increased expenditures on non-aided highway functions by the amount y2yA. Thus although the grant was nominally restricted to expenditure on X, a fraction -*was y3y4 actually diverted to other uses. The response to CNC aid will be quite different in cases where the grant ceiling is sufficiently large so as to cause the break point in the post-grant budget line to fall to the right of the income-con- sumption curve. For example, a CNC grant ceiling of y3y6 dollars will produce budget line y3e434 with equilibrium occurring at the break point e4. In this case, the BU shifts all of its pre-grant expenditures on highway commodity X to the non-aided functions, using only federal grant money for expenditure on the aided function. Thus CNC aid with a sufficiently high grant ceiling results in a greater total expenditure on highway commodity X than an equivalent amount unconditional grant. This situation can be easily identified, since none of the BU's own resources would be observed to support the aided highway function. The analysis of conditional, matching grants (both open and close- ended) presented in sections III.3.ii and III.3.iii assumed that the BU's pre-grant equilibrium included positive levels of consumption of highway commodity X, and other highway functions Y. This section con- cludes with a discussion of the response to CMC and CMO grants in cases 172 where the BU has not previously allocated any resources to the aided function. In terms of figure 111.3.7, we assume an initial equilibrium at e3=(O,y3). This solution obtains if the indifference curves (U1, ... U4) are everywhere less steep than the budget line y3J, i.e.: S9U 9X < P V X > 0 3Y Introduction of a conditional matching, open-ended grant is represented by the budget line y3K, and yields a new equilibrium at e4=(x4, y4)i Expenditures on highway commodity X in this case total y0y5 dollars. Of this amount, yy3 dollars derive from the BU's own resources, re- presenting a diversion of expenditures originally devoted to the non- aided function. The remainder of the total post-grant expenditures on X, y3y5 are supplied by the federal government. If the grant had been of the CMC variety, equilibrium would occur at either e4 or the break point in the CMC budget line, whichever comes first. It should be noted that of all the grant structure/response patterns discussed in the previous sections the case presented here is the only one in which the post-grant reallocation of the BU's resources always involves an increase in expenditures on the aided function from the BU's own revenues 1. Assuming that the slope of the indifference curve 04 at y3 is steeper than the new budget line y3K. 173 ANALYSIS OF RESPONSES TO GRANTS FOR FUNCTIONS NOT PREVIOUSLY UNDERTAKEN BY STATE GOVERNMENTS Ye. X6 7 K Figure 111.3.7 v. Summary of the Responses to Alternative Grant Structures 17 In the preceding sections, an attempt has been made to provide a descriptive theoretical framework for the analysis of State Highway expenditure responses to alternative Federal- Aid grant structures. While it is clear that the model presented here presumes a degree of economic "rationality" that ignores the administrative and political realities of State High- way investment decision making, the analyses do advance a set of hypotheses that may be modified to account for specific quali- fications.1 To the extent that a relaxation of the underlying assumptions do not alter the fundamantal logic of the models, these analyses serve to place bounds on the expected pattern of State High- way expenditure behavior. Figure 111.3.8. a summarizes the relative impacts of alter- native grant structures on State Highway expenditures. The horizon- tal axis measures the magnitude of Federal grants, while the vertical axis describes the post grant total (Federal + State) expenditures on highway commodity X. It follows that point E describes the BU's pre-grant expenditure level on X. In comparing the responses to various grant programs, it is useful to distinguish between two different behavioral patterns: expenditure stimulation and expenditure substitution. The former 1 A discussion of the critical assumptions of the preceding analyses and possible modifications to the model results is presented at the end of this section vi. 175 SUMMARY OF STATE RESPONSES TO ALTERNATIVE FEDERAL GRANT STRUCTURES $ I TiTAL (sTare + FEDERAL) fKPeAJpiTU 0A HIGH L)6AY COMMODITY EC: CMC grant response locus EI: CMO grant response locus EJ: UNC grant response locus EH: CNC grant response locus Figure III.3.8.a r expenditure stimulation j expenditure a substituion '2 ToTAL AVAILABLE FEDERAL A(P BXPENDITUARES or x and y or I ~ 4W 0+01g I -. Sb a Figure III.3.8.b I A f1s, I f-E0 4 case obtains when the effect of the Federal grant is to increase 176 State expenditures on the aided highway function from own sources. In other words, in these situations the State reallocates resources from non-aided functions to expenditure on the aided highway cate- gory. The contrary case, expenditure substitution obtains whenever total post-grant expenditures on the aided function increase by less than the amount of the Federal grant. The allocational con- sequence here is a decrease in the level of State expenditures on the aided function with a commensurate increase in expenditure on non-aided functions. In terms of figure III.3.8.a, the expen- diture stimulation and expenditure substitution response patterns are indentified by the regions lying to the left and right respec- tively of the line EF. It is evident that of the four grant responses shown in figure III.3.8.a only conditional matching (either open or close-ended) may induce expedditure stimulation on the aided function. The curve EG traces the expenditure response to succeeding by higher levels of CMC grant funding (at a matching ratio of CD ). We assume that AD at the pre-grant price of highway commodity X (Af_ ),the BU was in the AC-- elastic portion of its demand for X.i For grant levels below OP. dollars, the CMC grant is allocationally equivalent to the equiva- lent amount UNC grants, (c.f. section III.3.iii) and thus curve EC begins along the same locus as EJ in the expenditure substitution 1 This is indicated in figure III.3.8.b by the negative slope of the price consumption curve OB' at the pre-grant equilibrium Z0. 177 region. Beyond the grant ceiling OP, the CMC grant yields equili- bria at the break points along line segment Z5Z1 (figure III. 3. 8.b), with expenditures on highway commodity X from the BU's own re- sources increasing at the margin. When the grant ceiling reaches the level 0P2, the BU's expenditures on highway commodity X net of grants equals its pre-grant allocation to X (as indicated by point Zl). Thus, above this level of Federal aid, the CMC grant serves as an expenditure stimulant. Expenditures on X from the BU's own revenues exceed their pre-grant level, ultimately reaching a maxi- mum increase of G dollars at a grant ceiling of OP3. Beyond the grant ceiling OP3, no further reallocation of expenditures between highway commodity X1 and other functions Y occurs. In a similar fashion, we can construct the curve EI to suggest the locus of expenditure responses to conditional, matching, open- ended grants with succeedingly higher matching ratios. In this case, the higher the Federal matching ratio of the CMO grant, the greater will be the amount of Federal money expended by the BU. Moreover, since the BU was assumed to be initially in the elastic portion of its demand for highway commodity X, expenditures on the aided func- tion begin in the expenditure stimulation region above the threshold line EF. Unitary price elasticity corresponds to aid OP3 (matching ratio C), beyond which X expenditure substitution obtains at the AD margin. Ultimately, beyond Federal aid levels of OP5 dollars (matching ratio CE),the CMO grant yields an expenditure substitution 178 AE response, with post-grant expenditures on X from the BU's own sources falling below their pre-grant level. The limiting case here is a CMO grant with a 100% Federal share--in other words a conditional non-matching grant. Thus, as the Federal share payable approaches 100%, the curve El approaches the response locus EH associated with conditional, non-matching close ended grants. The response to unconditional block (i.e. non-matching) grants exhibits the most significant expenditure substitution behavior. In this case, a fraction of the UNC grants would be expected to be devoted to highway commodity X as a direct substitute for the BU's own X expenditures. The curve EJ traces the response locus to UNC grants with succeedingly higher grant ceilings. This curve lies entirely in the expenditure substitution response region, its slope depending on the BU's marginal propensity to consume highway com- modity X with higher levels of income.1 For UNC aid beyond the level OP4 dollars, the BU substitutes its entire pre-grant expenditures on X to non-aided activities Y, exclusively using Federal aid to purchase highway commodity X. 1 The marginal propensity to consume (MPC) is defined as the inverse slope of the income-consumption curve AA'. Two limiting cases serve to place bounds on the UNC response locus Ed. If the income-consumption curve is vertical (MPC=0), then each Federal-aid dollar is substituted one-for-one with the BU's own expenditures on X. The UNC grant response locus in this case is defined by EK in figure III.3.8.a. Conversely, if the MPC=co(income-consumption curve horizontal), then each Federal-aid dollar is fully expended on highway commodity X with pre-grant X expenditures remaining fixed. The case is represented by the UNC grant response locus EF. 179 The expenditure response to conditional, non-matching, close- ended grants is similar to the UNC grant response. As shown by response locus EH, CNC grants are allocationally equivalent to UNC grants below the funding level EP4 dollars. At that point, leakage of grant money into non-aided highway activities (as measured by HIH2, the vertical distance between EH and the 450 line OH) has reached the level of pre-grant expenditures on highway commodity X (OE). Further leakage is prevented as additional levels of CNC funding is wholly devoted to X at the margin, and response locus EH diverges from Ed. Table 111.3.3 summarizes the most significant findings of the preceding analysis. Of paramount importance is recognition of the fact that changes in the structure of a Federal-aid grant program may result in fundamental changes in the recipient government's allocation of resources among alternative transportation commodities. In this context our analysis framework can be used to address ques- tions such as: 1) What is the least expensive means for the Federal government to achieve a specified target expenditure by the recipients on the aided highway functions? 2) For a given ceiling on Federal highway aid, which grant program stipulations would be most favored by the recipient government? Grant Response Pattern 180 Response Locus (Figure III.3.8.a) For relatively bigh matching ratios EI approaches EH at high and large grant ceilings, the allo- Federal grant levels cative difference between condition- al matching and non-matching grants are insignificant. IL Conditional close-ended matching Segment EG2 on response grants may be allocationally equi- locus EG valent to unconditional block 2 grants for sufficiently low grant ceilings. In these cases, the grants result in expenditure sub- stitution on the aided function. Only conditional matching grants Segment EI, on response (either open or close-ended) can locus EI. 3 be expectdd to increase expendi- Segment G3G on response tures on the aided function by locus EG more than the amount of the grant. Unless the grant ceiling is not Response locus EG, and binding, CMC grants have a lesser segment EG on response stimulatory impact than a CMO locus EI grant with the same matching ratio. The specificity requirement on a Segment EHI on response 5 conditional non-matching close- locus EH ended grant may have no alloca- tive significant 6 Expenditure stimulation will be Not shownbreatest where CMO grants are ap- plied to highway functions not previously undertaken. SUMMARY OF GRANT RESPONSES Table 111.3.3 It is not surprising to note that the answers to these two 181 questions indicate a conflict in the preferences of the donor and donee governments. If one of the goals of the Federal government is to maximize the "return" on their grant (in terms of achieving the greatest expenditure on the aided function for a given level of Federal aid), they will always prescribe matching provisions on their highway grant programs. The States, on the other hand, would alwaysl find unconditional or block grants preferable to conditional grants with the equivalent ceiling. Another related finding of our theoretical analysis is that under certain circumstances grant programs with categorical restric- tions are allocationally equivalent to block grants (c.f. lines 1,2 and 5 of table 111.3.3). In these instances, the grant pro- grams should be evaluated in terms of their income-redistributive characteristics (e.g. whether they channel higher levels of aid into poorer States), rather than in terms of their allocative ef- ficiency characteristics. These issues will be discussed in greater detail in section 111.4. vi. Qualifications on the Theoretical Analyses The validity of the theoretical findings derived in the pre- ceding sections ultimately rests on the practicality of the under- lying assumptions of our model. Basically, there are three crucial assumptions upon which our theoretical analysis rests: 1 Except under certain restrictive conditions. See line 2 of table 111.3.3. 182 1) There is an identifiable behavioral unit at the State level that expresses a consistent set of preferences among alterna- tive transportation services. 2) These preferences may be represented by a map of continuous indifference curves 3) Grant money receives no special treatment beyond the stipula- tions made by the Federal government. The first of these assumptions is perhaps the most difficult to justify. Clearly, our reference to a "behavioral unit" ignores the existence of the numerous political agencies and private forces whose choices among alternative transportation projects often con- flict. It is certainly true that on any given transportation pro- ject, it would be simplistic to presume that a single individual or a monolithic agency solely determines the investment decisions. However, our model deals with overall budget behavior--that is, decisions on the level of expenditure to be devoted to generic transportation activities. We do not distinguish between the scale or location of individual highway projects, but only between the overall expenditure levels on aided and non-aided highway activities. In this context, our assumption boils down to an assertion that a single State agency (e.g. a State Highway Department/Commission or Depart- ment of Transportation) sets forth an investment policy determining the allocation of revenues amongst transportation investment alter- natives in broad, generic categories. 1 183 It is nonetheless the case that in any given year, these cate- gorical investments are comprised of a finite set of discrete pro- jects whose individual cost may represent a sizable fraction of the total investment. The implications here relate to the second as- sumption of our analysis, that the indifference curves are continuous functions of categorical highway expenditures. To the extent that the demands for alternative highway commodities are expressed in terms of discrete investment levels, the indifference curves will be piecewise linear rather than continuous. We assume that this qualification does not fundamentally alter the expenditure response patterns indicated by our models. The validity of the third assumption is not testable in any empirical sense. However, there are two reasons to suspect that the receipt of grant money may have the effect of shifting the recipient government's indifference map. 2 The first reason is the commonly held notion that it is "bad politics" to turn down a Federal grant. This view argues that Federal grants are "some- I For example, this policy might be expressed in terms of decisions to spend a certain fraction of revenues on maintenance, another frac- tion on the State Primary Highway System, and a third fraction on the State Secondary Highway System. In some States these "decisions" are actually dictated by statute. In others, a State highway agency makes these decisions on a (multi-) year to (mlti-) year basis. 2 It should be noted that an indifference map describes the trade- offs amongst alternative goods irrespective of the prices of those goods. As discussed in the previous sections, changes in the prices of the aided highway functions enter into our model through shifts in the budget line, not the indifference map. 184 thing special," or "free money," to be spent at all costs. Clearly, if this is the case, the States will behave differently than our models predict. There is another possible explanation for a deviation from our models'predictions which relates to "spin-off effects." Sup- pose a State must choose between a major intercity freeway projectl costong $100 million, and an arterial route costing $10 million. After weighing the costs and benefits, assume the arterial route were strongly preferred. At this point, however, the Federal government offers to pay 90% of the freeway costs. With the costs equalized, the State would choose between the two projects solely on the basis of benefits. Let us assume that the State still prefers the arter- ial project. If that were the extent of the decision, the grant offer would be declined. However, this decision could be reversed by a broader view of benefits. In a macro-economic context, the freeway project has the advantage of bringing an additional $90 million into the State's economy (which translates into increased income and employment). Thus the macro-economic context for aid recipients may be a vital factor in expenditure decisions and grant response. The implication of the "free money" or "spin-off effect" arguments is that Federal highway grants may induce a greater expen- diture stimulation response than our models would predict. But in order for this to be the case, we would have to observe the I This exapfple is placed in the setting of project selection, but the same arguments apply to the broader question of overall bud- get allocation. 185 States making expenditures on the aided highway functions less than or just equal to amount required to match a full close-ended Federal matching grant (see section III.3.v). Our model would appear to be valid in cases where an expenditure substitution response is associated with the Federal grant. In cases where our model pre- dicts an expenditure stimulation response to a Federal highway matching grant, the arguments advanced above indicate that the model results may understate the expenditure levels on the aided highway functions. As will be discussed in detail in section 111.4, the majority of States exhibits an expenditure substitution response to Federal highway grants. 186 111.4 The Analytics of State Responses to Federal Grants: The Benefit/Cost Investment Model The previous section discussed the analytics of State responses to Federal grants in terms of the allocation of highway resources amongst alternative expenditure categories. The basis of this discussion was that States allocate resources so as to maximize their perceived benefits (utility). The question of highway resource allocation can be approached from a somewhat different perspective. In particular, this section will present a benefit/cost investment model which focuses on the level of resources raised from a States own sources, in response to a variety of Federal highway grant structures.1 i. A Hypothetical Example Assume that a particular State has developed a set of candidate highway projects, and is prepared to expend funds on these projects up to the point where the benefit/cost ratio on the "last" project is just equal to 1.0. More explicitly, we assume that the State has ranked the projects in order of 1. For an application of this approach, see Miller, Edward, "The Economics of Matching Grants: The ABC Highway Program," National Tax Journal, Vol. 27, No. 2, June, 1974. 187 decreasing benefit cost ratio as shown in figure 111.4.1.2 For the hypothetical values displayed in figure 111.4.1 the State is willing to expend a total of $10 million to imple- ment projects 1 through 10. At this point, assume the Federal government steps in and offers a grant of $G with the provision that this grant must be matched dollar for dollar by the State government (i.e. the matching rate is 50%). It may be argued that there are three possible responses to the presence of the Federal grant, depending on the size of the grant G: Case I. $0< G 4$5M: Pure Income Effect This case applies where the sum of the Federal grant G and the State's matching share is less than the total amount the State was apparently willing to expend on highways in the absence of Federal grants. For example, assume the Federal grant offered is $3.M After providing for the required matching share, the State has expended $6.M This leaves a remainder of 2. It has often been noted that optimal project selection does not necessarily simply consist of those projects with the highest benefit/cost ratios. (For example, see Pecknold, Wayne M., Evolution of Transport Systems: An Analysis of Time- Staged Investment Strategies Under Uncertainty, Unpublished Ph.D. Thesis, M.I.T. Department of Civil Engineering, 1970, and Newman, Lance, A Time-Staged Strategic Approach to Trans- portation System Planning, Unpublished S.M. Thesis, M.I.T. Department of Civil Engineering, 1972). In the presentation that follows, we nonetheless make the assumption that States will not choose to implement projects whose perceived B/C ratio is less than unity. ILLUSTRATIVE EXAMPLE 188 OF THE BENEFIT/COST INVESTMENTMODEL Project No. B/C Total Cost (Millions of Dollars) 1.6 2.3 .7 10.0 - Cost of projects with B/C > 1.0 1.2 .6 .3 5.0 - Cost of projects with .5 .6 B/C( 1.0 .9 1.1 1.0 5.0 - Cost of projects with B/C 4.5 Figure III.4 1 1 2 Region I 10 7.6 6.9 1.0 11 12 Region 2 17 18 19 .97 .84 .50 .46 .41 Region 3 24 .23 189 projects costing $4M whose B/C ratio exceeds unity. Since, the Federal grant has been exhausted there is no incentive to expand the highway program beyond the previously determined level of $10.M Thus, the net effect of the $3M Federal grant has been to reduce the level of resources expended from the State's own sources. Total highway expenditures remain unchanged, as the State's own expenditures are reduced by just the amount of Federal grant. This situation represents the case of a pure income grant, where the close-ended grant is not of sufficient magnitude to create a perceived price reduction at the margin. As far as the State is concerned, the grant has had the effect of providing an additional $3M of income to be expended on other State services or "spent" on tax relief. Admittedly, this conclusion presents a somewhat extreme case. While the overall characterization of this type of grant as an income subsidy remains valid, realistically it is not necessarily the case that State expenditures on highways would be reduced dollar for dollar by the amount of the Federal grant. For one thing, it should again be noted that because of the indivisibility and "lumpiness" of highway investments, the presence of additional highway revenue might substantially alter the project mix (and therefore the total expenditure level) of an optimal highway investment program. Another mitigating factor here is the restriction in most States against expenditure 190 of earmarked highway revenue on non-highway projects. The consequence of this restriction (and particularly in the short run where changes in State revenue raising sources - e.g. tax rates, are not possible) is that at least part of the additional revenue may be expended on the aided highway category, thus increasing total expenditures on this function. More importantly however, is the fact that any expansion in total expenditures on the aided highway category results from the chosen allocation the additional income derived from the grant as opposed to any perceived price reduction on the aided function. By the same token, it is likely that expenditures on non-aided (highway) functions will be increased from the additional income afforded by the grant. Case II. $5M< G4$7 .5M Price Plus Income Effect For the hypothetical situation depicted in figure 111.4.1, once G exceeds the level of $5 million, the grant introduces both a price and income effect on the State's allocation decisi3ns.1 1. A price effect refers to changes in the allocation of re- sources deriving from a change in the perceived price of one or more expenditure items. Allocational shifts also derive from an income effect where the State allocates additional income on highway commodities whose perceived prices remain unchanged. A grant may introduce a pure income effect or a combination of a price effect and income effect. For a more detailed discussion of these concepts see Henderson J.M. and R.E. Quandt, Microeconomic Theory: A Mathematical Approach, McGraw-Hill Book Company, New York, 1958. 191 To see this, assume the Federal grant offered, G is $7 million. Since the State was apparently willing to expend $10 million from its own sources, it is clear that at least $5 million of the grant will be used. At this point total expenditures amount to $10 million, all projects with B/C greater than one have been programmed, and $2 million of Federal grants remain available. The remaining Federal grant has the effect of reducing the cost of additional highway construction to the State by one-half. In other words, the perceived B/C ratio of projects remaining on the candidate list increase by a factor of two. Since the B/C ratio of projects in Region 2 (see figure 111.4.1) fall in the range 0.5 to 1, the availability of Federal grants increase the perceived B/C ratio of these projects over unity. Following the simple criterion that all projects with (perceived) B/C 1 will be prograrrned, it is clear that the State will employ the remaining Federal grant, bringing total expenditures on the aided function to $14 million. Once the entire Federal grant has been employed, there is no longer any incentive for expansion of the highway program, since the State must now bear the full cost of projects whose B/C ratio is less than one. While the net effect of this grant has been to increase total expenditures, for a Federal investment of $7 million, total expenditures increase by only $4 million (from $10 million in the 192 absence of grants to $14 million with the grant). The expendi- ture increase derives from the price effect of the matching grant at the margin (i.e. at the point where the State decides to program projects in region 2 of figure IIM.4.1). It should also be noted that total expenditures from the State's own sources decrease from $10 million in the pre-grant situation to $7 million in the post-grant situation. As in Case I, the saving in State resources may be spent on other services, or translated into tax reductions. Case III G>$ 7 .5M: No Effect at the Margin Following the same reasoning as presented in Case II, it is clear that the State will not have an incentive to employ Federal grants in excess of $7.5 million. Since all projects in region 3 of figure 111.4.1 have a B/C ratio less than 0.5, the availability of 50% Federal matching grants will not bring the perceived B/C ratio of region 3 projects over one. Thus, for this hypothetical example, the maximum grant level that will willingly be employed by the State is $7.5M (this amount will cover half the costs of all projects in region 1 and region 2). At this grant level, total expenditures on the aided function amount to $15M divided evenly between State and Federal funds. This situation represents an increase in total expenditures by $5M, but a decrease in State's own expenditures by $2.5 193 ii. A Diagrammatic Description These three cases can be summarized diagrarnatically as in figure 111.4.2. We assume that the State expresses a demand for highway construction represented by the demand schedule D1D1. Thus, for the full price of highway construction (i.e. in the absence of grants), the State will purchase Q1 units of highway at a total cost of ObcQ1 dollars. Case I of our previous discussion is represented by the price line arsp. In particular, 50% matching grants are available up to a ceiling of Q0 highway units. Beyond this level of highway expenditure, the State again faces the full price of highways. As previously noted, the State response to this grant is to maintain its previous produc- tion scale of Q, units. Total expenditures from the State's own sources is indicated in the figure by area OarQ1 (the full cost borne by the State of highway construction up to the level Q). This represents a decrease in State expenditures by Q0 rdQ1 dollars. For the larger grant ceiling described in Case II, the relevant price line is depicted by aefp, The response in this instance is to expand production up to Q2 highway units at a total cost to the State of OaeQ2 dollars. As in the previous situation, State expenditures decrease from the pre-grant situa- tion - in this case by the difference between areas abcd and QadeQ2 ' Finally, the price line corresponding to Case III is 194 DIAGRAMMATIC DESCRIPTION OF THE BENEFIT/COST INVESTMENT MODEL ufir PRfaC oF IGNLwI F-Acikrits 1 p4 e -C P 'In A- TZ z ,trr'K VC i 4* 0 QQ( 3 PMWW+ 1 Cp0f4t~OiO Gi Qz Q ~~q(AA13?rTl OF HiR~n &MS s o 5TA~Tr EKftOPWUtES 10 _ _E AbwkcZ oF &RSwT -4TtWE~eEAPD(TI(&s ArTCR aN6Ars. Figure 111.4.2 0 / / 7 /7 / // / /7 7/ / / 4- / - a - firz z -m-4 T T X V 'lr"r ILlI I % 0 195 shown as amkp. Since this price line intersects the demand schedule D1D,, the State will expand its highway program only as far as Q 3 units, leaving Q3gmQ4 dollars of the Federal grant un- expended. Total State expenditure in this case is OagQ3, a decrease of abcd - QdgQ3 from the pre-grant situation. M11. Conclusions From the Benefit/Cost Investment Model An immediate conclusion that can be reached from the preceding analysis is that: Whereas the Federal government provides categorical grants presumably for those types of activities in which it perceives a national interest in stimula- ting expenditures (i.e. in inducing construction that may not have been undertaken in the absence of the grant), the net result may be the expansion of expenditures (or contraction through tax relief) in other (non-aided) areas in which the Federal govern- ment has no officially stated interest. This conclusion derives from the income effect of close-ended matching grants, which under certain conditions such as Case I of the preceding analysis, serve only as a non-cate- gorical income subsidy to the States.1 In fact, in the preceding hypothetical example, regardless of the ceiling of a 50% Federal matching grant, post-grant State expenditures decrease from their pre-grant level (and thus the savings incurred may be expended in 1. As described in Section 111.3, as long as the grant ceiling of a close-ended matching grant is low enough so as to be non-binding on the States investment calculus, the categorical restrictions of the grant are irrelevant. The allocational consequences of a grant of this type are identical to a simple block grant of like amount. 196 other areas). This expenditure response pattern need not have been the case however. As shown in figure 111.4.2 (and in the analysis describing figure 111.4.1), the States demand for highway facili- ties, expressed by the schedule D301 represents inelastic demand. That is, a decrease in price by one-half results in less than a doubling of total expenditures. It is entirely possible that a State's expressed demand for highway construction may be elastic, for example as depicted by the schedule D2D2 in figure 111.4.2. In this case total State expenditures following the offer of a 50% Federal matching grant with a ceiling in excess of OahQ4 dollars exceed pre-grant expenditures by the amount QdhQ4 - abcd (c.f. Section III.3.ii). However, regardless of the elasticity properties of the State's expressed demand for highway facilities, if the Federal grant in question has the properties described in Section III.4.ii as Case I, the unambiguous conclu- sion is that the categorical restrictions of the matching grant are non-binding, resulting in a stimulation of State expenditures on non-aided functions. For grants with ceilings sufficiently large to fall into the categories described as Case II and Case III, State expenditure response indeed depends on its elasticity of demand for highway construction. For these cases, elastic (inelastic) demand will result in a increase (decrease) of State expenditures frpm their pre-grant levels.1 In the next section, a brief analysis of actual highway expenditure data will be presented to illustrate the conclusions discussed above. 1. Several factors influence the price elasticity of a State's demand for highway construction including the level and growth in traffic on State roads, and tax capacity of the State (i.e. the propensity of the State to tap additional revenue sources or the willingness to increase levies on existing revenue sources. In the context of the illustra- tive examples presented in this section, the price elasticity as expressed by the State's response to a Federal matching grant is determined solely by the number of projects in region 2 of figure 111.4.1. Specifically, if in developing a list of mutually exclusive candidate projects for its highway investment program, a State perceives numerous projects marginally unattractive in benefit/cost terms (i.e. projects with B/C slightly less than one), then a relatively small Federal price subsidy may elicit a large expansion in the State's highway investment program (representing price elastic demand for highway facilities). 197 198 111.5 Observed Expenditure Patterns: The Impact of the ABC and Interstate Programs The analysis in Section 111.4 proceeded on the basis of a State developing a highway investment program in the absence of Federal highway grants, and then altering their investment decisions in response to the offer of Federal matching grants. Three possible response patterns were described (Cases I, II and III), each dependent on the matching provisions and magni- tude of the grant offer. In examining data indicating the States' total expenditure levels on Federal Aid System construction and Federal highway grant availability, it is clear that we are merely observing the States' expenditure responses to Federal highway grants rather than - in any direct fashion - observing how expenditure decisions changed due to the existence of Federal grants. However, by simply comparing the magnitude of Federal grant availability, and the level of expenditure from the State's own resources (on Federal Aid Systems), it can be straightfor- wardly inferred which of the three previously cited expenditure response patterns obtain (c.f. Section III.4.ii). For grants which have a pure income effect (Case r), we should observe a State consistently expanding their own highway expenditures beyond that level minimally required to match avail- able Federal grants. In this case, the size of the grant is not 199 of sufficient magnitude to introduce a perceived price reduction at the investment margin. By inference, this type of grant simply provides additional non-categorical income to the State, which may be expended on any highway function. If on the other hand, the data indicate that State expenditures consistently just equal the minimal amount required to match available Federal grants, then a price plus income effect may be inferred. In this case (Case II), the grant has had the effect of stimulating additional expenditures on the aided category, and increases in the size of the Federal grant may be expected to further stimulate State expenditures. 1 Finally, if the data indicates that States consistently do not exhaust all available Federal Aid, then it is clear that Case III obtains. It should be noted that we can imediately rule out the relevance of Case II since in only one isolated instance has a State (actually, "State" in question was Washington, D.C., who forfeited a portion of available Inter- state aid in 1971) failed to obligate the entirety of available Federal highway grants. i. Data Analysis of the ABC Highway Program Table 111.5.1 displays (for each of the 48 mainland 1. As opposed to (small) increases in Case I - type grants. where total expenditures on the aided function would not be expected to increase significantly. EXCESS FRACTIONSTATE ALA ARIZ ARK CALI COLO CONN DEL FLOR GEO IDA ILL IND IOWA KAN S KENT LOUS ME. MD. MASS MICH MINN MISS MSRI MONT NEB. NEV. N.H. N.J. N.M. N.Y. N.C. N.D. OHIO OKLA ORE. PENN R.I. S.C. S.D. TENN TEX. UTAH VER. VA. WASH W.V. WISC WYo. 0.289507 0.375106 0.235334 0.636863 0.188915 0.645065 0.360464 0.578587 0.196594 0.086208 0.142846 0.122115 0.472978 0.237851 0.401687 0.519069 0.203455 0.693403 0.454965 0.387245 0.359732 0.314645 0.389025 0.053528 0.109797 0.193299 0.321408 0.245089 0.128208 0.530505 0.263533 0.033898 0.545156 0.255555 0.364490 0.532504 0.197607 0.276288 0.270003 0.421665 0.391798 0.194422 0.293234 0.516324 0.477908 0.573908 0.430931 0.157235 TIME PERIOD: 1954-1970 Source: Yearly Editions of HIGHWAY STATISTICS (1954-1970), U.S. Bureau of Public Roads, Washington, D.C. Table 111.5.1 STATE EXPENDITURES OVER AND ABOVE MINIMAL MATCHING REQUIREMENTS EXPRESSED AS A FRACTION OF TOTAL EXPENDI- TURES ON "ABC" SYSTEMS 200 201 States, over the time period 1954-1970) expenditures over and above minimal matching requirements, expressed as a fraction of total expenditures on "ABC" systems. More significantly, each table entry is defined as: ef = (ETPF) I[ 1 -F HPF (12) MF ET where: ef = excess fraction (i.e. the table entries) ET = total expenditures by a given State over the 17 year sample period on ABC Systems (State and Federal monies) 1 MF = Federal matching share for a given State PF= Payments of Federal ABC monies from theHighway Trust Fund to a given State over the 17 year sample period The term in brackets in equation (13) expresses the expen- diture level from the States' own sources required to qualify for receipt of PF Federal Aid dollars. Thus, the numerator expresses 1. As shown in figure , the Federal share payable is not equal for all States. The 13 Public Land States receive ABC grants with Federal shares payable ranging from 53.5% (Washington) to 95.0% (Alaska). The remaining States all are subject to 50/50 ABC grants. Additionally the Federal share of grants to Public Land States change slightl from year to year in response to these States 'totalacreage of National Parks, Indian Reservations, etc. The data in figure 111.5.1 employed the Federal share payable in 1962 - the median year in the 17 year sample period. 202 the States' own excess expenditures beyond minimally required matching monies. The excess expenditure fractions in table 111.5.1 range in value from 3.4% in North Dakota to 69.4% in Maryland. In the latter case, of the total (State plus Federal monies ABC system investment by Maryland, between 1954 and 1970 nearly 70% represented expenditures net of minimal matching require- ments. In fact, only three of the forty eight States (Idaho, Montana and North Dakota) had excess expenditures totaling less than 10% of the their total ABC expenditures. The inescapable conclusion here is that for the great majority of States, the ABC grant program has served the role of non-categorical income subsidies. Neither the categorical restrictions, nor the matching provisions have been allocationally significant. In terms of the States' investment calculus, the determination of total ABC system expenditures have been based on the full cost of the marginal project rather than a price subsidized (50%) cost. Inferentially, it makes little difference whether the Federal share payable were 50% or some higher value - say 70%.l To see this, consider the example of New York's ABC 1. In fact, the Federal share payable on ABC systems was increased from 50% to 70% effective July 1, 1974. 203 system expenditure and grant availability in 1963 (table 111.5.2) Given a 50% Federal matching share, it would cost New York $60,315,000 to match the Federal payments made available. But considering that New York was willing to expend over $200 million on ABC system construction (from its own sources), it makes little difference whether the first $60 million or the first $26 million went towards matching available Federal funds. Only the price at the margin is important. Thus it is apparent that for New York and most other States, we should expect increases in ABC grants to have a relatively small impact (through an income effect) on total ABC systems expenditures. ii. Data Analysis of the Interstate Highway Program As discussed in Section 11.2 , the Interstate highway program differs in three important respects from the ABC highway program. In magnitude, Federal grants for the Interstate program exceeded ABC grants over the period 1954-1970 by 231%. Additionally, the basic Federal share payable for the Interstate program amounts to 90% as compared to a 50% share payable towards ABC projects. But perhaps the most fundamental difference - at least in terms of States' expenditure responses to Federal grants - is the fact that, unlike the ABC program, the Interstate program represents a closed system. Total system mileage and general corridor locations for the system were 204 ABC System ExpenditureslGrants New York: 1963 (1000's of dollars) 50% Federal 70% Federal Share Share Federal payments 60315 Required State matching funds 60315 25849 States' own expenditures 200964 "Excess expenditures" 140649 175115 Percentage excess expenditure 53.8% 67.0% Table 111.5.2 205 determined years before the first Federal dollar was expended on the system. Moreover, Federal Interstate grants are awarded to the States on the basis of the relative cost to complete their portion of the approved system, unlike ABC grants which are fixed without regard to the level of investment chosen by the State. For these reasons, it may be inferred that States have little incentive to expand Interstate highway construction sig- nificantly beyond the level provided for by the Federal grants. This expectation is borne out by the data in table 111.5.3 indi- cating the States' expenditures over and above minimal matching requirements, expressed as a fraction of total expenditures on the Interstate system over the period 1954-1970 (refer to equation 13). The excess expenditure fractions range from a low value of 0l (North Dakota) to a high value of 37.7% in Rhode Island. It is immediately clear that relative to expendi- tures made on the ABC system, most States expend little more than the minimally required amount necessary to qualify for 1. The negative value appearing for North Dakota indicates an error in the data reported in HIGHWAY STATISTICS. Note that an excess expenditure fraction less than zero would suggest a State not meeting its minimal matching requirement for the receipt of Federal Funds. We shall assume that the excess expenditures for North Dakota are essentially zero. EXCESS FRACTION ALA ARIZ ARK CAL I COLO CONN DEL FLOR GEO IDA ILL IND IOWA KANS KENT LOUS ME. MD. MASS MICH MINN Miss MSRI MONT NEB. NEV. N.H. N.J. N. M. N. Y. N. C. N. 0. OHI O KLA ORE. PENN R.I. S.C. S.D. TENN TEX. UTAH VER. VA. WASH W.V. WISC WYO. 0.033706 0.141695 0.042172 0.260211 0.093779 0.105866 0.119580 0.113527 0.116668 0.067219 0.057098 0.116334 0.175011 0.065520 0.071806 0.056850 0.055336 0.095672 0.166204 0.112119 0.067162 0.055157 0.000028 0.003678 0. 081 941 0.076883 0.038050 0.081553 0.094687 0.071708 -0. 043332 0.028562 0.097182 0.092277 0.042853 0.093673 0.376995 0.025138 0.047225 0. 041191 0.104352 0. 174613 0.026371 0. 009704 0.104955 0. 096852 0.150828 0.055882 TIME PERIOD: 1954-1970 Source: Yearly Editions of HIGHWAY STATISTICS (1954-1970), U.S. Bureau of Public Roads, Washington, D.C. Table 111.5.3 STATE EXPENDITURES OVER AND ABOVE MINIMAL MATCHING REQUIREMENTS EXPRESSED AS A FRACTION OF TOTAL EXPENDI- TURES ON INTERSTATE SYSTEMS STATE 206 207 receipt of Interstate grants. Fully thirty three out of the forty eight States devote less than 10% of their total Interstate investment towards expenditures beyond the minimal matching requirement. And with the exception of California and Rhode Island, all States exhibit an excess expenditure fraction less than 20%. Thus, it may safely be concluded that for the vast majority of States, Interstate grants have been characterized by a price and income effect. Following the analysis of Section 111.4., we may infer that Interstate grants have induced State expenditures on projects that would not have been made in the absence of grants. And by the same token, small increases in the level or price subsidization of Interstate grants may be expected to stimulate additional expenditures on the Interstate system from the States' own resources. 208 III.6 Summaryand Conclusions This chapter has attempted to define both the normative and positive analytic issues involved in an investigation of the Federal Aid Highway Program (FAHP). Two related findings merit particular attention: - the design of the FAHP should be related to the objec- tives the Federal government hopes to accomplish through its grant program - States' expenditure responses depend significantly on the structural characteristics of Federal grants. The former finding derives from the discussion in Section 2 on the normative aspects of the Federal Aid Highway Program. Summarily, it should be noted that the selection of the appropri- ate mathcing ratio - indeed the very choice of a Federal matching grant as opposed to a block grant must be related to the perceived fiscal problem the grant attempts to rectify. This type of per- spective gives direction to arguments for and against alterations to the existing FAHP. For example, it may be argued that the stipulations in the 1973 Federal Aid Highway Act allowing for the construction of mass transit facilities under the same grant provisions as the Urban (highway) System1 is not the appropriate form of transit aid. The relevant issue here is that the primary rationale for 1. Close-ended categorical matching grants with a Federal share payable of 70% 209 Federal highway grants is entirely different from the rationale fore transit aid. In the former case, the existence of signi- ficant interstate benefit spillovers call for external financing to move towards an efficient allocation of highway resources. In the latter case, it is primarily the fiscal disparity between different cities (i.e. the ability of a city to raise sufficient revenue to provide for a given level of transit service) that indicates the need for Federal financing. As discussed in Section 2, in the one instance, Federal matching grants are in order; in the other, block funding is more appropriate. The second major finding of this chapter is the relationship between State expenditure responses, and structural characteris- tics of Federal grants. It has been shown that categorical match- ing grants will always stimulate greater expgnditure levels than non-categorical block grants of like amount. In fact, Section 5 presented evidence that the ABC program has failed to serve as a stimulus for additional construction on the aided systems. In light of this finding it is important to question the objectives of the ABC highway grant program. If the intent of Federal grants for the ABC system was to "accelerate the construction of Federal-aid highway systems .... since many of such highways or portions thereof, are in fact inadequate to meet the needs of local and interstate commerce"I, the program has apparently failed 1. Subpart A, Title 23, United States Code, Chapter 1, Section 101(b): Declaration of Policy. 210 to do so. By the same token, the ABC grant program does not appear to be necessary to ensure a minimal level of provision of such systems (c.f. Section III.2.iv), since the great majority of States invest funds far in excess of their minimal matching require- ments. Indeed, the primary consequences of the ABC grant program appears to be merely to have provided the States with additional highway revenue - an outcome that could be achieved in a more straightforward manner by the institution of non-categorical block grants. 1 Needless to say, it is important to verify the theoretical findings in this chapter with empirical evidence. The remaining chapters of this thesis will discuss a series of econometric models designed to assess the impacts of the Federal Aid Highway Program on State highway expenditures. 1. Although this assertion reraises the initial question posed in this section: What are the objectives to be accomplished by the FAHP. CHAPTER IV 211 DEVELOPMENT OF THE TOTAL EXPENDITURE MODEL IV.l Introduction There are two fundamental dimensions of States' highway expendi- ture behavior: long run revenue or total expenditure policy formulation, and short run allocation (programming) determination. The distinction between revenue policy as a "long-run" phenomenon and allocation policy as a "short-run phenomenon derives from the fact that changes in the determinants of State highway revenue(e.g., tax rates, bond sales, etc.) tend to be infrequent relative to the expression of a State's allocation policy (e.g., year-to-year capital budgeting decisions). The empirical models developed in this research attempt to explain the factors influencing States' total highway expenditures, and allocation decisions amongst alternative highway expenditure categories. Naturally, the central focus of the research is an evaluation of how Federal grants have affected States' expenditure behavior. In this chapter, the development of the total expenditure model (TEM) is presented. Attempting to build on the common use of "Needs Studies" as a long run fiscal planning device, Section 2 presents a derivation of the TEM based on capacity utilization theory. The major focus of this model is to trace States' total highway expenditure responses to the presence of Federal highway grants. Following the derivation of the model, Section 3 explores the estimation problems inherent in the use of a pooled data set. 212 While it would have been desirable to estimate the TEM for each State individually -- as 48 separate time series -- lack of sufficient historical data precluded this approach. Accordingly, we describe a practical approach to estimating the model with both time series and cross sectional data. Section 4 describes the definitions and sources of data employed in our TEM estimation. In many instances, data which would have been desirable from a theoretical standpoint was not directly available. The use of proxy information is fully described in this section. Next, a short discussion is presented on considerations for interpreting the empirical results. Hypotheses to be tested are discussed in terms of the signs and magnitudes of specific parameter estimates. Section 6 describes the actual estimation results of the total expenditure model. Several alternative specifications are presented and applied to an 2xperiment where the entire sample was divided into two distinct subsets. The results convincingly demonstrate the States' differing expenditure responses to the Interstate and ABC grant programs. Finally, the major results and policy implications derived from the estimation of the total expenditure model are set forth in Section 7. 213 IV.2 Derivation of the Model It is convenient to conceptualize States' highway expenditure behavior in terms of two dimensions: 1. decisions relating to the determination of the magnitude of the States' highway budget in any given year, and 2. decisions relating to the allocation of that budget amongst alternative types of highway expenditure categories (e.g. Interstate, Primary System, maintenance, administration, etc.) In fact, it may be argued that this analysis perspective is not merely an artificial construct. While the administrative and political realities of altering tax rates and debt obligation (and thus altering total expenditure levels) inhibit quick adjustments to changes in costs and demand,I the program selection (programming) process operates on a relatively short cycle time.I We focus here on the derivation of a model to explain the derivation of a model to explain the first of the two dimensions of State behavior: the determination of total highway expenditures. An immediate starting point is an examination of the "Needs Study" process. The highway needs process has been incorporated into the U.S. Department of Transportation's biennial National Transportation Studies, required of all States as of 1968. But prior to this time to this time several States conducted explicit internal highway needs studies for their own fiscal planning purposes at varying intervals. In its simplest terms, a (highway) needs study involves the Highway bond sales are usually issued over a two to five year period. The average duration between tax rate adjustments is ever longer. Over the fifteen-year period, 1951-1965, the average duration between the States' tax rate adjustments was somewhat over ten years. determination of the desired ("needed") level of highway physical 214 plant based on structural and functional deficiencies in existing inventories, present and future design standards, traffic growth rates, and anticipated highway functional classification. Highway needs studies do not represent a radically innovative methodology to guide States' investment behavior. In fact, conceptually the needs study process may be considered as a specific application of the general economic theory explaining the investment behavior of a behavioral unit (be it a firm, industry or State Highway Department). This is an important point, since we are attempting to model the highway investment behavior of States, regardless of whether they conducted explicit needs studies during the course of our analysis period (1957 - 1970). The most general statement of the factors influencing total highway investment behavior (of which a needs study is one application) may be expressed by: (1) Rt = f(Kt - Kt-) where R = total revenues devoted to highway expenditure (State plus Federal funds) K* = desired capital stock in year t Kt-1 = actual capital stock at the end of year t-l Equation (1) asserts that the level of (total highway) investment in a given year t is a function of the gap between a "desired level of highway plant" at the end of year t and the existing level of capital stock at the beginning of year t. The conceptual basis of this investment relation has been 215 advanced under the general heading of "capacity utilization theories." Most commonly, the dependent variable is expressed in terms of (a firm's) investment in capital stock. In our application, we are more interested in a State's total (capital plus non-capital) highway investment. However, equation (1) remains perfectly general. We would expect higher levels of total highway investment to be associated with higher "gaps" between desired and existing highway plant. Note that Rt in equation (1) is just the sum of the States' own resources R and the amount of available Federal highwayt grants Gt (2) Rt = R0 + Gt t But Gt is equal to the sum of unexpended Federal grants in years t-1, t-2, . . . and Federal grants made available in year t: (3) Gt = UBGt-1 +gt where UBGt-1 = unexpended balance of Federal grants as of the end of year t-l gt = highway grants made available in year t Substituting equations (2) and (3) into equation (1) yields: (4) Rt = f(K* - Kt-1 ) - (UBGt 1 + which expresses the revenues raised for highway expenditure in a For a good summary of the various applications of these theories, see Kuh, Edwin, CAPITAL STOCK GROWTH: A MICRO-ECONOMETRIC APPROACH, North Holland Publishing Company, 1971, especially Chapter 2. 216 State in year t as a function of the gap between desired and actual highway capital stock and Federal grants. The capacity utilization theory expressed by equation (4) has a clear relationship to the classical Needs Study Process of long run fiscal planning. In effect, we are arguing that States adjust their long run highway investment policy in response to their perception of highway "needs" (K* in our terminology), the existing inventory (Kt-I) of highways, and the available level of external funding (Gt). Needless to say, the empirical measurement of "desired" (and even actual) capital stock represents a formidable conceptual problem. Several factors influence a State's perception of highway needs1 (desired capital stock), including traffic and congestions levels, demographic characteristics, and a variety of institutional char- acteristics. Symbolically, we assume desired capital stock -- "needs" -- can be expressed as: I It should be emphasized that our modelling framework does not assume that State highway expenditures will be adjusted to meet the cost perceived highway needs from year to year. On the con- trary, the expenditure model employed here explicitly recognizes the continuing existence of a "jap_" between perceived needs and actual highway capacity. It is the existence of this discrepancy between desired and actual highway plantthat influences State de- cisions on the magnitude of total highway investment. Presumably, the greater the gap between "needs" and existing inventory in any given year, the greater will be the expenditures in that year. (5) K = Kt (SEC, IC) 217 Where SEC= a vector of socio-economic characteristics of a State (e.g., urban density, pop- ulation, traffic conges- tion levels, per capita income, and various State growth measures) Where IC= a vector of institutional characteristics describing a State's hi hway financing conventions e.g., the ex- tent of local participation in highway maintenance and construction, the extent of toll road finance, and the degree of debt-service financing Introducing equation (5) into (4) leads to the basic form of the total investment model estimated in this study: (6) Rt = f(Kt (SEC, IC) - Kt 1) - g(UBG + gt where f and g are assumed to be linear functions of the arguments Note that the last term above is written as a function, rather than the simple sum of UBGt-1 and gt as in equation (4). The reason for the more general specification here is to allow for an explicit test of the ef- fect of Federal grants. In other word, equation (6) permits an assess- ment of the impact of Federal grants on the level of total hig wa expenditures derived from States' own sources. The major hypothesis to be evaluated empirically is relative degree of expenditure stimulation resulting from Interstate versus non-Interstate grants. In the hypo- thetical model presented in Chapter III, preliminary data analysis in- dicated that Interstate grant increases would most likely be associated with increases in States' own expenditures. This behavior was contrast- 218 ed with the ABC grant program, where it was hypothesized that States would view increases in ABC grants as a substitute for their own expenditures on these Federal Aid Systems. The empirical results presented in Section IV.6 will validate the theoretical hypotheses. 218%s IV.3 Estimation Techniques for the Total Expenditure Model While it would have been desirable to estimate the total expenditure model (TEM) for each State individually (i.e. as forty-eight separate time series), lack of sufficient historical data precluded this approach. The specification of the TEM incor- porated as many as twelve explantory variables (including the con- stant term). Given only fourteen years in our analysis period (1957- 1970), individual State estimation is clearly infeasible. Accordingly, the possibility of grouping our observations in a pooled data set consisting of time series and cross-sectional data merits special attention. One of the first investigations of this problem was advanced by Theil and Goldberger,I who demonstrated that the estimation of time series parameters can be designed to incorporate additional information oabtainable from cross-sectional data. In principle, the reasons for pooling data ar - s mpl3: provided that we cna take proper statistical account of individual regional and/or time effects that may be present in the data, the use of pooled data (by virtue of the large increase in available degrees of freedom) yields more effecient model paramter estimates. In our application, the use of pooled data increases the number of available observations from 14 (years) to 672 (14 years x 48 States). Theil, Henri, and A.S. Goldberger, "On Pure and Mixed Statistical Estimation in Economics," International Economic Review, Volume II, No. 1, January, 1961 To clarify the statistical problems inherent in estimating 219 models employing pooled data, let us rewrite equation (6) of Section IV.2 in matrix form to stress the fact that an observation is specific to a particular State and year: R0 R0 1R~' (7) R0 = = X + u 0R R0 RNT X - - X(K)ku11 11 11 XO) -.-. - X(K) u 1T 1T 1T + O)x(K) uNINl ll kiNI NT NTuNT 220 where: N = number of States (48) in the sample T = number of years (14) in the sample K = number of explanatory variables in the model R = a vector of observations (NTxI) of total highway expenditures from State n's own sources in year t Thus we have observations on N (=48) States, n = 1, 2 . .,'N taken over T (=14) years, t = 1, 2, . . . T. Our dependent variable R is assumed to be explained by K truly exogenous varibales X. The statistical properties of our parameter estimates B, and indeed the very meaning of our model is determined by what we assume about the properties of the residual vector U. The standard assumptions of econometric theory (i.e. if ordinary least squares (OLS) are to yield best linear unbiased parameter estimates) are that the residuals are distributed with mean 0 and variance a I. However, if a model is estimated with pooled data, there are strong reasons to suggest that these assumptions are not valid. When cross section and time series observations are combined in the estimation of a regression equation, it is likely that certain systematic shift effects are present in the data. Specifically, we refer to the presence of factors not explicitly accounted for by the included explanatory variables which nonetheless influence the dependent variable. 221 Two categories of "extraneous influences" may be present. One relates to the presence of pure regional effects -- i.e. factors outside the model which serve to determine the behavior of individual States. Growth rate policies, political culture variables, "belief in the future,"2 and auto/transit biases are examples of factors that, although important in determining individual State expenditure behavior, are difficult to explicitly model at the aggregate level of analysis considered in this thesis. A second extraneous influence relates to the presence of time dependent shifts -- i.e. those factors which may affect all States at any given point in time, but vary from year to year. The most obvious examples of this affect are macro-economic influences: interest rates, degree of inflation/ regression, unemployment rates, etc. A common method to account for these "extraneous influences" is to introduce explicitly into the equation individual shift variables. The rationale for this approach is that the observations contain an additive effect specific to the individual State or year. To account for such effects, dy variables corresponding to 1Kuh, Edwin, and J.R. Meyer, "How Extraneous are Extraneous Estimates," The Review of Economics and Statistics, Volume 39 (November, 1957). 2The importance of this factor was discussed by Mead, Kirtland, DESIGN OF A STATE WIDE TRANSPORTATION SYSTEM PLANNING PROCESS: AN APPLICATION TO CALIFORNIA, Unpublished Ph.D. thesis, M.I.T. Civil Engineering Department. each State or yearI may be explicitly introduced into the model. 222 The problem with this approach is that it reduces the degrees of freedom by N without adding in any real sense to the explanatory power of the model. Moreover, it is often found that the dummy variable approach "overcompensates" for the individual effect by drastically reducing the magnitude and significance of the explanatory variables. 2 Error Component Analysis Another technique to account for the.presence of individual State and/or time shift effects is with error component analysis.3 Since we are assuming the presence of economic forces specific to an individual State and/or year, not otherwise accounted for in our model specification, it is reasonable to expect that these forces "show up" in the residual term. To state this formally, we assume 1Obviously it would not be possible to introduce a specific dummy variable for each State and for each year. The most common practice is to focus on the presece of regional effects by introducing explicit State dummy variables. For an example of this approach, see Balestra, Pietro, and M. Nerlove, "Pooling Cross Section and Time Series Data in the Estimation of a Dynamic Model: The Demand for Natural Gas," Econometrica, Volume 34, Number 3 (July, 1966). 2This is particularly true of those variables that vary significantly from State to State, but exhibit little variance in any given State over time. The dummy variable approach was attempted in this research and abandoned for the above reason. For a further discussion of this point, see Balestra and Nerlove, op. cit., especially pages 590 - 593. 3Balestra and Nerlove, op. cit., Theil and Goldberger, op. cit., Kuh, op. cit. 223 each residual Unt may be decomposed into three statistically independent components: an individual State effect 1n, a time shift effect t , and a remainder vnt : (8) u nt Pn + t1 + Since the residuals are assumed to tve zero mean, and the components of untare independently distributed, it must also be true that: (9) E[pn] = E[6t] = E[vnt1 = 0 We further assume that there is no serial correlation among the error components, and that they are independent from one State and year to another: E[v ntlin] = 0 (10) E[vnt6t] = 0 E[vn6t] = 0 E[vntvn't' 10 2 Ef lip,] E[6t6tII 16 if n=n' and t=t' otherwise if n=n' otherwise if t=t' otherwise Accordingly, we may express the variance-covariance (an NTXNT matrix) 0 of the residuals (ant) by: E[untunt w2 w 2 w 2 1 w2 w2- 224 where: S0 - 0 0 T 0 0 0 P = (12/IG2 = S/2 *6 Equation (11) follows directly from our assumption that the covariance of all the cross products of the error components are identically 0. Note that the variance-covariance matrix .11 has a repetitive block structure. The diagonal blocks are T x T, and represent the variance-covariance structure of the individual State effect and remainder error component. The off-diagonal blocks, also T x T are all diagonal matrices, whose single parameter T represents the time shift effect. It is clear from the form of equation (11) that the variance- 225 covariance of the residuals derived from estimation on pooled data is not scalar. Accordingly, although ordinary least squares estimates of the coefficients would be unbiased and consistent, they would not be the most efficient (i.e. least variance estimators. In fact, the best linear unbiased estimators are the generalized least squares parameter estimates GLS which explicitly incorporate the non-scalar variance-covariance matrix: (12) GLS = (X'Q'X)'1 X'2'R0 A straightforward technique for deriving generalized least square estimators where the error term structure assumes the form of equation (8) has been advanced by Zellner.I Essentially, the technique involves a two-step estimation procedure: first estimate the model with ordinary least squares (OLS), and use the OLS residuals and equation (11) to determine the parameters of J1. Second, a generalized least squares estimation is performed by making the appropriate transformation of the original data. In our application, a simplified generalized least squares esti- mation procedure was adopted. Specifically, no account was taken of the separate time effect 6t . This error component was dropped for two reasons. First, allowing for a time shift effect would "greatly Zellner, A., "An Efficient Way of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias," Journal of the American Statistical Association, Volume 57 (1962). .226 complicate the analysis without adding any essential generality." It is obvious from the form of equation (11) that the development of generalized least squares estimators requires inverting an NTXNT matrix. Although the form of 2 inclusive of 6t is sparse (c.f. equation (11)], the inverse matrix Q-1 does not assume or simple pattern.2 In fact, inversion of a 672X672 matrix proves to be unwieldy and expensive. A second reason for dropping the individual time shift effect is that when estimations were performed using time shift dummy variables, the parameter estimates of these dummy variables did not prove to be significant. In short, the most important "extraneous influence" in our estimation problem was the presence of an individual State shift effect. The application of our simplified error component estimation procedure was straightforward. Following the notation of equation (11), we now assume that: 0 o - - 0 (13) Q = a2 * * 0 0 01 Balestra and Nerlove, op.cit., p.504. 2That is, there was no simple (and inexpensive) way to invert Remembering that each T x T matrix w is specified in terms of a 227 single parameter p, it may be shown that - can be estimated as a function of OLS residual estimates:? N T (14) -_ n~ti - a2(=n=t= t'= t ' n=l t=l nt N T (T-1) 62 where: Uj = OLS residuals for State n nt (=1,... ,N) in year t ,=l,...,T) 82 = estimated variance of the OLS regression The actual estimation of generalized least squares (GLS) estimates involves OLS estimation on suitably transformed data. The first step is to determine the Choleski decomposition2 h of Q-1 defined as: (15) h'h = -1 The original observations X and R are then premultiplied by the Choleski decomposition matrix to define X and P (16)( = hX R = hR Equation (1941 simply expresses the average value of all those elements of ulu' corresponding to where p appears in our assumed structure of 02 2 For an operational algorithm for determining Choleski darnos n matrices, see Faddeev, D.K., and Fadeeva, V.N., COMPUTATIOAL M ODS OF LINEAR ALGEBRA, W.H. Freeman, San Francisco, 1963. It follows directly that OLS estimation on the transformed data 228 yields GLS estimates of our model coefficients.1 In summary, the estimation of the total expenditure model followed a simplified error component analysis which explicitly allows for the presence of individual State shift effects in our pooled data set. Once the structure and properties of the residuals are specified [equation ( 8)], GLS estimation involves a straight- forward application of a two-step procedure employing OLS residuals to estimate the parameter of an assumed structure of the non-scalar variance-covariance matrix. I a OLS = (' '~'R= (X'h'hX)alX'h'hRo But from (15), h'h =-1 Thus BOLS = (X'Q'lX)-lX'Q-IRO = SGLS IV.4 The Data Set and Modelling Considerations Returning to the basic form of the total expenditure model derived in Section IV.2, we noted that States' own highway expenditures were functionally related to perceived investment needs, existing highway inventories and Federal grant availability: (17) While equation (17) suggests the basic explanatory relationship, the problem remains to specify the socio-economic factor (SEC), and institutional characteristic (IC) arguments of the highway needs term Kt. Moreover, a practical means of representing existing inventories Kt-1, and Federal grant availability must also be determined. This section will discuss the definitions end sources of each of the variables incorporated into the estimated total expenditure model. Several alternative specifications of the total expenditure model were estimated in this research using both deflated and undeflated data. The basic form of the model is presente in Figure IV.4.l. The first eight variables in the model correspond to the set of socio-economic and institutional characteristics which influence a State's perception of "desired" highway ca;acity. The variable KSTK serves as a proxy for existing highway inventories [i.e. the measure of Kt-i in (17)]. Finally, the availability of That is, expenditure levels, Federal grants and per capita income variables were deflated by the consumer price index. 229 THE TOTAL EXPENDITURE MODEL 230 0 MFC R a0 + a1I*SPOP + a2 *UFAC + a3 *GPOP + a 4 *PCY VMT + a 5 *GINI + a6 *RLTOT + a7 *TOLPCT + a8 *BIPTCX + a9 *KSTK + a10 *AVNIGP + a11 *AVIGP + U where R 0= State expenditures on highways exclusive of Federal per capita grants a- ao = constant term a1 = estimated coefficients VMT = State vehicle miles of travel SPOP = State Population MFC = State motor fuel consumption UFAC = percent of population residing in urban areas GPOP = State population growth rate PCY = per capita State income GINI = index of income inequality KSTK = present discounted value of highway capital stock per capita RLTOT = percent of total expenditures (all units of government) contributed by local (i.e., county and municipal) governments BIPTCX = percent of total capital expenditures provided for by debt financing AVNIGP = apportioned "ABC" grants (three year moving average) per capita AVIGP = apportioned Interstate grants (three year moving average) per capita U = error term Figure IV.4.1 231 Federal highway aid is represented by AVNIGP and AVIGP -- a three-year moving average of non-Interstate and Interstate grants respectively. i. The Socio-Economic Descriptors Five variables were employed to describe the socio-economic characteristics of each State: a basic State size variable (SPOP or MFC or VMT), a measure of urbanization (UFAC), an indicator of State growth (GPOP), and two income characteristics (per capita income PCY, and income distribution GINI). a. SPOP, MFC and VMT It is reasonable to expect that, ceteris paribus, State expenditures should increase with increasing levels of traffic demand. For one thing, higher traffic levels will generate increasing levels of earmarked State highway revenue. But more fundamentally, higher levels of auto use require increased construction, maintenance policing and aministrative expenses. Three alternative measures of State size were employed as a proxy for the scale of auto travel. The first indicator, State population (SPOP), was derived from yearly editions of the Survey of Buying Power.1 SPOP was entered into the model with a one year lag -- i.e. State expenditures during year t were related to population at Sales Management, SURVEY OF BUYING POWER, 1950 - 1970 (Yearly Editions), Bell Brothers Publications. This publication is the only source of year-to-year, State- by-State socio-economic descriptor data. The Census Bureau does not publish population, income or growth indices for each State on a yearly basis. The Survey of Buying Power's data base is adjusted to conform with the decennial census data. 233 the end of year t-l. Two alternative State size variables were also tested in the TEM estimations. Vehicle miles of travel (VMT) is perhaps the most direct measure each State's traffic levels. The only source of this information is from yearly editions of the Federal Highway Administrations HI3HWAY STATISTICS. Two problems are encountered in the use of this data. First, the data itself is not directly observed or collected, but estimated from gasoline sales statistics, and assumptions on average vehicle mix (i.e. truck/auto split) and gasoline consumption rates. Secondly, the data, is not published on a yearly basis. Over the course of our fourteen year analysis period, the FHWA published VMT data for only four years (1959, 1962, 1965 and 1968). For our purposes, intermediate (yearly) values of the VMT data were determined by simple straight line interpolation. Motor fuel consumption (MFC), the third alternative State size measure, was also derived from the FHWA Highway Statistics yearly publications, The data was entered into the model net of fuel deployed for agricultural, marine or aviation use. As with the two previous measures, a simple one year lag was employed. b. UFAC The degree of urbanization (UFAC) is an important factor in determining highway investment behavior (i.e. in terms of explaining perceived highway investment needs K) for several reasons. First, it is a measure of the "compactness" of a State as it serves to distinguish between largely rural/agricultural/sparsely populated States and densely populated urban/industrialized States (see 234 PERCENT OF POPULATION RESIDING IN URBAN PLACES WITH GREATER. THAN 5000 RESIDENTS_(1970) Urbanization IndexState State Urbanization Index Alabama Arizona Arkansas California Colorado Connecti cut Delaware Florida Georgia Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland MasSdchusetts Michigan Minnesota Mississippi Missouri Montana 58 74 48 86 75 76 66 75 56 50 82 64 56 64 47 b5 52 72 82 73 65 42 69 53 Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahomo Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming Source: Sales Management, SUl Brothers Publication RVEY OF BUYING POWER 1970, Bill Table IV.4.1 60 75 57 87 72 84 42 41 73 66 63 71 84 42 43 54 79 77 40 58 68 40 65 63 b- 235 Table IV.4.1). Secondly, it serves to identify States with highly concentrated urban areas where per lane mile construction costs are relatively high. On balance, we would expect the degree of urbanization to negatively influence States' per capita highway expenditures. There are two reasons for this. The first reason relates to the indivisibility and "lumpiness" of highway investments. As a State's population decentralizes (e.g. to previously unpopulated places), the need for highway route mileage increases. However, even the minimal provision of two lane rural roadways incurs a relatively large capital outlay.I Secondly, the more urbanized States have been subject to an increasing presence of community opposition to urban roadway construc- tion. The urbanization index UFAC is defined as the percent of a State's population residing in areas with greater than 5000 residents. The data was derived from yearly editions of the Survey of Buying Power and was entered into the TEM with a one year lag. 1That is, highway construction is charaterized by high fixed costs. Moreover, highway construction and maintenance rise less than proportionately to increases in the number of lanes (for a given route distance). 236 c. GPOP As an indicator of the rate of State growth, a measure of yearly population change was computed from the basic population data described in Section IV.4.i.a. Ceteris paribus, one would expect higher population growth rates to be associated with higher highway investment levels. As it turned out, the population growth rate data was characterized by extreme variability and proved to be a poor explanator of highway investment behavior. d. PCY and GINI Two separate measures of State income--per capita income and a measure of income inequality--were employed in the estimation of the total expenditure model. Per capita income (PCY) is correlated positively with auto usage (See Section II.3.ii), and thus we should expect increasing State income to lead to increasing State highway expenditure levels. PCY data was derived from yearly editions of the Survey of Buying Power. The GINI Index of Income Inequality is derived from Lorenz income distribution curves.1 As shown in Figure IV.4.2, the Lorenz curves describe the degree of homogeneity in household income within a State. If each household earned exactly the State average income level, then the Lorenz curve would be a straight line rising at 450 from the horizontal (i.e. 20% of the households earn 20% of total income, 40% of households earn 40% of total income, etc.) As the Lorenz curve plots the percentage of households, ranked 1Samuelson, Paul, ECONOMICS, McGraw-Hill Book Company, New York, 8th Edition, 1970. 237 LORENZ CURVES Percent of Total State Income IJA -Lorenz Curves Figure IV.4.2 238 fromypoorest up on the horizontal axis and the percentage of income they earn on the vertical axis, it is clear that as the degree of income inequality increases, the Lorenz curves become increasingly concave. This suggests a measure of income inequality related to the area between a Lorenz curve and the 450 (perfect income homogeity) line (e.g. see the shaded area in Figure IV.4.2). In particular the GINI Index of Income Inequality (GIII) is defined as area bounded b a Lorenz curve (18) GIII = and the 45 line area under the 450 line The GINI index varies between 0 and 1 with higher index values indicat- ing a greater degree of income inequality. The actual GINI indices developed for this research were constructed from piecewise linear Lorenz curves. The Survey of Buying Power data described the number of households in each State (and each year in the 14 year sample period) in each of five income categories -- $0 - 2499, $2500 - 4999, $5000 - 7499, $7500 - $10,000 and $10,000 and over. The GINI index serves to indicate two characteristics of the States. First the GINI index provides a measure of the number of low income households in each State. For a given level of per capita income, a State with a high GINI index value would have a relatively large number of low (and high) income households. Thus we are accouting for the possibility that the average income level as well as the distribution of income in a State will affect the level of auto 239 usage (and thus ultimately affect the level of State highway expendi- ture). The GIII also conveys a rough measure of regional characteris- tics. From Table IV.4.2, which displays the GINI index for each of the forty-eight mainland States in 1963 (the mid-year in our 14-year sample period), southern/agricultural/rural States tend to have a higher degree of income inequality than northern/industrial/urbanized States. ii. The Measurement of Highway Capital Stocks The development of time series information on a State's highway capital stock presents a formidable task. An imediate problem is to select the units to describe the capital stock, and the economic conventions to be employed in measuring the change in value productivity of vintage stocks over time. On theoretical grounds, it is clear that the best measure of capital stock is output capacity. In terms of evaluating highway investment behavior, it may be argued that a State's investment decisions are based, at least in part, on the perceived gap between the demand for existing highway service (e.g. vehicle miles of travel), and the existing supply of the highway plant. Implicit in this decision-making process is the notion of level of service. Herein lies the problem in measuring highway physical plant. The capacity of a highway system, and the quality of the output (i.e. level of service) are inherently related. This relationship stands in contrast to the capital stock measurement problem of manufacturing production processes where output is normally of uniform quality. The only 240 MEASURES OF INCOME INEQUALITY1963 State Gini Index of Income Inequality Oklahoma 43.1 Florida 42.8 Kentucky 42.5 Alabama 42.3 Louisiana 42.0 Tennesee 41.9 Texas 41.6 Arizona 41.6 Deleware 41.3 Virginia 40.5 New Mexico 40.2 Iowa 40.2 Mississippi 40.1 Georgia 39,9 North Carolina 39.8 Oregon 39.7 Vermont 39.1 Minnesota 39.0 Missouri 38.9 Kansas 38.9 Washington 38.7 West Virginia 38.5 South Dakota 38.4 New York 38.4 Nebraska 38.3 Nevada 38.2 Ohio 38.1 Maine 37.8 Pennsylvania 37.7 Illinois 37.6 Indiana 37.5 Maryland 37.4 Michigan 37.4 Rhode Island 37.3 South Carolina 37.3 Colorado 37.3 Massachusetts 37.2 Table IV.4.2 241 State Gini Index of Income Ineuality North Dakota 37.0 Idaho 37.0 Wisconsin 36.8 Arkansas 36.4 Connecticut 36.1 New Jersey 36.1 New Hampshire 35.6 Utah 35.2 Montana 35.0 Wyoming 34.8 California 32.0 Table IV.4.2 (contd.) 242 practical problem in capital stock measurement in this case is the selection of an appropriate depreciation formulation to measure the declining value productivity of older capital stocks. From the above remarks, it is clear that a complete descrip- tion of highway capital stock requires knowledge of the highway system's value-in-use -- ie. a comprehensive inventory of the physical (e.g. roadway width, surface quality, geometric design, etc.) and operating characteristics (i.e. speeds over the roadway at existing demand levels) of the highway system. Unfortunately, this data is not available on a time series basis. Moreover, for the few years in which comprehensive inventory data exists,1 the data set is excessively unwieldy, as it represents a large sample, section-by-section description of all State-adminis- tered highway mileage. Considering the fact that this type of information has been largely unavailable to State planners and decision-makers on a year-to-year basis, the relevant question for this analysis is to find a relevant proxy measure for value-in-use highway capital stock, drawing on available time series data. The primary source of highway mileage data examined in this study is drawn from the yearly editions of Highway Statistics, IHighway system inventory data has been collected as part of indivi- dual State Highway Needs Studies (HNS). The Federal government required HNS of all States as of 1968. Prior to the time, several States conducted HNS on their own at irregular intervals. 243 published by the U.S. Bureau of Public Roads. Unfortunately, the organization of this data does not lend itself inediately to proxy measures of highway capital stock suitable for investment analyses. The most important data gap is the lack of information on the vintage distribution of the States' highway plant. Thus, it is not immediately apparent how to depreciate the value-in-use of existing capital. Moreover, yearly additions to States' highway route mileage are reported in units of route mileage rathern than lane mileage, with no distinction made between projects on new rights-of- way, and projects designed to improve existing rights-of-way (e.g. major resurfacing of existing mileage, lane widening, addition of new lanes to existing ROW, etc.). Clearly, any attempt to measure capital stock in terms of capacity output requires data in lane mileage, rather than route mileage terms. The data on total existing lane mileage is sketchy. In all cases, the mileage figures are reported in discrete categories-- 2 lanes, 3 lanes, and 4 lanes or more--so that the data are imprecise in the highest lane category. Attempts to identify lane mileage figures with specific Federal-Aid Systems is complicated by lack of data on Federal Aid Secondary lane mileage. The lane mileage (LM) data is broken down into Interstate LM, Federal-Aid Primary LM, and State Primary System IM. The latter category includes portions of all of the Federal Aid System mileage as well as State system mileage not 1For example, the number of vehicles per day that can be accomodated on the State-administered road system at a given average speed. incorporated on the Federal-Aid Systems. 244 In summary, attempts to employ mileage data as a proxy measure of highway capital stock is complicated by a lack of information on the vintage distribution of highway plant, and an incomplete stratification of lane mileage by Federal and non-Federal- Aid System. Given the above-mentioned difficulties in applying mileage data to the task of measuring capital stock, it is desirable to investigate the use of historical capital expenditure data as a proxy measure of existing highway stock. An immediate issue in applying expenditure data is the proper accounting of the decline of capital productivity over time. As it turns out, the proper treat- ment of expenditure data as a capital stock proxy measure is far less difficult than the use of the available mileage data. The methodology for constructing highway capital stock measures requires some attention to the choice of an appropriate depreciation methodology. Depreciation refers to the loss in value of a currently held asset. Two types of depreciation functions are commonly found in the literature: market value functions and efficiency loss functions. The former measure indicates the decline in resale value 1The benefits of using physical measures of capital stock (i.e. elimination of price delator affects, and the ease of identifying stock retirements) are obvious. Nonetheless, the investment behavior literature is replete with studies employing capital expenditure proxies of capital stock. The main reason for the use of expenditure data is that it is generally more readily available than physical measures of capital. of fixed plant over time, while the latter measure reflects the 245 losses in efficiency due to wear on the fixed plant. The more relegant measure for highway investment studies is the efficiency loss function. The techniques for deriving depreciated highway capital stock measures in this study were based on methodology developed by Jack Faucett Associates.1 The methodology involves applying an efficiency loss depreciation function (ELDF) to the time series of State highway expenditures. The Faucett study hypothesizes that the efficiency loss of highway systems increases over time (i.e. as a highway approaches the end of its service lifd2 The actual ELDF employed takes the form of the lower segment of a rectangular hyperbola: (19) D(t) = SL tSL -at where D(t) = percent of a highway system's remaining productivity t = the age of a highway SL = the service life of a highway a = a parameter of the effciency loss depreciation function (Otacl) This formula generates a family of depreciation functions as a function of the parameter a (See Figure IV.4.3). Following the conventions of the Jack Faucett study, a 20-year service life was Jack Faucett Associates Inc., CAPITAL STOCK MEASURES FOR TRANSPORTA- TION, Volume 1, Report No. JACKFAU-71-04-1, 1971. As manifested by the increasing level of required maintenance expendi- tures and/or the decreasing level of highway productivity (as measured by vehicle capacity). 246 DEPRECIATION FUNCTIONS percent of remaining increasing productivity values of a D(t) D(t) =SL-tSL-at Figure IV.4.3 was assumed for State highway system construction expenditures, 247 and the ELDF parameter (a) was set to 0.8. The efficiency loss depreciation function was applied to a thirty-four year time series1 of State highway system expenditures to generate the depreciated highway capital stock measures per capita (KSTK)for each State and each year in the 14-year sample period. iii. Descrigtors of Financing Conventions and Institutional Characteristics Three descriptors of State hiqhway financing conventions were employed in this study: the extent of local participation in highway finance (RLTOT)2, the importance of toll roads in generating State highway revenues (TOLPCT)3, and the degree of debt service highway financing (BIPTCX). Since the dependent variable in the total expenditure model exclusively measures State highway expenditures, we should expect that higher degrees of local participation (as measured by RLTOT) in the provision and maintenance of highway facilities will be associated with lower expenditure levels from State resources. In 1The expenditure time series covered the period 1937 - 1970. Expen- diture data was derived from yearly editions of HIGHWAY STATISTICS. 2RLTOT is defined as the ratio of municipal and county highway expendi- tures to total (all units of government) highway expenditures. 3TOLPCT is defined as the percentage of a Stage's highway revenue derived from highway tolls. 4BIPTCX is defined as the ratio of bond interest to State highway construction expenditures. other words, to the extent that a State delegates its highway 248 authority to lower units of government, State highway expenditures should decrease. The other two indicators of institutional characteristics, TOLPCT and BIPTCX, reflect the degree of flexibility in the States' highway finance program. For a given State gas tax rate, the increasing use of toll road or debt service financing allows a State greater opportunity to raise higher levels of highway revenue. Thus we should expect TOLPCT and BIPTCX to positively influence State highway expenditure levels. Each of the three financing convention variables, RLTOT, TOLPCT and BIPTCX, were derived from yearly editions of the FHWA's HIGHWAY STATISTICS. iv. The Highway Grant Terms Two important characteristics distinguish the treatment of the Federal highway grant terms in our total expenditure model from previous empirical highway expenditure studies (See Section 1.3) First, the Federal-Aid Highway Program was broken down into two distinct components: Interstate System grants, and grants on the non-Interstate ("ABC") Systems. The theoretical analyses of Chapter III indicated the strong likelihood of differing State expenditure responses to these two grant types. In fact, it was hypothesized that the Interstate program grant structure would most likely induce expenditure stimulation in contrast to the hypothesized expenditure substitution response to ABC grants. The modelling emplications of these hypotheses are twofold. First, it was considered desirable to explicitly test these hypotheses by 250 separating out the two distinct grant types. Second, it was considered likely that the simple inclusion of a total grant term would "wash out" any empirically identifiable grant response.I A second characteristic distinguishing this study from previous research is in the treatment of the multi-year grant availability problem. As discussed in Chapter II, Federal highway grants are made available over a "grace period" extending from one-half year before the beginning of the fiscal year of the authorization to two years beyond the end of that fiscal year. The use of three year movingaverages on the grant terms was employed to represent the grace period FAHP feature. Moreover, the use of moving averages partly accounts for the fact that States may not fully and immediately adjust to changes in Federal highway grant availability. The basic Federal grant data was obtained from yearly editions of HIGHWAY STATISTICS. Apportionments for the years 1969 and 1970 were adjusted downward in accordance with the imposed OMB fiscal control totals (See Section IV.2). The grant terms were 1All of the studies cited in the literature survey of Chapter I included only a total highway grant term. Several estimations of our TEM were conducted with a single total grant term. As expected, the estimated grant parameter was extremely small and had a large standard error (See Section IV.6). 2Specifically, the three year moving averaged grant terms Gt were computed as -1 Gt= j(Gt+Gt-1 t-2) for t = 1954, . . ., 1970 where Gt = States' grant apportionments in year t. 251 expressed as averaged Interstate grants per capita (AVIGP) and averaged non-Interstate grants per capita (AVNIGP). v. Price Delflators This study conducted estimations on both (price) deflated and und2flated data. Specifically, all of the terms in the total expenditure model whose units are expressed in dollars were adjusted by the consumer price index (See Table IV.4.3) according to the following relationship: (20) d CPI where: Vd = price deflated variable V = value of variable in absolute terms CPI= consumer price index In addition to deflating the dependent (highway expenditure) variable, the following explanatory variables were deflated by the Consumer Price Index: per capita income (DEFPCY), highway capital stocks (DEFKSTK), Interstate grants (DEFIG), non-Interstate grants (DEFNIG), and total grants (DEFTG). 252 Consumer Price Index (1970 base) Consumer Price Index .689 .700 .725 .745 .751 .762 .771 .779 .788 .799 .812 .835 .859 .896 .944 1.000 Source: U.S. Department of Transportation, 1974 NATIONAL TRANSPORTATION STUDY: HIGHWAY PLANNING PROGRAM MANUAL, Table 11-3 Table IV.4.3 Year 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 253 IV.5 Research Strategy and Considerations for Model Interpretation i. The Total Expenditure Model: Considerations for Model Interpretation As indicated in the previous section, the basic form of the total expenditure model describes the relationship between States' own per capita highway expenditures, and a set of variables representing States' socio-economic and institutional characteristics (serving as proxies for the "desired" level of highway inventories), a measure of existing highway plant (with a one-year lag) and measures of available Federal highway grants (divided into Interstate and non-Interstate categories). Before presenting a discussion of the emprical results, it is important to clarify the hypotheses which the total expenditure model can address. Consider first the estimated coefficients of the Federal grant (per capita) terms (refer to Figure IV.4.1 ). Following the discussion presented in Chapter III, it is clear that sign and magnitude of these coefficient estimates will serve to distinguish the substitution or stimulation effects of Federal highway grants. To see this consider the following possible values of the grant term (a ) coefficient estimates:1 The following comments are relevant to the analysis of both the Interstate and non-Interstate grant terms. 254 1. a (- 1 -9-- A value of a less than one would indicate that States reduce their own highway expenditures by more than one ddllar for each additional grant dollar received. This type of behavior is highly improbable as it would imply that Federal highway grants have served to reduce total highway expenditures. 2. a9 = - 1.0 This case is symbolic of perfect expenditure substitution wherein each additional dollar of Federal grants is associated by exactly a one dollar reduction in the level of the States' own expenditures. It follows that, in this instance, total highway expenditures (State plus Federal funds) do not change in response to changes in the level of Federal grants. 3. - 1 ( a (0 Coefficient values in this range represent an expenditure substitution response. Like the previous situation, States' own expenditures decrease in response to increases in Federal grants, but in this case not on a dollar for dollar basis. In other words, a coefficient estimate in the range - 1 to 0 indicates that total expenditures will 255 increase but by less thanI the amount of Federal grant increases. 4. a > 0 This grant response is characteristic of expenditure stimulation. In other words, each additional dollar of Federal highway grant elicits an increase in States' own expenditures. It is only for this range in coefficient values (i.e. a 9-0) that total highway expenditures can be expected to increase by more than increases in the level of Federal grant funding. A second hypothesis to which the total expenditure model can be addressed is a test of the effect of the level of current highway inventories on total highway expenditures. It is commonly found that the higher the existing stock of capital goods, the lower will be the current desired and actual level of capital investment. While this behavior may pertain in our case, it should be noted that the dependent variable in the empirical model measures capital (i.e., highway construction expenditures) as well as non-capital (e.g. maintenance, administration, highway police and safety, etc.) expenditures. In general, non-capital expenditures tend to increase with increasing levels of existing highway inventory. Thus, the single coefficient of the existing inventory variable 1Except if a is identically 0 in which case, total expenditures would incregse by exactly the amount of Federal grant increase. 256 (KSTK) does not distinguish between capital and non-capital expenditure responses to changes in KSTK. For this reason it is entirely possible to obtain a positive coefficient estimate for the highway inventory variable. One final note of the form of the model pertains to the interpretation of the parameter estimates of the socio-economic descriptor variables. Since the dependent variable in our model is expressed in terms of expenditures per capita, it is not necessarily true that a negative coefficient on a socio-economic variable implies that total expenditures decrease with increasing levels of that variable. For example, a negative sign on the population variable (SPOP) might indicate that highway expenditures do not increase at the same rate as population increases (and thus per capita expenditures decrease). Nonetheless, such a coefficient estimate may still imply that total highway expenditures would increase in absolute terms in response to population increases. ii. Data Set Stratification The theoretical analysis developed in Section III. 4 advanced the hypothesis that the stimulatory impacts of the Federal Aid Highway Program would be greaest in those cases where States expend little more than the minimally required highway matching funds. It was for this reason that the TEM included separate terms for Interstate and non-Interstate grants (the latter grant type less binding than the former). But even within each grant program there exists some variation in the extent to which States 257 exceed minimal matching requirements. (For example, see Tables 111.5.1 and 111.5.3). To further test the notion that (ceteris paribus) the magnitude of Federal highway grants relative to State expenditure levels plays an important role in influecning State investment behavior, we divided our data set into two distinct groups. In particular, one subset was defined as the seven States with conspicuously low Interstate highway expenditures over and above minimal Interstate System matching requirements. These seven States whose "excess" Interstate expenditures amounted to less than 4% of their total Interstate investment over the fourteen-year analysis period 1957 - 1970, were Alabama, Missouri, Montana, New Hampshire, North Carolina, North Dakota, South Carolina, Cermont and Virginia (Table 111.5.3). The second data subset set was comprised of the 41 remaining States. Thus each of the alternative total expenditure model specifications was estimated on the full pooled data set and two data subsets. In terms of the estimated parameters of the TEM, the hypothesis that States experiencing more binding Federal highway grants exhibit stronger stimulatory expenditure responses would be borne out if the coefficient of the Interstate grant term is larger for the seven State sample than for the 41 State sample. The empirical models do validate this hypothesis as will be described in in the next section. 258 IV.6 Empirical Results In general, the empirical results of the total expenditure model estimations corroborate the theoretical hypotheses advanced in sections 111.5, and IV.4. A total of 34 alternative specifications of the total expenditure model were estimated in this research, representing the inclusion of different sets of variables the use of both deflated and undeflated data, the representation of Federal aid by a single total grant variable or as two terms stratified by grant type, and the estimation of the model on the entire data sample as well as two distinct data subsets. Appendix A presents a complete listing of the estimation results. The purpose of this section is to highlight the major findings of the model estimations, and integrate the empirical results with the theoretical hypotheses advanced earlier. In the figures that follow, each regression run is described by a four character model number 11 12 ni n2 where: S - grant terms stratified by type (Interstate and 11 = non-Interstate) IT - single total grant term 12 = U- undeflated data set ID - price deflated data set (1 - 48 State/14 year pooled sample n, j 2 - 7 State/14 year pooled sample 3 - 41 State/14 year pooled sample n2 = 1,2, ... - model specification number Figures IV.6.1 through IV.6.4 present the results of the generalized least squares estimation of the TEM using undeflated data on the full 48 State/14 year sample. In particular, Figure IV.6.2 considers the addition of one explanatory variable -- the ElltAIll.-RU3wULIS TOTAL EXPENDITURE MODEL GfRE RALlZEDt-LlASf-2LIARL EzUjAIL.ELJi&t.b) 2L 5a~2l&)------ S~ I FSTTIMAYF VA IJF STANDFAR'l ERPR- T-STATI STIC rySrTrPT \IVAtIUF STtNiDApfl CPPOR T-ST\TTSTTC -2 AL A --52IL --- S ------UEA----QY------G1N1L 9.A6 -0.650F-96 9.468 -0.601 0.019 '.635 5.58 0.732F-17 1.124 0.031 0.001 0.124 1.78 8.74 8.41 19.53 17.94 4.8 21- TOT -0.'31 0. o 36 8.96 TO. PC T 0.457 0.069 6.62 A.YN IGP p -1.146 0.091 12.55 AVIOP (.6 19 0.0 43 14.39 Figure IV.6.1 E5 TJ M AL _U31LI-S TOTAL EXPENDITURE MODEL aQ !LS.3'1-Za1 .GENLAU2.-.LA-SQUAELS E=.SAIS il L ii-=J&U2-=_ . _ . . ESTIMATE VA LUE STANDARD FPQ(IP T-STATISTIC cST IMATF VALUF STANOAQD E2RAIR '-STATISTIC P LA-------ELY-----N .9P -&.597E-06 10.639 -0.599 0.0117 0.613 5.55 0.796F-)7 1.206 0.03' 0.001 0.123 1.62 7.51 8.82 19.61 17.26 4.97 Q[LTQ T .fl 37 8.95 TfL PCT 0. 355 .0 'I 4.917 AVNIGP -1.123 0.097 11.61 AVIGP 0.608 0.043 14. 14 arIP rx( 0. 088 9.955 I.58 Figure IV.6.2 r.-) a') C0 - - - - - - - - - - - Wppmumm-pmmm P.%LIt AI l-RLLLS TOTAL EXPENDITURE MODEL .DEL-UaALLb G5,NF. ALILfEQ-LI Aall -. 5QUARfi - .QSAK-- S1A 1 --------- - L----.-----------------1--- ESTIMATF VALUE 10.01 -0.137E-33 9360 -0.600 0.018 0.696 STAnAPf FPOqR 5.66 J0173F-04 1.12S 0.031 J.001 0.126 T-cTTTISrTTC 1. 77 7.91 8.30 19.16 17.73 4.81 RLTnT TOLPCT AVNIGP AVI~G ;ST!"A T E VALUF -0.3AG 3.410 -1.135 0.620 STtNPAP) F2P'R 0.036 .070 0.093 0.043 T-sTATISTIC .17 9.83 12.?? 14.25 Figure IV.6.3 N3 -- A EL.Ih1OL-SULL5 TOTAL EXPENDITURE MODEL _!MQlEl . ,_ TU12 GENEBALILE EASI.S2UA&REi -~ ~ ESTIMATF VALUE STINOAnD FPRCR T-STATISTIC FSTIMATF VALIJF STANDAPF EPROR T--S TA'I STTC -. ENU.AUL-SE E l UE!- 20.84 -0.314E-J6 16.553 -C.458 0.013 O.A-7 6.C4 C.844F-07 1.814 C.032 0.001 0.135 3.45 3.72 9.13 14.C7 12.79 2.950 PL TfT -0.418 I 3.t? TOL PCT 3.178 0. 098 1.83 AVTGP 0.039 0.C35 1.11 BI p O.?59 0.056 4.40 Figure IV.6.4 N) Nl") on= mm No, am. 4pdw - A-6.206-d=6 .-a owl. -Aw- 263 degree of debt service financing to the basic set of nine right hand side variables included in Figure IV.6.1.1 Figure IV.6.3 employs vehicle miles of travel instead of population as the measure of State size. And Figure IV.6.4 includes only a single Federal aid term - total available highway grants, rather than the stratified grant terms employed in the previous specifications. The total expenditure model was also estimated for two subsets of the full pooled data set. Specifically, Figure IV.6.5 presents the estimation results of one specification of the TEM for the seven states with conspicuously minimal Interstate expenditures over and above required matching funds (c.f. section IV.5). Figure IV.6.6 presents the corresponding model estimation results for the forty one other States. The remaining estimation results derive from the use of price deflated data on all variables whose units are expressed in dollar terms. Specifically, Figures IV.6.7 through IV.6.8 represent the basic nine variable specification (c.f. Figure IV.6.1) of the price deflated TEM for the full pooled data set, the 7 State sample and the 41 State sample respectively. The most important empirical findings from the total expenditure model are presented in summary fashion below. i. The Federal Grant Terms The most striking finding from the total expenditure model is that the ABC grant program has elicited a significant expenditure 1See section IV.4 for a definition of the variables listed in the following fugures. E511AI12 S.AL15 TOTAL EXPENDITURE MODEL G E FNE R ALIZ.E -L EA.S!.5.UA dF -S AI ..-El_9.._nB-=.-ti216.-L..- ..5 - ..1 5 - - -- Q-.2 .2. ------------ -- - -- -- -- -- ------------ FSTIMATE VALUE STANDAPO ERROR T-C TATTST IC FSTIMATF VALUF ST ANDAP0 FFP1R T-CTATISTIC S iIMC22-2..---KU-UE AC.J ILL-- 97.82 -0.668E-06 0.209 -1.340 0.006 .542 8.94 f.737E-06 fl.307 0.227 0.002 0.114 IC.90.91 0.69 5.90 3.66 4.74 _LTCT -. e 127 1.41 TA PCT 2.772 0.492 5.64 AVNIGP -0.310 0.161 1.92 C.657 0.061 10.75 Figure IV.6.5 Ei.lmAll2 NEEM5AIS TOTAL EXPENDITURE MODEL -!aJE LJVLa.AII31 .GENEtALtLLDLA.L-SQUARL& F-STAT: Ffl0.964) = 241.3I SFF = 5.14 RSO = (794 rSTIMATF VALUE STANOARD FRROR T-STATTSTIC ESTTMATF VALtIF STANUAPD ERROR T-STATIST TC 16.15 5.55 2.91 U 31 -t *5?4 -,1. r 4 l~or41 12.75 -0.478F-06 .724E-07 6.60 TOL PCT 0.368 3*171 5.21 Figure IV.6.6 N) -1, ..AIEAU.. -0.637 C.034 18.50 PC V 0.018 3.001 17.32 GIN? 0.693 0.122 5.67 S.?74 1.032 8.02 AYNIGP -0.856 0 e 114 7.51 0.439 C.057 7.68 a-* -ALJ6-.AJ6.w- .-.F- ---- o .-. LUIA.MA12Ui_&L.2IS. TOTAL EXPENDITURE MODEL M-2DEL-N.-I DI iENEAL.EDLSA._LQU A a F-STAT: Ft 9.66?) r '48.72 SEE = 6.92- RSO = 0.772 FSTIMATE VALIJE STANDARD ERPrlR T-STAT!STIC CCBSIA NI [2.12 7.16 1669 --- j.El --.- _ -0.85TE-06 O.943E-07 9.039 ESTIMATE VALHE STANDAP) FOPoFR T-STATISTIC Figure IV.6.7 n.LEa5.I& 8 .028 1.050 7.65 -0.738 0.040 18.66 12EEEfmlX. 0.O22 0.001 17.52 0.771 0.159 4.84 "LTT -C.4?0 0.046 9.27 TPLPCT 0.598 U.089 6.75 DEFGf -1.103 0.092 14.43 DE F IQ 9.642 0.045 12.03 Am. AM Aw - -oubL426JON6 .w.'JWm.& Lmmd6 801,4 dw- am.& - -Jm&AL-WL own _________-0- m-.- --- -.0 W--ddmvmmmmmmmmp E$LL IAIL26L..EiUUS. TOTAL EXPENDITURE MODEL L .fUELDAQ.SDJ21 GENEALJLEDL EA SIS.QUARE S F-S TM:AFT9 l288) 28.00 SEE = 7.5 RS = 0 741 CONSTANT FSTIMATF VALUE STANPAPD ERROR T-STATISTIC FSTIMTF VALIuE STANAPD ERROR T-STATISTIC 121.10 9.36 12.93 RLTOT -o .185 06.nit t.*81 Spnp -0.623E-06 0.879E-06 3.71 TOLPCT 3.590 0.532 7.15 Figure IV.6.8 tIFAC -1.783 0.236 7.56 F PC Y 0.010 0.002 4.97 DEFKSTK 0.776 0.368 2.10 DE FNIG -0.295 0 .132 2.24 -1NL. -0.679 0.099 6.87 0.666 0.058 11.50 . _k-0-A _-60- -_w _mm 4140 _1__ _ _ _ _ _ _-o b4MW mmvo nwapmbon&AA Mnn it 9A 4" - - - - - - - - - - - - - - - - - - - - - - - - - - -;A -Am L _ _ "- _ U_- -_A d-- _ -- wm- _ - -mm JESILfAII l&.ES.ULIS TOTAL EXPENDITURE MODEL frQQL-h.&HjA31 JRALL IQE AS-iUARL F-STAT: Ft 9.5641=236.03 SEE 6.60- RSQ =O.9L ESTTMATF VALUE STANDARD ERROR T-STATISTIC 19.62 7.10 2.76 -0.648F-06 0.928E-07 6.98 .E.SKI& 8.696 1.065 8.16 ESTTMATE VALUE STANDARD EPROR T-STATISTIC Figure IV.6.9 00 -0.778 0.044 17.64 .DEE.EC. 0.023 0.001 17.01 0.869 0.157 5.55 RLTCT -0.686 0.053 12.99 T1L9PCT 0.444 0.091 4.87 DEFNIG -0.867 0.116 7.48 DEF IQ 0.440 0.060 7.33 . wm. .mm _W .W m o P--......-........_4- - -dm.40--.. .. .......... -ww.wm 269 substitution response amongst the States, as opposed to the Interstate grant program which has been associated with expenditure stimulation. Taking the nation as a whole, the coefficients of the non-Interstate grant terms in all of the specifications employing undeflated data fall in the range -1.123 to -1.146 (Figures IV.6.1-IV.6.3). In light of the discussion in the previous section, where it was indicated that grant coefficient values less than -1 represented highly implausible behavior, each of these coefficients were tested for the statistical significance of their difference from a value of exactly -1.0.1 In none of the cases, did the coefficient values differ significantly from a value of -1.0 (at the 5% significance level). Thus for all practical purposes, the total expenditure model indicates that the States exhibit a perfect expenditure substitution response to Federal ABC grants. It is clear that this type of behavior does not characterize the response to Interstate grants. Again referring to figures IV.6.1 through IV.6.3, it can be seen that the Interstate grant coefficients are all significantly greater than 0, ranging in value from .608 to .630. Taking the nation as a whole, this would indicate that an increase in Interstate grants by one dollar would elicit an increase in State expenditures by approximately 60. 'The test involves the formulation of the following t statistic: a - 1.0 9 where se is the standard error of the grant coefficient. se (a ) For example, using the values given in Figure IV.6.2 for the estimate of the AVNIGP coefficient, t = 1.123-1.0- = 1.27 < 1.64 = t.05,662 (single tailed test) 0.097 270 The same behavioral pattern is evident from an examination of the estimation results employing price deflated data (Figure IV.6.7). In fact, the estimated values of the grant terms from the deflated and undeflated data sets are remarkably similar. For the full 48 State/14 year price deflated data set, the coefficients of the non-Interstate grant terms were all slightly less (but not significantly different) than -1.0, while the Interstate grant coefficients assumed values around 0.60. The inclusion of just a single grant term AVTGP representing a three year moving average of total per capita highway grant availability did not yield significant results. From Figure IV.6.4, the estimated coefficient of the total grant term is 0.039 (indicating mild expenditure stimulation) but this value is not significantly different from 0 at the 5% significance level. These results are not surpirsing in view of our findings that Interstate and ABC grants have essentially opposite effects on State highway expenditure behavior. It is interesting to note that previous empirical studies of State expenditure behavior have failed to distinguish between different highwaygrant types. For example in a 1971 study by O'BrienI employing a 48 State/9 year (1958-1966) pooled data set, the estimated coefficient of total highway jrants was also found to be mild by stimulative (0.067) but not significantly different from O'Brien, Thomas, "Grants-In-Aid: Some Further Answers," National Tax Journal, Vol. XXIV, No. 1 (March, 1971) 271 0. The more interesting conclusion however is not that increasing total Federal grant availability has induced higher State expenditure levels, but that highway grants with significantly different structural characteristics have been associated with significantly different State expenditure responses. ii. Differences in Grant Term Coefficients Between the Two Data Subsets It was hypothesized in chapter III of this research summary that the potential of a grant to stimulate expenditures from States' own sources is greatest in cases where the matching and appointment provisions of a grant are "bindinq."1 To test this hypothesis, the full sample of observations was divided into two groups (see IV.5.ii) From Figures IV.6.5 and IV.6.6, it is evident that the seven States exhibiting the lowest excess Interstate expenditures were more sensitive to increases (or decreases) in Interstate grant funding than the remaining forty-one States. Specifically the Interstate grant coefficient for the seven State sample assumed a value of .657 compared to a value of .439 for the remaining forty-one State sample. 2 While all of these parameter estimates exemplify expenditure stimulation, it appears that increases in Interstate grants to States coming closest to minimally matching available Federal (Interstate) aid will elicit a greater expenditure response than the response from In the sense that State is found to minimally meet its required matching expenditures. 2A similar pattern was indicated for the runs employing the data subsets with deflated values (see Figures IV.6.8 and IV.6.9). 272 other States. Perhaps even more striking a result along these lines is the difference in the non-Interstate (i.e. ABC) grant term coefficients between the two data subsets. For example, comparing Figures IV.6.5 and IV.6.6 the coefficient of the non-Interstate grant term assumed values of -.31 (seven State sample) and -.86 (forty-one State sample). One of the reasons for the stronger expenditure substitution response manifested by the forty-one State sample is that, on average they were characterized by a higher "excess fraction" (see section I11.5) of ABC System expenditures than the States comprising the seven State sample. Referring to Table 111.5.1, 33% of the total ABC System investment by the 41 State sample represented expenditures over and above minimal ABC matching requirements as compared to a figure of 29% for the seven State sample. iii. Interpretation of the Coefficient Estimates of the and Institutional Descriptor Variables a. State Size Variables Results from the total expenditure model indicate that per capita highway expenditures (from States' own sources) decrease with increasing State population (SPOP) and urbanization (UFAC). This pattern runs throughout the estimation results presented in Figures IV.6.1 to IV.6.9. For example, the TEM estimation using undeflated data on the full pooled data set indicates that (Figure IV.6.1): And thus, following the reasoning of Section III, would be more prone to view ABC grants as a substitute for their own ABC System expenditures. 274 (21) R0PC = 9.96 - 0.65.10-6 SPOP - 0.60 UFAC + . . . Thus, an increase in State population by one million or an increase in urban density1 by one percent is associated with approximately a 60t per capita decrease in State highway expenditures. This does not imply that total (i.e. not per capita) highway expenditures (R0) decrease with increasing population. We can express total State highway expenditures R0 as: K (22) R = RPC. SPOP = (a0 + 2 - a)SPOP + Iak k=2 where a = estimated constant term = estimated coefficient of the population variable The change in total (own) State highway expenditures with respect to SPOP is qiven by: K (23) D R = a + 2a * SP0p + lak SPOP k=2 Thus the change in total expenditures with respect to SPOP will be positive as long as: K (24) a + 2a * SPOP + Yak> 0 k=2 Using the estimated coefficients in figure 4 and the average value of the variable SPOP2 yields: (25) a R = 9.96 - 2 *0.65 *10-6 . 0.38* 107 +- -. + 3 SPOP = 4.94 > 0 1Percent of a State's population residing in urban places greater than 5000 persons. 20ver the 14 year sample period, the 48 State average population was 3.8 million. 275 This implies that population increases increase States' own highway expenditures by $4.94 per person. b. The Income Measures Two separate measures of State income--per capita income and a measure of income inequality--were employed in the estimation of the total expenditure model. Per capita (State) income (PCY) is correlated positively with auto usage and thus we should expect increasing State income to lead to imcreasing State highway expenditure levels. This hypothesis is borne out by the estimation results. For example, referring to fiqure IV.6.1, an increase in per capita income by one dollar would be associated with a 1.8* increase in per capita State highway expenditures. As discussed in section IV.4, the second income measure employed in this study -- the GINI index of income inequality-- provides an indication of both the distribution of State income, and a rough measure of regional characteristics.1 The estimation results indicate that higher levels of income inequality are associated with higher per apita State highway expenditures. For example, referring to figure IV.6.1, an increase in the GINI index by one unit would lead to a 61* per capita increase in State highway expenditures. c. Institutional Characteristics Three descriptors of State highway financing conventions were employed in this study: the extent of local participation in highway finance (RLTOT), the importance of toll roads in generating 1Namely that States with greater income inequality (higher levels of GINI) tend to be Southern/rural/agricultural in nature. 276 State highway revenues (TOLPCT), and the degree of debt service highway financing (BIPTCX). Since the dependent variable in the total expenditure model exclusively measures State highway expenditures, we should expect that higher degrees of local participation (as measured by RLTOT) in the provision and maintenance of highway facilities will be associated with lower expenditure levels from State resources. In other words, to the extent that a State delegates its highway authority to lower units of government, State hiahway expenditures should decrease. The other two indicators of institutional characteristics, TOLPCT and BIPTCX reflect the degree of flexibility in the States' highway finance program. For a given (State) gas tax rate, the increasing use of toll road or debt service financing allows a State greater opportunity to raise higher levels of highway revenue. Thus we should expect TOLPCT and BIPTCX to positively influence State highway expenditure levels. These hypotheses were borne out by the estimation resilts of the total expenditure model. For each percentage increase in the ratio of local to total expenditures, State per capita highway expenditures decrease by more than 304 (see Figure IV.6.1 - IV.6.4). Increases in the percentage of toll road financing induce as much as a 47t (per 1% increase in TOLPCT) increase in per capita State highway expenditures. And the use of debt service financing was associated with higher per capita highway expenditures--on the order of a 64 increase for each percentage increase in BIPTCX (see Figure IV.6.2). 277 d. The Existing Inventory Measure The estimation results indicate that higher levels of existing inventory at the beginning of a year lead to higher levels of expenditure on highways during that year. For example, referring to figure IV.6.1, an increase in depreciated capital stock per capita of $1.00 would lead to a $9.48 increase in State per capita highway expenditures. There are two explanations for this finding. First, the higher the level of existing capital stocks, the higher will be the required level of non-capital expenditures (e.g. maintenance, admini- stration, highway police and safety etc.) to support the existing facilities. Second, it may be hypothesized that the increasing provision of highway facilities tends to divert and attract additional auto ridership which in turn leads to higher levels of highway expen- diture. In summary, the estimation of the total expenditure model generally confirmed the behavioral hypotheses advanced earlier. Most significantly, it was shown that states have viewed the Federal "ABC" grant program as a substitute for their own expenditures as contrasted with the Interstate highway program which has served to stimulate States' own highway expenditure levels. Table IV.6.1 summarizes the effects of each of the variables included in the TEM on State highway expenditure levels. iv. The Deflated Data Set It is common practice in empirical studies dealing with time series information to express all monetary data in real dollar 278 Variable SPOP UFAC PCY GINI KSTK RLTOT TOLPCT BIPTCX AVNIGP DIRECTION OF THE INFLUENCE OF THE EXPLANATORY VARIABLES ON TOTAL STATE HIGHWAY EXPENDITURES Direction of Influence on Total State Highway Expenditures + + + + + + AVIGP + +: indicates that increasing levels of the variable are associated with increased highway expenditure levels -: indicates that increasing levels of the variable are associated with decreased highway expenditure levels Table IV.6.1 279 terms for two reasons. First, price deflation converts expenditure data to a common base, indicative of the fact that one dollar of highway investment in 1957 differs from a one dollar investment in (for example) 1970 in terms of corresponding physical output. Secondly, price deflation introduces some notion of the price of the provision of highway facilities in models where it is difficult or infeasible to include an explicit price term. In our application, the choice of an appropriate price deflator was complicated by the fact that inflation rates differed significantly among the various highway activities undertaken by States. For example, over the last two decades price increases' have been more rapid for Federal aid highway construction than for maintenance and operational activities. 1 Moreover the structure of the total expenditure model does not distinguish between individual expenditure items; the dependent variable merely measures total highway expenditures. As described in section IV.5, a somewhat simplistic approach to price deflation was adopted in this research. All data whose units are expressed in dollar terms were deflated by the Consumer Price Index. Examples of estimation results using deflated data are shown in Figures IV.6.7 - IV.6.9.2 The results do not differ significantly 1Federal Highway Administration (FHWA) Notice HHO-34, "Highway Main- tenance and Operation Cost Trend Index," 12/14/72. FHWA Office of Highway Operations, PRICE TRENDS FOR FEDERAL-AID HIGHWAY CONSTRUCTION, Second Quarter, 1973. 2These Figures correspond to the undeflated model runs shown in Figures IV.6.1, Iv.6.5 and IV.6.6 respectively. 280 from the estimation runs on the undeflated data set. All of the variables maintained the same sign and roughly the same magnitude, the largest difference occurring in the coefficient of the population variable. Most significantly, estimation of the TEM with the price deflated data set again corroborated the basic finding that the ABC grant program has been associated by expenditure substitution, while the Interstate grant program has induced State expenditure stimula- tion.1 v. Tests of Equality Between Coefficients in the Two Data Subsets The empirical results reported in the previous paragraghs have been based on the use of a pooled 48 State/14 year data set as well as two data subsets comprising seven and forty one States (over 14 years) respectively. This raises two related statistical issues: - the validity of pooling our seven State sample with the forty one State sample, and - the significance of the difference between the estimated coefficients (taken as a whole) from the seven and forty one State samples In effect, while we have attempted to account for individual State preferences by the GLS error component procedure (section IV.3), it may nevertheless be the case that as a group, our seven State sample exhibits significantly different behavior than the 41 State IFor example, referring to Figure IV.6.7 representing estimation of the TEM on the 48 State deflated data set, the coefficient of the ABC grant term (DEFNIG) was - 1.103, while the coefficient of the Interstate grant term (DEFIG) assumed the value . 642 281 sample. To state this premise formally we wish to test the null hypothesis H0: (26) 1 = B2 where: 6 = the set of regression coefficients from a sample with T1 (=7 States x 14 years = 98) observations 62 = the set of regression coefficients from a second sample with T2 (=41 States x 14 years = 574) observations. The null hypothesis leads directly to the specification of a restricted model where no allowance is made for differing values of 6.1 and s2 (27) Ro = 1R XIU1 = Xs + u 2 X ju2 where i refers to the subset of T observations on own expenditures R, explanatory variables Xi. 1 and residual terms u. In an obvious extension of (27), the unrestricted model with explicit allowance for differing 61 and 62 may be written as: In fact the restricted model (and notation) referred to here is just our original model specification presented in equation (17). 282 R0 X 0 8u (28) R- = [; 0I VJ h R L 2 L2 2j where u. = residuals from the unrestric- model The test of the equality (in the statistical sense) between H and B2 may be expressed by an F-statistic and is presented here without proof:I (u'u - u*'u*) / k - (29) F(k,T1+T2 -2k) = __________ u*I'u / (T1+T2 - 2k) where k = the number of variables in our model u'u = the sum of squared residuals from the restricted model u*'u* = the sum of squared residuals from the unrestricted model T. = number of observations in sample i F(k,T1+T2-2k) = the computed F-statistic with parameters (degrees of freedom) k and T+T2-2k In our application, construction of the relevant F-statistic is straightfoward. The sum of squared residuals (SSR) from Fisher, Franklin M., "Tests of Equality Between Sets of Coefficients in Two Linear Regressions: An Expository Note," Econometrica, Vol. 38, No. 2 (March, 1970) 283 the unrestricted model derives from summing the squared resid- uals from the separate regression runs on the two data subsets. Thus for example, referring to Figures IV.6.1, IV.6.5, and-IV.6.6, where the Standard error of estimate (SEE) from the 48 State (restricted) sample, and the 7 and 41 State (unrestric- ted) sample are 5.37, 6.57, and 5.14 respectively,1 the corresponding F-statistic is computed as: 19450 - (4230 + 15164) F(10,652) = 10 - 0.18 19394 652 Since this computed value of F is significantly less than the critical value of the F distribution at the 5% significance level (F 05 (l0,l000) = 1.84), we are unable to reject the null hypothesis that 6l = g2. In other words, the practice of pooling our observations -- at least in terms of com- bining our 7 and 41 State sample for the given specification of the TEM (Figure IV.6.1) on the undeflated data set appears valid. The computed F-statistic for each of the alternative specifications explored in this thesis is prsented in Table: IV.6.2 1As presented in the Figures, the sum of squared residuals is equal to SEE squared times the number of observations in the sample. 284 TESTS OF SELECTED SUBSET COEFFICIENT EQUALITIES (Table entries represent computed F-statistics for the model numbers appearing in Appendix A) Undeflated Data Model No. F-Stat Deflated Data Model No. F-Stat Stratified Grant Terms SUlI 0.18* SDll 355 SUl2 1.75* SD12 1.44* Total Grant Term Only TUll 6.94 TDl 4.26 TUl2 4.93 TDl2 5.48 * not significant at the 5% level Table IV.6.2 285 IV.7 Summary and Conclusions The estimation results of the total expenditure model (TEM) generally confirmed the previously advanced theoretical hypotheses regarding the differing impacts of the Interstate and non-Interstate gramt programs, the expected responses among States whose expenditures are low relative to Federal grant availability, and the influence of the socioeconomic and institutional characteristic variables. While the data set used in calibrating the models describe condi- tions over the fourteen year period 1957-1970, the empirical finding may be interpreted in the broader sense of suggesting guidelines for future Federal-Aid Highway Program (FAHP) policy. Toward this end, we have shown that a major component of the FAHP has not been significantly influential in stimulating State highway expenditures. To the extent that States view a grant as a substitute for their own expenditures, one must view the Federal-aid from the perspective of its value as a tax- relief program rather than its merits in accomplishing an explicit reallocational goal. Along these lines we have shown (see chapter II) that the Interstate Highway Trust Fund is financed by non-progressive excise taxes, and apportioned in a somewhat arbitrary fashion which fails to accomplish a significant redistribution of State income. In conjunction with the theoretical analyses of chapter III, the empirical results of this chapter demonstrate that substitutive vs. stimulative impacts of Federal aid (at least for aid in the form of close-ended, conditional matching grants) depend critically on the level of Federal grants in relation to State expenditures on the aided system. 286 We have focused on the differing structural characteristics between the Interstate and non-Interstate grant programs and the corresponding differences in State expenditure responses. But these results have general applicability. Close-ended, conditional matching grants whose provisions are not binding on current or projected State expenditure levels may be expected to be viewed as a substitute for States' own i nvestments. From a Federal policy stand points the empirical findings in this chapter raise several important points. First, with our clearer understanding of the dynamics of State expenditure responses to Federal- aid, the fundemental issue of the objectives of the Federal Aid Highway Program is called into question. In effect, the imposition of Federal highway taxes and the pursuant distribution of categorical highway grants represents an explicit expression of Federal policy. It is not the intent of this research to argue the economic viability of the Federal governments support for particular highway facilities.1 For example, our findings demonstrate the success of the Interstate grant program in "accelerating" the construction of Federal Aid Systems (as measured by increasing State highway expenditure levels), if in fact the intent of the this program was to stimulate highway expenditures. However, it remains open to question whether the ensuing expenditure response to the Interstate grant program represents an economically viable investment of funds by benefit/ cost or other relevant investment criteria. Our concern has been to merely trace expenditure responses, not to evaluate their economic consequences, as this latter point has been adequately treated in the literature. Se for example Friedlaender, Ann F., THE INTERSTATE HIGHWAY SYSTEM, North Holland Publishing Company, Amsterdam, 1965, especially chapter 3. 287 Suffice it to say that the restrictions on the use of Federal funds for only certain types of facilities tends to identify those projects whose provision is deemed to be in the national interest. Guaranteeing a minimally acceptable provision of important transportation facilities or stimulating road construction necessary for interstate commerce are valid Federal objectives. But we have shown that for the ABC program, the former objective may not be appropriate, and the second objective is not being accomplished. To be sure, the Federal Aid Highway Program is characterized by other (non-allocational) consequences--ensuring adherence to Federal labor and contracting regulations, promoting the implementation of transportation planning and process guidelines, and redistributing income. An in fact, we are arguing that greater attention needs to be paid to these "ancillary" impacts in view of the failure of specific components of the FAHP to effect a significant increase in State highway expenditures. Our results indicate that restructuring the FAHP with a relaxation of the specificity of the categorical restrictions, and eliminating the built-in matching provisions would not significantly alter State expenditure levels. In fact, over our analysis period, the ABC program has effectively operated as a non- categorical block grant system. As described in section II.2.viii, the 1973 Highway Act has incorporated several provisions designed to reduce the specificity of the FAHP, most notably in terms of increasing the allowable fund transfers between distinct Federal Aid Systems, and providing Urban System aid for transit as well as highway construction. The logical 288 extension of the 1973 provisions would be to completely remove all categorical and matching provisions from those components of the FAHP where it is either not the intent or not a reasonable expectation (given projected State expenditure levels and Federal grant availa- bility) for Federal grnats to stimulate State expenditure levels. 289 CHAPTER V DEVELOPMENT OF THE SHORT RUN ALLOCATION MODEL V.1 Introduction In this chapter, we present a model to explore the factors influencing States' highway budget allocation. We have already traced the impacts of Federal grants and socio-economic and institutional characteristics on total highway expenditures. The empirical analysis of chapter IV has been useful in verifying our hypotheses on the substitution and stimulation effects of Federal highway grants. Now w: turn our attention to the issue of the determinants of expenditure levels devoted to specific types of highway activities. Again, the central focus of the research is the evaluation of how Federal grants have affected States' expenditure behavior. The short run allocation model (SRAM) developed here can be used to asses for example the impacts of Interstate grants on Interstate highway expenditures. Alternatively, we can investigate whether increasing Federal highway grant availability on any of the Federal and highway systems has been associated with increases or decreases in highway maintenance or State highway system construction. In short, the SRAM allows us to explore the dynamics of States' expenditure behavior in terms of decisions relating to the allocation of a fixed budget amongst alternative types of highway expenditures categories (e.g. Interstate, Primary System, maintenance, administration, etc.). 290 Section 2 develops the derivation of the short run allocation model, building on the consumer allocation theory presented in section 111.3. The derivation discusses the appropriate treatment of alternative grant structures, and fixed State highway budget constraints. The resulting estimatable equations take the form of a share model with six distinct structural equations -- one for each expenditure category. Section 3 discusses the statistical problems inherent in estimating a share-type model. Essentially, since the sum of the expenditure shares must equal 1.0, the six equations are not independent. This section develops an estimation technique which explicitly accounts for t'e joint interaction between shares. Section 4 presents the definitions and sources of data employed in the SRAM. Much of this data was also used in the estimation of the total expenditure model (Chapter IV). Thus particular attention will be given to data not previously described. The estimation results from the SRAM are presented in section 5. As with the empirical analysis of total expenditures, estimations of the SRAr were performed on a full pooled 48 State/14 year data set as well as two selected data subsets representing differing Interstate expenditure behavior. The empirical results from the SRAM are not easily or directly interpretable. Accordingly, section 6 discusses the application of derivatives and elasticities to explain State highway expenditure behavior. This section presents a derivation of the derivative and elasticity measures as functions of the estimated SRAM coefficients and evaluates the behavioral implications of the actual results. 291 An obvious extension of the previous section is to incorporate the findings from the total expenditure model (TEM) into the empirical analysis of allocation behavior. At this point we are able to explain both dimensions of State highway expenditure behavior: - decisions relating to the determination of the magnitude of States' highway budget in any given year, and - decisions relating to the allocation of that budget amongst alternative highway activities. Accordingly, section 7 presents the results from the TEM and SRAM in terms of derivatives and elasticities of expenditures on each of the six highway categories, as a function of the explanatory variables employed in the analysis. The results of this analysis are contrasted with the hypotheses advanced in the theoretical models of State highway expenditure behavior developed in chapter III. Finally, section 8 presents the conclusions and policy irplications stemming from the empirical analyses developed in Chapters IV and V. 292 V.2 Derivation of the Short Run Allocation Model. Before setting forth the analytical derivation of the short run allocation model, it is important to describe the nature of the decision environment we are attempting to model. It is convenient to conceptualize States' highway expenditure behavior in terms of two dimensions: the determination of total highway expenditure levels, and decisions relating to the allocation of total expenditures amongst broadly defined highway activities (e.g. Interstate construction, maintenance, etc.) It should be clear at this point that we are not attempting to explain the decision process governing project selection at the aggregate level of analysis adopted in this research. In modelling States' expenditure behavior, our data does not distinguish between decisions to implement a construction or maintenance project in a specific reqion within a State. Indeed, it may well be argued that the complexity of individual project evaluation -- from decisions relating to corridor determination to detailed location studies and the formulation of specific construction versus maintenance policies -- requires an analysis at a more detailed level than that adopted in this research. Nonetheless, the expression of States' investment behavior in terms of generically defined highway activities remains a valid and important analysis issue. This is particularly true from the perspective of the Federal government. The Department of Transportation administers several highway grant programs restricted to use on a variety of broadly defined highway activities. Our interest in developing the short run allocation model is to explain 293 the impact of the FAHP on States' expenditure levels on aided and non-aided highway activities rather than investigating the dynamics of the decision process governing individual project selection. In light of these observations, we may assert that States allocate their fixed highway budget with consideration of existing traffic levels, highway stock in place, socio-economic and institutional characteristics, and available Federal aid, so as to maximize their perceived benefits (utility). The formal statement of this behavioral representation takes the form: (1) max U this research. We do not attempt to trace the dynamics of project selection involving the resolution of conflicting preferences among several decision-makers. Only the aggregate level of expenditures on all Interstate projects or maintenance projects are considered here. Moreover, the analysis is not normative in the sense that no attempt is made to reflect societal preferences. 295 Accepting these provisions, we may proceed to derive estimatable highway investment functions from our generalized utility speci- fication. Specifically, we are not direcly concerned with the utility function itself, but with the conditions under which this function 4s maximized. Adopting a Cobb-Douglas utility function specification and dropping the subscript t represting time (for clarity), we may rewrite equation (1) as: n max U = U(E 1 , E2 ,...E ) = T En i=l n (2) s.t. E R where = parameters ("weights") of the utility function First order maximization conditionsI may be determined by the Lagrange multiplier technique. Thus defining: (3) TI = II- X( Z Ej - R) , the function U will be maximized when: DU = al - =0 S = a - X = 0 (4) rU = E - R = 0 Forming the ratio of any two of the first n equations of (4) yields 1 The second order maximization conditions on the function U are guaranteed by our assumption of utility funCtions convex to the origin. 296 -or- E. - E. for i=l,...,n(5) a E 1 a j Summing over the index i, we get (6) Za. E. = E.= R 1 (a. 3 Rearranging terms, we may write: (7) E E.a. i=1 From (7) it is immediately apparent that at optimality, the States' observed expenditure shares (the left hand side of equation 7) are a function of their utility function parameters a. . In fact, for the special case of utility functions homogeneous to degree one, the model has the property that the parameters of the utility function are just equal to the shares of each expenditure category The basis for the development of estimatable investment relations is that the parameters of the utility function, a. represent "weights" -- i.e. the relative importance a State attaches to expenditures on each of the highway categories. Thus we may consider each a to be a function of several exogenous variables describing traffic patterns, existing highway stock, socio-economic 1 Tresch (op.cit.), in his study of State expenditure behavior estimated investment functions based on utility functions homogeneous to degree one. We will not make any a priori assumptions on the homogeneity properties of the States' utility functions. 297 and institutional characteristics, and Federal grant availability. Formally: (8) = f (Z, U.) V where Z = set of independent variables in function f U = error term in f. Using the functional representation of (8) in equation (7), we may write the jth expenditure share s. as (9) S. = E = f(zU) Ef i (Z,9U ) i=1 So far the derivation of the SRAM has centered on the rationale for the general form of the model. Equation (9) represents the basic structural equation of our model. The left hand side of the equations are the directly observable highway expenditure shares in each State and year. And the right hand side factors are a set of exogenous explanatory variables. However as written, equation (9) is highly non-linear, and therefore unsuitable for OLS or GLS estimation. Rather than employing costly non-linear estimation procedures, we may perform a simple transformation on our structural equations to put them in the form of a linear system. Specifically, we "normalize" each share s. by a selected share sk (10) S. E. f.(Z,U.) skEk k(Zk Taking the logarithms of both sides of equation (10) leads to: in i ) = in [ f.(Z,U.) ] - in [ fk(ZUk (k k 298 The last step in our derivation requires an assumption on the functional form of f.. In our research, the SRAM was estimated for two alternative forms of f., product form: (12) = LH Z 1 U. if.3 1 i and exponential form: (13) feji e j i f. It should be clear that substituting either of the two functional forms of f. into equation (11) leads directly to an estimatable specification of the short run allocation model: (14) E,. Inl. n Z.. lnZ +U. - U (E k J1 j E ki ki + a k i4j ick (product form specification of f.) -or- (15) E. In = E .. Z.. - Z 3 k Zki + U.-U (E k) i- 1 i i c ki ki J k iEJ isk (exponential form specification of f.) In this form, our n basic structural equations (see equation 9) have been transformed into n-l log-linear equations. The variables of the "normalizing share" k appear identically in each of the remaining n-l equations. In order to determine a unique set of parameter estimates for the kth share we must constrain the Bl to be euqal in each of the remaining shares. This may be accomplished by performing a constrained estimation as represented by the matrix form in figure V.2.1.' Two more problems must be addressed before proceeding to the actual estimation of the short run allocation model. First of course is the selection of the exogenous variables to be incorporated in the analysis. The discussion has thus far been concerned only with the form of the model. And in fact, the theory does not dictate which variables should comprise the functions f.. Section V.4 will discuss the a priori reasoning behind the specification of each of our share equations. The second analytical issue relates to the proper treatment of Federal grants in constructing the dependent (share) variables. In chapter III, we presented a detailed discussion on the price and/or income effects associated with alternative types of Federal grants. In terms of our empirical analysis, modelling alternative grant structures requires the correct specification of the numerator and denominator in our expenditure share terms. To see this, we may rewrite the budget constraint of equation (1) of this section in terms of prices and physical output measures, rather than in the form of expenditures E. on alternative highway activities: 1 Figure V.2.1 is displayed for the exponential form specification. 299r fI CONSTRAINED ESTIMATION FORM FOR THE SHORT RUN ALLOCATION MODEL 1 Z1 ,2 0 0 --- --- 0 s i in - Sk s 2In - n n-1 s k 0 0 *-- 0 0 0 0 z k, Zk,2 Zk1 Zk,2 0 -- Z 1z -2 *-Zkl Z -k-- Figure V.2.1 06) C C f z 2,1 2,2 ------ . 01 $11 f12 21 22 n-12 -1 k2 + Ul-Uk U2-Uk t-i uk CONSTRAINED ESTIMATION FORM FOR THE SHORT RUN ALLOCATION MODEL --- e 0 0 (16) n = 0 EE. =Z p.X. = R i=1' i= 1 1 where P= price of highway activity i X. = some physical output measure of highway activity i (e.g. lane miles) R= states' own highway resources (i.e. exclusive of Federal grants) Equation (16) expresses a budget constraint in the absence of the availability of Federal grants, so that expenditures E and resources R0 represent States' own funding. The introduction of a Federal grant will alter the form of the budget constraint (and the corresponding expenditure shares) in one of two ways, depending on the structure of the grant. Conditional Matching Grants - Open Ended In this case the price of the aided category is reduced by the Federal share payable. Assume for example that an open ended matching grant is provided for highway commodity 1, with the Federal government assuming g% of all expenditures on this function. Budget constraint (16) now takes the form:1 This follows from tracing through the derivation presented in equations (2) through (7). Tresch (op.cit.) presents a good discussion of these points in chapter 2 of his thesis. 301 (17) p1X (1-g) + pn X0302 i=2 The first term in (17) represents States' own expenditures on the aided category. Thus, the budget constraint is still satisfied strictly in terms of States' own resources R0. It can be shown that the derivation of our SRAM in this case would lead to a specification of the numerator in the first expenditure share in terms of States' own expendi tures. I Block Grants - Close Ended This type of grant does not alter States' perceived prices of highway activities. However the total resources available to a State are increased by the amount of the grant. Thus (18) n n = R0 + GZE. Z p.X. i=l 1 1il where G = the level of Federal grant funding. As is evident from equations (14) and (15), our normalizing procedure renders the dependent variable in the estimatable SRAM equations in terms of a ratio between expenditure categories. Since we never deal explicitly with allocation shares, our task here is to determine the proper form for representing the share numerators- i.e. expenditures on each highway category. This task boils down to determining whether these expenditures should enter the model exclusive or inclusive of Federal grants. 303 Proper representation of expenditure shares in this case calls for the specification of expenditures inclusive of-Federal grants. The type of Federal highway grant encountered in this research, close-ended conditional matching grants is, in a sense a hybrid of our two above cases. We have detailed the argument (section 11I.3.V) that as long as States exceed minimal grant matching requirements, a close ended conditional matching grant is allocationally equivalent to a like amount conditional block grant. Moreover, we have shown that for the ABC program, and to a lesser extent for the Interstate program as well, State expenditures have in fact far exceeded minimal matching requirements (see figures 111.5.1 and 111.5.3). Accordingly, we have chosen to model the dependent variables in the SRAM as if Federal highway aid were provided on a conditional block grant basis (i.e. States expenditures enter the model inclusive of Federal grants). For the Interstate grant program, our modellinq convention may be somewhat suspect. In certain States, Interstate expenditures have apparently been set at a level indicative of a "corner solution" (see figure V.2.2). In other words, when State expenditures just equal minimal grant matching requirements (as indicated in figure V.2.2 by the tangency of utility curve UU1 at the break point in the close-ended matching grant budget line R a R/ ), it is unclear whether small changes in the level of Interstate grant funding would result in States reacting along the locus of budget line R bR 1 (as2 2(as our modelling convention assumes) or R bR2/ 304 CORNER SOLUTIONS IN THE SRAM LA Figure V.2.2 305 Fortunately our convention of modelling Interstate grants as conditional block grants should not create any major problems. All States have exceeded minimal Interstate matching requirements over the course of our fourteen year study period. Although these "excess" expenditures are often relatively small, it should be noted that the Federal matching rate for the Interstate program -- as high as 95% -- approaches conditional block funding (100%) in any event. It is useful at this point to summarize our development of the short run allocation model. The model is appealing for several reasons. First it derives from an explicit representation of State expenditure behavior that takes explicit account of the joint inter- action between expenditure shares. The incorporation of a budget constraint in our analysis recognizes the fact that the decision to increase expenditures in one activity must be compensated with reduced expenditures in at least one other activity. Second it provides a convenient framework for evaluating any number of allocation categories. For example, while we have not chosen to divide our highway construction categories (e.g. Interstate, Primary, Secondary Systems) into urban and ruralcomponents, dividing aggregate categories into several subcategories is easily facilitated. Finally, the SRAM takes explicit account of alternative grant structures. In fact our adoption of a utility function with no a priori assumptions on homogeneity properties guarantees that the expenditure shares sum to one regardless of the parameter estimates of the SRAM. 306 Although our application was restricted to the representation of Federal aid as conditional block grants, the analysis framework is perfectly general in the way it treats differing grant structures. 1 For example, Tresch (op.cit.) employed a model similar to the SRAM to evaluate the impacts of open-ended conditional matching Welfare grants. 307 V.3 Statistical Properties and Estimation Procedures In the derivation of the short run allocation model presented in the previous section, care was taken to account for the joint interaction between State highway allocation decisions. Specifically, our explicit representation of a States' highway budget constraint implies that the decision to increase highway expenditures on one activity (share) must be "compensated" by a decrease in expenditures devloted to at least one other activity. The choice of this analysis framework places special requirements on both the manner in which the individual structural equations enter the model, and the proper estimation techniques to ensure efficient, unbiased parameter estimates. We have already briefly discussed the former issue. Because the sum of a States' expenditure shares must equal 1.0, it is clear that the individual share equations are not independent. Operationally, this implies that it is not possible to separately estimate each share equation. In fact, as displayed in figure V.2.2, the entire set of expenditure shares are estimated in one equation. This matrix representation of the SRAM ensures proper treatment of the joint interaction between allocation decisions, and provides a unique set of estimates for the coefficients of the "normalizing share" While the structure of the short run allocation model has appealing theoretical properties, it is clear that our behavioral assumptions create inherent problems in obtaining efficient and unbiased parameter estimates. Specifically, in light of the inter- 308 action between shares, it is generally not appropriate for the estimation procedure to ignore these interrelationships as ordinary least squares must necessarily do.) To clarify the statistical problems inherent in estimating the SRAM, it is convenient to rewrite the error term specification in figure V.2.2 as Unts to emphasize the representation of our individual observations in terms of a specific State, year and share. In this notation: n = 1, ...N = State number t = 1, ...T =year s -1, ...S = share number In the pooled data set where the 48 States and 14 years are combined in a single regression, the variance-covariance matrix of the residual terms may be written as: (19) = E[untsunts] The "interrelationships" between shares imply a covariance between the residuals of our individual structural equations. Thus the variance-covariance matrix of the error terms is not scalar, and ordinary least squares estimation is not appropriate. 309 ~~1 C 12 Gs 21 22 2s si s2 Wss where: .. - an NTxNT matrix of variances and covariances between the residuals of the N States over T years for share i (i=1,...S) = an NTxNT matrix of covariances J between the residuals of share i and share j for N States and T years. Following the discussion of the previous section, it is reasonable to assume that within a State in a given year, errors across expenditure categories (shares) are correlated. This statement merely expresses in econometric terms the basic SRAM premise that allocation decisions are interrelated. As a computational necessity, we have been forced to qualify the above statement by assuming that errors are independently distributed across States and years and inter-share covariance terms are distributed identically for all States and years: 310 (20) ( %, if n=n' and t=t' E[Untsun'nt's] = 0 if n/n' and/or tjt' $ss if n=n' and t=t' and s=s' While the simplification in the assumed error structure represented by equation (20) may be questioned, it must be remembered that we are dealing with an extremely large variance-covariance matrix. The ultimate use of generalized least squares estimation requires the inversion of the NTSxNTS matrix G. In our application where M=48, T=14 and S=5, S1 (3360x3360) contained over 11 million elements. We have attempted to model the most significant behavioral interactions in keeping with an operation estimation procedure. 2 1 Actually, the short run allocation model incorporated six distinct expenditure categories. But as discussed in section V.2, our "normalizing" procedure transforms transforms the basic structural specification into a single regression equation with S-1 shares 2 Perhaps the most dubious assumption inherent in equation (20) is that within a given State, errors are distributed independently over time. It may also be hypothesized that (at least for bordering States) within a given year for a given share (particular- ly for the Interstate share), errors between States are correlated. We have actually tried to explicitly model these interactions. These experiments proved to be exceedingly expensive and impractical. Substituting the assumptions inherent in equation (20) in 311 equation (19) yields the basic structure of the variance-covaraince matrix of the SRAM residual terms. Using the notation of equation (19) we may now assert the basic form of Q : (21) (22) wss wss ss 0 0 Ess' 0 0 0 - $ss 0 - Ess'. 0 ss -'-0 .0'0 0 * - ss The development of generalized least squares parameter estimates, given the assumed structure of the variance-covariance matrix (equations 21 and 22) is straightforward. Following the procedure outlined in section IV.3, we first perform an OLS estimation of the short run allocation model. Using the OLS estimates of the residual terms Unts, and the assumed structure of the variance covariance 312 matrix, we may derive the parameters of a by: N T (23) $ss = unts s=1,..S n=l t=1 1 N T (24) Yss' =untsunts SS N T n =l t=l ^n s t ' s 1-2 , ... ,2S The estimates of Sss and Ess, are then employed in determining the Choleski decomposition of 2 (see equation (15) of chapter IV). Finally, our original data set is transformed by the Choleski decomposition matrix and another regression is performed to produce generalized least squares parameter estimates. In summary, we have attempted in this section to derive an operational procedure for estimating efficient and unbiased parameter estimates of the short run allocation model. Particular attention has been given to the proper econometric treatment of the assumed interaction between expenditures on individual highway activities. The next section presents the actual specification of variables employed in the SRAM that was estimated in this research. Equations (23) and (24) express the average value of all elements of Unts ts corresponding to where$s or s appear in our assumed structure of Q. 313 V.4 Modelling Considerations and Data Requirements The short run allocation model consists of six distinct structural equations corresponding to expenditures devoted to Interstate System construction, Primary System construction, Secondary System construc- tion, non-Federal-Aid System construction, maintenance activities (an all road systems) and on "other" category capturing State expenditures administration, highway police and safety, bond interest and grants to local governments. These six shares are representative of the three major Federally aided highway activities, and the three major non-aided State highway functions. As such, we are able to trace not only how a Federal grant effects expenditures on the aided functions, but the resulting tradeoff and complementary allocation responses among all major activities as well. The dependent variable in each of the SRAM (structural) equations represents the share of a State's total expenditures devoted to a particular highway activity. The explanatory variables, as in the total expenditure model (Chapter IV) fall into four categories: socio-economic indicators (e.g. population and per capita income), highway system characteristics (e.c. highway capital stocks and congestion levels), institutional characteristics (e.g. local govern- ment participation and toll road financing conventions), and Federal grant availability. The actual form of the short run allocation model is displayed in Figure V.4.1 for the product form specification.1 Several A similar specification of variables was also employed in estimating an exponential form model (c.f. equation 13). characteristics of the SRAM are immediately apparent. First, we 314 have represented Federal highway grant availability in terms of each of the major Federal-Aid-Systems - Interstate, Primary and Secondary.1 Contrastingly, the total expenditure model of the previous chapter disaggregated grant availability only in terms of an Interstate and non-Interstate designation. A second characteristic of the SRAM is that individual constant terms have been incorporated in all but one of the share equations. The exclusion of a constant from the maintenance equation (which in fact was chosen as our "normalizing share") was dictated by the fact that in a shares-type model specification the matrix of explanatory variables will not be of full column rank if a particular variable appears in each structural equation.2 Finally, it should be noted that in estimating the short run allocation model, the maintenance equation was chosen to normalize each of the five remaining shares in the manner described by equation (10). The choice of a particular normalizing share will Grants for extensions of the Federal Aid Primary and Secondary Systems in urban areas ("C" funds) were added to terms representing Primary-andSecondary System grant availability. This modelling convention reflects the fact "C" funds may be used for either Primary or Secondary system construction. 2 Thus it may also be noted that the population variable, SPOP appears in all but the share representing construction expenditures on non-Federal-Aid Systems (see Figure V.4.1). 315 in general affect the empirical results.1 Ultimately, the mainten- ance equation was selected as the normalizing share for no other reason than that expenditure data on this function appeared to be less reliable than for the remaining categories.2 Before presenting the estimation results derived from the SRAM, it is useful to set forth a brief description of the variables employed in each of the expenditure shares. Figure V.4.1 displays the form of the entire set of SRAM equations. Regardless of which equation is chosen as normalizing share, our estimation procedures should provide efficient and inbiased para- meter estimates. Nonetheless, for a given data sample, we may expect small differences in the estimated model parameters depending on the choice of a normalizing share. 2 Some variability exists in the States' data reporting conventions. A project considered to be a maintenance activity in one State might be reported as a construction expenditure by another State. THE SHORT RUN ALLOCATION MODEL E T E p a a,, a a a. a a 10SPOPIIUFACIz KSTK 13 TOLPCT 14AVIG 1 5 AVNIG 16 a 20SPOPa21UFACa22KSTKa23AVPGa24AVIGa26 - a SPOPa 31UFACa32GINIa33TSPMRa34PCCRMTa35AVSGa36AVIGa37 ET 30 EN= a4UFACa41PCCRMTa42RLTOTa43AVIGa44 L T 40 EM a SPOPa51 KSTKa52FPCMFa53RLTOTa 54AVTGa55 E T 50 r = a6 SpP0 a61 PCY a62KSTKa62RLTOT a63AVGa64 T Figure V.4.1 L&) SHARE I: SHARE 2: SHARE 3: SHARE 4: SHARE 5: SHARE 6: E = total State Interstate expenditures (State and Federal) 317 E = total Primary System expenditures ES = total Secondary System expenditures EN = non-Federal-Aid System construction expenditures EM = maintenance expenditures E0 = "other" expenditures (administration, grants to local govts., mi scel'Idneous expenditures) ET = totai expenditures: sum of the above expenditures SPOP = State population UFAC = percent of population residing in urban areas KSTK = present discounted value of highway capital stock TOLPCT = percent of total State revenues raised on State-administered toll roads AVIG = apportioned Interstate grants (three year moving average) AVNIG = apportioned "ABC" grants (three year moving average) AVPG = apportioned Primary System grants (three year moving average) AVSG = apportioned Secondary System grants (three year moving average AVTG = apportioned total grants (three year moving average) GINI = index of income inequality TSPMR = State rural primary system mileage PCCRMT = percent of rural primary system mileage carrying more than 10,000 ADT PCMF percent of total primary system mileage carrying more than 5,000 AUi RLTOT = percent of total expenditures (all units of govt.) contributed by local governments PCY = State per capita income aij = estimated coefficients Figure V.4.1 (contd.) I 318 Equation 1 - The Interstate Construction Share' Six variables in addition to a constant term were employea in the Interstate construction expenditure share equation. State size and urban density are characterized by the variables SPOP and UFAC respectively. With regard to the latter variable, we may expect higher levels of urban density to positively influence Interstate expenditure allocations, in light of the sharply increased costs of urban versus rural highway construction of Interstate standards.2 A measure of existing highway stock in place is afforded by the variable KSTK, derived accordina to the conventions Presented in section IV.3. An institutional characteristic bearing particular importance on a States' Interstate expenditure behavior is the extent of toll road financing, TOLPCT. In the early years of the Throughout the following presentation, unless otherwise indicated the definitions and sources of data employed in the SRAM are the same as previously described in the development of the total expenditure model (see section IV.3). 2 The relatively high costs of urban Interstate construction stem from the marked difference between ROW acquisition costs in urban and rural areas. Moreover, Interstate expenditures are particularly sensitive to land costs, since this System's design standards require more ROW than other highway systems. Interstate program, several States chose to finance Interstate 319 highway construction through the use of revenue bonds based on toll road operation. In fact the responsibility to construct and maintain these Interstate route segments was often delegated to a quasi-public Turnpike Authority.1 As such, all toll-financed Interstate activities are not reported in our data as State expenditures. Accordingly, we should expect the extent of toll-road financing (TOLPCT) to negatively influence a States' allocation of resources to construction on the Interstate System. The final two variables in the Interstate equation reflect Federal grant availability on the Interstate (AVIG) and non-Inter- state (AVNIG) Systems. Results from the total expenditure model (TEM) indicate that Interstate grants tend to stimulate State (total) expenditures. The SRAM allows us to determine the extent to which these grants have increased States' allocations specifically to Interstate construction. The States' Interstate expenditure response to the presence of non-Interstate grants may actually take one of two directions. On the one hand, we might expect increasing levels of non-Interstate grants to "draw away" resources that would otherwise have been devoted to Interstate construction. However, as we have shown in chapter IV, the ABC grant program has been viewed by the States as a substitute for their own ABC expenditures. In 1 It should also be noted that toll-financed Interstate roads are not eligible for Federal aid as stipulated by Title 23, United States Code, Section 301. 320 this perspective, increasing levels of ABC grants may "free up" State resources that may be allocated on Interstate construction as well as other State highway activities. In the SRAM, we will appeal to the data to verify the latter hypothesis. Equation 2 - The Primary System Construction Share This equation contains the same socio-economic and highway capital stock measures employed in the Interstate equation. However, we should expect the States' Primary System expenditure responses to these variables to differ from the expected responses expressed by the Interstate share equation. For example, the urban density measure should not exhibit as marked a positive influence on Primary System expenditures because of the previously noted difference in Primary System and Interstate System right of way requirements. Federal aid availability in this equation was represented by two terms -- the level of Primary System grants (AVPG) and the level of Interstate System grants. The direct effect of Primary System grants on State Primary System expenditures must be positive.1 1 Note that the dependent variables in the SRAM reflect total expen- diture levels inclusive of Federal arants. Even assuming that States need not raise their expenditure levels on the Primary System to match increasing Federal Primary System grant availability (because current State expenditure levels far exceed minimal matching requirements), it is extremely unlikely that States would decrease their own resource allocation to the Primary System by more than the amount of Federal grant increases. This point will become clearer in section V.6 where elasticity measures are presented for the SRAM. Suffice it to say here that we expect small increases in Primary System grant availability - say 1% - to increase States' Primary System expenditure allocation, but most likely by an amount less than 1% (indicative of a substitutive grant response). 321 The more irportant question is how these grants have influenced States' own resource allocation on the Primary System. The empirical results presented in the following sections will serve to verify our previous hypotheses on the substitutive expenditure impacts of Primary System grants. As for the States' Primary System expenditure res- ponse to Interstate grants, we should expect a negative influence. That is, our findings to this point suggest that the Interstate grant program has increased State highway investment levels. The SRAM estimation results will indicate the extent to which these increased investment levels have come at the expense of resource allocation to other State highway activities. Equation 3 - The Secondary System Construction Share Eioht variables (including the constant term) were used to express the factors influencing States' Secondary System allocation decisions. Since the relative importance of the Secondary System in a State's highway network is greatest in the predominantly rural/ agricultural States,1 we should expect the population variable SPOP, and the urban density measure UFAC to negatively influence Secondary System expenditure allocation. By the same reasoning the GINI index of income inequality (which was shown to be highest in rural/agricul- tural States -- see figure IV.4.2) should relate positively to Secondary System expenditure levels. 1 As noted in section II.2.iii, the Federal-Aid Secondary System comprises farm-to-market roads, rural mail routes, public school bus routes, local rural roads, county roads, and township roads. 322 In addition to these socio-economic indices, two descriptors of the States' rural highway systems were included in the Secondary System SRAM equation. The first, total State rural highway mileage (TSPMR), indicates the scale of the existing rural highway network. A second measure, PCCRMT provides a measure of the level of congestion on the States' rural roads.2 Specifically, this variable represents the percent of a State's rural highway mileage carrying more than 10,000 vehicles per day. We should expect hinher levels of rural highway traffic to influence a State to increase Secondary System construction expenditures. 1 This variable describes total State (i.e. exclusive of roads under county or municipal jurisdiction) highway mileage. Data were derived from yearly editions of the Federal Highway Administration's HIGHWAY STATISTICS (op. cit.) 2 HIGHWAY STATISTICS (op. cit.) reports traffic volume data in terms of seven distinct ADT categories, ranqing from a State's mileage carrying less than 5000 ADT to the number of miles bearing greater than 40000 ADT. The variable PCCRMT was derived from this source by dividing the rural mileage carrying greater than 10000 ADT, by total rural mileage. 323 The final two variables in the Secondary System share equation describe Federal grant availability for the Secondary (AVSG) and Interstate (AVIG) Systems. The expected expenditure responses in this instance should follow our discussion of hypothesized grant response in the Primary System equation. Specifically, increased in Federal Secondary aid should raise States' Secondary expenditures, but by an amount less than a grant increase. Interstate grants on the other hand may be expected to decrease States' Secondary expenditure levels. Equation 4 - The Non-Federal Aid System (MFAS) Construction Share In addition to their construction of Interstate, Primary and Secondary System highways, States also (wholly) finance the construction of roads apart from the Federal-Aid System designation. This activity represents a relatively minor expenditure of funds (averaging less than 10% for our 48 State/14 year sample), and most commonly represents rural highway construction. Four variables (and a constant term) were included in this expenditure share. Perhaps the most significant factor explaining the level of non- Federal-Aid System expenditures is the degree of local highway participation in highway finance (RLTOT). States differ markedly in the extent to which counties and municipalities assume the authority to construct and maintain local road networks. Since the SRAM is structured strictly in terms of State activities, we would expect RLTOT to negatively influence (State) expenditures on non- Federal Aid System roads. The parameter estimate of the urban density measure, UFAC should also be negative, reflecting the high incidence of non-Federal Aid System construction in rural areas. 324 Our discussion so far provides the basis for the expected signs of the parameter estimates of the two remaining variables included in this expenditure share -- the degree of rural road congestion (PCCRMT) and Federal Interstate grant availability (AVIG). Again noting the relatively high incidence of NFAS construction in rural areas, we should expect the presence of rural road congestion to induce higher expenditure levels on this activity. Increases in Interstate grant availability should, on the other hand decrease State expenditures on NFAS construction, as States devote an increasing share of their highway budget to expenditures on the aided function. Equation 5 - The Maintenance Expenditure Share The maintenance expenditure share contains five explanatory variables -- State population (SPOP), depreciated highway capital stocks (KSTK), a highway congestion measure (PCMF), the extent of local participation in highway finance (RLTOT) and the level of total Federal grant availability (AVTG). As in the previous share equation, to the extent that a State delegates highway authority to county and municipal governments, (State) maintenance expenditures should decrease. That is, we should expect a negative coefficient for the RLTOT term. Although we might expect both of the highway system characteristics variables, KSTK and PCMF to positively influence States' maintenance expenditures, this response pattern need not necessarily pertain. We refer here to the differing State policies regarding the performance of highway maintenance activities. If all States practiced a uniform maintenance policy,1 then increasing 325 congestion levels and/or increasing highway capital stocks would increase highway maintenance requirements. But we may also observe that some States adopt a highway policy favoring construction (as opposed to maintenance) expenditures. Thus, relatively high levels of existing capital stock actually (may) signal an explicit policy of constructing highway facilities "at the expense" of maintenance operations.2 Similarly, higher congestion levels may induce States to increase construction expenditures rather than maintenance operations. The SRAM allows for a specific test of these conflicting hypotheses. We have also included a term in the maintenance share equation representing total Federal highway grant availability. The intent here is to assess whether the presence of Federal aid has tended to divert State expenditures from non-aided (i.e. maintenance) highway activities. For example, attempting to implement a specific policy to maintain uniform road surface quality. See Findakly, H.K., A DECISION MODEL FOR INVESTMENT ALTERNATIVES IN HIGHWAY SYSTEMS, Unpublished ScD Thesis, Department of Civil Engineering, Massachusetts Institute of Technology, September, 1972. 2 As reported in our data, a major resurfa project would be recorded as a construction expenditure. Maintenance expenditures are reported for patching, sealing and filling of road surfaces. 326 Equation 6 - The "Other" Expenditures Share The final share in our SRAM formulation captures expenditures on all other State highway activities not included in the first five equations. Specifically, this category is comprised of expenditures on administration, highway police and safety, debt service payments, and grants to local governments. Five variables (plus a constant term) were incorporated in this SRAM equation. The first three, SPOP, PCY and KSTK should all positively influence "other" expenditures since States with relatively high populations, per capita incomes and existing highway networks can be expected to support relatively large highway-related administrative organizations ( e.g. State Highway Departments and State Departments of Transportation). As in our previous share equations, the delegation of highway authority to lower units of government should decrease the administrative requirements of State highway organizations. This effect is captured in the variable RLTOT, which should be associated with a negative coefficient estimate. Finally, a total Federal-aid term was included (AVTG) to evaluate the impacts of Federal highway grants on the performance of States' administrative and other higheay activities. 327 V.5 Empirical Results -- Parameter Estimates of the SRAM As in the empirical analysis of the total expenditure model, lack of sufficient time series data precluded statistically reliable State by State estimation of the short run allocation model. Thus three separate pooled data regressions were performed,1 corresponding to: - the entire set of observations on the 48 States over 14 years (1957-1970). - a subset of time series observations on the seven States exhibiting the lowest level of Interstate expenditures over and above minimum matching requirements, and - the subset comprising observations on the 41 remaining States over the 14 year period 1957-1970. As described in section V.2, estimation of the SRAM was performed for two alternative specifications of the individual structural (share) equations - a product form model, and an exponential form model. These data-set stratifications are similar to the modelling strategy followed in chapter IV. The seven States with conspicuously low "excess" Interstate expenditures were Missouri,'Montana,: North Carolina, North Dakota, South Carolina, Vermont and Virginia. 328 The complete set of estimation results from the short run aallocation model are reproduced in Figures V.5.1 - V.5.8. In these figures, the results are displayed for each of the six expenditure shares.I In each share equation, the figures indicate the individual parameter estimates, standard errors and t-statistics in that order. Figures V.5.1 and V.5.2 display the model parameters from the product form specification on the full pooled data set using OLS and GLS estimation respectively. The next four figures correspond to OLS and GLS estimation of the two data subsets of the SRAM in the product form specification. Finally, Figures V.5.7 and V.5.8 display the respective OLS and GLS estimations of the exponential form SRAM on the full pooled data set. The empirical results from the short run allocation model are most easily interpreted in terms of elasticities and derivatives of the categorical expenditures with respect to the explanatory variables incorporated in our analysis. This will be our task in the next two sections of this chapter. 1 The notation used in the figures to denote expenditure share equations is as follows: INT- Interstate construction, PRI - Primary System construction, SEC - Secondary System construction, NON - non- Federal Aid System construction, MNT- maintenance, and OTH - all other expendi tures. SHARE MODEL ESTIMATION RESULTS SPECIFICATION: PRODUCT FORM MODEL REGRESSION METHOD: F-STAT: F(37,3323)=25.97 ORDINARY LEAST SQUARES 6 SEE= 1.037 RSQ= 0.200 CONSTANT SPOP UFAC KSTK TOLPCT AVIG AVNIG -0.36E 01 -0.14E 01 0.46E 00 -0.59E 00 -0.78E-01 0.98E 00 -0.27E-01 INT 0.15E 01 0.17E 00 0.17E 00 0.16E 00 0.28E-f1 0.33E 00 0.22E 00 -2.51 -8.49 2.72 -3.76 -2.73 2.93 -0.12 CONSTANT SPOP UFAC KSTK AVPG AVIG -0.42E 01 -0.12E 01 -0.83E-C3 -0.40F 00 0.66E 00 0.13E 00 PRI 0.14E 01 0.16E 00 0.17E 00 0.16E 00 0.21E 00 0.33E 00 -2.95 -7.48 -0.00 -2.55 3.07 0.38 CONSTANT SPOP UFAC 61I1 TSPMR PCCRMT AVSG AVIG -0.17E 01 -0.11E 01 -0.15E 00 -0.86E-01 0.26E 00 0.67E-02 0.45E 00 -0.58E-01 SEC 0.19E 01 0.13E 00 0.18E 00 0.32E 00 0.10E 00 0.42E-01 0.19E 00 0.34E 00 -0.88 -7.87 -0.85 -0.27 2.49 0.16 2.35 -0.17 CONSTANT UFAC PCCRMT RLTOT AVIG -0.97E 01 -0.77E 00 0.21E 00 -0.49E 00 -0.89E-01 NON 0.12E 01 0.17E 00 0.34E-01 0.66E-01 0.50E 00 -7.91 -4.38 6.20 -7.42 -0.18 SPOP KSTK PCMF RLTOT AVTG -0.86E 00 -0.14E 00 0.37E-01 -0.97E-UI 0.21E 00 MNT 0.10E 00 0.93E-01 0.30E-01 0.34E-01 0.49E 00 -8.54 -1.55 1.22 -2.88 0.43 CONSTANT -0.10E 02 OTH 0.19E 01 -5.41 SPOP -0.1OE 03. 0.15E 00 -6.78 PCY 0.94E 00 0.22E no 4.23 KSTK -0.75E 00 0.19E 00 -3.95 Figure V.5.1 CA) ro RLTOT 0. 11E-01 0.65 E-01 0.16 AVTG 0.54E 00 0.51E 00 1.06 %J I L- %-f I 1 9 %.# V% I I w 1 11 6 1 4 'k %Lf S.F %0 %d I - I I %.R %-A L- L- SHARE MODEL ESTIMATION RESULTS SPECIFICATION: PRODUCT FORM MODEL REGRESSION METHOD: GENERALIZED LEAST SQUARES F-STAT: F(37,3323)=56.815 SEE= 0.!q7 RSQ= 0.354 CONSTANT SPOP UFAC KSTK TOLPCT AVIG AVNIG -0.70E 01 -0.15E 01 0.44E 00 -0.19E (0 -0.82E-01 0.12E 01 0.15E 00 INT 0.16E 01 0.24E 00 0.89E-01 0.19E 00 0.14E-01 0.25E 00 0.14E 00 -4.52 --6.27 L.92 -1.03 -5.72 4.84 1.09 -CONSTANT SPOP UFAC KSTK AVPG AVIG -0.58E 01 -0.63E 00 -0.16E 00 0.86E-01 0.71E 00 -0.92E-01 PRI 0.14E 01 0.16E 00 0.74E-01 0.13E 00 0.99E-01 0.16E 00 -4.12 -4.01 -2.10 0.69 7.14 -0.57 CONSTANT SPOP UFAC GINI TSPMR PCCRMT AVSG AVIG 0.27E 01 -0.541 00 --0.24E 00 0.33E 00 0.31E 00 0.3EE-01 0.31E 00 -0.11E 00 SEC 0.17E 01 0.9E-01 0.78E-O1 0.14E CO 0.46E-01 0.18[-01 0.77E-01 0.81E-01 1.56 -7.94 -3.13 2.31 6.7-4 2.07 3.97 -1.34 CONSTANT UFAC PCCRMT RLTOT AVIG -0.48E 01 -0.85E 00 0.19E 00 -0.52E 00 0.23E 00 NON 0.12E 01 0.34E 00 0.60E-01 0.11E 00 0.36E 00 -4.06 -2.48 3.21 -4.57 0.63 SPOP KSTK PCMF RLTOT AVTG -0.90E 00 0.23E 00 -3.91 0.26E 00 0.18E 00 1.46 0. 78E-02 0. 26E-01 0.30 -0. 71E-01 0. 23E-01 -3.10 KSTK -0.93E-01 0.71 E-01 -1.31 RLTOT AVTG -0,18E-02 -0.25E 00 0.22E-01 0.73E-01 -0.79 -3.44 Figure V.5.2 MNT CONSTANT -0.14E 02 OTH 0.11E 01 -8.02 SPOP 0.23E 00 0.55E-01 4.18 PCy 0.82E Co 0. 85E-01 9.66 0.57E 00 0.37E 00 1.51 wa L46) C0 SHARE MODEL ESTIMATION RESULTS SPEC I F I CA TIOtN: PRODUCT FORM MODEL REGRTS[9N METHOD: F-STAT: F(37, 453)=12.44 ORDINARY LEAST SQUARES 9 SEE:= 0. 793 RSQ= 0. 468 CONSTANT -0.35E 01 INT 0.48E 01 -0.74 CONS TANT -0.13E 01 PRI 0.47E 01 -0.28 SPOP UFAC -0.18E 01 0.48E-0) 0.34E 00 0.56E 00 -5.22 0.09 S POP -0.13E 01 0.33E 00 -4.13 KSTK TOLPCT AVIG AVLN Q -0. 20F 00 0.31E-01 0,81E 00 0.30E 00 0.31E 00 0.60E-01 0.79E 00 0.47E 00 -0.64 0.52 1.03 0.64 UFAC KSTK AVPG AYIG 0.58E 00 -0.iOE CO 0.64E 00 0.73E-02 0.56E 00 0.31E 00 0.44E 00 0.77E 00 1.04 -0.34 1.45 0.01 CCONSTANT 0.35E 0] SEC G.54E 01 0.64 SPOP -0.14E 01 0.36E 00 -3.99 UFAC Giii 0.14E 01 -0.28E 00 0.64E 00 0.95E 00 2.18 -0.29 TSPMR PCCRWIM 0.]7E 01 -0.12E 00 0.77E 00 0.14E 00 2 23 -0.86 AVSG AVIQ -0.59E 00 -0.14E-01 0.79E 00 0.82E 00 -0.?5 -0.02 CONSTANT UFAC. 0.34E 01 -0.t2E 01 NON C.51E 01 0.56E 00 0.6E -2.12 MNT PCCRMT RTOT AVIG 0.49E 00 -0.28E 00 -0.91E 00 0.10E 00 0.15E 00 0.13E 01 4.84 -1.93 -0.72 SPOP KSTK PCMF RLTOF AVTG -0.79E 00 0.50E-02 0.54E-01 -0.85E-01 0.18E-01 0.22E 00 0.13E 00 0.74E-91 0.76E-01 0.12E 01 -3.68 0.03 0.73 -1.13 0.02 CONSTANT SPOP 0.18E 01 -0.10E 01 0TH 0.48E 01 0.29E 00 0.38 -3.53 PCY 0.70E-01 0.60E 00 0.12 KSTK R .TOT 0.27E 00 -0.55E-01 0.40E 00 0.14E 00 0.66 -0.38 Figure V.5.3 AVTG 0.75E-01 0.12E 01 0.06 Co CO SHARE MODEL ESTIMATIONRESULTS SPECIFICATION: PRODUCT FORM MODEL REGRESSION ME1HOD: GENERALIZED LEAST SQUARES F-STAT: F(37, 453)=17.321 SEE= 1.039 RSO= 0.550 CONSTANT -0.94E 01 INT 0.64E 01 -1.48 SPOP -0.16E 01 0.29E 00 -5.37 CONSTANT -0.31E 01 PRI 0.62E 01 -0.50 SPOP -0.80E 00 0.22E 00 -3.63 UFAC 0. 61E 00 0.26E 00 2.31 KSTK AVPG AVIG .19E 00 0.48E 00 -0.18E 00 .18E 00 0.21E 00 0.38E 00 1.06 2.25 -0.49 CONSTANT 0.80E 01 SEC 0.70E 01 1.15 SPOP -0.10E 01 0.19E 00 -5.59 UFAC 0.97E 00 0.28E 00 3.51 GINI -0.19E 00 0.41E 00 -0.46 TSPMR 0.13E 01 0.33E 00 3.94 PCCRMT AVSG AVIG -0.24E-01 -0.32E 00 -0.73E-01 0.60E-O1 0.34E 00 0.32E 00 -0.40 -0.94 -0.23 CONSTANT UFAC PCCRMT RkTOT AVIG 0.24E 01 -0.62E 00 0.36E 00 -0.35E 00 -0.13E 01 NON 0.66E 01 0.11E 01 0.18E 00 0.25E 00 O.13E 01 0.36 -0.59 1.99 -1.38 -1.02 SPOP KSTK PCMF RLTO AVTG -0.69E 00 0.32E 00 0.12E 00 -0.58E-01 -0.62E-01 MNT 0.24E 00 0.18E 00 0.51E-01 0.48E-01 0.77E 00 -2.84 1.78 2.42 -1.22 -0.08 -CONSTANT_.SPOP PCY_ 1 KYTK RLQTh_ AVT G 0.97E 00 -0.32E 00 0.28E 00 0.45E 00 -0.94E-01 -0.22E 00 OTH 0.65E 01 0.15E 00 0.20E 00 0.16E 00 0.49E-01 0.43E 00 0.15 -2.21 1.37 2.87 -1.92 -0.51 Figure V.5.4 UFAC 0.12E 00 0.33E 00 0.35 KSTK 0.13E 00 0.23E 00 0.59 TOLPCT 0. 22E-01 0. 36E-01 0.60 AVIG 0.R1E 00 0.50E 00 1.62 AVNIG 0.14U 00 0.29E 00 0.47 SHARE MODEL EST IMATION RESULTS SPECIFICATION: PRODUCT FORM MODEL REGRESSION METHOD: F-STAT: F(37,2833)=19.81 ORDI'iARY LEAST SQUARES 7 SEE= 1.058 RSO= 0.183 CONSTANT SPOP VFAC KSTK TOLPCT AVIG AVNIG -0.34E 01 -0.12E 01 0.32E 00 -0.57E 00 -0.13E 00 0.94E 00 -0.15E 00 INT 0.16E 01 0.20E 00 0.19E 00 0.18E 00 0.34E-01 0.37E 00 0.25E 00 -2.16 -5.80 1.71 -3.09 -3.92 2.53 -0.60 CONSTANT SPOP UFAC KSTK AVPG AVIG -0.44E 01 -0.10E 01 -0.16E 00 -0.44E 00 0.68E 00 0.11E 00 PRI 0.15E 01 0.18E 00 0.19E 00 0.18E 00 0.24E 00 0.37E 00 -2.88 -5.81 -0.85 -2.45 2.78 0.30 CONSTANT SPOP UFAC GINI TSPMR PCCRMT AVSG AVIG -0.23E 01 -0.94E 00 -0.44E 00 0.33E-01 0.25E 00 0.32E-01 0.56E 00 -0.93E-01 SEC 0.21E 01 0.15E 00 0.20E 00 0.34E 00 0.11E 00 0.46E-nl 0.22E 00 0.38E 00 -1.10 -6.30 -2.14 0.10 2.18 0.70 2.59 -0.24 CONSTANT UFAC PCCRMT RLTOT AVIG -0.11E 02 -0.73E 00 0.1SE 00 -0.45E 00 0.73E-01 NON 0.13E 01 0.20E 00 0.36E-01 0.73E-01 0.56E 00 -8.24 -3.70 5.07 -6.17 0.14 SPOP KSTK PCMF RLTOT AVTG -0.80E 00 -0.19E 00 0.23E-01 -0.56E-01 0.28E 00 tiNT 0.11E 00 0.10E 00 0.34E-01 0.37E-01 0.55E 00 -7.05 -1.82 0.69 -1.51 0.51 CONSTANT SPOP PCY KSTK RLTOT AVTG -0.94E 01 OTH 0.21E 01 -4.46 -0.90E 00 0.17E 00 -5.20 0.72E 00 0.24E 00 2.94 -0.77E 00 0.21E 00 -3.59 -0 .96E-03 0.73F-01 -0.01 0.59E 00 0.56E 00 1.05 Figure V.5.5 GaGa Ga SHARE MODEL ESTIMATION RESULTS SPECIFICATION: PRODUCT FORM MODEL REGRESSION METHOD: GENERALIZED LEAST SQUARES F-STAT: F(37,2833)=49.481 SEE= 1.000 RSQ= 0.359 CONSTANT SPOP UFAC KST K TOLPCT AVIG AVNIG -0.79E 01 -0.11E 01 0.26E 00 -0.25E 00 -0.14E 00 0.11E 01 0.96E-01 INT 0.17E 01 0.22E 00 0.87E-01 0.18E 00 0.16E-01 0.25E 00 0.14E 00 -4.71 -4.72 3.02 -1.37 -9.27 4.60 0.69 CONSTANT SPOP UFAC KSTK AVPG AIIG -0.70E 01 -0.53E 00 -0.30t 00 -0.53F-02 0.81E 00 -0.44E-f1 PRI 0.15E 01 0.16E 00 0.84E-01 0.14E 00 0.11E 00 0.18E 00 -4.72 -4.2f: -3.62 -0.04 7.18 -0.25 CONSTANT SPOP UFAC GIUI TSPMR PCCPMT AVSG AVIG 0z25E 01 -0.51F 00 -0.39F 00 0.38E 00 0.32E 00 0.40E-01 0.30F 00 -0.48F-01 SEC 0.19E 01 0.72E-01 0.SfE-01 0.15E 00 0.50E-01 0.20E-01 0.89E-01 0.93E-01 1.33 -7.07 -4.39 2.48 6.54 2.02 3.35 -0.52 CONSTANT UFAC PCCRMT RLTOT AVIG -0.47E 01 -. 71E 00 0.16E 00 -0.49E 00 0.48E 00 NON 0.12E 01 0.39E 00 0.66E-01 0.13E 00 0.45E 00 -3.84 -1.82 2.51 -3.87 1.08 SPOP KSTK PCMF RLTOT AVTG -0-64E 00 0.12E 00 -0.40E-01 -0.21E-01 0.63E 00 MNT 0.21E 00 0.17E 00 0.26E-C1 0.23E--02 0.37E 00 -3.05 0.74 -1.56 -0.92 1.69 CONSTANT SPOP PCY KSTK RLTQT AVTG -0.13E 02 OTH 0.19E 01 -G.98 0.21E 0E0 0.64E-01 3.21 0.63E 00 0.90E-01 6.99 -0. 78E-01 0. 79E-01 -1.00 0.24E-01 -0.47 -0.12E 00 0. 91E-01 -1.34 wt W' Figure V.5.6 SHAREMODEL ESTIMATION RESULTS SPECIFICATION: EXPOPENTIAL FORM MODEL REGRESSION METHOD: F-STAT: F(37,3323)=23.745 ORDINARY LEAST SQUARES SEE= 1.046 RSO= 0.186 CONSTANT SPOP -0.29E 00 -0.32E-06 INT 0.20E 00 0.43E-07 -1.44 -7.47 UFAC 0.88E 00 0.32E 00 2.72 KST(K 0.37E 00 0.17E 00 2.14 TOL PC',- -0.66E 01 0.11E 01 -6.07 AVIG AVNIG 0.48E-08 -0.10E-07 0.13E-07 0.16E-07 0.36 -0.63 CONSTANT SPOP 0.13E 00 -0.35E-06 PRI 0.20E 00 0.47E-07 0.65 -7.35 UFAC -0.59E 00 0.32E 00 -1.86 KSTK -0.59E-01 0.17E 00 -0.34 AVPG 0. 29E-07 0. 23E-07 1.27 -0. 16E-08 0.13E-07 -0.12 CONSTANT SPOP UFAC GINi TSPMR PCCRMT AVSG AVIG -0.27E-01 -0.37E-06 -0.12E 01 -0.16E 00 0.14E-04 -0.30E 01 0.24E-07 0.15E-08 SEC 0.35E 00 0.4?E-07 0.33E 00 0.80E 00 0.79E-05 0.86E 90 0.2E-07 0.13E-07 -0.08 -8.94 -3.73 -0.21 1.80 -3.54 0.86 0.11 CONISTANT UFAC ?CCRMT RLTOT AVIG -0.14E 31 -0.14E 01 0.33E 01 -0.55E 31 -0.95E-08 NON 0.20E 00 0.33E 00 0.81E 00 0.46E GO 0.13E-07 -6.93 -4.22 4.01 -11.97 -0.72 ^POP KSTK PCMF RLTOT AVTG -0.29E-0F -C.43E-O1 -0..39E 00 -0.13E 01 -C.22E-08 MNT 0.24E-07 0.10E 00 0.19E 00 0.24E 00 0.13E-07 -12.14 -0.42 -2.05 -5.50 -0.17 CONSTANT $POP PCY K$TK RLTOT AVTG -0.41E 00 -0.33E-06 OTH 0.20E 00 0.34E-07 -2.09 -9.78 0. 18E-03 0.81E-04 2.22 -0.32E 00 0.20E 00 -1.61 0.74E 00 0.47E 00 1.59 0. 21E-08 0.13E-07 0.16 Figure V.5.7 WA w, SHARE MODEL ESTIMATION RESULTS SPECIFICATION: EXPONENIAL FRM MODEL REGRESSION METHOD: GENERALIZED LEAST SQUARES F-SrAT: F(37,3323)=41.469 SEE= 1.003 RSQ= 0.285 CONSTANT SPOP UFAC KSTK TOLPCT AVIG AVNIG -0.45E 00 -0.18E-06 0.90E 00 0.62E 00 -0.67E 01 0.27E-07 0.13E-07 INT 0.20E 00 0.46E-07 0.18E 00 0.21E 00 0.64E 00 0.12E-07 0.13E-0/ -2.28 -3.92 4.88 3.02 -10.49 2.34 1.04 CONSTANT SPOP UFAC KSTK AVPG AVIG 0.59E 00 -0.13E-06 -0.72E 00 0.44E-01 0.46E-07 0.13E-07 PRI 0.21E 00 0.36E-07 0.15E 00 0.15E 00 0.14E-07 0.86E-08 2.88 -3.65 -4.70 0.28 3.37 1.51 CONSTANT SPOP UFAC GITJI TSPMR PCCRfIT AVSG AVIG -0.57E 00 -0.97E-07 -0.10E 01 0.40E 00 0.16E-04 -0.23E 01 0.26E-07 0.62E-08 SEC o.33E 00 0.14E-07 0.15E 00 0.36E 00 0.35E-05 0.35E 00 0.11E-07 0.27E-08 -1.70 -7.04 -6.86 1.12 4.65 -6.56 2.45 2.29 CONSTANT UFAC PCCRMT RLTOT AVIC -0.58E 00 -0.98E 00 0.15E 01 -0.53E 01 0.24E-17 NON 0.19E 00 0.64E 00 0.14E 01 0.81E 00 0.13E-07 -3.05 -1.S4 1.01 -6.56 1.78 SPOP KSTK PCMF RLTOT AVTG -0.15E-06 0.22E 00 -0.39E 00 -0.12E 01 0.20E-07 VINT 0.41E-07 0.19E 00 0.15E 00 0.17E 00 0.12E-07 -3.56 1.15 -2.53 -Ii.83 1.75 CONSTANT SPOP PCY KSTK RVTOT AVTG -0.14E 01 OTH 0.19F 00 -7.35 -0. 24E-07 0. 13E-07 -1.82 0.39E-03 0.31E-04 12.64 -0.51E 00 0. 79E-01 -6.46 0.46E 00 0.16E 00 2.83 0.36E-08 0.25E-08 1.44 Figure V.5.8 337 However, several properties of the actual regression results should be noted here. Our generalized least squares estimation technique significantly improved the efficiency of the parameter estimates. For example, comparing figures V.5.1 and V.5.2 the Standard Error of Estimate (as noted by SEE in the figures) decreased from 1.037 in the OLS estimation to 0.997 for GLS estimation. More importantly, 25 of the 37 parameters in the SRAM had higher t-statistics in the GLS estimation than in OLS estimation. The signs of the parameter estimates proved to be generally consistent with the a priori hypotheses advanced in section V.4. For example, referring to the third share equation in Figure V.5.2, it was found that a State's Secondary System expenditures tend to decrease with population, urbanization and Interstate grant availability, and increase with the level income inequality, rural highway mileage and congestion levels, and Secondary System grant availability.1 A full discussion of the implications of the entire set of SRAM parameter estimates will be deferred to the next section. Finally, it should be noted that the product form specification of the SRAM provided somewhat more efficient parameter estimates than the exponential form specification. Comparing Figures V.5.2 and V.5.8, it may be seen that the F-statistics, Standard Error of Estimate, R-squared, and 24 of the 37 paramters' t-statistics 1 These findings may be compared with our a priori hypotheses advanced in section V.4 338 were higher for the product form SRAM specification. For this reason, further analysis of the exponential form SRAM was abandoned. Estimations of the exponentail form model were not performed on our two data subsets. Furthermore, the policy implications of the SRAM regression results found in the next two sections are all based on the findings from the product form model. V.6 Evaluation of the Elasticities and.Derivatives From the Short Run Allocation Model The estimation results from the short run allocation model are not immediately interpretable in a direct or simple fashion. Our immediate concern is not with the estimation coefficients themselves but with how the model predicts changes in expenditure allocation with respect to the variables incorporated in the analysis. A convenient way to describe these changes is with derivatives and elasticities. In our application, the derivative of an expenditure share with respect to a variable in the SRAM may be defined as: (25) = .( . a -2 af (Z,E) axk 1Hk if,) ax k where s = expenditure share j Xk = explanatory variable k a = parameters of the utility function f. = structural (share) equation in the SRAM The second and third terms of this equation follow directly from our derivation of the SRAM (c.f. equation 9). For our purposes here, the form of equation (25) has two important characteristics. First, it is clear that the derivatives are expressed as a function of the parameter estimates of the short run allocation model. And second, it may be seen that the variables included in any one share will have an effect on the derivatives (and elasticities) of all the shares in the SRAM. 339 340 Formally, this statement may be expressed as: (26) S as.(26)s.~p = 0 * k i=.1 k where S (=6) = number of shares in the SRAM Equation (26) emphasizes the tradeoffs inherent in a State's resource allocation decision process. Given a fixed budget, the decision to increase expenditures on one activity must be compensated by a decrease in the resources devoted to at least one other highway function. For example if an increase in Interstate grants stimulates additional State expenditures on Interstate construction (as indicated by a positive derivative of the Interstate share with respect to Interstate grants), then expendi- tures on some other function(s) must decrease (as indicated, for example, by a negative derivative of the non-Federal-Aid System expenditure share with respect to Interstate grants). ' Appendix B develops a detailed derivation of the derivatives and elasticities of the short run allocation model. Our purpose here is to highlight the more significant policy implications of the SRAM. It should be remembered that at this point we are concerned only with allocation decisions. The same comments apply to the interpretation of the SRAM elasticities. The elasticities of the SRAM n are defined as = as. X DXk s 341 from Figure V.6.1 that in the short run (i.e. fixed State budget), a one dollar increase in Interstate grant availability is associated with a $1.11 increase in total (State plus Federal) expenditures on that system. However, it is also apparent that the same one dollar increase in Interstate grants results in a decrease in expenditures devoted to all other categories except maintenance. Moreover, Figure v.6.1 indicates that Interstate grant increases effect a more significant reallocation of State resources than grants for the Primary and Secondary Systems. In particular, note that the derivative of Secondary System expenditures with respect to Secondary grants is only 1.04. If States matched Secondary grants dollar for dollar, ithen we would expect to find a derivative of 2.0. It appears then that in the short run, States only minimally increase their own Secondary expenditures in response to increasing Secondary System grant availability. To a lesser extent, the States' short run reaction to increases in Primary System grant availability is also character- ized by less than a dollar for dollar matching response, as indicated by the derivative value of 1.72. Both these findings substantiate our earlier comments on the non-binding nature of ABC grants. In particular, since States have been expending more 1We have previously noted that Secondary (and Primary) grants are provided on a 50% Federal matching basis. In the Interstate grant program, the Federal government assumes 90% of project costs. 342 In the next section, we will intergrate the results of the SRAM with the total expenditure model to describe the impacts of Federal grants and other factors on both total State highway expenditures and interfunction allocation. We begin our analysis of the SRAM with a presentation of the model derivatives. Figure V.6.1 displays the derivatives from the product form SRAM estimated (GLS) on the full 48 State/14 year data set. Each column represents a highway activity, and the row entries correspond to each of the explanatory variables in the SRAM.I The most striking finding from this figure is that changes in the level of grants on a given Federal-Aid System affect not onl the State's expenditures on that System, but significantly alter the expenditure shares of other Federal-Aid Systems and the remaining highway activities as well. For example, it is clear See Figure V.4.1 for a definition of the explanatory variables. The column headings are defined as INTERSTATE-Interstate System construction expenditures, PRIMARY-Federal-Aid Primary System construction expenditures, SECONDARY-Federal-Aid Secondary System construction expenditures, NONFASYST-non-Federal-Aid System con- struction expenditures, MAINT-maintenance expenditures, and OTHER-administrative and other miscellaneous expenditures. 343 FORTY-EIGHT STATE SAMPLE SHORT RUN MODEL DERIVATIVES SHARE VAR IADLE SPOP UFAC PCY GINI KSTK TSPMR PCCRMT P CM F TO L PUT R LTOT AVIG AVPG AVSG INTERSTATE -0.105E 02 0.402E 08 -0.474E 04 -0.524E '7 -0.172E 08 -0.221E 03 -0.17?E 08 -0.398E 06 -0.103E 09 0.61E 07 0.111E 01 -0.317E 30 -0.17OE-01 PRIMARY -0. 753E -n.136E: -0. 335E -0. 371E O.808E -0. 157E -0.122E -0. 281E 0.287E 0.468E -0.374E 0.172E -0.354E 00 08 04 07 P7 03 08 06 08 07 00 01 00 SECONDARY 0.578E -0. 100E -0.170E O.167E 0.940E 0.77E 0.147E -0.142E 0.145E 0.237E --C.iS7E -0. 286E 0.1041"E 00 08 04 c8 06 03 08 06 08 07 cc 00 01 Figure V.6.1 344 FORTY-EIGHT STATE SAMPLE SHORT RUN MODEL DERIVATIVES SHARE VARIlAnLE SPOP UFAC PCY GINI KSTK TSPMR PCCRMT IPMtF TO L PUT R L T OT AVIG APG AVSG I NTERSTATE -0.105E 02 0.4O2E 08 -0.474C 04 -0.5241E '7 -0.172E 08 -0.221E 03 -0.172E 08 -0.398E 06 -0.103E 09 0.661E 07 0.111E 01 -0.317E 30 -0.17CE-01 PRIMARY -0. 753E -n.136-: -0. 335E -0.371E O.808E -0. 15 7E -0.122E -0. 281E 0.287E 0.468E -0.374E 0. 172E -0. 354E 00 08 04 07 ..7 03 08 06 08 07 00 01 00 SECONDARY 0.578E -0. 100E -0.1 70E 0.167E 0.940E 0.737E 0.147E -0. 142EE 0. 145E 0.237E -C.1SIE -0.286E 0. 1041E 00 08 04 c 8 06 C3 0 f 06 08 07 c0 00 01 Figure V.6.1 (contd.) 345 than the minimal matching requirements for these Systems, they need not increase their own expenditures in order to satisfy the matching requirements of additional ABC aid. And, in fact, our results indicate that short run expenditure increases on the Primary and Secondary Systems do not match (dollar for dollar) increases in ABC grants. Contrastingly, our SRAM results indicate that the short run state response to increasing Interstate aid is to increase their own expenditures by slightly more than the minimally required state matching share. Referring to figure v.6.1, the derivative of total (State plus Federal) Interstate expenditures with respect to Interstate grants is 1.11. Thus, for each dollar increase in Federal Interstate grant availability, we can expect (in the short run) an eleven cent increase in State resources devoted to Inter- state construction. In addition to the direct effect of Federal aid, (that is the effect of a Federal-Aid System grant on expenditures on the same System), Federa'-aid also influences short run expenditures on other highway activities. To begin with, Figure V.6.1 indicates that each dollar increase in Interstate grant availability induces a 37 cent and 20 cent decrease in short run expenditures on the Primary and Secondary Systems respectively. Similarly, increases in Primary (or Secondary) System grants result in a decrease of States' resource allocation to the Interstate and 346 Secondary (or Primary) Systems. These "cross-derivatives"I are useful in suggesting the complementary and substitutive allocation characteristics manifest in States' highway expenditure behavior. For example, Figure V.6.1 indicates that (in the short run): -- Interstate grant increases induce greater decreases in Primary System construction expenditures than in Secondary System expenditures (i.e. States view Interstate roads as a closer substitute for Primary System roads than Secondary System roads). -- Primary System grant increases have tended to draw approximately equal resources from Secondary and Interstate System expenditures. ("cross-derivatives" equal to -.317 and -.286 respectively.) -- Secondary System grant availability has had the least reallocational impact of any of the Federal Aid System grants. This is particularly true of the effect Secondary grants on Interstate System expendi- tures. From Figure V.6.1, it may be seen that each dollar increase in Federal-Aid Secondary System grant availability decreases States' Interstate expenditures by less than two cents. 1 That is, the derivative of State expenditures on one activity with respect to Federal grants on another highway activity. 347 -- Interstate grant increases have tended to increase States' maintenance expenditures at the rate of approximately five cents per grant dollar. This is an interesting finding in light of the often expressed hypothesis that Federal aid availability has resulted in a decrease in States' expenditures on non-aided activites,1 (e.g. maintenance). In fact, Interstate grants have tended to accelerate Interstate construction, which in turn has led to increasing maintenance require- ments. Maintenance standards on the Interstate System are measurably higher than on other road types. This is because the Interstate System is designed for higher driving speeds and thus require maintenance of smooth roadys, wide rights-of-way and modern traffic service devices (signs, lighting). Several other findings concerning States' short run expendi- ture behavior may be inferred from Figure V.6.1. In each of the paragraphs below, the model implications are followed by the relevant derivative from Figure V.6.1 in parentheses. -- State maintenance expenditures increase with increasing levels of existing highway inventory, KSTK (.138 x 107), the level of highway congestion, PCMF 1For example, see Maxwell, J.A., "Federal Grant Elasticity and Distortion", National Tax Journal, Volume XXII, Number 4 (December , 1969). 348 (.122 x 107) and the amount of Federal Interstate grants (.495). -- The share of the States' budget devoted to the non- aided expenditure categories (non-FederalMid System construction, maintenance and "other") tends to decrease with increasing levels of any of the Federal Aid System grants.1 This is particularly true of the change in administration, highway police and safety and other miscellaneous (i.e. "other") expenditures in response to increases in the grant availability on the Interstate (-.561), Primary (-.899) and Secondary (-.637) Systems. -- Increasing levels of urbanization tend to increase State expenditures on the Interstate System (.402 x 108) and decrease expenditures on the Primary (-.136x108), Secondary (-l.OOxlO8) and non Federal- Aid (-.118x108) Systems. The explanation here is that the relatively large right of way requirements of the Interstate System, and the high price of urban (versus rural) land result in significantly higher Interstate The important exception of the effect of Interstate grants on maintenance expenditures has already been noted. 349 System costs in densely populated states. As might be expected, State expenditures on the rural-oriented road systems (the Secondary and non-Federal-Aid Systems) decrease with higher levels of urbanization. -- State expenditures on maintenance and non-Federal-Aid System construction decrease with increasing levels of local participation in highway finance (derivatives equal -.146x108 and -.445x1&7 respectively.) These two activities are commuonly delegated (to a greater or lesser degree) to county and municipal highway authorities. Thus to the extent tht lower govern- mental agencies assume the financial responsibility for maintenance and local road construction, State expenditures on these activities decrease. By the same token, the resources "freed up" by the delegation of highway responsibility to lower governmental units result in increasing State expenditure levels on those functions under exclusive State control (as evidenced by the positive derivatives of expenditures on the Federal-Aid Systems with respect to RLTOT). -- The SRAM results substantiate the hypothesis advanced in section V.4 that the degree of toll road financing (as measured by the variable TOLPCT) would negatively 350 influence States Interstate expenditures. In fact, of all the expenditure categories in the SRAM, only the Interstate share had a negative derivative (-.103x109) with respect to TOLPCT. In summary, this section has explored short run State highway resource allocation behavior. The derivatives of the short run allocation model generally corroborated the hypotheses advanced in section V.4. Most notably, it was found that Primary and Secondary System grants do not induce a dollar for dollar matching response by the States in the short run. Here again we have drawn attention to the fact that although the ABC grant program is characterized by matching provisions, these provisions are not binding on States allocation behavior. Contrastinoly, it was shown that the Interstate grant program has induced States to expend slightly more than the monomally required 10% State share, substantiating our earlier coments on the more binding nature of the Interstate grant program's matching provisions. A more complete listing of the derivatives and elasticities derived from the short run allocation model is presented in Appendix C.1 The empirical results in this section were discussed in terms of SRAM derivatives. The elasticities of the SRAM corroborate our general findings. In the next section where we investigate States' long run highway allocation behavior, our empirical results will be evaluated both in terms of model derivatives and elasticities. 351 V.7 Integration of the Results from the Total Expenditure Model and the Short Run Allocation Mode: Lon9 Run Responses This section extends the analysis of the previous section by considering the derivatives and elasticities of expenditures on each of the six highway categories with respect to the variables employed in both the short run allocation model and the total expenditure model. We refer here to long run derivatives (or elasticities) since the analysis allows for the influence of each of the variables on short run allocation as well as total expenditure levels. For example, the results of the short run analysis in section V.6 indicated that the share of Interstate expenditures increases in response to increasing Interstate grant levels. 1 But we have also seen from our total ex- penditure model (Chapter IV) that Interstate grant increases have tended to increase States' total expenditure levels. Thus to measure the total effect of Interstate grants (or any other variable), we must apply the predicted shifts in (short run) allocation shares to the predicted change in (long run) total expenditures. In short, this section attempts to integrate our findincs from the short run alloc- ation model and the total expenditure model. The two models of State highway expenditure behavior developed in this thesis take the form: More specifically, we have shown that Interstate grants have increa- sed short run State Interstate expenditures. Given the fixed budget consumption of our short run analysis, it follows that the States' share of resources devoted to Interstate construction has increased. 352 short run allocation model (SRAM) E. f-(27) s =R = R gg where s= E. = R = f i share of expenditures devoted to category j expenditures on category j total (State & Federal) expenditures structural equation in the SRAM total expenditure model (TEM) (28) R0pc = o+ E8 Xm m where R0 = Xm States per capita highway expenditures exclusive of Federal grants TEM explanatory variables m = TEM parameter estimates. It may be noted that the dependent variable in the TEM (Rp) ispc related to the form of the total expenditure term R in the short run allocation model. The former represents States' own per capita highway expenditures whereas the latter term is simply total highway expenditures (inclusive of Federal payments). Thus, by definition: (29) R = SPOP (R+pc + Fpc) where SPOP = State population Fpc = per capita Federal payments to the States. 353 Assuming that States ultimately expend all Federal grants made available, any differences between Federal highway payments Fp and Federal highway grants can be attributed to short run, transient responses. In the long run, it can be assumed that Federal payments will eventually "settle down" to the rate of Federal grant availa- bility. Thus in a long run static situation: (30) FPC = GPC where GPC = per capita Federal grant availability. But per capita highway grants were included as an explanatory variable in the total expenditure model. Thus employing the conventions of equations (29) and (30) in equation (27), we can rewrite the total expenditure model as: (31) R = ( + ZmXm + (1+Gpc SPOP exclusive of grant terms where R = total (inclusive of Federal grants) State highway expenditures e = TEM parameter estimate of the Federal grant terms GPC= per capita Federal highway grants. Equation (31) transforms our original TEM specification which served to predict States' own per capita highway expenditures, into a form which describes States total (inclusive of Federal grants) highway Particularly if Federal grant availability does not significantly change from year to year. 354 expenditures R. In fact, the definition of R in equation (31) is precisely the required form for interpretation of our allocation model. Thus, rewriting equation (27), we get (32) E= Six R where s.= a highway expenditure share as defined in ' the SRAM and R = total State highway expenditures as defined by the transformation of the TEM represented by equation (30). Finally, given the form of equation (32) we can define the long run derivatives of our expenditure categories E. with respect to the explanatory variables Xk: (33) 3E aXk aR as. = s X + R The corresponding long run Xk9 Ei/Xk is simply: 3 Xk=. ~X F(34.) = _E xk TEAk axk r j elasticity of E. with respect to variable kXk (s R R )s. _ i sj + R Xk3. k 3 as ax X 3 E. RI k X aR _sXk R Wak s. axk3 - R/Xk + qsj/Xk From the form of these equations, it is apparent that long run expenditures on a particular highway category E increase in response 3 to a change in an explanatory variable Xk if: 355 - the share of expenditures devoted to category j increased by more than an attendant percentage decrease in total expenditures, - total expentirues increase (in percentage terms) by more than an attendant decrease in the expenditure share devoted to highway category j, or - both total expenditures and the share of expenditures devoted to category j increase. Figure V.7.l1 displays the long run derivatives derived from the two expenditure models. The interpretation of the derivatives of expenditures with respect to the Federal grant variables deserve particular attention since these results provide strong evidence on the substitution/stimulation impacts of the Federal-Aid Highway Program. It is apparent that of the three Federal grant programs evaluated in this thesis, only the Interstate grant program had the effect of increasing State expenditures by more than the minimally required State matching share. Specifically, our results indicate that each dollar increase in Interstate aid is associated with a $1.57 increase in total Interstate expenditures, implying an increase in States' own Interstate expenditures by 57t. In fact recalling 1 The derivatives in this Figure were derived from the parameter estimates of the "SUll" specification of the total expenditure model (see Figure IV.6.1) and the GLS estimation of the SRAM (see Figure V.5.1). 356 FORTY-EIGHT STATE SAMPLE LONG RUN MODEL DERIVATIVES SHARE VARIABLE SPOP UFAC PCY GINI KSTK TS PMR PCCRMT PCMF TOLPCT RLTOT AV I G AV PG AVSG INTERSTATE 0.507E 01 0.395E 08 0.147E 05 -0.460E 07 -0.686E 07 -0.221E 03 -0.172E 08 -0.398E 06 -0.103E 09 0.627E 07 0.157E 01 -0.317E 00 -0. 170E-01 PRIMARY 0.103E 02 -0.140E 08 0.104E 05 -0.325E 07 0.154E 08 -0.157E 03 -0.122E 08 -0.281E 06 0.290E OF 0.444E 07 -0.516E-01 0.172E 01 -0.354E 00 SECONDARY 0.615E 01 -0.103E 08 0.526E 04 0.170E 08 0.464E 07 0.707E 03 0.147E 08 -0.142E 06 0.147E 08 0.225E 07 -0. 336E-01 -0.286E 00 0.104E 01 Figure V.7.1 357 FORTY EIGHT STATE SAMPLE LONG RUN MODEL DERIVATIVES SHARE VARIABLE SPOP UFAC PCY GI NI KSTK TSPMR PCCRMT PCMF TOLPCT RLTOT AV I G AVPG AVSG INTERSTATE 0.507E 01 0.395E 08 0.147E 05 -0.460E 07 -0.686E 07 -0.221E 03 -0.172E 08 -0.398E 06 -0.103E 09 0.627E 07 0.157E 01 -0.317E 00 -0. 170E-01 PRIMARY 0.103E 02 -0.140E 08 0.104E 05 -0.325E 07 0.154E 08 -0.157E 03 -0.122E 08 -0.281E 06 0.290E 08 0.44 4E 07 -0.516E-01 0.172E 01 -0.354E 00 SECONDARY 0.615E 01 -0.103E 08 0.526E 04 0.170E 08 0.46 4E 07 0.707E 03 0.147E 08 -0.142E 06 0.147E 08 0.225E 07 -0. 336E-01 -0.286E 00 0.104E 01 Figure V.7.1 (contd.) 358 the results of our total expenditure model analysis, and the short run allocation model analysis, our findings here are representative of a State response to increasing Interstate aid wherein States increase both their own total highway expenditures, and the share of those expenditures devoted to Interstate construction. This behavior stands in contrast to the States' response to increasing Secondary System grant availability. Note from Figure V.7.1 that the derivative of Secondary System expenditures with respect to Secondary System grants is only 1.04. The implication here is that each additional Federal Secondary System grant dollar increases State expenditures by only four cents -- far less than the increase that would pertain if States were matching increasing Federal Aid on a dollar-for-dollar basis.I In a similar fashion our results concerning the States' reaction to increasing Primary System aid suggest a less than a dollar-for- dollar expenditure matching response. The relevant derivative value here indicates that each dollar increase in Primary System aid induces only a 724 increase in States own expenditures on that System (derivative value equal to 1.72). These results reflect our findings from the empirical analysis of the total expenditure model (see section IV.6). That is, the increases in Primary and Secondary System expenditures in response to additions to grants on these 1 We again note that over our analysis period, Primary and Secondary System grants were provided on a 50% Federal, 50% State matching basis. 359 FORTY EIGHT STATE SAMPLE LONG RUN MODEL ELASTICITIES SHARE !NT ERSTATE 0.330 0.396 0.623 -0.029 -0.067 -0.031 -0.011 -0. 001 -0.059 0. 028 1.232 -0. 070 -0.002 PRIMARY 0.943 -0.198 0.623 -0. 029 0.214 -0.031 -0.011 -0.001 0.023 0. 028 -0.057 0.534 -0.045 SECONDARY 1.117 -0.287 0.623 0.302 0.127 0.277 0. 026 -0. 001 0.023 0. 028 -0.074 -0.176 0.261 Figure V.7.2 VAR I ABLE SPOP UFAC PCY GINI KSTK TSPMR PCCRMT P CMF TOLPCT RLTOI AVI G AVPG AVS G 360 FORTY EIGHT STATE SAMPLE LONG RUN MODEL ELASTICITIES SHARE NONFASYST 1.662 -0.890 0.623 -0.029 0.127 -0. 031 0.183 -0. 001 0.023 -0. 489 0.198 -0. 130 -0.026 MAINT 0.407 -0.042 0.623 -0.029 0.387 -0.031 -0.011 0.007 0.023 -0.043 0.440 -0.062 0.001 OTHER 1.987 -0.042 1.440 -0.029 0.034 -0. 031 -0.011 -0.001 0.023 0.025 -0. 146 -0. 226 -0.066 Figure V.7.2 (contd.) VARIABLE SPOP UFAC PCY G I N I KSTK TS PMR PCCRMT PCMF TOLPCT RLTOT AVI G AVPG AVSG 361 Systems stem not from increases in States' own total expenditures,1 but from increases in the share of a States' resources devoted to these Systems. Contrastingly, additional Interstate System aid has had the effect of increasing both the States' total expenditures, and the share of their expenditures devoted to Interstate construction. The same general findings are evident from an examination of Figure V.7.2 showing the long run elasticities from the two expenditure models. It may be seen that a one percent increase in Interstate grants leads to a 1.23% increase in long run State Interstate expenditures. In other words, the fraction of total expenditures representing Federal grant decreases with increasing levels of Interstate aid. Conversely, the direct elasticities of Primary and Secondary expenditures with respct to grants for these Systems are less than one. These elasticities -- .53 for the Primary System and .26 for the Secondary System indicate that Federal grants comprise an increasingly larger fraction of total (State plus zederal) expenditures on these Systems. Thus, on the Primary and Secondary Systems, States' own expenditures have increased at approxi- mately only one-half and one-fourth of the respective percentage In fact, we have shown that the States' response to ABC grants is characterized by expenditure substitution. That is each additional ABC grant dollar is associated with a decrease in States' own expenditures by one dollar. 362 rate increases in Federal aid (for these Systems).1 The elasticities (or derivatives) of categorical highway expenditures with respect to the other variables included in the expenditure models generally conform with expected State behavior. The indicated responses to each of these variables are summarized below. Socio-Economic Characteristics As expected, increasing levels of State population (SPOP) and per capita income (PCY) positively influence the expenditure levels on all the highway categories. Highway travel within a State increases with population and personal income. Therefore, we should expect higher levels of SPOP and PCY to increase the States' construction, maintenance and administrative expenditure requirements.2 It should be kept in mind in interpreting the results that elastici- ties express percentage changes in the expenditure levels on each highway category. Thus for example, while the elasticity of main- tenance expenditures with respect to population increases (.497) is 1 Note that States' own Interstate expenditures have increased at a greater percentage rate than increases in Interstate aid. These findings are all the more significant when it is recalled that for several years in our analysis period, States own Interstate expen- ditures exceeded their ABC System expenditures (see Figure 11.2.1) and the States' required matching share is lower on the Interstate than on the Primary or Secondary Systems. 2 Moreover for a given gas tax rate, increasing highway travel provides States with higher levels of earmarked highway revenue. 363 greater than the corresponding elasticity for the Interstate System (.3i0), in absolute terms increases in Interstate expenditures (in response to changes SPOP) exceed those for highway maintenance.I The measure of urbanization (UFAC) positively influenced Inter- state System expenditures, reflecting the sharply increased cost of Interstate highway construction in urban areas. The elasticity of the remaining five shares with respect to UFAC were all negative, most notably for the "lower order" (Sconary and non-Federal Aid) Systems. GINI, the indicator of State income distribution had a positive elasticity only for Secondary System expenditures. This result reflects the fact that the rural States tend to have the greatest degree of income inequality, and thus commit relatively higher expenditure levels on the rural-oriented Secondary System. Highway System Characteristics Two measures of existing highway inventories (KSTK-depreciated highway capital expenditures and TSPMR - State rural highway mileage) and two indicators of highway congestion levels (PCCRMT--percent of heavily traveled rural mileage and PCMF--percent of heavily traveled total mileage) were incorporated in the analysis. As might be expected, increasing levels of highway inventories positively influenced maintenance and "other" (non-capital) expenditure levels. In fact only Interstate expenditures exhibited a negative elasticity 1 As manifested by the corresponding derivative values (Figure V.7.1) of 5.07 for the Interstate category and 3.65 for the maintenance category. 364 with respect to KSTK. Secondary System expenditures exhibited a positive elasticity with repsect to rural highway mileage; again indicating the rural orientation of the Secondary System. Although the measures of highway congestion did not prove particularly significant, the elasticities with respect to PCMF and PCCRMT indicate reasonable expenditure responses. In particular expenditures on the predominantly rural highway systems (Secondary and non-Federal Aid Sustems) exhibited a positive elasticity with respect to the level of rural highway congestion (PCCRMT). And maintenance expenditures were positively influenced by the general measure of State-wide concestion (PCMF). Institutional Characteristics The variable measuring the extent of local participation in highway finance (RLTOT) exhibited neaative long run elasticities for the non-Federal Aid System and maintenance expenditure categories. Thus higher expenditure levels (presumably on highway maintenance and non-Federal Aid System construction) by counties and municipali- ties has the effect of "freeing up" (State) resources for the performance of exclusive State highway functions (Federal Aid System construction and administrative and other activities). The second indicator of State highway financing conventions--the extent of toll road financing (TOLPCT) did not appear to signifi- cantly influence the allocation of State resources. However, the results indicate that increasing use of toll roads has tended to decrease Interstate expenditures while increasing the level of expenditure on all other highway categories. As noted earlier, 365 this finding stems from the common State practice of delegating Interstate System financing responsibility to quasi-public toll- financed Turnpike Authorities. 366 V.8 Summary This chapter has presented an empirical analysis of the State highway allocation behavior in both a short run and long run context. The empirical model of short run highway allocation was derived from a utility maximization representation of State expenditure behavior. The model has the desirable property of explicitly accounting for State budget constraints and thus focuses on the inherent tradeoffs States must face in programing expenditures on alternative highway activities. A generalized least square estimation technique was developed to take proper statistical account of the joint interaction between States highway expenditure shares. The short run analysis explored allocation behavior under the assumption that State budget levels were fixed. The results demon- strated the relative importance of the Interstate grant program in influencing States allocation decisions. The results from the short run allocation model were then integrated with the empirical findings of the total expenditure model (Chapter IV) to develop measures of States' long run highway allocation behavior. The results demon- strate that Federal grants for the Primary and Secondary Systems have not significantly increased States' own expenditures on these Systems. Specifically, it was shown that States have not had to increase their own expenditures on a dollar-for-dollar matching basis with increased Federal funding. This behavior contrasted with State responses to the Interstate grant program, where it was shown that increasing Federal aid has increased both total State expenditures and the share of the States' budgets devoted to Interstate 367 construction. It was also shown that increases in Federal grant availability have generally decreased State expenditures on non-aided activities. One exception of interest was the finding that Interstate grant increases have led to increases in States' maintenance expenditures, indicative of the relatively large maintenance requirements associ- ated with that system. The predicted expenditure responses to changes in the State socio-economic indicators, highway system characteristics and institutional characteristics generally corroborated our a priori hypotheses. The policy implications of our empirical findings will be explored in the next chapter. 368 CHAPTER VI SUMMARY AND CONCLUSIONS VI.l Summary of the Thesis This study has investigated the impacts of the Federal Aid Highway Program on State highway expenditures. Our concern through- out the conduct of the research has been to focus on this issue from a national policy perspective. In simplest terms, the moti- vation of the research was a consideration of the design of, and response to Federal and highway financing. Our starting point was a review of the mechanics of State and Federal highway finance. Special attention was given to the unique aspects of the Federal Aid Highway Program (FAHP) and the attendant implications for empirical modelling. First, we took note of the widespread use of earmarked Trust Funds at both the Federal and State levels. This finding allowed us to restrict our modelling attention solely to the dynamics of State higway expenditure behavior.1 Second, our review of the highway finance environment pointed out the significant differences between the structural characteristics of the various Federal highway grant programs--most notably between the Interstate and ABC highway grant programs. The modelling implications here were twofold. 1 That is, unlike other State activities financed from general tax revenues, we have been able to "separate out" highway expendi- ture decisions from the overall State budgetary process. This modelling convention is discussed in detail in Chapter II. 369 First, it became apparent that the models of State expenditure behavior should explicitly account for the possibility of differ- ing State responses to the availability of grants on the Inter- state and ABC highway Systems.1 And second, the existence of several distinct highway grant types suggested the importance of in- vestigating the inherent tradeoffs States must face in programing expenditures on alternative highway activities. In other words, it was deemed important to trace the impact of the Federal Aid Highway Program on both the total level of States' highway expendi- tures and the allocation of State resources amongst Federally aided and non-Federally aided highway activites.2 Following the review of the Federal and State highway finance environment, we proceeded to develop a theory of State highway expenditure behavior. Our purpose here was to draw attention to the premise that State highway expenditure behavior depends not only on the level of available Federal grants-in-aid, but on the structural characteristics of the grant programs as well. rowards this end, Chapter III started out with a normative dis- This convention represents a departure from previous analytical analyses in this area. None of the studies cited in the liter- ature review in Chapter I chose to evaluate the separate State expenditure responses to grants on the different Federal Aid Highway Systems. In section IV.6.1, we argue that failure to account for differing State responses to the Interstate vis-a-vis ABC highway grant programs obscures a fundamental characteristic of the Federal Aid Highway Program, and indeed yields misleading results. 2 Here too, our modelling convention differs from previous empirical studies. As noted in Chapter I, the existing literature contain many examples of evaluations of States' total expenditure respon- ses to grants or States' allocation behavior. This thesis has at- tempted to present an integrated treatment of the impacts of the FAHP on both dimensions of State expenditure behavior. 370 cussion of the considerations involved in designing a Federal highway grant program to achieve specific national objectives. A distinction was drawn between proposing changes to the existing structure of the FAHP because the initial justification for the Federal role in highway finance is no longer (or hasanever been) valid, or because the structure of the FAHP is not compatible with the accepted goals of the Federal role in highway finance. While the normative analysis was not conclusive,1 the thesis does argue that the issues involved in the design of a Federal grant program are not simply a matter of political expediency. The adoption of a revenue sharing program (for example) will have significantly different allocational consequences than the pro- vision of Federal aid on an open-ended categorical, matching grant basis. Thus the normative analyis stresses the importance in gaining a better understanding of the dynamics of State expendi- ture responses to alternative Federal aid grant structures. Accordingly, the remainder of Chapter III was devoted to the development of a theory of State highway expenditure behavior. A typology of alternative grant types was introduced, and evaluated in terms of their impact in stimulating State expenditures on aided functions or in effecting a substitution response wherein States would reduce their own highway expenditures in response to 1 The normative analysis is limited by the difficulty in ascer- taining a unique, consensual national highway policy. Congres- sional debate is not normally conducted at an abstract (policy) level. Moreover, Federal highway objectives are not static. 371 increasing levels of Federal aid. Two modelling frameworks were introduced, one based on an extension of consumer allocation theory, and the other deriving from an application of a simple benefit/cost investment criterion. Although these two models ostensibly differed with respect to their underlying assumptions, in fact the conclu- sions drawn from both approaches were quite similar. That is, both analyses stressed the notion of price and income effects introduced by Federal grants, and proceeded to demonstrate how State expendi- ture responses differ according to the presence of one or both of these grant characteristics. The theoretical models were then used to investigate the historical grant and expenditure levels on the Interstate and ABC highway programs. The theoretical analy- ses suggested that for the Interstate program, Federal grants have stimulated State expenditures that would most likely not have been made in the absence of the grant program. This behavior was contrasted with the experience in the ABC program, where it was hypothesized that Federal grants have had a relatively insignificant impact in determining States' total expenditure levels. The theoretical models were useful in suggesting both the appropriate framework for structuring the empirical models and the expected empirical results. Our purpose in the remainder of the thesis was to validate our theoretical hypotheses with econometric models. Two models were advanced, treating in turn the impacts of the FAHP on total State highway expenditures, and on the allocation of States' highway budgets. The total expenditure model (TEM) derived from a capacity utilization investment theory relating 372 States' highway investment levels to existing highway capital stocks, proxy measures of desired highway capital stocks, and the availa- bility of Federal aid. The empirical results strongly corroborated the theoretical hypotheses regarding the differential impacts of the Interstate and ABC highway grant programs. The empirical model dealing with the second dimension of State highway expenditure behavior--the short run allocation model (SRAM) was derived from a utility maximization representation of State decision making. The results demonstrated the differential im- pacts of the various grant programs on States' short run budget allocation amongst Federally aided and non-aided highway activities. Finally, the empirical results from the short run alloca- tion model were integrated with the findings of the total expendi- ture model to develop measures of the States' long run highway allocation behavior. These results were consistent with our a priori hypotheses of State highway expenditure behavior. 373 VI.2 Policy Implications of the Empirical Findings As the main focus of this thesis was to explore the impacts of the FAHP on State expenditure behavior, we begin our discussion here with the policy implications of estimation results of the Feder- al grant terms included in the two expenditure models. We have shown that the Interstate grant program has effected more signifi- cant State expenditure responses than the ABC grant program. Specifically, we have traced the responses to Federal grants in terms of both States' total expenditure levels and short run State budget allocation amongst aided and non-aided highway activi- ties. For the former dimension of State behavior, the empirical models have demonstrated that the Interstate programs have been associated with increases in total (State plus Federal) expendi- tures by more than the amount of increases in Federal Interstate aid. Thus we concluded that the Interstate grant program has had the effect of stimulating State highway expenditures.1 This response pattern was contrasted with the ABC program, where the theoretical and empirical models have demonstrated that States have substituted their own highway expenditures for the receipt of increasing levels of Federal ABC aid. Regarding the second dimension of State highway expenditure behavior, we have demonstrated that the various Federal grant pro- grams have had a differential impact on States' allocation of their 1 Furthermore, we have shown that the resulting increase in States' total highway expenditures derive mainly from increasing resource allocation to Interstate construction and maintenance activities (presumably in large measure in the Interstate system). 374 highway resources. Although all of the Federal highway grant programs considered in this thesis were shown to stimulate States' short run budget allocation to Federal-Aid System construction activities, our results indicate that short run impacts of Primary and Secondary System grants exhibit a less than dollar-for-dollar matching response by the State.I Contrastingly, the Interstate grant program was shown to increase States' short run Interstate expenditures by more than the minimally required matching share. In fact, based on our theoretical analyses (see Chapter III), none of our empirical findings were unexpected. The empirical analy- ses served to validate our a priori hypotheses, and placed dimen- sions on the pattern of State responses to the FAFP. More important- ly perhaps, the empirical research provides evidence which suggests policy recomnendations for altering the present structure of the Federal-Aid Highway Program. Specifically, with our clearer understanding of the dynamics of State expenditure responses to Federal aid, the fundamental issue of the objectives of the Federal Aid Highway Program is called into question. The imposition of Federal highway taxes and the pursuant distribution of categorical grants represents an explicit expression I Since the matching ratio of ABC aid over our analyses period was 50% (except for the "public land States"; see Chapter II), our results indicate that even in the short run, States can "absorb" additional Federal aid without having to increase their own expenditures by the required State matching share. In Chapter II, we demonstrated that this response pattern could obtain only if States were histocially expending more than their minimally required matching share on the Federal-Aid Systems. 375 of Federal policy. In particular, the restrictions on the use of Federal funds for only certain types of facilities serves to iden- tify those projects whose provision is deemed to be in the national interest. It may well be argued that guaranteeing a minimally ac- ceptable provision of important transportation facilities or stimu- lating road construction necessary for interstate commerce are valid Federal objectives. But we have shown that for the ABC pro- gram, the former objective may not be appropriate, and the second objective is not being accomplished. In short, our results indi- cate that restructuring the Federal Aid Highway Program with a relaxation of the specificity of the categorical restrictions, and eliminating the built-in matching provisions would not significant- ly alter State expenditure levels. Since the ABC program has (over our analysis period) effectivejy operated as a non-categorical block grant system, the detailed provisions (matching ratios, categorical restructions, etc.) of the FAHP are unnecessary and wasteful. To be sure, the FAHP is characterized by other (non-allocation- al) consequences--ensuring adherence to Federal labor and contracting regulations, promoting the implementation of transportation planning and process guidelines, and guaranteeing that Federally-funded roads conform to certain safety standards. None of these "ancil- lary" impacts are tied to the particular structure of the FAHP. They are merely conditions States must satisfy in order to be eligible for the receipt of Federal highway monies. Indeed, we are arguing 376 that greater attention needs to be paid to exploiting these "ancillary" benefits in view of the failure of specific components of the FAHP to achieve significant allocational goals. We have already noted (section II.2.viii) that the Federal Aid Highway Act of 1973 has incorporated several provisions de- signed to reduce the specificity of the FAHP, most notably in terms of increasing the allowable fund transfers between distinct Federal Aid Systems, and providing Urban System aid for transit as well as highway construction. The logical extension of the 1973 provisions would be to completely remove all categorical and matching provisions from those components of the FAHP where it is either not the intent or not a reasonable expectation (given projected State expenditure levels and Federal grant availability) for Federal grants to stimu- late State expenditure levels. As we noted in Chapter III, categorical matching grants are most appropriate in situations where the Federal government perceives a national interest in promoting investment on specific types of highway facilities. Thus we argue that the criteria to be considered in the design of the structure of the FAHP (specifically in terms of the provision of categorical aid) is the existence of identifiable investment needs1 on specific highway facilities. The analyses I The Interstate System was a case where States would not have heavily invested on this System in the absence of Federal cate- gorical grants. Moreover, it may be argued that the Interstate Systemis characterized by significant "benefit spillovers" (see Chapter III) due to its value in enhancing interstate commerce and national defense. Thus, grants for the Interstate System may be viewed as a case where categorical aid was appropriate. Other 377 developed in this thesis suggest that categorical aid for broadly defined functional highway classes, for example the Federal Aid Primary System is not justified. A related issue is the question of the advisability of the existing taxation scheme and distribution formulas characterizing the existing FAHP. We have shown that the gasoline excise tax is at best proportional (for journey to work travel) and at worst regressive (for vacation and business intercity travel). Moreover, the analyses in Chapter II suggests that the apportionment formulas currently in effect fail to accomplish a significant redistribution of income from wealthier to poorer States. While the FAHP's main objectives are not directly related to achieving more desirable income redistribution,1 the generally recognized importance of transport systems in promoting economic growthand regional develop- ment suggests that more attention needs to be given to income dis- tributive properties of FAHP apportionment formulas. In line with our conclusion that the numerous highway categorical matching instances where categorical grants might be appropriate include high risk/new technology projects where categorical "demonstration" grants serve to overcome States' reluctance to invest in un- tested technology, or, more generally any instance where the Federal government perceives a national interest in accelerating expenditures on specific project types (e.g., TOPICS, and the "Priority Primary Routes" designated in the 1972 Highway Act). I There are more efficient Federal policies to achieve significant income redistribution, for example direct transfer payments (Revenue Sharing) with income-based distribution formulas. 378 grants be consolidated into a block grant system, it is recommended that the Department of Transportation give consideration to a restructuring of the FAHP apportionment formulas. Towards this end, the income and tax effort-based distribution formulas of the Federal government's General Revenue Sharing program merit particular im- portance. The second aspect of income inequality inherent in the current FAHP--the gasoline excise tax--also deserves DOT's attention in de- veloping future Federal highway policy. The issue here involves the income distribution characteristics, the revenue potential and the price distortion characteristics of alternative taxation schemes. While the gasoline tax possesses undesirable income dis- tribution characteristics, it nonetheless represents an efficient and relatively stable revenue source,2 and connotes a rough measure of equity. 3 In order to mitigate its perverse income distribution, DOT should consider supplementing the existing gasoline tax with an excise tax on automobiles where the tax rate would be progressive- ly higher for larger engine vehicles. This scheme would have the I Since the FAHP apportionment formulas are currently administered on a System-by-System basis, a grant consolidation program would require a change in apportionment policy in any event. 2 In the sense that demand for gasoline/auto travel is price in- elastic. 3 In the sense that the tax burden on an individual is proportional to his usage of highway facilities. 379 merits of promoting progressive taxation and enhancing the Federal government's objective of reducing gasoline consumption. 380 VI.3 Limitations of the Empirical Approach and Directions for Further Research The empirical analyses conducted in this thesis could be ex- tended in several fruitful directions. First, more attention could be given to investigating the specifics of the variation in highway investment behavior between States. Data limitations precluded the possibility of applying our expenditure models (the short run allocation model and the total expenditure model) on a State-by-State basis. While we did take proper statistical account of interstate behavioral variation in the pooled data sample, more research is necessary to investigate causal factors underlying differences in State behavior. Along these lines, more attention could be given to political and institutional factors. Does a State's highway expenditure behavior change significantly after it has formed a multimodal Department of Transportation? Are there significant cultural and regional effects present--that is for example, do Southern States express a different outlook on the provision of public services that the New England States and is so, why?1 Is there a difference in expenditure behavior that is attributable to differing State political organization, as for example between States where the Legislature exerts strong highway policy influence and States where the Executive branch (Governor) 1 Some of these questions were examined in our highway expenditure models through the use of "dummy variables." None of these experiments produced conclusive results. 381 assumes a major role in highway policy formation? These are all important questions that can only be addressed by adopting a more disaggregate analysis framework than the one applied in this thesis. The approach we did adopt reflected a focus on the highway investment issue from a national polic p2er- spective. A second area where future research would be fruitful involves exploring the validity of the assumptions underlying our empirical models. Our models have assumed States exhibit "rational economic behavior" in the sense that allocation and expenditure decisions are based on the desire to maximize States' perceived utility (or benefit). While this view of the motivations for State decision- making is quite general and non-restrictive, it would be instruc- tive to conduct in-depth interviews with responsible State highway officials to validate our assumptions. Such interviews would be useful in both gaining further insight into the factors (variables) to be included in future model development and checking the reason- ableness of our empirical results.1 Finally, our modelling approach could be extended in a fore- casting environment to assess the impacts of future Federal policy alternatives. Along these lines, the policy recommendations ex- pressed earlier in this chapter (grant consolidation and an alteration 1 The Federal Highway Administration has reviewed the major empirical results developed in this research, and has indicated general agreement with our findings based on their own in-house analyses. 382 in the taxation and grant distribution characteristics of the FAHP) as well as other alternative program variants could be evaluated against baseline predictions of the consequences of con- tinuing the existing FAHP. BIBLIOGRAPHY 383 Advisory Commission on Intergovernmental Relations, STATE-LOCAL FINANCES: SIGNIFICANT FEATURES AND SUGGESTED LEGISLATION, 1972 Edition Advisory Commission on Intergovernmental Relations, SPECIAL REVENUE SHARING: AN ANALYSIS OF THE ADMINISTRATION'S GRANT CONSOLIDATION PROPOSALS, December, 1971 Advisory Commission on Intergovernmental Relations, IMPACT OF FEDERAL PROGRAMS ON LOCAL GOVERNMENT, ORGANIZATION AND PLANNING, 1962 Ainsworth, K.G., "Comments on Monypenny's Federal Grants-in -Aid to State Governments: A Political Analysis," National Tax Journal, Volume XIII, Number 3 (September, 1960) Balestra, P., and M. Nerlove, "Pooling Cross Section and Time Series Data in the Estimation of a Dynamic Model: The Demand for Natural Gas," Econometrica, Volume 34, Number 3 Barr, J.L. and O.A. Davis, "An Elementary Politidal and Economic Theory of Expenditure of Local Governments," Southern Economic Journal, Volume 34, Number 1 (October, 1966) Birkhead, Guthrie S., METROPOLITAN ISSUES: SOCIAL, GOVERNMENTAL, FISCAL, Brookings Institution Reprint Number 61, Washington, D.C., 1962 Bishop, George A., "Stimulative Versus Substitutive Effects of State School Aid in New England," National Tax Journal, Volume XVII, Number 2 (June, 1964) Break, George F., INTERGOVERNMENTAL FISCAL RELATIONS IN THE UNITED STATES, The Brookings Institution, (Studies of Government Finance), Washington, D.C., 1967 Burch, P., HIGHWAY REVENUE AND EXPENDITURE POLICY IN THE UNITED STATES, Rutgers University Press, New Brunswick, New Jersey, 1962 Dearing, C.I., and W. Owen, NATIONAL TRANSPORTATION POLICY, The Brook- ings Institution, Washington D.C., 1949 DeGarmo, E. Paul, ENGINEERING ECONOMY, The MacMillan CompanyNew York, New York, 1960 384 Dorfman, Robert, PRICES AND MARKETS, Foundations of Modern Economics Series, Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1967 Dresch, S.P., "An 'Alternative' View of the Nixon Revenue Sharing Program," National Tax Journal, Volume XXIV, Number 2 (June, 1971) Due, John F. and A.F. Friedlaender, GOVERNMENT FINANCE: ECONOMICS OF THE PUBLIC SECTOR, Richard D. Irwin Inc., Homewood, Illinois, Fifth Edition, 1973 Faddeev, D.K. and V.N. Faddeeva, COMPUTATIONAL METHODS OF LINEAR ALGEBRA, W. H. Freeman Inc., San Francisco, California, 1963 Ferman, Gerald, OUTPUT ANALYSIS: THE DISTRIBUTION OF GRANTS-IN- AID 1957-1967, Working Paper Number 10, Denter for the Study of Federalism, Temple University, Philadelphia, Pennsylvania, 1974 Findakly, H.K., A DECISION MODEL FOR INVESTMENT ALTERNATIVES IN HIGHWAY SYSTEMS, Unpublished ScD Thesis, Department of Civil Engineering, Massachsuetts of Technology, September, 1972 Friedlaender, A. F., THE INTERSTATE HIGHWAY SYSTEM, North Holland Publishing Co., Amsterdam, 1965 Friedlaender, A.F., "The Federal Highway Program as a Public Works Tool," in Ando, A. et al, STUDIES IN ECONOMIC STABILIZATION, The Brookings Institution, Washington, D.C., 1968 Gabler, L.R., and J.I. Brest, "Interstate Variations in Per Capita Highway Expenditures," National Tax Journal, Volume XX, Number 1 (March, 1967) Gallamore, Robert E., (Reprint of) Testimony Before the Subcomit- tee on Roads of the Senate Public Works Committee, February 15, 1973 Gramlich, E.M., "Alternative Federal Policies for Stimulating State and Local Expenditures: A Comparison of Their Effects," National Tax Journal, Volume XXI, Number 1 (June 1968) Haskell, M.A., "Notes and Memoranda: Federal Grants in Aid-Their Influence on State and Local Expenditures," Canadian Journal of Economics and Political Science, Volume XXX, Number 4 (November, 1964) 385 Haveman, R.H., and J. Margolis (editors) PUBLIC EXPENDIUTRES AND POLICY ANALYSIS, Markham Publishing Company, Chicago, Illinois, 1970 Henderson, J.M. and R. E. Quandt, MICROECONONIC THEORY: A MATHE- MATICAL APPROACH, McGraw-Hill Book Co., 1958 Highway Research Board, HIGHWAY FINANCING: 10 REPORTS, Highway Research Record Number 20, 1963 Jack Faucett Associates Inc., CAPITAL STOCK MEASURES FOR TRANSPOR- TATION, Report Number JACKFAU-71-04-1, Volumes I, II, and III, Chevy Chase, Maryland, June, 1972 Johnson, D.W.,.and C.M. Mohan, "Revenue Sharing and the Supply of Public Goods," National Tax Journal, Volume XXIV, Number 2 (June, 1971) Kuh, Edwin, CAPITAL STOCK GROWTH: A MICROECONOMETRIC APPROACH, North Holland Publishing Co., Amsterdam, 1971 Kurnow, Ernest, "Determinants of State and Local Expenditures Recon- sidered," National Tax Journal, Volume XVI, Number 3 (September, 1963) McFarland, W.F., ECONOMIC EFFICIENCY IN HIGHWAY EXPENDITURES, Unpub- lished PhD Thesis, Tulane University, New Orleans, Louisiana, 1970 McMahon, W.W. and C.M. Sprenkle, "A Theory of Earmarking," National Tax Journal, Volume XXIII, Number 3 (September, 1970) Maxwell, J.A., "Federal Grant Elasticity and Distortion," National Tax Journal, Volume XXII, Number 4 (December, 1969) Maxwell, J.A., FINANCING STATE AND LOCAL GOVERNMENTS, The Brookings Institute, Washington, D.C., 1969 Miller, Edward, "The Economics of Matching Grants: The ABC Highway Program," National Tax Journal, Volume XXVII, Number 2 (June, 1974) Miller, Edward, "Short Run Responses to Changes in the Availability of Federal Funds," Unpublished Department of Transportation Paper (TPI-10), 1972 Miller, Edward, "Effects of Federal Grants in Aid on Local Expenditures," Unpublished Department of Transportation Paper (TPI-10), 1972 386 Miller, Edward, "The Effects of the Revenue Sharing Pass Through in Large Urban Areas," Unpublished Department of Transportation Paper (TPI-10) 1972 Miller, Edward, "Impacts of the ABC Program on Highway Investment," Unpublished Department of Transportation Paper (TPI-10) 1972 Miller, Edward, "Differences in Returns by Road System," Unpublished Department of Transportation Paper (TPI-10) 1972 Mogulof, M.B., "Regional Planning, Clearance, and Evaluation: A Look at the A-95 Process," American Institute of Planners Journal, Volume 37, Number 6 (November, 1971) Monypenny, P., "Federal Grants-in-Aid to State Governments: A Politi- cal Analysis," National Tax Journal, Volume XIII, Number 1 (March, 1960) Musgrave, R.A. and P.B. Musgrave, PUBLIC FINANCE IN THEORY AND PRACTICE, McGraw-Hill Book Co., 1973 Musgrave, R.A..(editor), ESSAYS IN FISCAL FEDERALISM, The Brookings Institution, Washington, D.C., 1965 Neuman, Lance, A TIME STAGED STRATEGIC APPROACH TO TRANSPORTATION SYSTEM PLANNING, Unpublished SM Thesis, Department of Civil Engineering, Massachusetts Institute of Technology, 1972 Oates, W.E., "The Dual Impact of Federal Aid on State and Local Govern- ment Expenditures: A Comment," National Tax Journal, Volume XXI, Number 4 (November, 1968) O'Brien, T., "Grants-in-Aid:Some Further Answers," National Tax Jour- nal, Volume XXIV, Number 1 (March 1971) Osman, Jack W., "The Dual Impact of Federal Aid on State and Local Government Expenditure," National Tax Journal, Volume XIX, Number 4 (December, 1966) Osman, Jack W., "On the Use of Intergovernmental Aid as an Expendi- ture Determinant," National Tax Journal, Volume XXI, Number 4 (December, 1968) Pecknold, Wayne M., EVOLUTION OF TRANSPORT SYSTEMS: AN ANALYSIS OF TIME STAGED INVESTMENT STRATEGIES UNDER UNCERTAINTY, Unpublished PhD Thesis, Department of Civil Engineering, Massachusetts Institute of Technology, 1970 387 Quandt, Richard E. and K.H. Young, "Cross-'Sectional Travel Demand Models: Estimates and Tests," Journal of Regional Science, Volume IX, Number 2 (1969) Roth, G.J., A SELF FINANCING ROAD SYSTEM, Institute for Economic Affairs, London, 1966 Sacks, Seymour and R. Harris, "The Determination of State and Local Government Expenditure and Intergovernmental Flow of Funds," National Tax Journal, Volume XVII, Number 1 (March, 1964) Scott, A.D., "The Evaluation of Federal Grants," Economica, Volume XIX, Number, 76 (November, 1952) Smerk, George M. , URBAN TRANSPORTATION; THE FEDERAL ROLE, Indiana University Press, Bloomington, Indiana, 1965 Smith, A.H., "State Payments to Lcoal Governments in Wisconsin," National Tax Journal, Volume XV, Number 3 (September, 1962) Smith, D.L., "The Response of State and Local Governments to Federal Grants," National Tax Journal, Volume XXI, Number 3 (September, 1968) Stanford Research Institute, BENEFIT/COST ANALYSIS OF HIGHWAY IMPROVE- MENT PROJECTS, SRI Project MU-7362, Stanford, California, December, 1969 Stockfisch, J.A., "Fees and Service Cahrges as a Source of City Revenues," National Tax Journal, Volume XIII, Number 2 (June, 1970) Strotz, R.H., "The Empirical Implications of a Utility Tree, Econo- metrica, Volume 25, Number 2 Teeples, R.K., "A Model of a Matching Grant-in-Aid Program With External Tax Effects," National Tax Journal, Volume XXII, Number 4 (December, 1969) Theil, Henri, OPTIMAL DECISION RULES FOR GOVERNMENT AND INDUSTRY, North Holland Publishing Co., Amsterdam, 1964 Theil, Henri and A.S. Goldberger, "On Pure and Mixed Statistical Estimation in Economics," International Economic Review, Volume 2, Number 1 (January, 1961) 388 U.S. Bureau of the Census, 1967 CENSUS OF TRANSPORTATION, Volume 1, National Travel Survey, Washington, D.C., July, 1970 U.S. Bureau of the Census, GOVERNMENTAL FINANCES IN 1953-1954 (Yearly editions to 1969-1970), Washington, D.C. U.S. Bureau of the Census, STATE GOVERNMENT FINANCES IN 1950 (Yearly edition to 1970), Washington, D.C. U.S. Bureau of Public Roads, HIGHWAY STATISTICS 1950 (Yearly editions to 1970), Federal Highway Administration, U.S. Department of Transpor- tation, Washington, D.C. U.S. Department of Transportation, Office of the Assistant Secretary For Policy and International Affairs, 1972 NATIONAL TRANSPORTATION REPORT, Washington, D.C., 1972 U.S. Department of Transportation, NATIONWIDE PERSONAL TRANSPORTATION STUDY: HOME-TO-WORK TRIPS AND TRAVEL, Volume 8, Washington D.C., August, 1973 U.S. Department of Transportation, ALLOCATION OF HIGHWAY COST RESPON- SIBILITY AND TAX PAYMENTS, Washington, D.C., 1969 U.S. Federal Highway Administration, FINANCIAL BACKGROUND FOR THE 1972 HIGHWAY NEEDS STUDY, Unpublished Report C-1, Washington, D.C., 1972 U.S. Federal Highway Administration, HIGHWAY FINANCE MANUAL, Washing- ton, D.C., 1972 Urban Mass Transportation Administration, CAPITAL GRANTS: FOR URBAN MASS TRANSPORTATION: INFORMATION FOR APPLICANTS, Washington, D.C., June, 1972 Wells, John D. et al, ECONOMIC CHARACTERISTICS OF THE URBAN PUBLIC TRANSPORTATION INDUSTRY, Institute for Denfense Analyses, Arlington, Virginia, February, 1972 Wilde, J.A., "Grants-in-Aid: The Analytics of Design and Response," National Tax Journal, Volume XXIV, Number 2 (June, 1971) Wilde, J.A., "The Expenditure Effects of Grant-in-Aid Programs," Na- tional Tax Journal, Volume XXI, Number 3 (November, 1968) 389 Winch, D.M., THE ECONOMICS OF HIGHWAY PLANNING, University of Toronto Press, Toronto, Ontario, 1963 Young, K.H., "The Synthesis of Time Series and Cross-Section Analyses: Demand for Air Transportation Service," Journal of the American Statistical Association, Volume 67, Number 339 , "The Public Finance Aspects of the Transportation Sector, A Staff Paper Prepared by the Office of Policy and Plan Development, U.S. Department of Transportation, Washington, D.C., May, 1971 , FINANCING STATE AND LOCAL GOVERNMENTS, Proceedings of the Monetary Conference, Nantucket Island, Massachusetts, June 14-16, 1970 ,Sales Management 's SURVERY OF BUYING POWER, (Yearly editions 1950-1970), Bill Brothers Publications, New York, New York 390 Biographical Summary Dr. Sherman was born in New York City on June 22, 1948. He pursued undergraduate studies at the Massachusetts Institute of Technology, receiving a Bachelor of Science degreee in Aeronautical and Astro- nautical Engineering in February, 1971. Dr. Sherman received a Master of Science degree in Transportation Systems Analysis from M.I.T. in June, 1971. His S.M. thesis was entitled "The Airport Access Problem: A Case Study Approach." Dr. Sherman remained at M.I.T. for his doctoral research, concentrating in the field of transportation economics. He submitted his Ph.D. dissertation en- titled "The Impacts of the Federal Aid HIghway Program on State and LOcal Highway Expenditures," in January, 1975. Dr. Sherman's research interests include a wide range of topics relating to transport economics. He is currently employed as a Senior Research Associate for Charles River Associates, Inc., where he is conducting research on Federal energy and environmental policy alternatives, and developing imporved methods for predicting urban travel demand patterns. He has worked as a consultant to the govern- ment of Venezuela, assisting in the development of capital budgeting procedures. Dr. Sherman has also consulted to the U. S. Department of Transportation in a variety of areas including developing proce- dures for assessing urban mobility, and assisting in the design of the National Transportation Study. 391 Appendix A Estimated Parameter Values of the Long Run Revenue Policy Model 392 This appendix presents a complete listing of the regression runs performed on the total expenditure model (TEM). In the figures that follow, each regression run is described by a four character model number, 1112nln2 where: = 4 12 ni= { n2 = S - grant terms stratified by type (Interstate and non-Interstate T - single grant term U - undeflated data set D - price deflated data set 1 - 48 State/14 year pooled data sample 2 - 7 State/14 year pooled data sample 3 - 41 State/14 year pooled data sample 1,2,..., - model specification number E3JAlL2ULESULLS TOTAL EXPENDITURE MODEL !QE_" .QLNhSU SENE RAL1ZfLLLEAS.I2UARtS E-:AIt.1- %k2tk12L55a&z------S LE--.2s3L---89502 a~--- aa~a - F STI MA T E VALUE STANPAPO ERRPP T-STATISTIC FSTrATE VALUE STANflAP) E PPOR T-STATTSTIC; '.A6 -0.650E-06 5.58 0.732F-O7 1.78 8.74 R I. TOT -0.319 0.f'36 8.86 TO L PCT 0.457 0.069 6.62 PrY C HNT -0.601 0.031 19.53 0.018 0.001 17.94 9.468 Ie.24 8.41 A VNIGP -1.146 3.091 12.55 0.605 0.124 4.88 0.6 19 0.043 14.39 w~ - m EU AlL2E.ULUis TOTAL EXPENDITURE MODEL .ENERA2 IL.LAi QUAEl F-STAT: F(10.661) = 238.10 SEE = x3 ~RS0 0 .182 CON STM'NT ESTIMATE VALUE STANDARD FP9PII T-STATISTIC FSTTMATF VALIIF STANOARD EQRDR T -STATISTIC 8.9P 5.55 1.62 RLTOT J . 37 a03 7 SPOW -0 .597E-06 0.796F-37 7.51 TOLPCT 0.355 0. C8 4.3? 0.017 0.001 17.26 0.613 0.123 4.97 10 .639 1.206 8.8? AVNIGP -1 *123 0.097 11.61 -00599 0.030 19.61 AVIGP 0.608 0.043 14.14 BI PTCX 0. 088 0.055 1.58 ko . " -.w .M WA.M-f mom .-~fi.A --__ _ -_ _ _ _ _6 _6 M M - - - - - - - - - - - -W - - -0..- -00 - qwft --M. om. -wpm awmmlmmpwmompommom EU.1_ ALL2 La.EaULIS TOTAL EXPENDITURE MODEL EQL.Na.sul3 GEN-rALIL.ED-LEAi.SQUARES F-STAT: F(1066I1) 231 5FF = 5.-34 R&D = 0.781 CONISTANT cpnp . - ---- o- la -- -MO- ------ FSTIMATF VLIF STANOAPD ERROR T-STATISTIC rSTIMATF VALUCf STANARDF EROR T-STATISTIC 6.73 5.70 1.18 RLTOT -0.333 0 r 36 9.1? -0 .649E-96 0*728'-07 8.91 TOLPCT 0.407 0.372 5.68 K STK IJFAC 0.018 0.001 17.98 &ILE. 0.656 0.125 5.24 q.872 t .t39 8.66 AVNIGP -1.146 0.091 12.61 -o .ss7 0.031 18.83 AVIGP 0.607 0.043 14.08 GOP -3.402 3. 172 2.34 cLn .d& M -1&d _6mw .. mum.- _ ._ - - - - _ _ - __ A&_-J6A - - - - - - - - - - - - - - - - - - - - - - - - - - - .- -MN.- - _ US Ilt ALi22-HEUL S TOTAL EXPENDITURE MODEL !QEt-tU~A' Ift IEUEALELLLEAS1-iQUARLS E= IiELi h -- 2 --- -- 5 1 --- 5 -- 2 3 CONSTANT- C~STTMATF VAIIF STANnAPI) FRPOR T-STATISTIC RSTYM-TF VALUIE STANrAF9 ERROR T-STATTSTIC 4.20 QLTDT -I?47 0.037 6.68 -S pr -. 6CRE-06 O.758F-i7 8.02 TiLPCT C. 784 0.086 3.29 12.852 1.193 10.76 AVNIGP -1.179 0.093 12.71 ALLEAL - -0.652 0.031 21.05 AVIGP 0.530 0.042 12.62 0.016 ).001 15.51 B I PTAX 0.059 0.053 1012 0.20 0.120 6.9? GPQP -0,.508 0.164 3.10 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - wiLw.EmwM- w1w -w-dmmo~ 49- -M 4M. At L.L.61 J9..w6 o64,64 .1p. -w. . . " ma.L-w. -.. . . - mwmppmv EiLLMALI22t-SaTS TOTAL EXPENDITURE MODEL ENE39AL LLL.DEAiIsQUA&LS =SAI- L2Th kztL_2-4LI2 R--$UE &-5fl-___Z2--1 E[STIMATE VALUF STA"FA' ERPPIP T-STAT! STTC ESTIMATP VALIIF cTANOAP D EP PR T-STATI 5TIr CQ 2ArL--BE C.-.-E E---!EAC---_ 1---GL 7.93 -0 .153E-05 9.315 -0.602 '.018 0.659 5.67 C.l04F-)6 1.130 0.031 0.001 0.126 1.4" 7.49 8.24 19.17 17.62 17.62 PL TCT -0.324 o. C 37 5.23 TfL PCT J.401 V0071 8.84 AVNIGP -1. 11 0.093 5.68 AI!GP 0.621 0,044 12.03 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - TOTAL EXPENDITURE MODEL G AF E1L.. .. su iEEALiLJEA ST_QUARE F-STAT3!1 F( 9.h? = '50.79 SEE= ~R&QE2~iItI Aaaa4 =1 -.--. - -_2 _ _ _ _ -- -- _--"- - Ek .C&N]iA.I_ ESTIMATE VALUE STMPANA ERPOR T-STATISTYC PSTIMATE VALUE STtNDAPD FRROR T-STATISTIC 10.01 5.66 1.77 RLTOT -0.330 0.036 9.07 -0.137E-33 0.173F-04 7.9' TOLPCT 3.410 0.070 5.83 A5!K.. 9.360 1 * 128I 8.30 AVNIGP -1.9135 0.093 12.22 .UEA.Q.. -0.600 0.031 19.16 0.018 0.001 17.73 AVIG 0.620 0.043 14.25 0.606 0.126 4.81 .... Mo -- G kflI M- .O--.- -...4. - - .. MwoO- -W ... d- TOTAL EXPE NDITURE MODEL -MQQN.A..S21 ENESALIZEID-L EASiQUAR i F-SrAr: E 9. RRI 2018 SF16 EE 6.57 fllN A NT c pnp K CIK FSTIMATE VALUE STANDAPP ERRIR T-CTATTST T FSTIMATE VALIUE STANQAP FPRfR T-STATISTIC 97.82 8.94 1 0.95 RLTCT -0.127 x cqo 1.41 -0.668E-06 0.737E-06 0.91 T9LPCT 2.772 0.492 5.64 RSO = 2m20 iFAC ECV . TMT -1.340 0.227 5.90 0.006 0.002 3.66 0.209 0.307 0.69 AVNIGP -0.311) 0.161 1.92 -0.542 o.114 4.74 0.657 0.061 10.75 WA 1 x _ - - . _ _ - -. - - - - - -- - - --. IN- _ - - - _ _ _ M 15LUAltl&ESiUUL TOTAL EXPENDITURE MODEL -I24LN-SU22 .G2 f3AU LL.EDLLAi1hS2UAES E-STAT: FIC'. 87) = 15.24 SEE = 6.11 RSQ = .697 FSTIMATF VALUE STANPAPf EPROR T-STATISTIC %-STIMTE VALUE STANOArD FRROR T-STATISTIC 73.5R -O.178E-O5 3.166 -0.616 0.003 -0.416 9.02 0.A65F-36 0.133 0.147 0.002 0.194 8.16 2.O 1.24 4.19 l.41 2.14 PL T'lT -0.032 3.090 o.91 T')L PC T 1.400 u.490 2.86 AVNIGP -0.379 0.208 1.8? AVIGP 0.571 0.091 6.26 9i PTCX 0.484 0.491 0.99 a .646 -;m .m6.&ibdl -U = _L _ _-m Wm__ _ _ _ _ __ _ _ _ _ _ __o _ _ - - - - - - - - - - - - - - - - - - - - - - W- TOTAL EXPENDITURE MODEL .GENEALI LElA.IA QUAfli F-STAT!F( fl.AS41 = 24t.3t SEE = 5 14 RSQ 0.794 --- ----- -- - ----- - - ----- CONSTANT- PSTIMATF VALUE STANDARD FRROP T-STATTSTIC E STIMATE VALUE STANDARD ERROR T-STATISTTC 16.15 5.55 2.91 RLTOT- -<.524 0 .C41 12.75 SPpp -0.478E-06 2.724E-07 6.60 TOLPCT 0.368 0.T71 5.21 .OJEAL.- -0.637 0.034 18.50 0.018 0.001 17.32 KSTK- 8.?74 1.032 8.02 -0.856 0.114 7.51 0.693 0.122 5.67 0.439 0.057 7.68 -Pb q U ."- .0- -.. I. -wo now.-ma-mm AN& JWMA-amx a- EULMA2N-REULIi TOTAL EXPENDITURE MODFI fQODL-Nia_.a2 GENE ALILE!LJEA.SSQUARfS RSQ = 0.799 FSTIMATE VALUE STANDAPD EfRlP T-STATIST IC L2N.IAN2I. 16.24 5.48 2.96 -0.5C8E-06 0.783E-37 6.49 ES T !NATF VALUE STANDAPD EPROR T-STATISTIC 10.050 1.125 8.93 -0.9631 0.034 18.53 3.018 0.001 16.99 RLTOT -2.534 0.043 12.32 0.683 0.121 5.65 TCL PCT 0.393 0.086 4.55 AVNMI-GP -0.919 0.120 7.64 0.415 0.057 7.30 -0.05? 0.056 0.93 -ME-M- 4 A&= AlOWNEWO - 4M d aWW4 aNW- --- AML-OL-L-.dt-.d6- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -. U- . - --PON-- dL-.-401W d ...S t~jMAUI.tLR3E.SU 15 TOTAL EXPENDITURE MODEL fzESERAL QJZEJLEA2.1 UAEES F-ST AT: Ff 8,66b3) z 2)l496 SE E _ .0 ERS z0.JZ Z ESTIMATE VALUE ST NPARD ERROP T-STATISTIC FSTIMATE VALUE STANnAPD ERROR T-STAT1STIC -CO ANI-IiSEQ._M--K... EAINL...0- 24.1? -0.454E-06 13.640 -0.454 0.014 3.307 6.17 0.807E-07 1.655 0.033 0.001 0.138 3.90 5.62 8.24 13.69 13.01 2.21 RLTOT -0.488 0.038 12.84 TOLPCT 0.482 3.378 6.14 A VT &P 0.038 3 .03? 1.17 CD) m.w_ _A - - - - - - - - - - - - - - - Ellbal N....ESals TOTAL EXPENDITURE MODEL LAUDE. TXUU12 .iGENEAL.LLEA I.5$QUARtS E=IAIJ1.EU. LE..QA........ .--.-..-- ESTIMATF VALUE STANDAPD FPRR T-STATISTIC 20.84 6.34 3.45 -0.3 14E-)6 C.844F-OT 3.72 FSTIMATF VALIJF STANDkPn EPROR T-STA T ISTTC 16.553 1.814 9.13 -0.458 C .032 14.C7 0.013 0.001 t2.?9 0.337 0.135 2.50 RL TOT -0.418 0.C3g 13.6? TOLPCT 0.178 0.098 1.83 AVTGP 0.039 0.035 1.11 B! PT c 0.?59 0.056 4.40 0. ampdolm- ---ad- 4 - -1dbAUW..m.m - E5iLeAllMQmESULIS TOTAL EXPENDITURE MODEL EfELALuQ12Uf ' ENERALLLEDLWA AB F-STAT: F( 9.662) = 199.56 SE E= 5.93 RSQ = 0.731 ESTIMATF VALIE STANPARn FRROR T-STATISTIC E ST IMAlI E VA UE STANDARD ERROp T-STATISTIC 19.96 6.23 3.19 RLTfT -0.Sfl? 0.038 13.18 52- 2E------ESTK -0.455E-)6 16.177 0.795E-7 1.756 5.72 9.21 TOLPCT 0.388 0.081 4. 80 AVTGP -0.004 0.033 0.11 .JIEAL. -0.461 0.033 12.96 0.015 0.001 13.30 .o 355 0.138 2.57 GPOP -0.543 0.191 2.85 4:0 C:) .- . t_ -- lgM SZo -mo-fd4mJ-rJ ---m--kfA-M 6&6L- -K JPC.L __-_.------... _.. _I_ W-- E5IefAlL.ESULT TOTAL EXPENDITURE MODEL .QDELQ..JUA F-NEHAUSTLLESSQUARSi F-STAT: F(10.6611 = 113.72 SEE = _5.7B RSO = 0.143 ESTIMATE VALAE STANa)4P ERROR T-STATISTIC FSTIMATC VALUF STANnAPQ ERROR -S T A TI'ST r _LN MAhl__ QI2__EI___UEA_---U0-----G- 8 36.41 -0.32?E-2i6 11.084 -0.534 0.012 0.618 6.9O 0.835E-07 1.411 0.034 0.001 0.136 5.27 3.86 7.85 15.66 10.74 4.53 RITOT -0.374 0.041 q,.16 TOL PCT 11.178 0.098 1.81 AVTGP 0.080 0.032 2.52 B IPT.X 0.252 0.058 4.33 -0.554 0.186 2.98 4P'b 0) -M*-MoM Aw -dlkb..E-.dLIL-dg-MJ6 m dmmw-dr- AM =Mmp - dM-146 A. A6 mg-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0 W-91- LM A2 L&JUEUj.S TOTAL EXPENDITURE MODEL tullE l-N...-l02 .G.ENE A1.E LWAI.lQUA5E F-STAT: Ff Ro R9) = I 9SFF = 7a1l RSQ = 0.9RD STITMATF VA LUE STNPAon FRRnRp T-SrTATJSTIC CNiIANI. p9.12 11 8.81 3.31 7F-05 0.1 16E- J5 2.74 T 1MAT F VA LUF ST ANFAPf ERROR T -STATISTIC .AVLi.. 2.680 0.611 4.38 .ALUEA.. -1.331 Pi. 216 6.06 ml--- 0.001 ).002 0.42 RL T G0T 7. 6 r 2.9C6 -0.647 0.208 3.10 TOLPCT 1.641 0. 189 8.67 0.725 * 101 7.15 0 l , --, I -JL. Abdll;,JLAd Z -W.- Amin... LJ.AL3L bd.A ALIb- - -- - -0- , iSIl!Ali~t-.ZLill TOTAL EXPENDITURE MODEL 1ED2EL.-Z Iu22 UNERALl E LtA.iQUAfE F-ATT F q pI= 1 56 SEE = 7m15 CPnp KS TK a~a~~-a- -a a~- - ~aa~ a - a~ -- rSTIMATF VALUE STJANAFD F RP IR T-STATISTIC CSTIMATE VAL(UF STANfAPD FRRIR T-CTAT!STTC 101.40 9.79 10.35 RL T CT- 13304 3.088 3.45 0.716E-06 '.338E-06 0.76 TOL PcT 3.?90 0.546 6.03 RSO = 2 1fF AC PC v (INYV -1.720 0.241 7.12 0.006 0.002 2.85 0.255 D0135 1 . 88 AVT GP C' .583 0.089 6.49 -0.416 0.218 1.91 BI pT n 0 085 0.096 0.89 0 -AL- - - - J-J6 -w- -- , - . TOTAL EXPENDITURE MODEL M112111. 11!3 GESETAFMO*DUL48 aSM2I 5A37 c-STAT: F( 8.565) = ?43.48 5FF = 5.37 RSO = 0.775 FSTIMATF VALIF STANPAPD ERR2P T-STATISTIC PS TIMATF VAlUt E STANfnADO FQPOR T-CTATISTIC 28.27 -G.357E-06 9.880 -0.528 0.015 0.458 5.60 J.739E-37 1.182 0.034 0.001 0.125 5.05 4.82 8.36 15.79 14.68 3.66 RL TOT --. 643 0. C4') 16.17 T JL PCT . 391 0.374 5.30 0.013 0.028 0.45 P- TOTAL EXPENDITURE MODEL MFDEL..Qa5U3Z tE5ERAU Zt2.LEAS L.3SUA&ES F-STAT! Fl 9.5641 = 21R.R5 5FF = S.34 RSO = 0.777 CTIMATF V ALLF STANDAP ERRR T-STAT!STIC ESTYMATE VALIUE STANDAR') EQPCR T-STATISTTC ?6.46 -).322E-06 10.556 -0.529 0.015 0.482 1.6 J.788E-07 1.239 0.034 0.001 0.124 4.7? 4.38 8.52 15.80 14.19 3.88 RLTlT -0.617 044 14. OC TOLPCTI 0.315 0.990 3.49 AVTGP 0.018 0 .032 0.56 fBIPTQ 0.068 0.057 1.20 C P- Ej1ALL2-_RtES&LLis TOTAL EXPENDITURE MODEL - 2 1~L L2t-2 .5S9 =2 2---S-2x.. F I6MA TF V41 hF 'fTANI f9Q f t F;-IQ T - T A fI 5T IC LST IMAT E VA[III3 SI TAN f) A P' 9 FVfPP T-S 1 t T J c j j &CB~tat 5.L ..-- DttE1 L- EAffi----QEEBEL - -- GNI 12.1? -0.857F-06 8.028 -p.738 9.o? 0.771 7.16 Q.94 3F-07 1 .050 0.04J 0.001 0.159 1.69 9.09 7.65 18.66 17.52 4.84 jL I '31 -C .4%0 0 .O4t 9.7 InI- PCT 0. 598 U.089 6.75 OF FNI -1.103 0.092 14.43 DE F ( 0.642 0.045 17.03 E1A112lQLEiUJJ& TOTAL EXPENDITURE MODEL B-E12LWN...L.112 LfJERE ALU2E.LJE 5_QUARE E-zMA~Lft12adt uIt3-2 fBl ---_L..-3k2t-----a&Q3&iL. Cfl TAFJT ESTIMATF VALUE STANDARD ERRfP T-STATISTIC CSTIMATE VALUIE STANDAPO E"ROP T-STAT!STIC n E FK ITK 11.33 -0.791F-06 11.286 7.04 0.101E-06 1.247 1.61 7.81 9.05 RL TDT -' . 395 0.047 8.40 TOLPCT 3.421 0.112 3*75 DEFNJG -1.123 0.096 11.60 -0.730 0.039 18.81 DEFIG 0.606 0.044 13.70 .ELE.LY. 0.022 0.001 16.95 RI l-PTCX- 3.118 0.071 1.67 0.790 0.156 4.80 40b - - - - - - - - - - - - - - - - - - - --- -_ _ _.& -mw. Nw. EalL! Al12!LRESUi TOTAL EXPENDITURE MODEL LEN BALI ZEDIA&U1UABLS F-STATz Fff0.AF 11 = 233.26 SFF = A.Rfl RSO = .-779 EST[MATF VALUE STANDARD FPRPR T-STATISTIC 8.3? 7.26 1.15 -0.361E-06 0.927F-07 9.28 flEEtESI& 10.389 1.167 8.90 DEFPCY GINI --. JA aa.---------. .U .. -0.715 0.040 18.03 0.023 0.001 17.74 3.808 0.129 5.07 FSTIMATE VALIUE STANDAPO FRROR T-SrTATISTC RLTfOT -0.442 0.046 qe.54 TOLPOT 0.494 0.091 5.39 DEFNIG -16148 0.091 12.59 DEFIG o .607 0.044 13.67 GPOP -0.530 0.218 2.43 0-4 L43 - - - - - - - - - - - - - - - ----m- ,-,- E ilT 12UItEEULLS. TOTAL EXPENDITURE MODEL mF-TT l O EF L - 644 E=STAT: E~lo6601 3222.67 SEE = 6.44 RSO = 0.R802 ESTIMATE VALUF STANDAPO ERROR T-STATISTIC -CC IANlI 33.23 7.64 4.34 -0 . 796E-06 0.963E-07 8.27 .2EEZI. 13.677 1.220 11.21 FSTIMATE VALUF STANDARD FPQJR T-STATI ST IC -0.801 0.039 20.44 .DEELX. 0.020 0.001 15.03 1.040 0.153 6.8! RLTOT -1.323 r.047 6.98 TOLPCT 0.327 0.110 2.97 DEFNIG -1.167 0.092 12.65 DEFIG 0.520 0.043 12.04 BI PTCX 0.087 0.067 1.30 GP9P -0.619 0.207 2.99 .- 441; Jo. As.- -.t- .. .aA.. --b _ j _ 4 0M_____ .--- - -.0 mom-w..-wmm-wmmmmmwmw... Mwww EiLLoAI1MLSES.uLu TOTAL EXPENDITURE MODEL ENERALZE-LEASit.SQUAREI F-' TAT: Ft Qo AR) = 28m00fl SEE= 7.50 RSO = O 741 . ZI- a 1 -- .na a--n-..-.- ABe- ---------- ee M FSTIMATF VALUE STANPAQD FRROR T-STATISTIC 121.10 9.36 12.9 -0.623E-06 0.F79E-06 3.71 -12EK1& 0.776 0.368 2.10 ESTIMATE VALUE STANPARO ERROR T-STATIST IC .IEA!L.. -1.783 0.236 7.56 0.010 0.002 4.97 -0.679 0.099 6.87 RLTOT -0.185 0.101 1. *83 TOLPCT 3.590 0.502 7.15 DEFNIG -0.295 0.132 2.24 DEFl 0.666 0.058 11.50 4C" mvdmpM-dw-dw -.--W -mv- .00 mmmlw.-M TOTAL EXPENDITURE MODEL NQELNQ(3-S 1222 GE&EBALLLQLA.SESQUA5E F-STAT: Ff10. 871 = 17t73 5FF = 7.46 I A^r' ESTIMATE VALUE STANDARD FPROR T-STATISTIC %-STIMATF VALUE STANDAPR F RP T-STATISTIC 87.41 10.94 7.99 RLT.T 0.092 0.10 q 0.84 -0. 179E-05 0 a 106F-05 1.68 TOLPCT 1.789 0.456 3.76 RSO = 0.77 - r- Dr v r TM T 0.005 0.002 ?.07 0.056 O .16c: 0.34 OFFNIG -0.433 0.206 2.10 -0.419 0.231 1.82 -0.859 0*176 4.88 9 FF It; 0.624 0.087 7.17 B! PTQX 0.492 0.549 0.90 -Jb a) -.- a-m-AL a;- -- I J A- dM6Jd-JL -go- - ' ' MIL -AL- Aw M J06 Jklw- - %up ..m - -wm w I--ELuC NI . ESIlfAlItLRE.SULIS TOTAL EXPENDITURE MODEL 2iE 9iEALEQWi S UA t F-STAT: F( 9.5641 = 236.03 SEE = 6.60- RSO = 0.790 rfnlNczTANT ESTTMATE VALIE STANPARD ERROR T-STATISTIC ESTTMATE VLUE STANDAPO FPRFR T-STATIST IC 19.62 7.10 2.76 RLTCT -0.686 0.053 12.99 -0.648F-06 0.928E-37 6.98 TDLPCT 0.444 0.091 4.87 nF FKI C TKt -0.778 0.044 17.64 I)EE-ec. 0.023 0.001 17.01 &nfa _ 0.869 0*157 5.55 8.696 1 .065 8.16 DEFNIG -0.867 0.116 7.48 DE F IQ 0.440 0.060 7.33 4'zb .immommaw-11116-d6w 6 A I ' -at A -M - .- mm A& 3bK -ML. -- "-Mo-mmw _,- ----- om 11FCar TOTAL EXPENDITURE MODEL tQ0F EL..NA SD2 GENERALLIED-EASE-SiLAEAES F-STAT: F(10.5631 = ?16A5 SEE = 6.55 RSO = 0.794 ESTIMATE VALUE STANPAP Y FRROR T-STATISTIC CDNSJ.AU 195 7.C4 2.78 -0.676E-06 0.101E-06 6.72 ESTIMATE VALUF STANDAPD ERROR T-STATISTIC DEEEKSI& 10.153 1. 152 8.81 SUEAC.- -0.771 0.044 17.60 DEER.YZ 0.023 0.001 16.57 0.861 0.155 5.55 -0.*697 0.056 12.44 TOL PCT 0.468 0.111 4.21 DEFNIG -0 .908 0.122 7.44 DEF IG 0.415 0.060 6.94 81 PTCX -0.053 0.072 0.73 4 :b ..- j 00 - - - - - - - - - - - M -.- d- -_-__.NM-_d----- go F-STAT: Ft R 6631 Eii L1fAUlQ!LBE&ULLS TOTAL EXPENDITURE MODEL = 21533 SEE = ltl -R&SQ _fQAZ Z_ ClNSTANT DE FKSTK. ESTIMATE VALuE STANDAP) EPQPR T-STATISTIC ESTIMATE VALUE STANDARD ERROR T-STATISTIC 30.59 7.81 3.92 RLTOT -0.638 0.048 13.27 -0.62 OE-06 0. 102E-06 6.06 TOLPCT 0.576 0.100 5.76 SPOP UFAC. OE EPC-Y 14.757 1.711 8.62 -GINI -0.551 0.042 13.11 0.018 0.001 12.92 0.359 0.175 2.04 DEFTG 0.017 0.033 0.52 Imw - - - - - - - - - - - - - - - - - - - - N . - - --Z= L -m-- -A -11 - -_ _ _ _ _ .P A L --- A M.=. -0 -.-96an A- w -P FiE LALTDL&E&LuLIS TOTAL EXPENDITURE MODEL .MDELJ.Q.STJ2LZ 2ENEaRAU..2 L l.SzJAafia F-STAT Ff 9.aA2) = 203mA SFF = 7.o46 RSO = 0.734 CONSTANT ESTIMATE VALUE STANDARD FRPOR T-STATISTIC E~STIMATE VALUF STANDARD ERROR T-STATISTIC 25.83 7.68 3.36 RLTOT -0.551 0.050 10.99 SP -0.441E-96 0. 108E-06 4.08 TOLPCT 0. 222 0.124 1.79 .JIEA. -0.561 0.041 13.55 QEELCY 0.017 0.001 12.17 2EFK&T 15.012 1.784 8.97 DEFTG o .044 0.035 1.27 0.427 0.172 2.48 BPTCX 0.331 0.076 4.38 ____-__- ~ ~ _ _ _dwSio " _ __OL -0 . L 0 fEUlLAUI.tL-&SULlS TOTAL EXPENDITURE MODEL mDDEL.5a. t1113 (&NERAJLIEDLE A .LSQUAR&E F-STAT: F i q*s i = 1, 9S76 SEF = .S7 -- a a _ -a6 __. .6w A . CONSTANT ESTIMATE VALUE STANPAPD FPROR T-STATISTIC ESTIMATE VALUE STANPARD ERROR T-STATISTIC 24.98 7.98 3.13 RLTOT -0.657 o.048 13.57 spnp -0.622E-06 0. 102E-06 6.12 1TOLPCT 0.496 0. 103 4.81 RSC = n.777 IFAr -0.529 0.042 12.49 * P.EERC. 0.019 0.001 13.19 DFFKSTK 15.419 1.712 9.00 DEFTG 0.004 0.032 0.13 0.447 0.176 2.54 GPOP -n .659 0.243 2.72 4 :Ib - - - - - - - - - - - _-_ _ -- - i -- -- -. om EU1leA112N-EULUS TOTAL EXPENDITURE MODEL GENELALILQEDEASL.SQUAES F-STAlv El t61I -= FF3.22 -SEE = 7f3 -RSU-= O4 ESTIMATE VALUE STANDAR ERROR T-STAT1STIC LDtSIAUI 45.66 A.71 5.24 -0.45 3F-06 0. 106E-06 4.27 11.789 1.437 8.20 FSTIMATE VALUE STANDARD EPROR T-STATISTIC UEAQ. -0.655 0.043 15.13 0.015 0.002 10.61 0.791 0.173 4.58 -L L -0.489 0.052 9.44 TJOL PC T 0.212 0.124 1.71 DEFTG 0.067 0.032 2.08 81 PTCX 0.315 0.074 4.24 GPOP -0. 736 0.236 3.12 N3b Aso. A.d .W.mo__..Go0- ft TOTAL EXPENDITURE MODl. MODEL N Z.D21 F S IETEtALlEDUIL.SQ2U A R.2 F - a I L 1B1 -12 l_. .. 3 E.2-.- 2. -------------------------- --------------------- ESTIMATE VALUE STANDARD ERROR T-STATISTIC CCNiiAI Q4.63 13.92 6.80 0.224E-05 0. t4E-05 1.58 ESTIMATE VALUE STANDAPD ERROR T-ST&TISTIC DfFFKSTK 2.180 0.671 3.25 iFAC- -1.09 7 0.250 4.40 DEEPCY 0.003 0.002 1.07 -0.619 0.271 2.28 RLTOT -0.?86 0.116 2.45 TOL PCT 1.322 0.129 10.25 DEFTG 0.563 o .094 6.00 4-)z E.IlaI.ON-REULI5 - _-. _ _ _ __J-.__ _ ---jL o ESily.All -REULIS TOTAL EXPENDITURE MODEL BUDELNO_.-XI22 fiENE ALLE ASflUARU F-cZTAT! Ft Q. RAI = 16A CFF = A. 92 RSO = nA?9 a~.~-a ~ Mad-a aa n~a~ ESTIMATE VALUE STANDARD ERROR T-STATISTIC ESTIMATE VALUE STANDARD ERROR T-STAT!STIC QaI AIs2 an EEKU uE cD e x---1-h~ 107.32 0.109E-05 0.372 -1.870 0.009 -0.381 11.0C 0.117E-05 0.140 0.275 0.002 0.278 9.10 0.93 2.66 6.81 3.50 1.37 RLTOT -0.368 0.110 3.36 TOLPCT 3.578 0.657 5.45 DEF3G 0.580 0.086 6.76 BIPTC 0.057 0.127 0.45 W-mm...kw s ATIhl-NA_.EULI TOTAL EXPENDITURE MODEL 2DfEL_.JTD31 fGLNERALI.E LFAS L ._ QUARES E-AIA.L 1...23DQ. FF = 6AR DEF KSTK- RQS = (1.772Am - --- _ .- .r --- - = - _ UFAC- OE EPCY FSTIMATF VALuE STANDAPO ERROR T-STATISTIC ESTIMATE VALUE STANDARD EPROP T-STATISTIC 34.84 7.15 4.87 SL T nT -O.8 34 0.058 16.40 -0.498E-06 0.948E-07 5.25 .10LC-T 0.479 0.095 5.05 DEFTG 0.001 o.029 0.04 4'-:1 10.351 1.217 8.51 GINI -0.643 0.043 15.00 0.019 0.001 14.41 0.574 0.160 3.59 .. J6 _ M _ _ _..._ . _ _ _ __~JA 16 oaw o__ EI5!IALLHLRtiULT TOTAL EXPENDITURE MODEL . D E LN.a2 G EBE~lZ LE A SI QMA CFE = C fmcT AN T oP nE cK rTK UFAC nFFPrY rl NT -a& ~~ ~ a~ a.- - - .. FSTTMATE VALUE STANTARD ERROR T-STATISTIC ESTIMATE VALUF STANDAI) ERRPOR T-STATISTIC 32.15 7.14 4.50 OR LTO T -0.OA1 0.056 14.21 -0.455F-06 0.101E-06 4.50 T...L PC T %.382 0.115 3.31 F-TAT:AT Ft Q.AA4I = 2t 2 RQ = 0 77S -0.641 0.043 15.00 0.019 0.001 13.93 11.340 1.290 8.79 DEFTG 0.002 0.032 0.05 0.612 0.159 3.86 0.082 0.073 [.12 4N) L- A *= I-10--I-L- -ZX2 %Jxa :-- - _ _ _.. .. aj__ L._ .- _ 0 ]" jLdj~d- - .I j L .-- - -..&Xaj 427 Appendix B Derivation of Derivatives and Elasticities from the Expenditure Mndels 428 This appendix sets forth the derivation of derivatives and elasticities from the long run revenue policy model, and the short run allocation model. Moreover, it will be shown how the results from these two models can be combined to indicate the total change- on both revenue and allocation- resulting from changes in the level of the explanatory variables. The short run allocation model takes the form If(1) .=E. = f where S. = share of expenditure devoted to category j E = expenditures on category j R = E = total expenditures (State and Federal I funds) f. = f(X) = n XJk or iejk Xk kej k We wish to derive the form of both the derivative of E. with respect to Xk ,DE. , and the elasticity of E. with respect to k kE 3 Xk X ks'n E /X k From (1) we get (2) = R j = R(X) jL. i f (X) 429 But R(X) is related to the estimated form of the long run revenue policy model. The long run revenue policy model takes the form: (3) Rown, -pc a + I RMXm m where Rown,.pc = total per capita expenditures from states own sources (i.e. exclusive of Federal payments to the States, F). a= estimated coefilcients Thus, R own, pcin (3) is related to R in (2) by: (4) R = SPOP *(Rown,p + FPC) where SPOP state population Fpc = Federal highway payments per capita Assuming a long run static solution1 whereby F = GPC where Gpc = per capita highway grants, 1. Assuming that the states ultimately expend all Federal grants made available, differences between GPC and FPC can be attributed to short run, transient responses. In the long run, it can be assumed that Federal payments will eventually "settle down" to the rate of Federal grant availability. (5) 430 the long run revenue policy model can be rewritten as: (6) R += (s+mXm+ (1 + ) Gpc )*SPOP Returning to equation (2) we can now define the derivative of E with respect to Xk as: (7) @E . Xk = Sij kX+ R s. ak The corresponding elasticity is simply: (8) Ej/Xk Xk E.3 SaE ax k R Xk x = E. ax ak xk 3 TR ) = Xk R a R aX k Xk 3 as. aXk - R/Xk + Sj/Xk 431 The Product Form Model In this case, the specification of each share takes the form: T1 Xkj k Ej n (9) s. = = ~dj where: n = share numerator d = share denominator k = estimated share modeljk coefficients Assume variable Xp appears in the share numerator and one or more of the fi in the share denominator. The derivative of the numera- tor with respect to Xp takes the form: aa- &1jkj n (10) = Jpp Xk jk Xp kjp kfp By the same reasoning, the derivative of the share denominator with respect to XP is: 432 (11) - I. p i p Using these results, we can now derive: 2 as. and(12) = d - n - p =(Y Gd-n - n f = s~ (1 - s) p p a. - sI Y s i/jI Returning to equation (7), the derivative of expenditures on category i with respect to variable Xp is: (13) aE = s n + {sR (1 - sQ )pp - s4 i } But from (6), If the variable in question X = SPOP, then apop= 0+ 2 S SPOP (14) 3E Thus, we can with respect (15) KE. axP = SPOP now state the final to variable X : = SPOP + The corresponding elasticity for simply: (16) /X p X SPOP R form of the derivative of E { s~ (I - s.) S. -s Ot 8 Ps } i hj the product form model is + (1-s.) S. - a s3 Jp iPi Ivi Special Cases: The Product Form Model In the derivation of the derivatives and elasticities of the expenditure models, on the preceding pages, it was assumed that the explanatory variables X enter into the allocation model as given in equation (9). In the actual estimated form of the models, there were two exceptions to this specification. The first concerns the highway grant variables, which enter several of the expenditure shares as either specific grant types (e.g. Interstate, Primary, Secondary) or as aggregates across 433 434 grant categories (e.g. total non-Interstate grants, total grants). We are interested in deriving the derivatives and elasticities of expenditures with respect to each of the categorical grant types. Since the derivation in this instance follows the same reasoning as in the preceding section, the results are presented without a detailed derivation. Let G I G, G s GNI GT - Interstate grants - Primary grants - Secondary grants - Gp + GS = non-Interstate grants - Total Grants From equation (6), it is clear that: -A(17) -G = (1 + ) SPOP, for g = I, P, S Using this result in equation (7), the derivatives of expenditures with respect to grant terms take the form: (18) aE. -tag = s.'(l + 6 )-SPOP + R { s -() -s g + yAjNI+ G - G ) s } A(OXj &* GNIczNI 435 for g = I, P, S and = 0 if g=I{l ifg= P or S The corresponding derivatives follow directly from equation (18): (19) (E /G (1 + 0g ) G SPOP + (1 -s R + G + taT - NI T GG(ig + 6i aiNI + aiT)si i j NI The second exception to the general derivation of elasti- cities and derivatives concerns the population variable, SPOP. This variable appears in several of the expenditure shares in both direct form, and as the denominator of the variable measuring capital per capita (KSTK). In this case, we can rewrite equation (9) as: S jSPOP- CAPTL jKSTK X jk XAk (20) S(Xk SPOP i (SPOP A iKSTK X i-- XkI k where: CAPTL = highway capital stocks 436 The derivative and elasticity of share s with respect to SPOP can be written respectively as: as. = LIISPOPI~2KSTK) s (l -si) - SPOP &iSPOP - &iKSTK 3 13 SPOP (22) 3Is /SPOP As noted in of total expenditures, (1i s) (&jSPOP ~ &IjKSTK) . s i(iSPOP - &iKSTK) itj the footnote on page , the derivative R with respect to population is: - +2U SPOP(23) Thus we can now state the form of the 'derivative and elasticity of E with respect to SPOP: (24) = Si( + 2 SPOP SPOP) + 14is.{(jSPOP 7 SjKSTK) (1 - s ) - .. i SPOP ~ -iKSTK)5i} (21) 437 SOP A A(25) TE./SPOP = - o ( + 2$Spop) + (&jSPOP - JKSTK) (1 - - j (&iSPOP - CiKSTK)*Si The Exponential Form Model The derivatives and elasticities from the exponential form allocation model differ from the previously presented results of the product form model. In this case, each share is specified as: (26) s. = k a IIe 'i hei Following the same reasoning as expressed in equations (10) through (12), the derivative of expenditure share j with respect to a particular variable Xp is given by: (27) as. = A s (1 - s) - s axJip 3 3j S. The corresponding elasticity is simply: (28) rsx = j X ( - s ) - Xp{j .S 438 Substitutin these results in equations (7) and (8), we get the derivative and elasticity of E with respect to X for the exponen- tial form allocation model: (29) = OP + R{& s (1 - si) - s a s} pp JjL (30) X SPOP + 0.X (1 - sj) - aX s R Special Cases: The Exponential Form Model As in the product type allocation model, the general form of the derivatives and elasticities for the exponential form allo- cation model do not apply in the case of the population variable and the highway grant terms. The derivatives and elasticities from the exponential model, for these special cases are presented below. (31) = (1 + ) SPOP + R{ s (1 - s ) (a. + gg 6 i JfNI + aJT) - si(ig + YiNI + iT 1The notation used here is identical to the definitions given in the section "Special Cases: The Product Form Model." 439 = -) SPOP + G {(1 - s.) (. + S ajNI + &jT ig5 for g = I, P, S and 6, 0 if g1I and 6~ ={ 1 i gII1 f 0I = s O +C 2SPOP SPOP) + ReKSTK-s6.{(1-s.) (&jSPOP- + 5SiNI jI+ &iT) s } LjKSTK) - SPOP iSPOP _ i S K ) SPOP + P = T(0 + 20po SPOP) + KSTK { 3(1 - s ) (jSPOP SPOP - aSPOP S -aiKSTK) si 5jIKSTK) - (32) T'E /G (33) aE.i (34) TE /SPOP 440 Appendix C Derivatives and Elasticities from the Two Expenditure Models 441 This appendix contains the derived elasticities and derivatives from the expenditure models described in Chapters IV and V. On the pages that follow, the tables are titled "Short Run" or "Long Run" Elasticities (or Derivatives). The short run measures pertain to the short run expenditure model (SRAM), where by definition the States' budgets are fixed. The long run elasticities and derivatives reflect the empirical analysis integrating the results of the SRAM and TEM, and thus describe States' long run expenditure responses to Federal grants (inter alia) where budget levels can change. The derivatives and elasticites are presented for both the product form and exponential form of the SRAM (see Chapter V.). 442 PRODUCT FORM SPECIFICATION OF THE SRAM FORTY EIGHT STATE SAMPLE SHORT RUN MODEL ELASTICiTIES SHAR E VARI ABLE SPOP UFAC PCY G I N I KS TK TS PMR PCCRMT PCM F TOLPCT RLTOT AVI G AV PG AVSG INTERSTATE -0.682 0.402 -0.201 -0.033 -0.169 -0.031 -0.011 -0.001 -0.059 0.029 0.873 -0.070 -0.002 PRI MARY 0.069 0.192 -0. 201 -0.033 0. 112 -0.031 -0. 011 -0.001 0.023 0. 029 -0.416 0. 534 -0.045 SECONDARY 0.105 -0.280 -0.201 0.298 0.026 0.277 0.026 -0.001 0.023 0.029 -0.433 -0.176 0.261 443 PRODUCT FORM SPECIFICATION OF THE SRAM FORTY EIGHT STATE SAMPLE SHORT RUN MODEL ELASTICITIES SHARE NONFASYST 0.650 -0.884 -0.201 -0.033 0.026 -0.031 0. 183 -0.001 0.023 -0.488 -0.161 -0.130 -0.026 MAI NT -0.515 -0.036 -0.201 -0.033 0.285 -0.031 -0.011 0.007 0.023 -0.041 0. 082 -0.062 0. 001 OTHER 0.975 -0.036 0.616 -0.033 -0.068 -0.031 -0.011 -0.001 0.023 0.028 -0.505 -0.226 -0.066 VARI ABLE SPOP UFAC PCY GiNI KSTK TS PMR PCCRMT PCMF TOLPCT RLTOT AVI G AVPG AVSG 444 PRODUCT FORM SPECIFICATION OF THE SRAM SEVEN STATE SAMPLE SHORT RUN MODEL ELASTICITIES SHAR E VARIABLE SPOP UFAC PCY GI NI KSTK TS PMR PCCRMT PCM F TOLPCT RLTOT AVIG AVPG AVSG INTERSTATE -0.573 -0.128 -0.049 0.022 -0.077 -0.150 -0.014 -0.021 0.015 0.189 0.774 -0.016 0.084 PRIMARY 0.126 0.366 -0.049 0. 022 -0.021 -0.150 -0. 014 -0.021 -0.006 0.189 -0.217 0. 379 0.035 SECONDARY 0.085 0.726 -0.049 -0.168 -0.211 1.150 -0.038 -0.021 -0.006 0. 189 -0.759 -0.105 -0.282 445 PRODUCT FORM SPECIFICATION OF THE SRAM SEVEN STATE SAMPLE SHORT RUN MODEL ELASTI C ITI ES SHARE VARIABLE NONFASYST MAINT OTHER spop 1-122 0.114 0.347 UFAC -0.867 -0.245 -0.245 PCY -0.049 -0.049 0.232 GINI 0.022 0.022 0.022 KSTK -0.211 0.110 0.238 TS PMR -0.150 -0.150 -0.150 PCCRMT 0.348 -0.014 -0.014 PCMF -0.021 0.103 -0.021 TOLPCT -0.006 -0.006 -0.006 RLTOT -0.161 0.131 -0.750 AVIG -0.962 -0.076 -0.186 AVPG - -0.375 -0.117 -0.149 AVSG -0.115 0.028 0.010 446 PRODUCT FORM SPECIFICATION OF THE SRAM FORTY ONE STATE SAMPLE SHORT RUN MODEL ELASTICITIES SHARE INTERSTATE -0.406 0.314 -0.162 -0.037 -0.174 -0.032 -0.010 0.005 -0.104 0. 024 0.781 -0.124 0.112 PRIMARY -0. 117 -0.254 -0.162 -0.037 0.070 -0.032 -0.010 0.005 0.041 0.024 -0.397 0.617 -0.157 SECONDARY -0.102 -0.339 -0.162 0. 343 0. 075 0. 292 0. 030 0. 005 0. 041 0. 024 -0.401 -0. 193 0. 140 VARIABLE SPOP UFAC PCY GINI KSTK TSPMR PCCRMT PCMF TOLPCT RLTOT AVIG AVPG AVSG 447 PRODUCT FORM SPECIFICATION OF THE SRAM FORTY ONE STATE SAMPLE SHORT RUN MODEL ELASTiCITIES SHARE VARIABLE SPOP UFAC PCY GINI KSTK TS PMR PCCRMT PCMF TOLPCT RLTOT AVI G AVPG AVSG NONFASYST 0.406 -0.663 -0. 162 -0.037 0.075 -0.032 0.155 0.005 0.041 -0.472 -0.006 -0.096 0.221 MAINT -0.361 0.050 -0.162 -0.037 0.200 -0.032 -0.010 -0.035 0.041 0.003 0. 102 -0.066 0.338 OTHER 0.690 0.050 0.465 -0.037 -0.003 -0.032 -0. 010 0. 005 0.041 0. 012 -0.441 -0. 217 -0. 253 448 PRODUCT FORM SPECIFICATION OF THE SRAM FORTY EIGHT STATE SAMPLE SHORT RUN MODEL DERIVATIVES SHARE INTERSTATE -.105E 02 0.402E08 -0.474E 04 -0.524E 07 -0.172E 08 -0.221E 03 -0.172E 08 -0.398E 06 -0.103E 09 0.661E 07 0.111E 01 -0.317E 00 -0.170E-01 PRIMPRY -.753E 00 -0.136E08 -0.335E 04 -0.371E 07 0.808E 07 -0.157E 03 -0.122E 08 -0.281E 06 0.287E 08 0.468E 07 -0.374E 00 O.172E 01 -0.354E 00 SECONDARY 0.578E 00 -0.100E 08 -0.170E 04 0.167E 08 0.940E 06 0.707E 03 0.147E 08 -0.142E 06 0.145E 08 0.237E 07 -0.197E 00 -0.286E 00 0.104E 01 VARIABLE SPOP UFAC PCY GINI KSTK TSPMR PCCRMT PCMF TOLPCT RLTOT AVIG AVPG AVSG 449 PRODUCT FORM SPECIFICATION OF THE SRAM FORTY EIGHT STATE SAMPLE SHORT RUN MODEL DERIVATIVES SHARE VAR I ABLE SPOP -J FA C PCY GINI KSTK TSPMR PCCRMT P CM F TOLPCT RLTOT AVIG AVPG AVSG NON FASYST 0.134E 01 -0.118E 08 -0.f633 E 03 -C.701E 06 0.351E 06 -0.296E 02 0.379E 08 -0.531E 05 0.-41E 07 -0.146E 08 -0. 273E-01 -0. 71E-01 -0.390E-01 MAINT -0.378E 01 -0.169E 07 -0.226E lL4 -0.250E 07 0.138E 08 -0.106E 03 -0.821E 07 0.122E 07 0.193E 08 -0.445E 07 0. 495E- 01 -0.135E 00 0.774 E -02 OT H E R 0. 131E -0. E10E 0.127E -0. 4558E -0. 601E -0. 193E -0. 150E -0.347E 0.35 4E 0.5143E -0.561E -0. 3 99 E -0. 637E 02 07 05 07 07 03 08 06 08 07 00 00 00 450 PRODUCT FORM SPECIFICATION OF THE SRAM SEVEN STATE SAMPLE SHORT RUN MODEL DERIVATIVES SHARE VARIABLE INTERSTATE PRIMARY SECONDARY SPOP -0.930E 01 0.150E 01 -.553E 00 U5AC -0.114E 08 0.238E 08 0.259E 08 PCY -0,888E 03 -0.649E 03 -0.356E 03 GIN! 0.231E 07 0,..69E 07 -0.710E 07 KSTK -0.481E 07 -0.957E 06 -0.52E 07 TSPMR -0.870E 03 -0.636E 03 O.268E 04 PCCRMT -0.412E 08 -0.301E 08 -0.448E 08 PcMP -0.102E 08 -0.746E 07 -0.409E 07 TOLPCT 0.525E 08 -0.155E 08 -0.851E 07 RLTOT 0.365E 08 0.267E 08 0.146E 08 AVIG 0.9572 00 -0.196E 00 -0.376E 00 AVPG -0.679E-01 0.118E 01 -0.179E 00 AVSG p.645E '0 0.194E 00 -O.66E 00 451 PRODUCT FORM SPECIFICATION OF THE SRAM SEVEN STATE SAMPLE Si-ORT RUN ICDEL DERIVATIVES SHARE VARIABLE SPOP UFAC PCY G1 N KS TK TS PMR PCCAIT P CM F TULPCT R L T AVIG AV PG AVSG ON FAS Y.ST 0.29 E -0. 124E -0. 143E O.371E -0. 213E -0.140E 0.165E -3.164E ~-O.500E -O.191E -0.257E -0 .142 E MAINT 01 08 03 06 07 03 09 07 07 07 00 00 00 0.109E 01 -0.129E 08 -0.524E 03 0.136E 07 0.407E 07 -0.5i14E 03 -0.243E 08 0.295E 08 -0.123E 08 0.149E 08 -0.53 2E-01 -C.295E 00 0.126E 00 C THE R 0.340E 01 -0.132E 08 0.255E 04 0.139E 07 0.899E 07 -0.526E 03 -0.249E 08 -0.517E 07 -0.128E 08 -0.874E 08 -0.139E 00 -0.384E 00 0. 465E-01 452 PRODUCT FORM SPECIFICATION OF THE SRAM FORTY ONE STATE SAMPLE SHORT RUN MODEL DERIVATIVES SHARE INTERSTATE. 0.799E 00 -0.865E 07 -0.509E 03 -0.799E 06 0.106E 07 -0.300E 02 0.293E 08 0.243E 06 0.864E 07 -0.139E 08 -0.908E-03 -0.566E-01 -0.644E-02 PRIMARY -0.252E 01 0.232E 07 -0.181E 04 -0.284E 07 0.997E 07 -0.106E 03 -0.666E 07 -0.586E 07 0.307E 08 0.266E 06 0.594E-01 -0.133E 00 0.398E-01 SECONDARY 0.972E 01 0.468E 07 0.104E 05 -0.571E 07 -0.306E 06 -0.214E 03 -0.134E 08 0.174E 07 0.618E 08 0.254E 07 -0.517E 00 -0.915E 00 -0.556E 00 VARIABLE SPOP UFAC PCY GINI KSTK TSPMR PCCRMT PCMF TOLPCT RLTOT AVIG AVPG AVSG 453 PRODUCT FORM SPECIFICATION OF THE SRAM FORTY ONE STATE SAMPLE ShORT RUN MODEL DERIVATIVES SHARE VARIABLE SPOP UFAC PCY GINI KSTK TSPMR FCCRMT PCMF TOLPCT RLTOT AVIG AVPG AVSG NONFASYST 0.799E 00 -0.865E 07 -0.509E 03 -0.799E 06 0.106E 07 -0.300E 02 0.293E 08 O.243E 06 O.864E 07 -O.139E 08 -0 .908E-03 -C.566E-01 -0.6L- 4E-02 MAINT -J.252E 01 0.232E 07 -0.181E 04 -0.284E 07 O.997E 07 -0.106E 03 -0.66FE 07 -C .586E 07 O.307E 08 0.266E 06 0.59 4E-01 -0.138E 00 0.398E-01 OTHER 0.972E 0.468E 0.IO4E -0.571E -0. 306E -0. 214E -3.134 E 0.174 E O.618E 0. 254E -0.517E -0.915E -. 5S6E 01 07 05 07 06 03 08 07 08 07 00 00 00 454 PRODUCT FORM SPECIFICATION OF THE SRAM FORTY EIGHT STATE SAMPLE LONG RUN MODEL ELASTICITIES SHARE VARIABLE SPOP UFAC PCY GINI KSTK TSPMR PCCRMT PCMF TOLPCT RLTOT AVI G AVPG AVS G INTERSTATE 0.330 0.396 0.623 -0.029 -0.067 -0. 031 -0. 011 -0.001 -0. 059 0.028 1.232 -0. 070 -0.002 PRIMARY 0.943 -0.198 0.623 -0.029 0. 214 -0. 031 -0.011 -0. 001 0.023 0.028 -0.057 0.534 -0.045 SECONDARY 1.117 -0.287 0.623 0.302 0.127 0.277 0.026 -0.001 0.023 0.028 -0.074 -0.176 0.261 455 PRODUCT FORM SPECIFICATION OF THE SRAM FORTY EIGHT STATE SAMPLE LONG RUN MODEL ELASTICITIES SHARE NONFASYST 1.662 -0.890 0.623 -0.029 0.127 -0.031 0.183 -0.001 0.023 -0.489 0.198 -0.130 -0.026 OTHERMAINT 0,497 -0.042 0.623 -0.029 0.387 -0.031 -0.011 0.007 0.023 -0.043 0.440 -0.062 0.001 1.987 -0.042 1. 440 -0.029 0.034 -0.031 -0.011 -0.001 0. 023 0.026 -0. 146 -0.226 -0.066 VARIABLE SPOP UFAC PCY GINI KSTK TSPMR PC C RMT PCMF TOLPCT RLTOT AVI G AVPG AVS G 456 PRODUCT FORM SPECIFICATION OF THE SRAM SEVEN STATE SAMPLE LONG RUN MODEL ELASTICITIES SHARE VARIABLE SPOP UFAC PCY GINI KSTK TS PMR PCCRMT PCMF TOLPCT RLTOT AVI G AVPG AVSG INTERSTATE 1. 326 -0.139 0.188 0.018 -0.075 -0.150 -0.014 -0. 021 0.016 0.189 1.159 0.031 0.110 PRIMARY 2.026 0.355 0.188 0.018 -0.019 -0.150 -0. 014 -0.021 -0.006 0.189 0.168 0.425 0.061 SECONDARY 1.985 0.715 0.188 -0.172 -0.209 1.150 -0.038 -0.021 -0.006 0.189 -0.374 -0.058 -0.256 457 PRODUCT FORM SPECIFICATION OF THE SRAM SEVEN STATE SAMPLE LONG RUN MODEL ELASTICITIES SHARE NONFASYST 3.021 -0.878 0.188 0.018 -0.209 -0.150 0.348 -0. 021 -0.006 -0.162 -0.576 -0.328 -0.089 MAINT 2. 014 -0.256 0.188 0. 018 0.113 -0.150 -0.014 0.103 -0.006 0.131 0.310 -0.071 0. 054 OTlER 2.247 -0.256 0.468 0.018 0. 240 -0.150 -0.014 -0.021 -0.006 -0.750 0. 200 -0.103 0. 036 VARIABLE S POP UFAC PCY GINI KSTK TSPMR PCCRMT PCMF TOLPCT RLTOT AVIG AVPG AVSG 458 PRODUCT FORM SPECIFICATION OF THE SRAM FORTY ONE STATE SAMPLE LONG RUN MODEL ELASTICITIES SHARE INTERSTATE 0. 754 0.307 0.690 -0. 033 -0.086 -0. 032 -0. 010 0.005 -0.104 0.021 1.098 -0. 115 0.115 PRIM ARY 1. 042 -0. 261 0.690 -0. 033 0.157 -0.032 -0. 010 0. 005 0.041 0. 021 -0. 080 0.626 -0.154 SECONDARY 1.057 -0.346 0. 690 0. 348 0.162 0.292 0.030 0.005 0.041 0.021 -0. 084 -0.184 0.144 VARIABLE SPOP UFAC PCY GINI KSTK TSPMR PCCRMT PCMF TOLPCT RLTOT A V I G AVPG AVSG 459 PRODUCT FORM SPECIFICATION OF THE SRAM FORTY ONE STATE SAMPLE LONG RUN MODEL ELASTICITIES SHARE VAR I A BLE SPOP UFAC PCY G I N I KSTK TSPMR PCCRMT PCM F TOLPCT RLTOT AVI G AVPG AVSG NONFASYST 1.565 -0.670 0.690 -0.033 0.162 -0. 032 0.155 0.005 0. 041 -0.475 0.312 -0.087 0.224 MA I NT 0.799 0. 043 0.690 -0.033 0.287 -0.032 -0.010 -0.035 0. 041 -0.0Oo 0.419 -0.057 0. 341 0 TH ER 1.850 0.043 1.318 -0.033 0.084 -0. 032 -0. 010 0.005 0.041 0.009 -0.124 -0.208 -0.249 460 PRODUCT FORM SPECIFICATION OF THE SRAM FORTY EIGHT STATE SAMPLE LONG RUN MODEL DERIVATIVES SHARE VARIABLE SPOP UFAC PCY GiNI KSTK TSPMR PCCRMT PCMF TOLPCT RLTOT AV I G AVPG AVSG INTERSTATE 0.507E 01 0.395E 08 0.147E 05 -0.460E 07 -0.686E 07 -0.221E 03 -0.172E 08 -0.398E 06 -0.103E 09 0.627E 07 0.157E 01 -0.317E 00 -0. 170E-01 PRIMARY 0.103E 02 -0.140E 08 0.104E 05 -0.325E 07 0.154E 08 -0.157E 03 -0.122E 08 -0.281E 06 0.290E 08 0.444E 07 -0.5 16E-01 O.172E 01 -0.354E 00 SECONDARY O.615E 01 -0.103E 08 0.526E 04 0.170E 08 0.464E 07 O.707E 03 0.147E 08 -0.142E 06 0.147E 08 0.225E 07 -0.336E-01 -0.286E 00 0.1O4E 01 461 PRODUCT FORM SPECIFICATION OF THE SRAM FORTY EIGHT STATE SAMPLE LONG RUN MODEL DERIVATIVES SHARE VARIABLE SPOP UFAC PCY GINI KSTK TSPMR PCC.RMT PCMF TOLPCT RLTOT AV I G AV PG AVSG NONFASYST O.342E 01 -0.119E 08 0.196E 04 -0.614 E 06 0.173E 07 -0.296E 02 0.379E 08 -0.531E 05 0.543E 07 -0.147E 08 0. 33 6E-01 -0. 791E-01 -0.390E-01 MAINT 0.365E 01 -0.201E 07 0.701E 04 -0.219E 07 0.188E 08 -0.106E 03 -0.821E 07 0.122F 07 0.196E 08 -0. 461E 07 0.267E 00 -0.135E 00 0. 774E-02 OTHER 0.267E 02 -0.368E 07 0.297E 05 -0.402E 07 0.302E 07 --0.193E 03 -0.J50E 08 -0.347E 06 0.358E 08 0.513E 07 -0.162E 00 -0.899E 00 -0.5&7F 00 462 PRODUCT FORM SPECIFICATION OF THE SRAM SEVEN STATE SAMPLE LONG RUN MODEL DERIVATIVES SHARE VARIABLE INTERSTATE PRIMARY SECONDARY SPOP 0.215E 02 0.240E 02 .129E 02 UFAC -0.L24E 08 0.231E 08 O.255E 08 PCY 0.342E 04 0.250E 04 0.137E 04 GIN, 0.191E 07 0.140E 07 -0.726E 07 KSTK -0.466E 07 -0.8h6E 06 -0.523E 07 TSPIR -0.870E 03 -0.636E 03 O.268E 04 PCCRMT -0.412E 08 -0.301E 08 -0.448E 08 PCMF -0.102E 08 -0.746E 07 -0.409E 07 TOLPCT 0.546E 08 -0.140E 08 -0.770E 07 RLTOT 0.36 4E 08 0.266E 08 0.146E 08 AVIG 0.143E 01 0.152E 00 -0.185E 00 AVPG 0.130E 00 0.132E 01 -0.996E-01 AVSG 0.843E 00 0.339E 00 -0.787E 00 463 PRODUCT FORM SPECIFICATION OF THE SRAM SEVEN STATE SAMPLE LONG RUN MODEL DERIVATIVES SHARE VARIABLE NONFASYST MAINT OTHER SPOP 0.789E 01 0.193E 02 0.220E 02 UFAC -0.126E 08 -0.135E 08 -0.138E 08 PCY 0.531E 03 0.202E 04 0.516E 04 GINI 0.308E 06 0.113E 07 0.116E 07 KSTK -0.210E 07 0.416E 07 0.908E 07 TSPMR -0.140E 03 -0.5l14E 03 -0.526E 03 PCCRMT 0.165E 09 -0.2L43E 08 -0.249E 08 PCMF -0.164E 07 0.295E 08 -0.617E 07 TOLPCT -0.309E 07 -0.113E 08 -0.116E 08 RLTOT -0.5C2E- 07 0.14 9E 08 -0.875E 08 AVIG -0.115E 00 0.226E 00 0.149E 00 AVPG --0.225E 00 -0.178E 00 -0.264E 00 AVSG -0.110E 00 0.243E 00 0.166E 00 464 PRODUCT FORM SPECIFICATION OF THE SRAM FORTY ONE STATE SAMPLE LONG RUN MODEL DERIVATIVES SHARE VARIABLE SPOP UFAC PCY GINI KSTK TSPMR PCCRMT PCv= TOLPCT ALTOT AV I G AV PG AVSG INTERSTATE 0.115E 0.311 F 0. 168E -0. 540E -0.944E -0. 233E -0. 145E 0. 189E -0.1.72E 0. 479E 1.140E -0. 526E -0. 137E 02 08 05 07 C7 03 03 07 09 07 01 00 00 PRIMARY 0.112E 02 -0.186E 08 0.118E 05 -0.380E 07 0.121E 08 -0.164E 03 -0.102E 08 0.133E 07 0,475E 08 0.337E 07 -0. 719E-01 0.202E 01 -0.318E 00 SECONDARY 0.566E 01 -0.123E 08 0.589E 04 0.202E 08 0.622E 07 O.748E 03 0.156E 08 0.661E 06 0.237E 08 0168E 07 -0.3 74E-01 -0.295E 00 0.106E 01 465 PRODUCT FORM SPECIFICATION OF THE SRAM FORTY ONE STATE SAMPLE LONG RUN MODEL DERIVATIVES SHARE VARIABLE SPOP UFAC PCY G I N I KSTK TSPMR PCCRMT PCMF TOLPCT RLTOT AVIG AV PG AVSG NOIFASYST 0.308E 01 -0.874E 07 0.216E 04 -0.696E 06 0.229E 07 -0.300E 02 0.293E 08 0. 243E 06 0.870E 07 -0.140E 08 0. 511E-01 -0. 514E-01 -0. 123E-02 MA NT 0.558E 01 0.199E 07 0.768E 0 ( -0.2 47E 07 0.14 3E 08 -0.106E 03 -0.666E 07 -0.586E 07 0.309E 08 -0.993E 04 0.?L44E 00 -C.120E 00 0.5 83E-01 OTHER 0. 260E 0.400E 0.295E -0. 498E 0.8 48E -0.214E -0.134E 0.174E 0. 622E 0. 198E -0. 145E -0. 878E -0. 519E 02 07 05 07 07 03 08 07 08 07 00 00 00 466 EXPONENTIAL FORM SPECIFICATION OF THE SRAM FORTY EIGHT STATE SAMPLE SHORT RUN MODEL ELASTICITIES SHARE VARIABLE SPOP UFAC PCY GINi KSTK TSPMR PCCRMT PCMF TOLPCT RLTOT AVI G AVPG AVSG INTERSTATE -0. 469 0.554 -0. 242 -0. 015 0.314 -0.014 0.007 0.008 -0.164 0.065 0.554 -0.057 0.012 PRIMARY -0.018 -0.415 -0.242 -0.015 -09.026 -0. 014 0.007 06008 0. 064 06065 -0.108 0.379 -0.058 SECONDARY 0.087 -0.579 -0. 242 0.138 -0.051 0.121 -0.082 0.008 0. 064 0.065 -0.435 -0.229 0.031 467 EXPONENTIAL FORM SPECIFICATION OF THE SRAM FORTY EIGHT STATE SAMPLE SHORT RUN MODEL ELASTICITIES SHAR E NONFASYST 0.308 -0.569 -0.242 -0.015 -0.051 -0. 014 0.063 0. 008 0.064 -1.345 0.404 0.086 0.071 MAl NT -0.157 0.017 -0.242 -0.015 0.077 -0.014 0.007 -0.0 54 0.064 -0.248 0.230 0.038 0.051 OTHER 0.554 0.017 0.740 -0.015 -0.351 -0. 014 0.007 0. 008 0.064 0.188 -0. 555 -0.182 -0.039 VARIABLE SPOP UFAC PCY GINI KS TK TS PMR PCCRMT PCMF TOLPCT RLTOT AVI G AVPG AVSG 468 EXPONENTIAL FORM SPECIFICATION OF THE SRAM FORTY EIGHT STATE SAMPLE SHORT RUN MODEL DERIVATIVES SHAR VARIABLE SPOP UPAC PCY GINI KSTK TSPMR PCCRMT PCM F TOLPCT RLTOT AVI G AV PG AVSG INTERSTATE -0. 721E O .553E -0. 570E -0. 243E 0. 319E -0.968E 0.106E 0.315E -0. 236E 0.145E O.704E -0. 258E 3.136E 01 08 04 07 08 02 08 37 09 0? 00 00 00 PRIMARY -0.191E 00 -0. 293E 08 -0.403E 04 -0.172E 07 -0.187E 07 -0.685E 02 0,747E 07 0.223E 07 0.79Y 08 0.103E 08 -0.9 71E-01 0.122E 01 -0.456E 00 SECONDARY 0.477E -0.207E -0. 204E 0. 776E -0. 188E 0.309E -0. 453E 0.113E 0. 401E 0.522E -0.198E -0. 372E 0.322E 00 08 04 07 07 03 08 07 08 07 00 00 00 469 EXPONENTIAL FORM SPECIFICATION OF THE SRAM FORTY EIGHT STATE SAMPLE SHORT RUN MODEL DERI VATI VES SHARE VARIABLE S POP UFAC PCY GINI KSTK TS PMR PCCRMT PCMF TOLPCT RLTOT AVI AVPG AVS G NONFASYST 0. 633E 00 -0.760E 07 -0. 761E 03 -0.325E 06 -0.700E 06 -0.129E 02 0.130E 08 0.421E 06 0.150E 08 -0. 404E 08 0.6 86E-01 0. 524E-01 0.105E 00 MAINT -0.115E 01 0.825E 06 -0.272E 04 -0.116E 07 0.373E 07 -0.462E 02 0.504E 07 -0.968E 07 0.535E 08 -0.266E 08 0.139E 00 0. 817E-01 0.270E 00 OTHER 0. 744E 0. 151E 0.152E -0. 212E -0. 312E -0. 846E 0.922E 0.275E 0.0 979E 0. 369E -0. 617E -0. 72 3E -0. 377E 01 07 05 07 08 02 07 07 08 08 00 00 00 470 EXPONENTIAL FORM SPECIFICATION OF THE SRAM FORTY EIGHT STATE SAMPLE LONG RUN MODEL ELASTICITIES SHARE VARI ABLE SPOP UFAC PCY GINI KSTK TS PMR PCCRMT PCMF TOLPCT RLTOT AVIG AVPG AVSG I NTh.RSTATE 0.543 0.547 0.583 -0.011 0.415 -0. 014 0.007 0.008 -0.263 J. 063 0.913 -0. 057 0.012 PR IMARY 0.994 -0. 421 0. 583 -0.011 0. 076 -0.014 0.007 0.008 0. 064 0. 063 0. 251 0. 379 -0.058 SECONDARY 1.098 -0.586 0.583 0.142 0.050 0.121 -0.082 0.008 0.064 0.063 -0.076 -0. 229 0.081 471 EXPONENTIAL FORM SPECIFICATION OF THE SRAM FORTY EIGHT STATE SAMPLE LONG RUN MODEL ELASTICITIES SHARE VARIABLE SPOP UFAC PCY GINI KSTK TS PMR PCCRMT PCMF TOLPCT R LTCT AVI G A V PG AVSG NONFASYST 1.320 -0.57T 0.533 -0.011 0. 050 -0. 014 i 0.063 0.008 0.064 -1. 346 0.762 0.086 0.071 MAI NT 0.855 0. 011 0. 583 -0. 011 0.179 -0. 014 0.007 -0.054 0. 064 -0. 250 0.589 0.038 0.051 OTHER 1.565 0.011 1.564 -0.011 -0.250 -0. 014 0.007 0.008 0.064 0.18 7 -0.196 -0. 182 -0.039 472 EXPONENTIAL FORM SPECIFICATION OF THE SRAM FORTY EIGHT STATE SAMPLE LONG RUN MODEL DERIVATIVES SHARE VARIABLE INTERSTATE PR IMARY SECONDARY SPOP 0.836E 01 0.108E 02 0.605E 01 UFAC 0.547E 08 -0.298E 08 -0. 210E 08 PCY O.137E 05 O.972E 04 0.492E 04 GINI -0.178E 07 -0.126E 07 0.799E 07 KSTK 0.423E 08 0.545E 07 0.183E 07 TSPMR -0.968E 02 -0.685E 02 0.309E 03 PCCRMT 0.106E 08 0. 747E 07 -0. 453E 08 PCMF 0.315E 07 0.223E 07 0.113E 07 TOLPCT -0.285E 09 0.797E 08 0.403E 08 RLTOT 0.142E 08 0o.101E 08 0.510E 07 AVIG 0.116E 01 0.226E 00 -0. 347E-01 AVPG -0. 258E 00 0.122E 01 -0.372E 00 AVSG 0.136E 00 -0.456E 00 0.322E 00 473 EXPONENTIAL FORM SPECIFICATION OF THE SRAM FORTY EIGHT STATE SAMPLE LONG RUN MODEL DERIVATIVES SHARE VARI ABLE S PO F UFAC PCY GI NI KSTK TSPMR PCCRMT PCMF TOLPCT RLTOT AVI G AVPG AVSG NONFASYST 0. 271E -0.769E 01 07 0.184E 04 -0.238E 06 0.681E 06 -0.129E 02 O.130E 08 0.421E 06 0.150E 08 -0.404E 08 0.129E 00 0. 524E-01 0.105E 00 MA INT 0. 628E 01 0.512E 06 0.656E 04 -0.851E 06 0.867E 07 -0.462E 02 0.50L4E 07 -0.968E 07 0.537E 08 -0.268E 08 0.357E 00 0. 817E-01 0.270E 00 OTHER 0. 211E 0.9 38E 0.322E -0. 156E -0. 222E -0.846E 0.922E 0. 275E 0.9 84E 0. 366E -0. 218E -0. 723E -0. 377E 02 06 05 07 08 02 07 07 08 08 00 00 00