The Effects of Scale Differences on Inferences in Accounting Research: Coefficient Estimates, Tests of Incremental Association, and Relative Value Relevance

Abstract

Firms' financial data vary considerably with the size of their operations. Such scale differences potentially confound several types of inferences, of which this paper analyzes three. This paper evaluates two potential solutions to these inference problems suggested by theory: (i) deflating the data by a proxy for scale; and (ii) including a scale proxy as an independent variable. First, simulations show that deflating the data more effectively mitigates coefficient bias than including that proxy as an independent variable. Reconciling this result with the opposing conclusion of Barth and Kallapur (1996, Contemporary Accounting Research) reveals that the prior results depend on assumptions that are economically and statistically unreasonable. Second, the deflation approach results in more accurate tests of incremental association in terms of mean squared error. Third, deflating by a scale proxy results in well-specified tests of relative association using Vuong's (1989) Z-statistic for non-nested models whereas including the scale proxy as an independent variable results in overstated significance. Given the additional advantages of deflation with respect to heteroscedasticity and the coefficient of determination (R2) demonstrated in prior studies, researchers should generally deflate their models when scale differences exist in the data.