Inference in linear panel data models with serial correlation and an essay on the impact of 401 (k) participation on the wealth distribution

Abstract

This thesis considers inference issues in serially correlated multilevel and panel data and presents a separate essay that examines the impact of 401(k) participation on wealth. The first chapter examines generalized least squares (GLS) estimation in data with a grouped structure where the groups may be autocorrelated. The analysis presents computationally convenient methods for obtaining GLS estimates in large multilevel data sets and discusses estimation of covariance parameters for use in GLS when the shock follows an AR(p) process. Standard estimates of the AR coefficients will typically be biased due to the inclusion of group level fixed effects, so a simple bias correction for the AR coefficients is offered which will be valid in the presence of fixed effects and group specific time trends. The chapter concludes with a simulation study that illustrates the usefulness of the derived methods. The second chapter further explores inference in serially correlated panel data by considering the asymptotic properties of a robust covariance matrix estimator which is advocated for use in panel data. The estimator has good properties when the cross-section dimension, n, grows large with the time dimension, T, fixed. However, many panel data sets are characterized by a non-negligible time dimension. Chapter 2 extends the usual analysis to cases where T [right arrow] [infinity symbol] showing that t and F tests based on the robust covariance matrix estimator display their usual limiting behavior as long as n [right arrow] [infinity symbol] with T.

(cont.) When T [right arrow] [infinity symbol] with n fixed, the results show that t and F statistics can be used for inference despite the fact that the robust covariance matrix estimator is not consistent but converges to a limiting random variable. The properties of tests based upon the robust covariance matrix estimator are examined in a short simulation study. The final chapter uses instrumental variables quantile regression to examine the effects of participating in a 401(k) on wealth. significant over the entire range of the asset distribution and that the increase in the lower tail appears to translate completely into an increase in wealth. However, there is evidence of substitution between net financial assets and other forms of wealth in the upper tail of the distribution. The results demonstrate that estimates of treatment effects which focus on a single feature of the outcome distribution may fail to capture the full impact of the treatment and that examining additional features may enhance our understanding of the economic relationships involved.