Random Coefficients Models

Abstract

This chapter deals with specification, estimation and inference within the framework of a random coefficient model in the presence of higher dimensional panel data. Most of the chapter is concerned with a three-dimensional setting with an extension to higher dimensions at the end. We discuss several estimation methods, starting with the GLS made feasible by a new procedure for the estimation of the variance-covariance components, as well as an extension of the MINQUE approach for this setting.We also derive the full Maximum Likelihood and a Restricted Maximum Likelihood estimators involving the maximization of the log-likelihood in a subset of the parameter space for an independent estimation of the variancecovariance elements. Furthermore, we design specification tests that allow to determine if the response coefficients are constant or varying. Additionally, we present different extensions of the linear model including unbalanced panels, correlated random components and correlation of the stochastic elements with the regressors. Finally, the chapter ends with brief discussions of non-linear and higher dimensional extensions as well as a simulation experiment comparing the performance of the above methods in a finite sample setting.