Random Coefficients Models

This chapter deals with specification, estimation, and inference within the framework of a random coefficients model for multi-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 estimation procedure for the variance-covariance components as well as an extension of the MINQUE approach. We also derive the full Maximum Likelihood, and a Restricted Maximum Likelihood involving the maximization of a restricted part of the log-likelihood that is free of the intercept and slope coefficients such that we obtain unbiased estimators of the variance-covariance 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, misspecification of the variance-covariance structure, 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.