Asymptotics for random effects models with serial correlation

Abstract

This paper considers the large sample behavior of the maximum likelihood estimator of random effects models. Consistent estimation and asymptotic normality as N and/or T grows large is established for a comprehensive specification which allows for serial correlation in the form of AR(1) for the idiosyncratic or time-specific error component. The consistency and asymptotic normality properties of all commonly used random effects models are obtained as special cases of the comprehensive model. When N or T \rightarrow \infty only a subset of the parameters are consistent and asymptotic normality is established for the consistent subsets.Panel data; error components; consistency; asymptotic normality; maximum likelihood.