Asymptotics for random effects models with serial correlation

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.