Quasi ML Estimation of the Panel AR(1) Model with Additional Regressors

Abstract

In this paper we discuss several limited information (LI) and full information (FI) random effects and fixed effects Quasi ML estimators (MLEs) for panel AR(1) models with additional regressors. We also consider related GMM estimators. All estimators are consistent for short (large N, fixed T) panels. The models allow for arbitrary initial conditions and heteroskedasticity and are extensions and generalizations of the models considered in Kruiniger (2013. Quasi ML estimation of the panel AR(1) model with arbitrary initial conditions. Journal of Econometrics 173, 175-188). Among other things, we distinguish between the case where the regressors are strictly exogenous, the case where some of them are predetermined with respect to the idiosyncratic errors, including the case where they are weakly exogenous, and the case where some regressors are contemporaneously correlated with the idiosyncratic errors; we consider the possibility that the regressors are correlated with the individual effects; and we discuss estimation of models with time-varying individual effects. We also discuss how to choose between a random effects and a fixed effects approach. When the distribution of the data is correctly specified, the LI MLEs have better finite sample properties than the corresponding GMM estimators and when the time-dimension, T, is not small relative to the cross-section dimension, N, Wald tests based on the QMLEs have better size properties than GMM based Wald tests. Finally, the LI QMLEs for dynamic models with additional predetermined regressors are more easily computed and more precise than the ss-LIMLE of Moral-Benito (2013. Likelihood-based estimation of dynamic panels with predetermined regressors. Journal of Business & Economic Statistics 31, 451-472) and also more easily computed and in finite samples often more precise than the FI QMLEs.

Keywords: control function, Generalized Method of Moments (GMM), predetermined regressors, Quasi Maximum Likelihood (QML), time-varying individual effects

JEL Classification: C12, C13, C23