Maximum Likelihood Estimation and Inference Methods for the Covariance Stationary Panel AR(1)/Unit Root Model

Abstract

This paper considers Maximum Likelihood (ML) based estimation and inference procedures for linear dynamic panel data models with fixed effects.
The paper first studies the asymptotic properties of MaCurdy’s [MaCurdy, T., 1982. The use of time series processes to model the time structure of earnings in a longitudinal data analysis. Journal of Econometrics 18, 83–114] First Difference Maximum Likelihood (FDML) estimator for the covariance stationary panel AR(1)/unit root model with fixed effects, viz. yi,t = ρyi,t−1 + (1 − ρ)µi + εi,t, under a variety of asymptotic plans. Subsequently, the paper shows through Monte Carlo simulations for panels of various dimensions the favourable finite sample properties of the FDMLE for ρ as compared to those of a number of alternative fixed effects ML estimators for ρ under covariance stationarity and normality of the data. The paper also discusses panel unit root test procedures that are based on the FDMLE. A Monte Carlo study conducted for one version of these tests reveals that it has very good size and power properties in comparison with alternative panel unit root tests.