Maximum likelihood estimation and inference methods for the covariance stationary panel AR(1)/unit root model

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.