Generalized Least Squares Inference in Panel and Multilevel Models with Serial Correlation and Fixed Effects

In this paper, I consider generalized least squares (GLS) estimation in fixed effects panel and multilevel models with autocorrelation. A complication which arises in implementing GLS estimation in these settings is that standard estimators of the covariance parameters necessary for obtaining the feasible GLS estimates will typically be inconsistent due to the inclusion of individual specific fixed effects. Focusing on the case where the disturbances follow an AR(p) process, I offer a bias-correction for the AR coefficients which is simple to implement and will be valid in the presence of fixed effects and individual specific time trends. I develop asymptotic properties of the bias-corrected estimator as the cross-section dimension goes to infinity with the time dimension fixed and as both the cross-section and time series become large. I also present asymptotic properties of the feasible GLS estimator in both asymptotics and derive the higher order bias and variance of the feasible GLS estimator in the second case. The usefulness of GLS and the derived bias-correction for the parameters of the autoregressive process is illustrated through a simulation study which uses data from the Current Population Survey Merged Outgoing Rotation Group files.