Cross-sectional quasi-maximum likelihood and bias-corrected pooled least squares estimators for short dynamic panels

Abstract

This paper proposes new estimators for the panel autoregressive (PAR) model of order 1 with short time dimensions and large cross sections. These estimators are based on the cross-sectional regression model using the first time series observations as a regressor and the last as a dependent variable. The regressors and errors of this regression model are correlated. The first estimator is the quasi-maximum likelihood estimator (QMLE). The second estimator is the bias-corrected pooled least squares estimator (BCPLSE) that eliminates the asymptotic bias of the pooled least squares estimator by using the QMLE. The QMLE and BCPLSE are extended to the PAR model with endogenous regressors. The QMLE and BCPLSE provide consistent estimates of the PAR coefficients for stationary, unit root and explosive PAR models and consistently estimate the coefficients of endogenous regressors. Their finite sample properties are compared with those of some other estimators for the PAR model of order 1. This paper’s estimators are shown to perform quite well in finite samples.