GMM Estimation of AR(1) Time Series Model with One Additional Regressor

Abstract

GMM estimators properties for panel data have been very well known in the econometric literature and it has been observed that for small sample cases, they perform well. The OLS (Ordinary Least Squares) is not applicable when lagged endogenous and exogenous variables are correlated with the error term. Hence, here an attempt is made to estimate AR(1) time series model with one additional regressor by considering First-difference GMM and Level GMM estimation methods proposed by Arellano and Bond (1991) and Arellano and Bover (1995) respectively. In order study the performances of the above mentioned estimators in comparison with the OLS estimator Monte Carlo simulation study is carried out. Further, a comparison among these estimators has been done in terms of bias and RMSE. Study disclose that for an autoregressive parameter, Level GMM estimator performs better than First-difference GMM and OLS estimators when T, the sample size is small and, the autoregressive parameter is close to unity. Whereas for the parameter of additional regressor, Level GMM estimator performs better than the other two mentioned estimators for all the values of and .