Abstract
This paper studies the asymptotic properties of standard panel data estimators in a simple panel regression model with error component disturbances. Both the regressor and the remainder disturbance term are assumed to be autoregressive and possibly non-stationary. Asymptotic distributions are derived for the standard panel data estimators including ordinary least squares, fixed effects, first-difference, and generalized least squares (GLS) estimators when both T and n are large. We show that all the estimators have asymptotic normal distributions and have different convergence rates dependent on the non-stationarity of the regressors and the remainder disturbances. We show using Monte Carlo experiments that the loss in efficiency of the OLS, FE and FD estimators relative to true GLS can be substantial.
Highlights
Econometricians have long been concerned with conditions under which the ordinary least squares (OLS) estimator is asymptotically e¢ cient
We show that when the error term is I(0) and the regressor is I(1), the FE estimator is asymptotically equivalent to the generalized least squares (GLS) estimator and OLS is less e¢ cient than GLS
This implies that GLS is the preferred estimator under both cases (i.e., regression error is either I(0) or
Summary
Econometricians have long been concerned with conditions under which the ordinary least squares (OLS) estimator is asymptotically e¢ cient. Structure on the disturbances, the OLS estimator is less e¢ cient than generalized least squares (GLS) This is well documented for the case of stationary autoregressive disturbances and stationary regressors. Phillips and Park (1988) showed that in a regression with integrated regressors, OLS and GLS are asymptotically equivalent. Showed the equivalence of the GLS and FE estimators in a simple panel data regression with time trend as a regressor. This paper extends the literature by studying the asymptotic properties of OLS, FE, ...rst di¤erence (FD) and GLS in the panel regression with an autocorrelated regressor and an autocorrelated remainder error (both of which can be stationary or nonstationary). We show that when the error term is I(0) and the regressor is I(1), the FE estimator is asymptotically equivalent to the GLS estimator and OLS is less e¢ cient than GLS (due to a slower convergence speed). All proofs are collected in an appendix available upon request from the authors
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