Quasi-Maximum Likelihood Estimators For Spatial Dynamic Panel Data With Fixed E¤ects When Both n and T Are Large

This paper investigates the asymptotic properties of quasi-maximum likelihood estimators for spatial dynamic panel data with …xed e¤ects when both the number of individuals n and the number of time periods T are large. We consider the case where T is asymptotically large relative to n, the case where T is asymptotically proportional to n, and the case where n is asymptotically large relative to T . In the case where T is asymptotically large relative to n, the estimators are p nT consistent and asymptotically normal, with the limit distribution centered around 0. When n is asymptotically proportional to T , the estimators are p nT consistent and asymptotically normal, but the limit distribution is not centered around 0; and when n is large relative to T , the estimators are consistent with rate T , and have a degenerate limit distribution. The estimators of the …xed e¤ects are p T consistent and asymptotically normal. We also propose a bias correction for our estimators. We show that when T grows faster than n, the correction will asymptotically eliminate the bias and yield a centered con…dence interval. JEL classi…cation: C13; C23 Keywords: Spatial autoregression, Dynamic panels, Fixed e¤ects, Maximum likelihood estimation, QuasiMaximum likelihood estimation, Bias correction We would like to thank participants of the Econometrics Seminar at The Ohio State University, the International Workshop on Spatial Econometrics and Statistics 2006 (Rome, Italy) and the Far Eastern Meeting of Econometric Society 2006 (Beijing, China) for helpful comments. Lee acknowledges …nancial support from NSF under Grant No. SES-0519204 and research assistantship support from the Department of Economics in The Ohio State University.