A Spatial Dynamic Panel Data Model with Both Time and Individual Fixed E¤ects

This paper establishes asymptotic properties of quasi-maximum likelihood estimators for spatial dynamic panel data with both time and individual …xed e¤ects when both the number of individuals n and the number of time periods T can be large. Instead of using the direct approach where we estimate both individual e¤ects and time e¤ects directly, we propose a data transformation approach to eliminate the time e¤ects so that the bias of the order O(n ) is avoided. When T is relatively larger than n, the estimators are p nT consistent and asymptotically centered normal; 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; when T is relatively smaller than n, the estimators are consistent with rate T and have a degenerate limit distribution. 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. This transformation approach has advantage over the direct approach especially when n is relatively small as the direct approach has the bias of order O(n ) remained. JEL classi…cation: C13; C23 Keywords: Spatial autoregression, Dynamic panels, Fixed e¤ects, Time e¤ects, Quasi-maximum likelihood estimation, Bias correction We acknowledge …nancial support for the research from NSF under Grant No. SES-0519204.