Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large

This paper investigates the asymptotic properties of quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects, 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 nT consistent and asymptotically normal, with the limit distribution centered around 0. When n is asymptotically proportional to T, the estimators are 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 T consistent, and have a degenerate limit distribution. The estimators of the fixed effects are T consistent and asymptotically normal. We also propose a bias correction for our estimators. We show that when T grows faster than n1/3, the correction will asymptotically eliminate the bias and yield a centered confidence interval.