A Unied Estimation Approach for Spatial Dynamic Panel Data Models: Stability, Spatial Cointegration and Explosive Roots

This paper considers a quasi-maximum likelihood estimation for the 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 di¤erent estimation methods depending on whether the data generating process has time dummy e¤ects or not and whether it is stable, spatial cointegrated, or explosive, we propose a data transformation approach which may eliminate time dummy e¤ects and unstable or explosive components. When T is relatively larger than n , which is the e¤ective sample size for each period after the transformation, the estimators are p n T consistent and asymptotically centered normal; when T is asymptotically proportional to n , the estimators are p n T consistent and asymptotically normal, but the limit distribution may not be properly centered; 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 approach has a uni…ed bias correction procedure that can be applied to di¤erent DGPs where the process might be stable or not. JEL classi…cation: C13; C23; R15