| This dissertation is composed of three papers about the theories and application of spatial dynamic panel data model with fixed effects. The first 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 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 n1/3, the correction will asymptotically eliminate the bias and yield a centered confidence interval. The second paper covers a nonstationary case where there are units roots in the data generating process. When not all the roots in the DGP are unity, the estimators rate of convergence will be the same as the stationary case, and the estimators can be asymptotically normal. But for the estimators' asymptotic variance matrix, it will be driven by the nonstationary component into a singular matrix. Consequently, a linear combination of the spatial and dynamic effects can converge with a higher rate. We also propose a bias correction for our estimators. We show that when T grows faster than n 1/3, the correction will asymptotically eliminate the bias and yield a centered confidence interval. In the third paper, a spatial dynamic panel data approach is proposed to study growth convergence in the U.S. economy. In neoclassical model, countries are assumed to be independent from each other, which does not hold in the real world. We introduce technological spillovers and factor mobility into the neoclassical framework, showing that the convergence rate is higher and there is spatial correlation. Exploiting annual data on personal state income spanning period 1961-2000 for the 48 contiguous states, we obtain empirical results consistent with the model prediction. |
