Spatial Dynamic Panel Data Models With High Order Time Varying Endogenous Weights Matrices

This paper investigates spatial dynamic panel data models with high order time-varying endogenous weights matrices. We consider the panel data when $n$ is large, and $T$ can be large, but small relative to $n$. In this case, the maximum likelihood estimation (ML) approach would be either infeasible or computationally complicated. Furthermore, under a heteroskedastic error term, ML is inconsistent in general. We propose the generalized method of moments (GMM) estimation and establish its asymptotic properties with the finite moments condition and many moments condition. Monte Carlo simulations show that the proposed estimators have satisfactory finite sample performances. We then apply our model to study the strategic interaction of firms' innovation in China. Empirical results show that market spillover has the greatest impact on R\&D expenditure, while technological spillover has the greatest impact on the total factor of productivity