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

In this paper, we study the spatial dynamic panel data models with high-order time-varying endogenous weights matrices. The quasi-maximum likelihood (QML) estimator is inconsistent under heteroskedastic errors and would be computationally complicated due to the evaluation of the Jacobian determinants in the likelihood function. To overcome these two issues, we propose the generalized method of moments (GMM) estimator and establish its asymptotic property under two scenarios: (i) finite T with large n, (ii) T can be large but small relative to n. We prove the consistency and asymptotic normality of these GMM estimators with finite or many moments. Furthermore, under homoskedastic errors, by designing appropriate moment conditions, the GMM estimator can be more efficient than the QML estimator. Monte Carlo simulations confirm that our proposed GMM estimators have satisfactory finite sample performances. We then apply our model to study multi-dimensional spillover effects of research and development (R&D) activities in China's listed firms. Empirical results show that market spillover dominates in the strategic interaction of R&D investments, while the technological spillover dominates in the innovation performance