Composite Quasi-Maximum Likelihood Estimation of Dynamic Panels with Group-Specific Heterogeneity and Spatially Dependent Errors

This paper proposes a new method to estimate dynamic panel data models with spatially dependent errors that allows for known/unknown group-specific patterns of slope heterogeneity. Analysis of this model is conducted in the framework of composite quasi-likelihood (CL) maximization. The proposed CL estimator is robust against some misspecification of the unobserved individual/group-specific fixed effects. Since our CL method is based on the idea of doing regressions involving common-group stochastic trends, no endogeneity problem will arise. Therefore, unlike existing methods the proposed estimator does not require the use of intrumental variables nor bias correction/reduction. Clustering and estimation of the parameters of interest involve a large-scale non-convex mixed-integer programming problem, which can then be solved via a new efficient approach developed based on DC (Difference-of-Convex functions) programming and the DCA (DC algorithm). Suppose that the number of time periods and the size of spatial domain grow simultaneously, asymptotic theory is derived for both cases where the covariates are stationary and nonstationary. An extensive Monte Carlo simulation is also provided to examine the finite-sample performance of the proposed estimator. Our method is then applied to study the long-run relationship between saving and investment rates. The empirical findings reconcile various empirical approaches to capital mobility in the literature; and there exists substantial capital mobility in some countries while no conclusion about capital mobility can be drawn in other countries. Applied economists can easily implement the method by using the companion software to this paper.