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

This paper proposes a novel method to estimate large panel data error-correction models with stationary/non-stationary covariates and spatially dependent errors, which allows for known/unknown group-specific patterns of slope heterogeneity. Analysis is based on composite quasi-likelihood (CQL) maximization which performs estimation and classification simultaneously. The proposed CQL estimator remains unbiased in the presence of misspecification of the unobserved individual/group-specific fixed effects; therefore, neither instrumental variables nor bias corrections/reductions are required. This estimator also achieves the `oracle' property as the estimation errors of group memberships have no effect on the asymptotic distributions of the group-specific slope parameters estimates. Classification and estimation involve a large-scale non-convex mixed-integer programming problem, which can then be solved via a new algorithm based on DC (Difference-of-Convex functions) programming - the DCA (DC Algorithm). Simulations confirm good finite-sample properties of the proposed estimator. An empirical application and a software package to implement this method are also provided.