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

TL;DR

This paper introduces a new composite quasi-likelihood method for estimating large panel data models with group-specific heterogeneity and spatially dependent errors, enabling simultaneous estimation and classification without bias from fixed effects.

Contribution

It develops a novel CQL estimator that remains unbiased under misspecification, achieves the oracle property, and includes a new algorithm for solving the complex estimation problem.

Findings

Estimator performs well in simulations with finite samples.

Method successfully applied to empirical data.

Software implementation provided for practical use.

Abstract

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.