Estimation and Specification Testing of Panel Data Models with Non-Ignorable Persistent Heterogeneity, Contemporaneous and Intertemporal Simultaneity, and Observable and Unobservable Dynamics

This paper proposes efficient estimation methods for panel data limited dependent variables (LDV) models possessing a variety of complications: non-ignorable persistent heterogeneity; contemporaneous and intertemporal endogeneity; and observable and unobservable dynamics. An important problem handled by the novel framework of this paper involves contemporaneous and intertemporal simultaneity caused by social strategic interactive effects or contagion across economic agents over time. The paper first shows how a simple modification of estimators based on the Random Effects principle can preserve the consistency and asymptotic efficiency of the method in panel data despite non-ignorable persistent heterogeneity driven by correlations between the individual-specific component of the error term and the regressors. The approach is extremely easy to implement and allows straightforward classical and omnibus tests of the significance of such correlations that lie behind the non-ignorable persistent heterogeneity. The method applies to linear as well as nonlinear panel data models, static or dynamic. Two major extensions of the existing literature are that the method works for time-invariant as well as time-varying regressors, and that these dependencies may be non-linear functions of the regressors. The paper then combines this modified random effects approach with two simulationbased estimation strategies to overcome analytical as well as computational intractabilities in a widely applicable class of nonlinear models for panel data, namely the class of LDV models with contemporaneous and intertemporal endogeneity. The effectiveness of the estimation methods in providing asymptotically efficient estimates in such cases is illustrated with three discrete-response econometric models for panel data.