Simple methods for consistent estimation of dynamic panel data sample selection models

Abstract

We analyse the properties of generalised method of moments-instrumental variables (GMM-IV) estimators of AR(1) dynamic panel data sample selection models. We show the consistency of the first-differenced GMM-IV estimator uncorrected for sample selection of Arellano and Bond (1991) (a property also shared by the Anderson and Hsiao,1982, proposal). Alternatively, the system GMM-IV estimator (Arellano and Bover, 1995, and Blundell and Bond, 1998) shows a moderate bias. We perform a Monte Carlo study to evaluate the finite sample properties of the proposed estimators. Our results confirm the absence of bias of the Arellano and Bond estimator under a variety of circumstances, as well as the small bias of the system estimator, mostly due to the correlation between the individual heterogeneity components in both the outcome and selection equations. However, we must not discard the system estimator because, in small samples, its performance is similar to or even better than that of the Arellano-Bond. These results hold in dynamic models with exogenous, predetermined or endogenous covariates. They are especially relevant for practitioners using unbalanced panels when either there is selection of unknown form or when selection is difficult to model.