Some estimators for dynamic panel data sample selection and switching models

We present estimators for panel data sample selection and switching models where the regression equations are dynamic and it is allowed for the existence of endogenous regressors and correlated individual unobserved heterogeneity. We consider two types of switching models under the names of observed dynamics switching and latent dynamics switching. The dynamic sample selection model implicitly assumes an underlining latent dynamics switching regime process. The type of methods presented are different Generalized Method of Moments (GMM) estimators for dynamic panel data sample selection and switching models that may combine estimation of the models both in first time differences and in level equations (with the corresponding sample selection correction terms under one or the other case). Therefore, we consider the possibility of applying System-GMM estimators for dynamic panel data to the case of sample selection and switching models. Depending both on estimation in levels or time differences and on the types of switching models considered (observed or latent) the sample selection correction terms present different degrees of complexity. Some of this complexity can be simplified if we are willing to impose stationarity assumptions, exchangeability conditions, and/or lack of individual heterogeneity in the selection equations determining the switching regimes. In the general setting neither stationarity, exchangeability, or lack of individual heterogeneity in the selection equations are imposed. To see the performance of the proposed estimators we perform a Monte Carlo study of the finite sample properties of different Generalized Method of Moments (GMM) estimators for dynamic panel data sample selection and switching models. Finally, we present an empirical example using Spanish data on wage settlements and strike outcomes. In an economic context in which workers may strike to obtain a wage concession, the strike decision is endogenous to the wage process and the wage equation is then affected by endogenous selection. We test this as well as alternative economic hypotheses in a dynamic context.