Panel data models with unobserved effects and endogenous explanatory variables

This dissertation consists of three essays that address issues of estimation in panel data models with unobserved effects and endogenous explanatory variables. The first essay considers estimation of correlated random coefficient (CRC) panel data models with endogenous regressors. This chapter provides a set of conditions sufficient for consistency of a general class of fixed effects instrumental variables (FE-IV) estimators in the context of a CRC panel data model. The usual FE-IV estimator turns out to be fairly robust to the presence of neglected individual-specific slopes. Monte Carlo simulations suggest the proposed FE-IV estimator of Population Averaged Effect (PAE) provided a full set of period dummy variables is included performs better than other estimators in finite samples for the case of (roughly) continuous endogenous explanatory variables.; The second essay continues studying a CRC panel data model from the first chapter but, in addition to allowing some explanatory variables to be correlated with the idiosyncratic error, the joint distribution of the endogenous regressors and the individual heterogeneity conditional on the instruments is allowed to depend on the instruments. The second essay uses a two-step control function approach to account for endogeneity and to consistently estimate average partial effects (APEs) in CRC panel data models with endogenous roughly continuous regressors. The simulation findings indicate that in the finite samples the control function approach to estimating the CRC balanced panel data model with time-constant individual heterogeneity performs better than other estimators under the considered conditions. The pro posed method is applied to the problem of estimating the APEs of annual hours of on-job-training on output scrap rates for manufacturing firms in Michigan.; In the third essay, a dynamic binary response panel data model that allows for an endogenous regressor is developed. This estimation approach is of particular value for settings in which one wants to estimate the effects of a treatment which is also endogenous. This model is applied to examine the impact of rural-urban migration on the likelihood that households in rural China fall below the poverty line. The empirical results that migration is important for reducing the likelihood that poor households remain in poverty and that non-poor households fall into poverty. Further, failure to control for unobserved heterogeneity leads to an overestimate of the impact of migrant labor markets on probability of staying poor of those who lived below the poverty lines.