Three essays in microeconometrics and applied microeconomics

The first essay develops and implements a semiparametric estimator for investigating, with panel data, the importance of human capital accumulation, nonseparable preferences of females, and child-care costs on female life-cycle fertility and on labor supply behaviors. It presents a model in which the agents' expectations are correlated with their future choices and provides a set of conditions under which statistical inferences are possible from a short panel. Under the assumption that observed allocations are Pareto optimal, a dynamic model of female labor supply, labor force participation, and fertility decision is estimated. In that model, experience on the job raises future wages and time spent nurturing children affects utility, whereas time spent off the job in the past directly affects current utility (or indirectly through productivity in the non-market sector). We show that an important determinant of life-cycle fertility and labor supply decisions is human capital accumulation.;The second essay considers the problem of identification and estimation in panel data sample selection models with a binary selection rule, when the latent equations contain possible predetermined variables, lags of the dependent variables, and unobserved individual effects. The selection equation contains lags of the dependent variables from the latent equations and other possible predetermined variables relative to the latent equations. We derive a set of conditional moment restrictions that are then exploited to construct a two-step GMM sieve estimator for the parameters of the main equation including a nonparametric estimator of the sample selection term. In the first step, the unknown parameters of the selection equation are consistently estimated using a transformation approach in the spirit of Berkson's minimum chi-square sieve method and a kernel estimator for the selection probability. This first estimator is of interest in its own right: it can be used to semiparametrically estimate a panel data binary response model with correlated random effects model without making any distributional assumptions. We show that both of our estimators (first and second stage) are N -consistent and asymptotically normal.;The third essay proposes a semi-structural method for estimating empirical auction models that are either too complex to be analyzed using a fully structural approach or when players are not following the prescribed Nash Equilibrium strategy. This approach allows one to draw inference about such models relative to a more developed benchmark model. As a consequence of the semi-structural approach, one is able construct a method for addressing the very important, though often neglected, issue of post-model validation. This framework would be useful in analyzing models of collusive behavior or other non-standard assumptions that may lead to asymmetric Nash Equilibrium strategies.