This project develops estimation methods that use simulations to overcome the computational burdens of numerically complex econometric models. This is a very important line of research because many economic problems are intractable even using supercomputers. Many applied economists must consciously design models to avoid computationally intractable aspects, even though the economics of the issue naturally lead in that direction. This project generalizes the simulated moments methods, uses it to solve complicated empirical economic problems and extends a new class of semi-parametric estimators for linear index models developed by the investigator under his previous NSF grant. The method of simulated moments is generalized to limited dependent variable models besides the conditional multinomial Probit model and to inference problems associated with approximating moment functions like the score of the log- likelihood. The research in computation addresses the existence and nondifferentiability of simulated moments estimators. The second part of the research is an empirical application of simulated moments estimation methods to the analysis of labor supply with nonlinear taxes. The third part of the research is about semi-parametric estimation of index models. Asymptotic distribution theory for a class of estimators for linear index models will be derived and the relationship between this family of estimators and others is explored.
