Title（问题）：On Inference of PSMD Estimators of Semi/Nonparametric Conditional Moment Models

Speaker（报告人）：Professor Xiaohong Chen, Professor Demian Pouzo

Yale University University of California, Berkeley

Time（时间）：2011年6月30日（周四）下昼3:15 — 4:15

Place（所在）：伟易博新楼217课堂

Abstract（摘要）：In this paper, we consider estimation and inference of functionals of unknown parameters satisfying (nonlinear) semi/nonparametric conditional moment restrictions models. Such models belong to the difficult (nonlinear) ill-posed inverse problems with unknown operators, and include nonparametric quantile instrumental variables (IV), single index IV regressions and nonparametric endogenous default model as special cases. We first establish the asymptotic normality of the penalized sieve minimum distance (PSMD) estimators of any functionals that may or may not be root-n estimable. We show that the profiled optimally weighted PSMD criterion is asymptotically chi-square distributed, which provides one simple way to construct confidence sets. We also establish the validity of bootstrap based confidence sets for possibly non-optimally weighted PSMD estimators. We illustrate the general theory by constructing confidence bands for a nonparametric quantile instrumental variables Engel curve in a Monte Carlo study and a real data application.