Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals and Nonclassical Measurement Errors

• Activity Number: 662
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Suyong Song*+
• Companies: University of Wisconsin-Milwaukee
• Keywords: Penalized sieve minimum distance ; Endogeneity ; Nonclassical measurement error ; Nonsmooth residuals ; Conditional independence

Abstract

We study two sets of semiparametric conditional moment models. The first models rely on standard instrumental variable but the second models rely on nonclassical instruments ensuring conditional independence of endogenous regressors and unobservable causes. Both models allow for possibly nonsmooth residuals which contain finite dimensional unknown parameters and infinite dimensional unknown functions, and allow for the unknown functions to depend on endogenous variables contaminated by nonclassical measurement errors. We provide sufficient sets of conditions to control for both endogeneity and measurement error in both models and show that one instrument is sufficient to identify parameter of interest. We propose a two-stage estimation procedure: sieve maximum likelihood estimation is used to estimate conditional density of endogenous variables given conditioning variables, and then penalized sieve minimum distance estimation is used to estimate parameters of interest. We establish root-n asymptotic normality for the estimator of the finite dimensional unknown parameters and nonparametric optimal convergence rate for the estimator of the infinite dimensional unknown functions.