Semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors

This paper develops a framework for the analysis of semiparametric conditional moment models with endogenous and mismeasured causes, which is of empirical importance. We show that one set of valid instruments is sufficient to control for both endogeneity and measurement errors of the causes of interest, which has been observed in linear parametric models. Two-step consistent estimators of the parameters of interest are proposed. We also show that the proposed estimators are consistent with a rate faster than n−1/4 under a certain metric, and the proposed estimators of the finite-dimensional unknown parameters obtain root-n asymptotic normality. Monte Carlo evidences show that the proposed estimators perform well under a variety of identification conditions. An application to instrumental variables estimation of Engel curves illustrates the usefulness of our method. It supports that correcting for both endogeneity and measurement errors on total expenditure is substantial in estimating economically meaningful Engel curves.