Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity

Abstract

This paper investigates identification and inference in a nonparametric structural model with instrumental variables and non-additive errors.We allow for non-additive errors because the unobserved heterogeneity in marginal returns that often motivates concerns about endogeneity of choices requires objective functions that are non-additive in observed and unobserved components.We formulate several independence and monotonicity conditions that are sufficient for identification of a number of objects of interest, including the average conditional response, the average structural function, as well as the full structural response function.For inference we propose a two-step series estimator.The first step consists of estimating the conditional distribution of the endogenous regressor given the instrument.In the second step the estimated conditional distribution function is used as a regressor in a nonlinear control function approach.We establish rates of convergence, asymptotic normality, and give a consistent asymptotic variance estimator.