SOME IDENTIFICATION ISSUES IN NONPARAMETRIC LINEAR MODELS WITH ENDOGENOUS REGRESSORS
In applied work economists often seek to relate a given response variable y to some causal parameter [mu]* associated with it. This parameter usually represents a summarization based on some explanatory variables of the distribution of y, such as a regression function, and treating it as a conditional expectation is central to its identification and estimation. However, the interpretation of [mu]* as a conditional expectation breaks down if some or all of the explanatory variables are endogenous. This is not a problem when [mu]* is modeled as a parametric function of explanatory variables because it is well known how instrumental variables techniques can be used to identify and estimate [mu]*. In contrast, handling endogenous regressors in nonparametric models, where [mu]* is regarded as fully unknown, presents difficult theoretical and practical challenges. In this paper we consider an endogenous nonparametric model based on a conditional moment restriction. We investigate identification-related properties of this model when the unknown function [mu]* belongs to a linear space. We also investigate underidentification of [mu]* along with the identification of its linear functionals. Several examples are provided to develop intuition about identification and estimation for endogenous nonparametric regression and related models. a
c1 Address correspondence to Gautam Tripathi, Department of Economics, University of Connecticut, Storrs, CT 06269, USA; e-mail: email@example.com.
a We thank Jeff Wooldridge and two anonymous referees for comments that greatly improved this paper.