SOME IDENTIFICATION ISSUES IN NONPARAMETRIC LINEAR MODELS WITH ENDOGENOUS REGRESSORS
研究了当解释变量存在内生性时，非参数模型中未知函数的识别问题，基于条件矩约束构建模型，探讨了线性空间下函数的识别性及其线性泛函的欠识别问题，并辅以实例说明。
In applied work economists often seek to relate a given response variable y to some causal parameter μ* 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 μ* as a conditional expectation breaks down if some or all of the explanatory variables are endogenous. This is not a problem when μ* 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 μ*. In contrast, handling endogenous regressors in nonparametric models, where μ* 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 μ* belongs to a linear space. We also investigate underidentification of μ* 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.We thank Jeff Wooldridge and two anonymous referees for comments that greatly improved this paper.