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Some Identification Issues In Nonparametric Linear Models With Endogenous Regressors

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  • Severini, Thomas A.
  • Tripathi, Gautam

Abstract

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.

Suggested Citation

  • Severini, Thomas A. & Tripathi, Gautam, 2006. "Some Identification Issues In Nonparametric Linear Models With Endogenous Regressors," Econometric Theory, Cambridge University Press, vol. 22(2), pages 258-278, April.
  • Handle: RePEc:cup:etheor:v:22:y:2006:i:02:p:258-278_06
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    References listed on IDEAS

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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