Some identification issues in nonparametric linear models with endogenous regressors

Thomas A. Severini, Gautam Tripathi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)258-278
Number of pages21
JournalEconometric Theory
Issue number2
StatePublished - Apr 2006

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics


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