# Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors

*Thomas A. Severini* and
*Gautam Tripathi* ()

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Thomas A. Severini: Northwestern University

No 2005-12, Working papers from University of Connecticut, Department of Economics

**Abstract:**
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 modelled 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 in order to develop intuition about identification and estimation for endogenous nonparametric regression and related models.

**Keywords:** Endogeneity; Identification; Instrumental variables; Nonparametric models. (search for similar items in EconPapers)

**JEL-codes:** C14 (search for similar items in EconPapers)

**New Economics Papers:** this item is included in nep-ecm

**Date:** 2005-04

**Note:** We thank Jeff Wooldridge and two anonymous referees for comments that greatly improved this paper.

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**Related works:**

Journal Article: SOME IDENTIFICATION ISSUES IN NONPARAMETRIC LINEAR MODELS WITH ENDOGENOUS REGRESSORS (2006)

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**Persistent link:** https://EconPapers.repec.org/RePEc:uct:uconnp:2005-12

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