SOME IDENTIFICATION ISSUES IN NONPARAMETRIC LINEAR MODELS WITH ENDOGENOUS REGRESSORS

Thomas A. Severini and Gautam Tripathi

Econometric Theory, 2006, vol. 22, issue 02, pages 258-278

Abstract: In applied work economists often seek to relate a given response variable y to some causal parameter * 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 * as a conditional expectation breaks down if some or all of the explanatory variables are endogenous. This is not a problem when * 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 *. In contrast, handling endogenous regressors in nonparametric models, where * 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 * belongs to a linear space. We also investigate underidentification of * 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.

Date: 2006
View citations in EconPapers

Downloads: (external link)
http://journals.cambridge.org/abstract_S0266466606060117 link to article abstract page (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:22:y:2006:i:02:p:258-278_06

Access Statistics for this article

More articles in Econometric Theory from Cambridge University Press
Address: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
Series data maintained by Mike Eden ().