Nonparametric identification using instrumental variables: sufficient conditions for completeness

Yingyao Hu and Ji-Liang Shiu
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Ji-Liang Shiu: Institute for Fiscal Studies

No CWP25/11, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract:

This paper provides sufficient conditions for the nonparametric identification of the regression function m(.) in a regression model with an endogenous regressor x and an instrumental variable z. It has been shown that the identification of the regression function from the conditional expectation of the dependent variable on the instrument relies on the completeness of the distribution of the endogenous regressor conditional on the instrument, i.e., f(x/z). We provide sufficient conditions for the completeness of f(x/z) without imposing a specific functional form, such as the exponential family. We show that if the conditional density f(x/z) coincides with an existing complete density at a limit point in the support of z, then f(x/z) itself is complete, and therefore, the regression function m(.) is nonparametrically identified. We use this general result provide specific sufficient conditions for completeness in three different specifications of the relationship between the endogenous regressor x and the instrumental variable z.

Date: 2011-06-25
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Citations: View citations in EconPapers (6)

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Related works:
Journal Article: NONPARAMETRIC IDENTIFICATION USING INSTRUMENTAL VARIABLES: SUFFICIENT CONDITIONS FOR COMPLETENESS (2018)
Working Paper: Nonparametric Identification Using Instrumental Variables: Sufficient Conditions For Completeness (2011)
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