A Flexible Nonparametric Test for Conditional Independence

40 Pages Posted: 11 Jun 2013

See all articles by Meng Huang

Meng Huang

Freddie Mac

Yixiao Sun

University of California, San Diego (UCSD) - Department of Economics

Halbert L. White, Jr.

University of California, San Diego (UCSD) - Department of Economics

Date Written: May 30, 2013

Abstract

This paper proposes a nonparametric test for conditional independence that is easy to implement, yet powerful in the sense that it is consistent and achieves n^{-1/2} local power. The test statistic is based on an estimator of the topological "distance" between restricted and unrestricted probability measures corresponding to conditional independence or its absence. The distance is evaluated using a family of Generically Comprehensively Revealing (GCR) functions, such as the exponential or logistic functions, which are indexed by nuisance parameters. The use of GCR functions makes the test able to detect any deviation from the null. We use a kernel smoothing method when estimating the distance. An integrated conditional moment (ICM) test statistic based on these estimates is obtained by integrating out the nuisance parameters. We simulate the critical values using a conditional simulation approach. Monte Carlo experiments show that the test performs well in finite samples. As an application, we test the key assumption of unconfoundedness in the context of estimating the returns to schooling.

Keywords: Conditional Independence, Generically Comprehensively Revealing, Nonparametric Test

Suggested Citation

Huang, Meng and Sun, Yixiao and White, Halbert L., A Flexible Nonparametric Test for Conditional Independence (May 30, 2013). Available at SSRN: https://ssrn.com/abstract=2277240 or http://dx.doi.org/10.2139/ssrn.2277240

Meng Huang (Contact Author)

Freddie Mac ( email )

8200 Jones Branch Road
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Yixiao Sun

University of California, San Diego (UCSD) - Department of Economics ( email )

9500 Gilman Drive
La Jolla, CA 92093-0508
United States
858-534-4692 (Phone)
858-534-7040 (Fax)

Halbert L. White

University of California, San Diego (UCSD) - Department of Economics ( email )

9500 Gilman Drive
La Jolla, CA 92093-0508
United States
858-534-3502 (Phone)
858-534-7040 (Fax)

HOME PAGE: http://www.econ.ucsd.edu/~mbacci/white/

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