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A Flexible Nonparametric Test for Conditional Independence

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  • Huang, Meng
  • Sun, Yixiao
  • White, Hal

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 root-n 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 Önite samples. As an application, we test the key assumption of unconfoundedness in the context of estimating the returns to schooling.

Suggested Citation

  • Huang, Meng & Sun, Yixiao & White, Hal, 2013. "A Flexible Nonparametric Test for Conditional Independence," University of California at San Diego, Economics Working Paper Series qt3pt89204, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt3pt89204
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    References listed on IDEAS

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    1. Halbert White & Karim Chalak, 2008. "Identifying Structural Effects in Nonseparable Systems Using Covariates," Boston College Working Papers in Economics 734, Boston College Department of Economics.
    2. Su, Liangjun & White, Halbert, 2007. "A consistent characteristic function-based test for conditional independence," Journal of Econometrics, Elsevier, vol. 141(2), pages 807-834, December.
    3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    4. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    5. Su, Liangjun & White, Halbert, 2008. "A Nonparametric Hellinger Metric Test For Conditional Independence," Econometric Theory, Cambridge University Press, vol. 24(04), pages 829-864, August.
    6. Su, Liangjun & White, Halbert, 2014. "Testing conditional independence via empirical likelihood," Journal of Econometrics, Elsevier, vol. 182(1), pages 27-44.
    7. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    8. Racine, Jeffrey S., 2008. "Nonparametric Econometrics: A Primer," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(1), pages 1-88, March.
    9. Boning, Wm. Brent & Sowell, Fallaw, 1999. "Optimality For The Integrated Conditional Moment Test," Econometric Theory, Cambridge University Press, vol. 15(05), pages 710-718, October.
    10. Powell, James L. & Stoker, Thomas M., 1996. "Optimal bandwidth choice for density-weighted averages," Journal of Econometrics, Elsevier, vol. 75(2), pages 291-316, December.
    11. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-1458, November.
    12. Griliches, Zvi, 1977. "Estimating the Returns to Schooling: Some Econometric Problems," Econometrica, Econometric Society, vol. 45(1), pages 1-22, January.
    13. Blackburn, McKinley L & Neumark, David, 1993. "Omitted-Ability Bias and the Increase in the Return to Schooling," Journal of Labor Economics, University of Chicago Press, vol. 11(3), pages 521-544, July.
    14. Su, Liangjun & White, Halbert, 2010. "Testing Structural Change In Partially Linear Models," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1761-1806, December.
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    Cited by:

    1. Yu-Chin Hsu & Ta-Cheng Huang & Haiqing Xu, 2018. "Testing for unobserved heterogeneous treatment effects in a nonseparable model with endogenous selection," Papers 1803.07514, arXiv.org.
    2. Su, Liangjun & White, Halbert, 2014. "Testing conditional independence via empirical likelihood," Journal of Econometrics, Elsevier, vol. 182(1), pages 27-44.
    3. Lu, Xun & White, Habert, 2015. "Testing For Treatment Dependence Of Effects Of A Continuous Treatment," Econometric Theory, Cambridge University Press, vol. 31(05), pages 1016-1053, October.
    4. Hoderlein, Stefan & Su, Liangjun & White, Halbert & Yang, Thomas Tao, 2016. "Testing for monotonicity in unobservables under unconfoundedness," Journal of Econometrics, Elsevier, vol. 193(1), pages 183-202.
    5. Lu, Xun & White, Halbert, 2014. "Testing for separability in structural equations," Journal of Econometrics, Elsevier, vol. 182(1), pages 14-26.
    6. repec:eee:ecolet:v:156:y:2017:i:c:p:162-167 is not listed on IDEAS

    More about this item

    Keywords

    Social and Behavioral Sciences; Physical Sciences and Mathematics; Conditional Independence; Generically Comprehensively Revealing; Nonparametric Test;

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