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A Flexible Nonparametric Test for Conditional Independence

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

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.

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Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt3pt89204.

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Date of creation: 01 May 2013
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Handle: RePEc:cdl:ucsdec:qt3pt89204
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  1. Su, Liangjun & White, Halbert, 2003. "A Consistent Characteristic-Function-Based Test for Conditional Independence," University of California at San Diego, Economics Working Paper Series qt4dv0837f, Department of Economics, UC San Diego.
  2. Racine, Jeffrey S., 2008. "Nonparametric Econometrics: A Primer," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(1), pages 1-88, March.
  3. Su, Liangjun & White, Halbert, 2014. "Testing conditional independence via empirical likelihood," Journal of Econometrics, Elsevier, vol. 182(1), pages 27-44.
  4. 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.
  5. 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.
  6. 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 521-44, July.
  7. Griliches, Zvi, 1977. "Estimating the Returns to Schooling: Some Econometric Problems," Econometrica, Econometric Society, vol. 45(1), pages 1-22, January.
  8. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November.
  9. Bierens, H.J. & Ploberger, W., 1995. "Asymptotic theory of integrated conditional moment tests," Discussion Paper 1995-124, Tilburg University, Center for Economic Research.
  10. Su, Liangjun & White, Halbert, 2010. "Testing Structural Change In Partially Linear Models," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1761-1806, December.
  11. 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.
  12. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
  13. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
  14. 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.
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