Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-23T23:04:00.523Z Has data issue: false hasContentIssue false
  • English
  • Français

A FLEXIBLE NONPARAMETRIC TEST FOR CONDITIONAL INDEPENDENCE

Published online by Cambridge University Press:  02 September 2015

Meng Huang ,
Yixiao Sun  and
Halbert White
Meng Huang*
Affiliation:
Freddie Mac
Yixiao Sun*
Affiliation:
UC San Diego
Halbert White
Affiliation:
UC San Diego
*
*Address correspondence to Meng Huang, Freddie Mac, 1551 Park Run Dr., McLean, VA 22102, USA; email: [email protected] or to Yixiao Sun, Department of Economics 0508, University of California, San Diego, La Jolla, CA 92093, USA; email: [email protected].
*Address correspondence to Meng Huang, Freddie Mac, 1551 Park Run Dr., McLean, VA 22102, USA; email: [email protected] or to Yixiao Sun, Department of Economics 0508, University of California, San Diego, La Jolla, CA 92093, USA; email: [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 an implication of the key assumption of unconfoundedness in the context of estimating the returns to schooling.

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 6 , December 2016 , pp. 1434 - 1482
Copyright
Copyright © Cambridge University Press 2015 

References

REFERENCES

Andrews, D.W.K. (1994) Empirical process methods in econometrics. In Engle, R.F. & McFadden, D.L. (eds.), Handbook of Econometrics, vol. IV, pp. 2248–2296. Elsevier.Google Scholar
Barnow, B.S., Cain, G.G., & Goldberger, A.S. (1981) Issues in the analysis of selectivity bias. In Stromsdorfer, W.E. & Farkas, G. (eds.), Evaluation Studies Review Annual, vol. 5, pp. 43–59. Sage.Google Scholar
Bierens, H.J. (1982) Consistent model specification tests. Journal of Econometrics 20,105–134.CrossRefGoogle Scholar
Bierens, H.J. (1990) A consistent conditional moment test of functional form. Econometrica 58, 1443–1458.CrossRefGoogle Scholar
Bierens, H.J. & Ploberger, W. (1997) Asymptotic theory of integrated conditional moment tests. Econometrica 65, 1129–1151.CrossRefGoogle Scholar
Bierens, H.J. & Wang, L. (2012) Integrated conditional moment tests for parametric conditional distributions. Econometric Theory 28, 328–362.CrossRefGoogle Scholar
Billingsley, P. (1999) Convergence of Probability Measures. Wiley.CrossRefGoogle Scholar
Blackburn, M. & Neumark, D. (1993) Omitted-ability bias and the increase in the return to schooling. Journal of Labor Economics 11, 521–544.CrossRefGoogle Scholar
Boning, W.B. & Sowell, F. (1999) Optimality for the integrated conditional moment test. Econometric Theory 15, 710–718.CrossRefGoogle Scholar
Dawid, A.P. (1979) Conditional independence in statistical theory. Journal of the Royal Statistical Society, Series B 41, 1–31.Google Scholar
Delgado, M. & Gonzalez-Manteiga, W. (2001) Significance testing in nonparametric regression based on the bootstrap. Annals of Statistics 29, 1469–1507.CrossRefGoogle Scholar
Fernandes, M. & Flores, R. (1999) Tests for Conditional Independence, Markovian Dynamics and Noncausality. Discussion paper, European University Institute.Google Scholar
Geenens, G. (2014) Probit transformation for kernel density estimation on the unit interval. Journal of the American Statistical Association 109(505), 346–358.CrossRefGoogle Scholar
Griliches, Z. (1977) Estimating the returns to schooling: Some econometric problems. Econometrica 45, l–22.CrossRefGoogle Scholar
Griliches, Z. & Mason, W.M. (1972) Education, income, and ability. The Journal of Political Economy 80(3), S74–S103.CrossRefGoogle Scholar
Hansen, B.E. (1996) Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 64, 413–430.CrossRefGoogle Scholar
Hoeffding, W. (1948) A class of statistics with asymptotically normal distribution. Annals of Mathematical Statistics 19, 293–325.CrossRefGoogle Scholar
Huang, M. (2009) Essays on testing conditional independence. Ph.D. dissertation, University of California. Available at http://escholarship.org/uc/item/15t6n3h6.Google Scholar
Lee, A.J. (1990). U-statistics: Theory and Practice. CRC Press.Google Scholar
Li, Q. & Fan, Y. (2003) A kernel-based method for estimating additive partially linear models. Statistica Sinica 13, 739–762.Google Scholar
Li, Q. & Racine, J.S. (2007) Nonparametric Econometrics. Princeton University Press.Google Scholar
Linton, O. & Gozalo, P. (1997) Conditional Independence Restrictions: Testing and Estimation. Discussion Paper, Yale University Cowles Foundation for Research in Economics.Google Scholar
Mincer, J. (1974) Schooling, Experience, and Earnings. Columbia University Press.Google Scholar
Powell, J.L., Stock, J.H., & Stoker, T.M. (1989) Semiparametric estimation of index coefficients. Econometrica 57, 1403–1430.CrossRefGoogle Scholar
Powell, J.L. & Stoker, T.M. (1996) Optimal bandwidth choice for density-weighted averages. Journal of Econometrics 75, 291–316.CrossRefGoogle Scholar
Robinson, P.M. (1988) Root-N-consistent semiparametric regression. Econometrica 56, 931–954.CrossRefGoogle Scholar
Song, K. (2009) Testing conditional independence via rosenblatt transforms. Annals of Statistics 37, 4011–4045.CrossRefGoogle Scholar
Stinchcombe, M. & White, H. (1998) Consistent specification testing with nuisance parameters present only under the alternative. Econometric Theory 14, 295–324.CrossRefGoogle Scholar
Su, L. & White, H. (2003) Testing Conditional Independence Via Empirical Likelihood. Discussion Paper, UCSD Department of Economics.Google Scholar
Su, L. & White, H. (2007) A consistent characteristic function-based test for conditional independence. Journal of Econometrics 141, 807–834.CrossRefGoogle Scholar
Su, L. & White, H. (2008) A nonparametric hellinger metric test for conditional independence. Econometric Theory 24, 829–864.CrossRefGoogle Scholar
Su, L. & White, H. (2010) Testing structural change in partially linear models. Econometric Theory 26, 1761–1806.CrossRefGoogle Scholar
White, H. & Chalak, K. (2008) Identifying Structural Effects in Nonseparable Systems Using Covariates. Discussion Paper, UCSD Department of Economics.Google Scholar
White, H. & Chalak, K. (2010) Testing a conditional form of exogeneity. Economics Letters 109, 88–90.CrossRefGoogle Scholar