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Testing Conditional Independence Restrictions

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  • Oliver Linton
  • Pedro Gozalo

Abstract

We propose a nonparametric test of the hypothesis of conditional independence between variables of interest based on a generalization of the empirical distribution function. This hypothesis is of interest both for model specification purposes, parametric and semiparametric, and for nonmodel-based testing of economic hypotheses. We allow for both discrete variables and estimated parameters. The asymptotic null distribution of the test statistic is a functional of a Gaussian process. A bootstrap procedure is proposed for calculating the critical values. Our test has power against alternatives at distance n -super-&minus1/2 from the null; this result holding independently of dimension. Monte Carlo simulations provide evidence on size and power.

Suggested Citation

  • Oliver Linton & Pedro Gozalo, 2014. "Testing Conditional Independence Restrictions," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 523-552, August.
    • Handle: RePEc:taf:emetrv:v:33:y:2014:i:5-6:p:523-552
    DOI: 10.1080/07474938.2013.825135
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    References listed on IDEAS

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    1. James Heckman & Hidehiko Ichimura & Jeffrey Smith & Petra Todd, 1998. "Characterizing Selection Bias Using Experimental Data," Econometrica, Econometric Society, vol. 66(5), pages 1017-1098, September.
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    Cited by:

    1. Hsu, Yu-Chin & Huang, Ta-Cheng & Xu, Haiqing, 2023. "Testing For Unobserved Heterogeneous Treatment Effects With Observational Data," Econometric Theory, Cambridge University Press, vol. 39(3), pages 582-622, June.
    2. Xiaojun Song & Haoyu Wei, 2021. "Nonparametric Tests of Conditional Independence for Time Series," Papers 2110.04847, arXiv.org.
    3. Wang, Hongfei & Liu, Binghui & Feng, Long & Ma, Yanyuan, 2024. "Rank-based max-sum tests for mutual independence of high-dimensional random vectors," Journal of Econometrics, Elsevier, vol. 238(1).
    4. Xuehu Zhu & Jun Lu & Jun Zhang & Lixing Zhu, 2021. "Testing for conditional independence: A groupwise dimension reduction‐based adaptive‐to‐model approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 549-576, June.
    5. Ai, Chunrong & Sun, Li-Hsien & Zhang, Zheng & Zhu, Liping, 2024. "Testing unconditional and conditional independence via mutual information," Journal of Econometrics, Elsevier, vol. 240(2).
    6. Su, Liangjun & Zheng, Xin, 2017. "A martingale-difference-divergence-based test for specification," Economics Letters, Elsevier, vol. 156(C), pages 162-167.

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