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Conditional Independence Restrictions: Testing and Estimation




We propose a nonparametric empirical distribution function based test of an hypothesis of conditional independence between variables of interest. This hypothesis is of interest both for model specification purposes, parametric and semiparametric, and for non-model 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^{-1/2} from the null; this result holding independently of dimension. Monte Carlo simulations provide evidence on size and power. Finally, we invert the test statistic to provide a method for estimating the parameters identified through the conditional independence restriction. They are asymptotically normal at rate root-n.

Suggested Citation

  • Oliver Linton & Pedro Gozalo, 1996. "Conditional Independence Restrictions: Testing and Estimation," Cowles Foundation Discussion Papers 1140, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1140

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    References listed on IDEAS

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    Cited by:

    1. Joeri Smits & Jeffrey S. Racine, 2013. "Testing Exclusion Restrictions in Nonseparable Triangular Models," Department of Economics Working Papers 2013-02, McMaster University.
    2. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    3. Cheng, Yu-Hsiang & Huang, Tzee-Ming, 2012. "A conditional independence test for dependent data based on maximal conditional correlation," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 210-226.
    4. Matos, João Manuel Gonçalves Amaro de & Fernandes, Marcelo, 2001. "Testing the Markov property with ultra high frequency financial data," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 414, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    5. Poirier, Alexandre, 2017. "Efficient estimation in models with independence restrictions," Journal of Econometrics, Elsevier, vol. 196(1), pages 1-22.
    6. Yanqin Fan & Oliver Linton, 1997. "Some Higher Order Theory for a Consistent Nonparametric Model Specification Test," Cowles Foundation Discussion Papers 1148, Cowles Foundation for Research in Economics, Yale University.
    7. Györfi, László & Walk, Harro, 2012. "Strongly consistent nonparametric tests of conditional independence," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1145-1150.

    More about this item


    Conditional independence; empirical distribution; independence; nonparametric; smooth bootstrap; test;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection


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