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Conditional Independence Restrictions: Testing and Estimation

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Abstract

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.

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File URL: http://cowles.econ.yale.edu/P/cd/d11a/d1140.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1140.

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Length: 47 pages
Date of creation: Nov 1996
Date of revision:
Handle: RePEc:cwl:cwldpp:1140

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

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

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References

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Citations

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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. 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.
  3. Imbens, Guido W. & Wooldridge, Jeffrey M., 2008. "Recent Developments in the Econometrics of Program Evaluation," IZA Discussion Papers 3640, Institute for the Study of Labor (IZA).
  4. Matos, João Manuel Gonçalves Amaro de & Fernandes, Marcelo, 2001. "Testing The Markov Property with Ultra High Frequency Financial Data," Economics Working Papers (Ensaios Economicos da EPGE) 414, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  5. Györfi, László & Walk, Harro, 2012. "Strongly consistent nonparametric tests of conditional independence," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1145-1150.

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