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Conditional Independence Restrictions: Testing and Estimation

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Author Info
Oliver Linton (Cowles Foundation, Yale University)
Pedro Gozalo (Brown University)

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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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Publisher Info
Paper provided by Cowles Foundation, 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: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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

Other versions of this item:

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

References listed on IDEAS
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    Other versions:
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  7. 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.
    Other versions:
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    Other versions:
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  18. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
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  27. repec:cup:etheor:v:11:y:1995:i:3:p:560-96 is not listed on IDEAS
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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, Graduate School of Economics, Getulio Vargas Foundation (Brazil). [Downloadable!]
    Other versions:
  2. Yanqin Fan & Oliver Linton, 1997. "Some Higher Order Theory for a Consistent Nonparametric Model Specification Test," Cowles Foundation Discussion Papers 1148, Cowles Foundation, Yale University. [Downloadable!]
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