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Testing Conditional Independence Restrictions

Authors: Pedro Gozalo and Oliver Linton
Date: 27 November 2013
Type: Journal Article, Econometric Reviews, Vol. 33, No. 5-6, pp. 523-552
DOI: 10.1080/07474938.2013.825135

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 −1/2from the null; this result holding independently of dimension. Monte Carlo simulations provide evidence on size and power.

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