Conditional Independence Restrictions: Testing and Estimation

Oliver Linton and Pedro Gozalo
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Pedro Gozalo: Brown University

No 1140, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

Keywords: Conditional independence; empirical distribution; independence; nonparametric; smooth bootstrap; test (search for similar items in EconPapers)
JEL-codes: C12 C14 C15 C52 (search for similar items in EconPapers)
Pages: 47 pages
Date: 1996-11
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Citations: View citations in EconPapers (11)

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