Testing conditional independence restrictions

Linton, O. and Gozalo, P.

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 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.