Abstract

This paper proposes a nonparametric test for conditional independence that is easy to implement, yet powerful in the sense that it is consistent and achieves n^{-1/2} local power. The test statistic is based on an estimator of the topological between restricted and unrestricted probability measures corresponding to conditional independence or its absence. The distance is evaluated using a family of Generically Comprehensively Revealing (GCR) functions, such as the exponential or logistic functions, which are indexed by nuisance parameters. The use of GCR functions makes the test able to detect any deviation from the null. We use a kernel smoothing method when estimating the distance. An integrated conditional moment (ICM) test statistic based on these estimates is obtained by integrating out the nuisance parameters. We simulate the critical values using a conditional simulation approach. Monte Carlo experiments show that the test performs well in finite samples. As an application, we test the key assumption of unconfoundedness in the context of estimating the returns to schooling.

Highlights

  • We propose a ‡exible nonparametric test for conditional independence

  • Dawid (1979) showed that some simple heuristic properties of conditional independence can form a conceptual framework for many important topics in statistical inference: su¢ ciency and ancillarity, parameter identi...cation, causal inference, prediction su¢ ciency, data selection mechanisms, invariant statistical models, and a subjectivist approach to model-building

  • We develop a ‡exible nonparametric test for conditional independence that is simple to implement, yet powerful

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Summary

Introduction

We propose a ‡exible nonparametric test for conditional independence. Let X; Y; and Z be three random vectors. Whereas Bierens (1982, 1990) and Bierens and Ploberger (1997) construct tests essentially by comparing a restricted parametric and an unrestricted regression model, the test in this paper follows a suggestion of StW, basing the test on estimates of the topological distance between unrestricted and restricted probability measures, corresponding to conditional independence or its absence. This distance is measured indirectly by a family of moments, which are the di¤erences of the expectations under the null and under the alternative for a set of test functions. The last section concludes and discusses directions for further research

The Null Hypothesis
An Equivalent Null Hypothesis in Moment Conditions
Heuristics for Rates
Xn 4 1 n n1
Assumptions
Stochastic Approximations
2: It follows from Lemmas 1 and 2 that p n h
The Test Statistic
Asymptotic Distribution of the Test Statistic
Calculating the Asymptotic Critical Values
A Rescaled ICM Test
Monte Carlo Experiments
Level and Power Studies
Comparison with Other Tests
Application to Returns to Schooling
Concluding Remarks
Full Text
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