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This paper proposes a new nonparametric test for conditional independence, which is based on the comparison of Bernstein copula densities using the Hellinger distance. The test is easy to implement because it does not involve a weighting function in the test statistic, and it can be applied in general settings since there is no restriction on the dimension of the data. In fact, to apply the test, only a bandwidth is needed for the nonparametric copula. We prove that the test statistic is asymptotically pivotal under the null hypothesis, establish local power properties, and motivate the validity of the bootstrap technique that we use in finite sample settings. A simulation study illustrates the good size and power properties of the test. We illustrate the empirical relevance of our test by focusing on Granger causality using financial time series data to test for nonlinear leverage versus volatility feedback effects and to test for causality between stock returns and trading volume. In a third application, we investigate Granger causality between macroeconomic variables.

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Abstract. In this paper, we propose a general method for testing inequality restrictions on nonparametric functions. Our framework includes many nonparametric testing problems in a unified framework, with a number of possible applications in auction models, game theoretic models, wage inequality, and revealed preferences. Our test involves a one-sided version of Lp functionals of kernel-type estimators (1 ≤ p < ∞) and is easy to implement in general, mainly due to its recourse to the bootstrap method. The bootstrap procedure is based on nonparametric bootstrap applied to kernel-based test statistics, with estimated “contact sets. ” We provide regularity conditions under which the bootstrap test is asymptot-ically valid uniformly over a large class of distributions, including the cases that the limiting distribution of the test statistic is degenerate. Our bootstrap test is shown to exhibit good power properties in Monte Carlo experiments, and we provide a general form of the local power function. As an illustration, we consider testing implications from auction theory, provide primitive conditions for our test, and demonstrate its usefulness by applying our test to real data. We supplement this example with the second empirical illustration in the context of wage inequality. Key words. Bootstrap, conditional moment inequalities, kernel estimation, local poly-nomial estimation, Lp norm, nonparametric testing, partial identification, Poissonization, quantile regression, uniform asymptotics

A nonparametric copula based test for conditional independence with applications to Granger causality

We construct a Kolmogorov-Smirnov test for the null hypothesis that the average treatment effect is non-negative conditional on all possible values of the covariates. The null hypothesis of our interest can be characterized as a conditional moment inequality under the unconfoundedness assumption, and we employ the instrumental variable method to convert the conditional moment inequality into unconditional ones without information loss. The Kolmogorov-Smirnov test is constructed based on these unconditional moment inequalities. It is shown that our test can control the size asymptotically, is consistent against fixed alternatives, and is unbiased against some N −1/2 local alternatives. Furthermore, our test is more powerful than Lee and Whang’s (2009) against a broad set of N −1/2 local alternatives. Monte-Carlo simulation results confirm our theoretical findings. Several interesting extensions are discussed too. JEL classification: C01, C12, C21

grants SEJ 2007-63098 is also acknowledged.

This paper proposes new nonparametric tests for treatment effects when the out-come of interest, typically a duration, is subjected to right censoring. Our tests are based on Kaplan-Meier integrals, and do not rely on distributional assumptions, shape restrictions, nor on restricting the potential treatment effect heterogeneity across dif-ferent subpopulations. The proposed tests are consistent against fixed alternatives and can detect nonparametric alternatives converging to the null at the parametric n−1/2-rate, n being the sample size. Finite sample properties of the proposed tests are examined by means of a Monte Carlo study. We illustrate the use of the proposed pol-icy evaluation tools by studying the effect of labor market programs on unemployment duration based on experimental and observational datasets.

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