Testing Conditional Independence via Rosenblatt Transforms

Kyungchul Song ()
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Kyungchul Song: Department of Economics, University of Pennsylvania

PIER Working Paper Archive from Penn Institute for Economic Research, Department of Economics, University of Pennsylvania

Abstract: This paper investigates the problem of testing conditional independence of Y and Z given λθ(X) for some unknown θ ∈ Θ ⊂ Rd, for a parametric function λθ(•). For instance, such a problem is relevant in recent literatures of heterogeneous treatment effects and contract theory. First, this paper finds that using Rosenblatt transforms in a certain way, we can construct a class of tests that are asymptotically pivotal and asymptotically unbiased against √n-converging Pitman local alternatives. The asymptotic pivotalness is convenient especially because the asymptotic critical values remain invariant over different estimators of the unknown parameter θ. Even when tests are asymptotically pivotal, however, it is often the case that simulation methods to obtain asymptotic critical values are yet unavailable or complicated, and hence this paper suggests a simple wild bootstrap procedure. A special case of the proposed testing framework is to test the presence of quantile treatment effects in a program evaluation data set. Using the JTPA training data set, we investigate the validity of nonexperimental procedures for inferences about quantile treatment effects of the job training program.

Keywords: Conditional independence; asymptotic pivotal tests; Rosenblatt transforms; wild bootstrap (search for similar items in EconPapers)
JEL-codes: C12 C14 C52 (search for similar items in EconPapers)
Pages: 52 pages
Date: 2007-09-05
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ppm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:pen:papers:07-026

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