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Testing for stochastic monotonicity

By Sokbae Lee, Oliver Linton and Yoon-Jae Whang

Abstract

We propose a test of the hypothesis of stochastic monotonicity. This hypothesis is of interest in many applications in economics. Our test is based on the supremum of a rescaled U-statistic. We show that its asymptotic distribution is Gumbel. The proof is difficult because the approximating Gaussian stochastic process contains both a stationary and a nonstationary part, and so we have to extend existing results that only apply to either one or the other case. We also propose a refinement to the asymptotic approximation that we show works much better in finite samples. We apply our test to the study of intergenerational income mobility

Topics: HB Economic Theory
Publisher: Wiley-Blackwell
Year: 2009
DOI identifier: 10.3982/ECTA7145
OAI identifier: oai:eprints.lse.ac.uk:30597
Provided by: LSE Research Online
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