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Testing for stochastic monotonicity

Authors: Sokbae (Simon) Lee , Oliver Linton and Yoon-Jae Whang
Date: 31 July 2008
Type: cemmap Working Paper, CWP21/08
DOI: 10.1920/wp.cem.2008.2108


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 diffcult 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 infinite samples. We apply our test to the study of intergenerational income mobility.

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Sokbae (Simon) Lee and Oliver Linton March 2009, Testing for stochastic monotonicity, Journal article

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