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Testing for stochastic monotonicity

  • Sokbae (Simon) Lee


    (Institute for Fiscal Studies)

  • Oliver Linton


    (Institute for Fiscal Studies and University of Cambridge)

  • Yoon-Jae Whang


    (Institute for Fiscal Studies and SNU)

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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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP21/08.

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Date of creation: Jul 2008
Date of revision:
Handle: RePEc:ifs:cemmap:21/08
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