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Testing for stochastic monotonicity

Authors: Sokbae (Simon) Lee and Oliver Linton
Date: 01 March 2009
Type: Journal article, Econometrica, Vol. 77, No. 2, pp. 585-602


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.

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Sokbae (Simon) Lee, Oliver Linton and Yoon-Jae Whang July 2008, Testing for stochastic monotonicity, cemmap Working Paper, CWP21/08

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