Testing for Stochastic Monotonicity

Sokbae (Simon) Lee (), Oliver Bruce Linton () and Yoon-Jae Whang ()

Econometrica, 2009, vol. 77, issue 2, pages 585-602

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. Copyright 2009 The Econometric Society.

Date: 2009
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Related works:
Working Paper: Testing for stochastic monotonicity (2008)
Working Paper: TESTING FOR STOCHASTICMONOTONICITY (2006)
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