Econometrica Vol. 77 No. 2 2009

Testing for Stochastic Monotonicity

Sokbae Lee¹; Oliver Linton²; Yoon-Jae Whang^3,4,5

¹ University College London · ² London School of Economics and Political Science · ³ Seoul National University · ⁴ Leverhulme Trust · ⁵ National University College

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.

DOI

10.3982/ecta7145

Volume

77

Issue

2

Pages

585-602

Language

en

Sources

openalex crossref

Cite

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