Journal
ECONOMETRICA
Volume 77, Issue 2, Pages 585-602Publisher
WILEY
DOI: 10.3982/ECTA7145
Keywords
Distribution function; extreme value theory; Gaussian process; monotonicity
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Funding
- Centre for Microdata Methods and Practice
- ESRC
- Korean government [KRF-2005-041-B00074]
- Economic and Social Research Council [ES/F015879/1, ES/F015232/1] Funding Source: researchfish
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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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