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Testing for Stochastic Monotonicity
Author(s) -
Lee Sokbae,
Linton Oliver,
Whang YoonJae
Publication year - 2009
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta7145
Subject(s) - infimum and supremum , gumbel distribution , monotonic function , mathematics , asymptotic distribution , statistical hypothesis testing , statistic , test statistic , mathematical economics , gaussian , econometrics , mathematical optimization , statistics , discrete mathematics , mathematical analysis , extreme value theory , physics , quantum mechanics , estimator
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.