Working Paper

Testing for stochastic monotonicity


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

Published Date

31 July 2008


Working Paper (CWP21/08)

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 diffcult 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 infinite samples. We apply our test to the study of intergenerational income mobility.

Latest version

Testing for stochastic monotonicity
Sokbae (Simon) Lee, Oliver Linton