Journal Article

Testing for stochastic monotonicity

Authors

Sokbae (Simon) Lee, Oliver Linton

Published Date

1 March 2009

Type

Journal Article

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.


Previous version

Testing for stochastic monotonicity
Sokbae (Simon) Lee, Oliver Linton, Yoon-Jae Whang
CWP21/08