Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Mar, 2009, Volume 77, Issue 2

Testing for Stochastic Monotonicity
p. 585-602

Sokbae Lee, Oliver Linton, Yoon‐Jae Whang

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 ‐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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Supplemental Material

Supplement to "Testing for Stochastic Monotonicity"

Mathematical proofs.

Supplement to "Testing for Stochastic Monotonicity"

File includes data and GAUSS programs for the application and simulation in the paper