Testing for stochastic monotonicity - Sokbae Lee; Oliver Linton; Yoon-Jae Whang (Centre for Microdata Methods and Practice (cemmap), 2008)
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.
Keywords: C14; C15; 330; Distribution function; Extreme Value Theory; Gaussian Process; Monotonicity; Statistischer Test; Stochastischer Prozess; Statistische Verteilung; Intergenerational Mobility; Einkommensverteilung; Theorie