This paper discusses testable implications of rank invariance or rank similarity, assumptions that are common in program evaluation and in the quantile treatment effect (QTE) literature. We nonparametrically identify, estimate, and test the counterfactual distribution of potential ranks, or features of the distribution. The proposed tests allow treatment to be endogenous, with exogenous treatment following as a special case. The tests essentially do not require any additional assumptions other than those to identify and estimate QTEs. We apply the proposed tests to investigate whether the Job Training Partnership Act training causes trainees to systematically change their ranks in the earnings distribution.

This paper proposes consistent testing methods for examining the effect of a policy treatment on the whole distribution of a response outcome within the setting of a regression discontinuity design. These methods are particularly useful when a policy is expected to produce treatment effects that are heterogeneous along some unobserved characteristics. The test statistics are Kolmogorov-Smirnov-type and are asymptotically distribution free when the data are i.i.d. The proposed tests are applied to three seminal RD studies (Pop-Eleches & Urquiola, 2013; Abdulkadiroglu, Angrist, & Pathak, 2014; and Battistin et al., 2009).