Testing for Rank Invariance or Similarity in Program Evaluation

Abstract

This paper discusses testable implications of rank invariance or rank similarity, assumptions that are common in program evaluation and quantile treatment eect (QTE) models. We nonparametrically identify and test the counterfactual distribution of individual potential ranks, or features of the distribution. The tests allow treatment to be endogenous, while essentially not requiring any additional assumptions other than those used to identify and estimate QTEs. We focus on testing ranks in the unconditional distribution of potential outcomes, and briey discuss testing for invariance or similarity of conditional ranks. The proposed tests are applied to the JTPA training program and Project STAR. For the former, we investigate whether job training causes individuals to systematically change their ranks in the earnings distribution; for the latter, we analyze the impacts of small classes and teacher aides on the gender performance gap in early childhood education. Also investigated is how these educational treatments interact with teacher experience in aecting students’ relative performance.