Generic inference on quantile and quantile effect functions for discrete outcomes

This paper provides a method to construct simultaneous con?dence bands for quantile and quantile effect functions for possibly discrete or mixed discrete-continuous random variables. The construction is generic and does not depend on the nature of the underlying problem. It works in conjunction with parametric, semiparamet-ric, and nonparametric modeling strategies and does not depend on the sampling schemes. It is based upon projection of simultaneous con?dence bands for distribution functions. We apply our method to analyze the distributional impact of insurance coverage on health care utilization and to provide a distributional decomposition of the racial test score gap. Our analysis generates new interesting ?ndings, and com-plements previous analyses that focused on mean effects only. In both applications, the outcomes of interest are discrete rendering standard inference methods invalid for obtaining uniform con?dence bands for quantile and quantile effects functions.