Generic inference on quantile and quantile effect functions for discrete outcomes

This paper provides a method to construct simultaneous con fidence bands for quantile and quantile eff ect 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, semiparametric, and nonparametric modeling strategies and does not depend on the sampling schemes. It is based upon projection of simultaneous con dfidence 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 fi ndings, and complements previous analyses that focused on mean e ffects only. In both applications, the outcomes of interest are discrete rendering standard inference methods invalid for obtaining uniform con fidence bands for quantile and quantile e ffects functions.