Nonparametric Analysis of Treatment Effects in Ordered Response Models

Abstract

This paper deals with the identification of treatment effects when the outcome variable is ordered. If outcomes are measured ordinally, previously developed methods to investigate the impact of an endogenous binary regressor on average outcomes cannot be applied as the expectation of an ordered variable, in its strict sense, does not exist, and a shift in focus to distributional effects is indispensable. Without imposing a fully fledged parametric model the treatment effects are generally not point-identified. Assuming a threshold crossing model on both the ordered potential outcomes and the binary treatment variable leaving the distribution of error terms and functional forms unspecified, it is discussed how the treatment effects can be bounded and inference on the bounds can be conducted.