Sharp Bounds on Heterogeneous TReatment Responses

Abstract

This paper aims to identifiy heterogeneous causal effects of an ordered discrete variable chosen by individuals, without relying on parametric assumptions. The proposed nonparametric restrictions have set identifying power of the value of the nonseparable structural function. When applied to an "unordered" binary endogenous variable, our model can be used to answer the question regarding whether a policy/treatment has a positive or negative impact on an individual when his/her ranking in the unobserved characteristic is given. The identification result is applied to examine the effects of Vietnam-era veteran status on earnings. The empirical findings show that when other observable characteristics are the same, military service had positive impacts for those with low earnings potential, while individuals with high earnings potential had negative impacts.