Testing for Unobserved Heterogeneous Treatment Effects with Observational Data

TL;DR

This paper introduces a nonparametric, easy-to-implement test for detecting unobserved heterogeneity in treatment effects within observational data, accommodating self-selection and monotonicity assumptions.

Contribution

It develops a novel Kolmogorov-Smirnov-type test for unobserved heterogeneous treatment effects under standard assumptions, with demonstrated finite-sample performance and practical applications.

Findings

Test rejects homogeneity in fertility effects on family income.

Test fails to reject homogeneity in Job Training Program effects.

Method performs well in Monte Carlo simulations.

Abstract

Unobserved heterogeneous treatment effects have been emphasized in the recent policy evaluation literature (see e.g., Heckman and Vytlacil, 2005). This paper proposes a nonparametric test for unobserved heterogeneous treatment effects in a treatment effect model with a binary treatment assignment, allowing for individuals' self-selection to the treatment. Under the standard local average treatment effects assumptions, i.e., the no defiers condition, we derive testable model restrictions for the hypothesis of unobserved heterogeneous treatment effects. Also, we show that if the treatment outcomes satisfy a monotonicity assumption, these model restrictions are also sufficient. Then, we propose a modified Kolmogorov-Smirnov-type test which is consistent and simple to implement. Monte Carlo simulations show that our test performs well in finite samples. For illustration, we apply our test to study heterogeneous treatment effects of the Job Training Partnership Act on earnings and the impacts of fertility on family income, where the null hypothesis of homogeneous treatment effects gets rejected in the second case but fails to be rejected in the first application.