Regression Discontinuity Design with Multivalued Treatments

TL;DR

This paper extends Regression Discontinuity Design to multivalued treatments, providing conditions for identification, estimation methods, and an application to health insurance effects.

Contribution

It introduces identification conditions and a practical Two-Stage Least Squares estimator for multivalued treatments in RDD.

Findings

Identification of treatment effects depends on treatment discontinuity independence.

Linear independence of treatment discontinuities enables weighted average effect identification.

The proposed estimator is implementable with standard software and validated through an empirical application.

Abstract

We study identification and estimation in the Regression Discontinuity Design (RDD) with a multivalued treatment variable. We also allow for the inclusion of covariates. We show that without additional information, treatment effects are not identified. We give necessary and sufficient conditions that lead to identification of LATEs as well as of weighted averages of the conditional LATEs. We show that if the first stage discontinuities of the multiple treatments conditional on covariates are linearly independent, then it is possible to identify multivariate weighted averages of the treatment effects with convenient identifiable weights. If, moreover, treatment effects do not vary with some covariates or a flexible parametric structure can be assumed, it is possible to identify (in fact, over-identify) all the treatment effects. The over-identification can be used to test these assumptions. We propose a simple estimator, which can be programmed in packaged software as a Two-Stage Least Squares regression, and packaged standard errors and tests can also be used. Finally, we implement our approach to identify the effects of different types of insurance coverage on health care utilization, as in Card, Dobkin and Maestas (2008).