The Devil is in the Tails: Regression Discontinuity Design with Measurement Error in the Assignment Variable

TL;DR

This paper addresses the challenge of identifying treatment effects in regression discontinuity designs when the assignment variable is measured with error, proposing conditions for identification and methods for estimation.

Contribution

It provides new identification conditions and estimation methods for RD designs with measurement error in the assignment variable, applicable to both discrete and continuous cases.

Findings

Identification is possible under certain conditions despite measurement error.

Proposed estimation procedures perform well in simulations.

Empirical application estimates Medicaid takeup effects.

Abstract

Identification in a regression discontinuity (RD) research design hinges on the discontinuity in the probability of treatment when a covariate (assignment variable) exceeds a known threshold. When the assignment variable is measured with error, however, the discontinuity in the relationship between the probability of treatment and the observed mismeasured assignment variable may disappear. Therefore, the presence of measurement error in the assignment variable poses a direct challenge to treatment effect identification. This paper provides sufficient conditions to identify the RD treatment effect using the mismeasured assignment variable, the treatment status and the outcome variable. We prove identification separately for discrete and continuous assignment variables and study the properties of various estimation procedures. We illustrate the proposed methods in an empirical application, where we estimate Medicaid takeup and its crowdout effect on private health insurance coverage.