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Identification in a regression discontinuity (RD) research design hinges onthe discontinuity in the probability of treatment when a covariate (assignmentvariable) exceeds a known threshold. When the assignment variable is measuredwith error, however, the discontinuity in the relationship between theprobability of treatment and the observed mismeasured assignment variable maydisappear. Therefore, the presence of measurement error in the assignmentvariable poses a direct challenge to treatment effect identification. Thispaper provides sufficient conditions to identify the RD treatment effect usingthe mismeasured assignment variable, the treatment status and the outcomevariable. We prove identification separately for discrete and continuousassignment variables and study the properties of various estimation procedures.We illustrate the proposed methods in an empirical application, where weestimate Medicaid takeup and its crowdout effect on private health insurancecoverage.

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