Identification in a regression discontinuity (RD) design hinges on the discontinuity in the probability of treatment when a covariate (assignment variable) exceeds a known threshold. If 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 challenge to treatment effect identification. This chapter 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.
We thank two anonymous referees, Orley Ashenfelter, Eric Auerbach, Matias Cattaneo, Eleanor Choi, Damon Clark, Kirill Evdokimov, Hank Farber, Marjolaine Gauthier-Loiselle, Jian Kang, Marta Lachowska, Lars Lefgren, Pauline Leung, Jia Li, Carl Lieberman, Andrew Marder, Alex Mas, Jordan Matsudaira, Alexander Meister, Stephen Nei, Andrew Shephard, Lara Shore-Sheppard, and especially Bo Honor and David Lee for helpful comments. We have also benefited from helpful suggestions given by the participants of the Princeton Labor Seminar, Princeton Political Science Methodology Seminar and the Advances in Econometrics conference at the University of Michigan. We thank David Card and Lara Shore-Sheppard for graciously sharing their data. Zhuan Pei gratefully acknowledges financial support from the Richard A. Lester Fellowship. Finally, we thank Yue Fang, Suejin Lee, Katherine Wen and Le Wu for outstanding research assistance.
Pei, Z. and Shen, Y. (2017), "The Devil is in the Tails: Regression Discontinuity Design with Measurement Error in the Assignment Variable", Regression Discontinuity Designs (Advances in Econometrics, Vol. 38), Emerald Publishing Limited, Bingley, pp. 455-502. https://doi.org/10.1108/S0731-905320170000038019
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