When the running variable in a regression discontinuity (RD) design is measured with error, identification of the local average treatment effect of interest will typically fail. While the form of this measurement error varies across applications, in many cases there is a group structure to the measurement error. We develop a procedure to make use of this group-specific measurement error structure to correct estimates obtained in a regression discontinuity framework using auxiliary data. This procedure extends the prior literature on measurement error on the running variable by leveraging auxiliary information in order to account for more general forms of measurement error. Additionally, we develop adjusted asymptotic variance and standard errors that take in consideration the variability introduced by the nonparametric estimation of nuisance parameters from auxiliary data.
Simulations provide evidence that the proposed procedure adequately corrects for measurement error introduced bias and tests using the new adjusted formulas exhibit empirical coverage closer nominal test size than ``naive'' alternatives. We provide two empirical illustrations to demonstrate that correcting for measurement error can either reinforce the results of a study or provide a new empirical perspective on the data.
C14, C21, I12, J65
Original Release Date: May 16, 2018
Department of Economics, Iowa State University
Bartalotti, Otávio; Brummet, Quentin; and Dieterle, Steven, "A Correction for Regression Discontinuity Designs with Group-Specific Mismeasurement of the Running Variable" (2018). Economics Working Papers: Department of Economics, Iowa State University. 18008.