A Correction for Regression Discontinuity Designs With Group-Specific Mismeasurement of the Running Variable

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 the measurement error structure is heterogeneous across different groups of observations. We develop a novel measurement error correction procedure capable of addressing heterogeneous mismeasurement structures by leveraging auxiliary information. We also provide adjusted asymptotic variance and standard errors that take into consideration the variability introduced by the estimation of nuisance parameters, and honest confidence intervals that account for potential misspecification. Simulations provide evidence that the proposed procedure corrects the bias introduced by heterogeneous measurement error and achieves empirical coverage closer to nominal test size than naive alternatives. Two empirical illustrations demonstrate that correcting for measurement error can either reinforce the results of a study or provide a new empirical perspective on the data.

Automated summary

This study introduces a novel measurement error correction procedure that addresses heterogeneous mismeasurement structures by utilizing auxiliary information. Adjusted asymptotic variance, standard errors, and honest confidence intervals are provided, with simulations showing that the proposed procedure corrects bias introduced by heterogeneous measurement error and achieves empirical coverage closer to nominal test size. Two empirical illustrations demonstrate the potential of correcting for measurement error to reinforce study results or provide new perspectives on data.