A Correction for Regression Discontinuity Designs With Group-Specific Mismeasurement of the Running Variable
提出一种新的测量误差校正方法，解决断点回归中分组变量测量误差异质性问题，利用辅助信息修正偏差，并提供调整后的标准误和置信区间。
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.