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Estimation of a treatment effect by a regression discontinuity design faces asevere challenge when the running variable contains measurement errors sincethe errors smoothen the discontinuity on which the identification depends. Theexisting studies show that the variance of the measurement errors plays a vitalrole in both bias correction and identification under such situations. However,the methodologies to estimate the variance from data are relativelyundeveloped. This paper proposes two estimators for the variance of measurementerrors of running variables of sharp regression continuity designs. Theproposed estimators can be constructed merely from data of observed runningvariable and treatment assignment, and do not require any other external sourceof information.

Estimating the Variance of Measurement Errors in Running Variables of Sharp Regression Discontinuity Designs