Random Measurement Error Does Not Bias the Treatment Effect Estimate in the Regression-Discontinuity Design

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Abstract
This article examines the regression-discontinuity (RD) design when there is random measure ment error and a treatment interaction effect. Two simulation issues -the specification of the pretest-posttest functional form and the choice of the point-of-estimation of the treatment effect- are examined Traditionally, an interaction effect in the general linear model has been con structed after centering the true scores by subtracting their mean. However, because the RD design has traditionally estimated the treatment effect at the cutoff, one is liable to obtain an apparently biased treatment effect that is actually attributable to the misspecification with regard to the point-of-estimation. Formulas are provided that allow one to control exactly in simulations the magnitude of a treatment effect at any point-of-estimation. These formulas can also be used for simulating the randomized experimental (RE) case where estimation is not at the pretest mean.