Regression Discontinuity Design with Continuous Measurement Error in the Running Variable

Since the late 90s, regression discontinuity designs have been widely used to estimate local treatment effects. When the running variable is observed with continuous errors, identification fails even if the dispersion of measurement errors is small. Assuming non-differential measurement errors, we propose a consistent nonparametric estimator of the LATE when the true running variable is observed in an auxiliary sample of treated individuals. Such auxiliary information is usually collected by agencies in charge of delivering the treatment