Identification in Regression Discontinuity Designs with Measurement Error

Abstract

This paper studies the identification of the treatment effect by the local polynomial estimator in regression discontinuity designs with measurement error. In the sharp design, when the measurement error is fixed, the treatment effect can be identified in some special cases if the treatment is based on the contaminated forcing variable, and cannot be identified if the treatment is based on the genuine forcing variable. If the measurement error is shrinking to zero, the treatment effect can be identified with a small extra bias and without efficiency loss if the treatment is based on the contaminated forcing variable; the treatment effect can be identified with efficiency loss and a large bias if the treatment is based on the genuine forcing variable and the treatment status can be observed; the treatment effect cannot be identified if the treatment is based on the genuine forcing variable and the treatment status cannot be observed unless the measurement error is extremely small. We extend the results to the fuzzy design. The Monte Carlo results confirm the theoretical analysis.