Regression Discontinuity Designs with Nonclassical Measurement Errors

This paper develops a nonparametric identification analysis in regression discontinuity (RD) designs where each observable may contain measurement error. Our analysis allows the measurement error to be nonclassical in the sense that it can be arbitrarily dependent of the unobservables as long as the joint distribution satisfies a few smoothness conditions. We provide formal identification conditions under which the standard RD estimand based on the observables identifies a local weighted average treatment effect parameter. We also show that our identifying conditions imply a testable implication of the continuous density of the observable assignment variable.