Regression Discontinuity Designs with Nonclassical Measurement Errors

We develop novel regression discontinuity inferences where the binary treatment and/or continuous assignment variable may contain measurement errors. For a measurement error of the binary treatment, the standard estimator is inconsistent for the causal parameter. To solve the problem, we develop a local linear generalized method of moments inference by using the availability of an exogenous variable. We then develop identification with a nonclassical measurement error for the assignment variable without additional information. We show that when some compliers accurately report their assignment values, the standard estimand may identify a meaningful causal parameter for them