When can we ignore measurement error in the running variable?
Yingying Dong, Michal Kolesár
Abstract
Summary In many applications of regression discontinuity designs, the running variable used to assign treatment is only observed with error. We show that, provided the observed running variable (i) correctly classifies treatment assignment and (ii) affects the conditional means of potential outcomes smoothly, ignoring the measurement error nonetheless yields an estimate with a causal interpretation: the average treatment effect for units whose observed running variable equals the cutoff. Possibly after doughnut trimming, these assumptions accommodate a variety of settings where support of the measurement error is not too wide. An empirical application illustrates the results for both sharp and fuzzy designs.
Topics & Concepts
TrimmingVariable (mathematics)Regression discontinuity designComputer scienceStatisticsObservational errorType I and type II errorsCutoffFuzzy logicInstrumental variableEconometricsInterpretation (philosophy)RegressionMathematicsAlgorithmArtificial intelligenceProgramming languageMathematical analysisPhysicsOperating systemQuantum mechanicsStatistical Methods and InferenceAdvanced Causal Inference TechniquesAdvanced Statistical Methods and Models