Design-Based Analysis of Regression Discontinuities: Evidence from an Experimental Benchmark

The appeal of regression-discontinuity (RD) design arises from its interpretation as a local natural experiment. However, even many flexible forms of parametric estimation do not yield simple and transparent analysis in the spirit of this interpretation. While influential work in econometrics has interpreted the estimand in RD designs as a limit of potential-outcome regression functions at a discontinuity, this definition of causal parameters leads to complicated estimators that introduce discretion in applied work. We emphasize a simpler estimand --- the average causal effect for units in a window around the discontinuity --- and a transparent, design-based estimator of this parameter. Yet, this estimator is justified by a particular chance model; and the source of stochastic variation is not always readily apparent in RD designs. We discuss two different models: one in which units' score on an assignment covariate is viewed as the realization a unit-level random variable, and another in which the source of chance variation is manipulation of the key threshold, with unit scores held fixed. Using data from an experimental benchmark and bootstrap simulations, we explore how the properties of different estimators vary across these chance models.