Limitless Regression Discontinuity

Abstract: Conventionally, regression discontinuity analysis contrasts a univariate regression's limits as its independent variable, $R$, approaches a cut-point, $c$, from either side. Alternative methods target the average treatment effect in a small region around $c$, at the cost of an assumption that treatment assignment, $\mathcal{I}\left[R<c\right]$, is ignorable vis a vis potential outcomes. Instead, the method presented in this paper assumes Residual Ignorability, ignorability of treatment assignment vis a vis detrended potential outcomes. Detrending is effected not with ordinary least squares but with MM-estimation, following a distinct phase of sample decontamination. The method's inferences acknowledge uncertainty in both of these adjustments, despite its applicability whether $R$ is discrete or continuous; it is uniquely robust to leading validity threats facing regression discontinuity designs.