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, $\mathrm{I}\left[\mathrm{R}<\mathrm{c}\right]$ , is ignorable vis-à-vis potential outcomes. Instead, the method presented in this article assumes “residual ignorability,” ignorability of treatment assignment vis-à-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.