Jumpy or Kinky? Regression Discontinuity without the Discontinuity

Regression Discontinuity (RD) models identify local treatment effects by associating a discrete change in the mean outcome with a corresponding discrete change in the probability of treatment at a known threshold of a running variable. This paper shows that it is possible to identify RD model treatment effects without a discontinuity. The intuition is that identification can come from a slope change (a kink) instead of a discrete level change (a jump) in the treatment probability. Formally this can be shown using L'hopital's rule. The identification results are interpreted intuitively using instrumental variable models. Estimators are proposed that can be applied in the presence or absence of a discontinuity, by exploiting either a jump or a kink.