Jump or Kink? Identification of Binary Treatment Regression Discontinuity Design without the Discontinuity

Standard Regression Discontinuity (RD) designs exploit a discontinuity (a jump) in the treatment probability to identify a local average treatment effect (LATE). RD identification fails or is weak when there is no jump or the jump is small. Unlike regression kink design (RKD), which requires a continuous treatment, this paper considers a binary treatment. This paper shows that without a jump, one can still identify a treatment effect utilizing a slope change (a kink) in the treatment probability. This paper provides weak and easily testable behavioral assumptions for identification based on a kink to be valid. While the standard RD model identifies a LATE for compliers, the kink identifies a limit form of the RD LATE, which can be viewed as a marginal treatment effect (MTE) or an average effect for marginal compliers. This paper further discusses a general model that utilizes either a jump, a kink or both for identification, and shows that a local two stage least squares (2SLS) estimator can be used regardless whether the treatment probability has a jump, a kink, or both. An empirical application is provided. JEL Codes: C21, C25