Difference-in-discontinuities Design

Abstract

This paper formalizes the difference-in-discontinuities design, a hybrid approach that combines the regression-discontinuity design and the difference-in-difference design. While this design is widely employed to mitigate the effects of confounding treatments co-occurring at discontinuities, few studies provide complete presentations of identifying assumptions and identified treatment effects. First, I formalize the difference-in-discontinuities design introduced by Grembi et al. (2016). Second, I formulate the difference-in-difference-in-discontinuities design. Importantly, under the standard assumptions, the diff-in-disc design identifies the local average treatment effect on the treated (LATT) at the discontinuity, contrary to Grembi et al. (2016) regarding the local average treatment effect (LATE).

Keywords: Difference-in-discontinuities, RD-DD, RD-DDD, RD-DID, Regression-discontinuity

JEL Classification: C10, C18, C21