Basics and Recent Advances in Regression Discontinuity: Difference versus Regression Forms

This paper reviews the basics of regression discontinuity (RD) design, whose hallmark is having a treatment determined by an underlying score (i.e., ‘running variable’) crossing a known cutoff or not. Following the basics, recent advances in RD are examined, where the topics are grouped into those related to score and those not. The former topics include multiple scores, measurement errors in score, integer score, and score-density continuity. The latter topics include regression kink (RK), high-order effects, and extending RD identification range (i.e., external validity). Detailed empirical examples are provided for the RD topics, but not for the RD basics which are fairly well-known these days. RD is simple, which can thus appeal even to lay audiences, and this review accordingly emphasizes the intuitive nature of RD and its applicability in practice. Practical and widely applicable techniques are given more coverage, whereas theoretically-motivated but less-practically-relevant ones are only briefly mentioned. The beauty of RD is in its simplicity, and temptation to make it too sophisticated should be resisted.