Regression discontinuity

In statistics, econometrics, political science, epidemiology, and related disciplines, a regression discontinuity design (RDD) is a quasi-experimental pretest-posttest design that elicits the causal effects of interventions by assigning a cutoff or threshold above or below which an intervention is assigned. By comparing observations lying closely on either side of the threshold, it is possible to estimate the average treatment effect in environments in which randomization is unfeasible. First applied by Donald Thistlethwaite and Donald Campbell to the evaluation of scholarship programs, the RDD has become increasingly popular in recent years.

The intuition behind the RDD is well illustrated using the evaluation of merit-based scholarships. The main problem with estimating the causal effect of such an intervention is the endogeneity of performance to the assignment of treatment (e.g. scholarship award): Since high-performing students are more likely to be awarded the merit scholarship and continue performing well at the same time, comparing the outcomes of awardees and non-recipients would lead to an upward bias of the estimates. Even if the scholarship did not improve grades at all, awardees would have performed better than non-recipients, simply because scholarships were given to students who were performing well ex ante.

Despite the absence of an experimental design, a RDD can exploit exogenous characteristics of the intervention to elicit causal effects. If all students above a given grade—for example 80%—are given the scholarship, it is possible to elicit the local treatment effect by comparing students around the 80% cut-off: The intuition here is that a student scoring 79% is likely to be very similar to a student scoring 81%—given the pre-defined threshold of 80%, however, one student will receive the scholarship while the other will not. Comparing the outcome of the awardee (treatment group) to the counterfactual outcome of the non-recipient (control group) will hence deliver the local treatment effect.

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