In statistics, econometrics, epidemiology and related disciplines, a regression discontinuity design (RDD) is a design that elicits the causal effects of interventions by exploiting a given exogenous threshold determining assignment to treatment. By comparing observations lying closely on either side of the threshold, it is possible to estimate the local treatment effect in environments in which randomization was unfeasible. First applied by Donald Thistlewaite and Donald Campbell to the evaluation of scholarship programs[1], the RDD has become increasingly popular in recent years[2].
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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 assignment to 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 marks 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 mark - for example 50% - are given the scholarship, it is possible to elicit the local treatment effect by comparing students around the 50% cut-off: The intuition here is that a student scoring 49% is likely to be very similar to a student scoring 51% - given the pre-defined threshold of 50%, 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.
The identification of causal effects hinges on the crucial assumption that there is indeed a sharp cut-off, around which there is a discontinuity in the probability of assignment from 0 to 1. In reality, however, cut-offs are often not strictly implemented (e.g. exercised discretion for students who just fell short of passing the threshold) and the estimates will hence be biased.
In contrast to the sharp regression discontinuity design, a fuzzy regression discontinuity design (FRDD) does not require a sharp discontinuity in the probability of assignment but is applicable as long as the probability of assignment is different. The intuition behind it is related to the instrumental variable strategy and intention to treat.
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