9 Regression Discontinuity Designs

A regression discontinuity design (RDD, for short) arises when the selection of a unit into a treatment group depends on a covariate score that creates some discontinuity in the probability of receiving the treatment. In this lecture we will consider both “sharp” and “fuzzy” RDDs.

Regression discontinuity designs are appropriate in cases where the probability that a unit is treated jumps at some specific value (\(c\)) of a running variable (\(X_i\)). The RDD is powered by the idea that jumps in the outcome (\(Y\)) that occur at the same value of the running variable can – under certain assumptions – be attributed to the causal effect of the treatment. The basic logic behind this is that we normally expect most outcomes to evolve smoothly, and so as long as we are able to model that smooth evolution to a sufficient degree of accuracy, we can calculate the difference in outcomes that occur at the cutoff and count that as the treatment effect.

There are good treatments (get it?) of the RDD in both the Mostly Harmless book, and the Mastering ’Metrics books, but it probably is easiest to gain intuition about these methods from seeing plenty of examples. The paper we covered during the lecture is this one by Andy Hall, which uses a very common RD setting – election results which lead to one type of candidate being elected rather than another type – but in an innovative way that speaks to some important debates in American Politics. For an example of population-threshold based RDDs, this paper by Andy Eggers is very nice. Eggers uses the fact that municipalities in France use one electoral system (Majoritarian) when they have a population of less than 3500 and another (PR) when they have more than 3500 people. Finally, this paper is really nice, where Ferwerda and Miller implement a geographic-RDD to investigate the causal effects of the Vichy regime in World War Two on the strength of the French resistance (you could also read this paper in which Kocher and Monteiro (2016) challenge the “as if random” interpretation of Ferwerda and Miller’s RDD setting.)

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