Statistical inference for the evaluation of policy interventions using regression discontinuity design

Much of public policy consists of interventions aiming to improve the lives of individuals or the performance of organizations. To evaluate whether such interventions fulfill their purpose, one needs to compare outcomes of individuals (or organizations) with access to the intervention (the "treatment group") to those without (the "control group"). For such a comparison to allow conclusions about the effects of the intervention, it is necessary for the treatment and control group to be as similar to each other as possible. A method which is generally considered to be among the most credible to make such comparisons is the regression discontinuity design (RDD).

The basic idea of RDD is to compare individuals who just reach a certain threshold, which let them receive the treatment, with individuals who lie just below this threshold, thereby not receiving the treatment. For instance, the result on a SAT test may determine if an individual is admitted to their desired education. To estimate the effect of being admitted, one can compare the individuals who reached the minimum score to gain admission with individuals who just missed that score. Because they had almost the same result on the SAT, one may expect these individuals to be comparable, which means that any differences in outcome (such as future wages) may be attributed to the treatment (being admitted to the desired education).

However, there are significant methodological challenges when using RDD, especially when the variable determining treatment (in this example, points on the SAT) can only can take a limited number of values. Such discrete-ness limits how close one can get to the threshold, and thus how similar treatment and control group are. Despite this situation being common, there is no consensus on which method should be used to deal with it. In this project, we develop a new methodology which enables scientifically rigorous conclusions without requiring overly strong assumptions about the process generating the data.