In the potential outcomes framework, a causal effect is the difference in potential outcomes between two different interventions simultaneously applied to the same unit (e.g., individual, school, city). Unfortunately, this definition requires that the same unit be observed simultaneously in two different states, a contradiction that Holland designated the Fundamental Problem of Causal Inference. In response to this problem, Rubin proposed a statistical solution that a population can be used to estimate the average causal effect of an intervention, relative to a control, across different units with the assumption that no unobserved variables confound the relationship between the exposure and outcome (i.e., exchangeability of units). The randomization of treatment assignments became the ‘gold standard’ method to create an expectation of exchangeability in units between two arms of any experiment.

Experiments can randomize intervention assignment to overcome the exchangeability assumptions, whereas non-experimental studies require several additional strong and untestable assumptions to measure causal intervention effects (see, (10)). Instances exist, however, when some arbitrary cutoff assigns an intervention to some people and does not affect others, which in expectation can create exchangeability of units around the threshold.

The rationale for the RD design is that there is no systematic difference in those who are just over the threshold (e.g., over age 21 years) and those who are just below (e.g., less than 21 years). Therefore, the ability to legally purchase alcohol, in this example, is based only on month of birth; essentially treatment is randomly assigned to some and not others.