In the first of a promised 3-part series, Mitch Abdon summarizes RDD in a helpful (and brief) post (here). As the post makes clear:
"RDD is a quasi-experimental method for evaluating program impact when observation units (example, households) can be sorted using some continuous metric (example, income) and program assignment is based on a pre-determined threshold or cutoff point of the sorting metric. Observations just below the cutoff are deemed similar to, and therefore, compare well to those just above the cutoff. In the absence of the program, one would expect that any shifts in outcome variables would happen smoothly alongside minor changes in the running variable. Thus, a large jump in the outcome variable, observed precisely at the threshold value of the running variable, after program intervention can be attributed to the program itself."