Getting a Little Jumpy: Regression
But when you start exercising those rules, all sorts of
processes start to happen and you start to find out all sorts
of stuff about people It's just a way of thinking about a
problem, which lets the shape of the problem begin to
emerge. The more rules, the tinier the rules, the more
arbitrary they are, the better.
Douglas Adams, Mostly Harmless
Regression discontinuity (RD) research designs exploit precise knowledge of the rules determining treatment. RD identification is based on the idea that in a highly rule-based world, some rules are arbitrary and therefore provide good experiments. RD comes in two styles, fuzzy and sharp. The sharp design can be seen as a selection-onobservables story. The fuzzy design leads to an instrumental variables (IV) type of setup.
Sharp RD is used when treatment status is a deterministic and discontinuous function of a covariate, xi. Suppose, for example, that