Regression discontinuity

In the design of experiments, regression discontinuity (RD) designs are designs that evaluate causal effects of interventions, in which assignment to a treatment is determined at least partly by the value of an observed covariate lying on either side of a fixed threshold.

The basic RD design is a two-group pretest-posttest model as indicated in the design notation. As in other versions of this design structure (e.g., the Analysis of Covariance Randomized Experiment, the Nonequivalent Groups Design), we will need a statistical model that includes a term for the pretest, one for the posttest, and a dummy-coded variable to represent the program.

Units are assigned to conditions based on a cutoff score on a measured covariate, gor example, communities that exceed a certain cutoff on arrests for drunk driving for young drivers per 100,000 receive treatment, and communities below that cutoff are in the comparison condition. The effect is measured as the discontinuity between treatment and control regression lines at the cutoff (it is not the group mean difference).

Advantages

When properly implemented and analyzed, RD yields an unbiased estimate of treatment effect (see Rubin, 1977). Communities are assigned to treatment based on their need for treatment, consistent with how many policies are implemented.

Disadvantages

Statistical power is considerably less than a randomized experiment of the same size. Careful attention to power is crucial. Effects are unbiased only if the functional form of the relationship between the assignment variable and the outcome variable is correctly modeled, including:
*Nonlinear relationships
*Interactions

The major problem in analyzing data from the RD design is model misspecification.

History

These designs were first introduced in the evaluation literature by Thistlewaite and Campbell (1960). With the exception of a few unpublished theoretical papers, these methods did not attract much attention in the economics literature until recently. Starting in the late 1990s, there has been a large number of studies in economics applying and extending RD methods.

Reference

* "Regression Discontinuity Designs: A Guide to Practice", Guido Imbens, Thomas Lemieux, NBER Technical Working Paper No. 337, Issued in April 2007
* David Lee, "Randomized Experiments from Non-random Selection in U.S. House Elections", in Journal of Econometrics, 142(2) 675-697 (http://www.princeton.edu/~davidlee/wp/RDrand.pdf)
* [http://www.socialresearchmethods.net/kb/statrd.php]
* [http://obssr.od.nih.gov/Documents/Conferences_And_Workshops/Conference_FY2004/Shadish.ppt]