Regression Discontinuity Design

The regression discontinuity design (RD or RDD) is often useful for the identification of treatment effects when a treatment is triggered by an arbitrary threshold. Cannonical examples include Campbell and Thistlewaite (1960) who use the old guidelines for the national merit scholarship which required a student score sufficiently high on the SAT. Those students around the threshold are conceptualized as conditionally randomly assigned to the scholarship "treatment." Sandra Black innovated by using geographic boundaries of school districts to estimate a parent's willingness to pay for a better school (1999). Starting here, you may find useful these two RD guides. One is Hahn, Todd, and Van der Klauww (Ecmta, 2008) who tend structural which is attached below. The other is Imbens and Lemieux (JOEcmt, 2008) which is here.

Unfortunately, the RD gives you an estimate reflective of the average effect at the threshold point. If the design is fuzzy, it is an even more restricted parameter, a local, local average treatment effect. This is often informative or of interest for its own sake, but its not everything in every situation.

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