Limitless Regression Discontinuity

Publication Date

March, 2014

Publication Type

Tech Report

Author(s)

Adam Sales, Ben B. Hansen

Abstract

Many universities place underperforming students on "Academic Probation" (AP), granting them support and threatening suspension if performance does not improve. In a study of the effect of AP on subsequent grade point averages (GPAs), Lindo, et al. (2010) noted that AP follows a regression discontinuity design (RDD): students whose first year GPAs (the "running variable") fall below a cutoff are put on AP. However, the standard RDD procedure suffered in their dataset from a number of problems, including a discrete running variable and a McCrary test failure. This paper presents a new approach to modeling RDDs, which solves these problems. Its idea is to disentangle the outcome from the running variable, producing a transformed version of the outcome; to model the transformed outcome as independent of treatment assignment; and to estimate treatment effects using permutation inference. Whereas standard RDD analysis relies on limits of outcomes' conditional expectation functions and assumes a continuous running variable, we model the transformed data as if they emerged from a randomized experiment. Our approach estimates effects for a specific sample of subjects, is robust to small samples and discrete running variables, and is amenable to solutions to a McCrary test failure.