Wanna Get Away? Regression Discontinuity Estimation of Exam School Effects Away From the Cutoff

Abstract

In regression discontinuity (RD) studies exploiting an award or admissions cutoff, causal effects are nonparametrically identified for those near the cutoff. The effect of treatment on inframarginal applicants is also of interest, but identification of such effects requires stronger assumptions than those required for identification at the cutoff. This article discusses RD identification and estimation away from the cutoff. Our identification strategy exploits the availability of dependent variable predictors other than the running variable. Conditional on these predictors, the running variable is assumed to be ignorable. This identification strategy is used to study effects of Boston exam schools for inframarginal applicants. Identification based on the conditional independence assumptions imposed in our framework yields reasonably precise and surprisingly robust estimates of the effects of exam school attendance on inframarginal applicants. These estimates suggest that the causal effects of exam school attendance for 9th grade applicants with running variable values well away from admissions cutoffs differ little from those for applicants with values that put them on the margin of acceptance. An extension to fuzzy designs is shown to identify causal effects for compliers away from the cutoff. Supplementary materials for this article are available online. Keywords: causal inference; conditional independence assumption; instrumental variables; treatment effects