Wanna Get Away? RD Identification Away from the Cutoff
In the canonical regression discontinuity (RD) design for applicants who face an award or admissions cutoff, causal effects are nonparametrically identified for those near the cutoff. The impact of treatment on inframarginal applicants is also of interest, but identification of such effects requires stronger assumptions than are required for identification at the cutoff. This paper discusses RD identification 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 illustrated with data on applicants to Boston exam schools. Functional-form-based extrapolation generates unsatisfying results in this context, either noisy or not very robust. By contrast, identification based on RD-specific conditional independence assumptions produces 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.
Our thanks to Parag Pathak for many helpful discussions and comments, and to seminar participants at Berkeley, CREST, and Stanford for helpful comments. Thanks also go to Peter Hull for expert research assistance. Angrist gratefully acknowledges funding from the Institute for Education Sciences. The views expressed here are those of the authors alone and do not necessarily reflect the views of the National Bureau of Economic Research or The Institute for Education Sciences.