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.

• Causal inference
• Conditional independence assumption
• Instrumental variables
• Treatment effects

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Joshua D. Angrist

Joshua D. Angrist, Department of Economics, MIT, Cambridge, MA 02142-1347 and NBER, Cambridge MA 02138-5398 (E-mail: [email protected]). Miikka Rokkanen, Department of Economics, Columbia University, New York, NY 10027 (E-mail: [email protected]). The authors thank their JSM session discussants and Alberto Abadie, Victor Chernozhukov, Yingying Dong, Ivan Fernandez-Val, Patrick Kline, Arthur Lewbel, and seminar participants at Berkeley, CREST, HECER, Northwestern, Stanford, the January 2013 Lech am Arlberg Labor Conference, the 2013 SOLE meetings, and the 2013 Human Capital, and Productivity conference at Warwick for helpful comments. Special thanks go to Parag Pathak for helpful notes along the way and to Peter Hull for expert research assistance. The authors gratefully acknowledge financial support from the Institute for Education Sciences (Under award R305A120269), the National Science Foundation (Under award SES-1426541), and the Arnold Foundation. The views expressed here are those of the authors alone.

Miikka Rokkanen

Joshua D. Angrist, Department of Economics, MIT, Cambridge, MA 02142-1347 and NBER, Cambridge MA 02138-5398 (E-mail: [email protected]). Miikka Rokkanen, Department of Economics, Columbia University, New York, NY 10027 (E-mail: [email protected]). The authors thank their JSM session discussants and Alberto Abadie, Victor Chernozhukov, Yingying Dong, Ivan Fernandez-Val, Patrick Kline, Arthur Lewbel, and seminar participants at Berkeley, CREST, HECER, Northwestern, Stanford, the January 2013 Lech am Arlberg Labor Conference, the 2013 SOLE meetings, and the 2013 Human Capital, and Productivity conference at Warwick for helpful comments. Special thanks go to Parag Pathak for helpful notes along the way and to Peter Hull for expert research assistance. The authors gratefully acknowledge financial support from the Institute for Education Sciences (Under award R305A120269), the National Science Foundation (Under award SES-1426541), and the Arnold Foundation. The views expressed here are those of the authors alone.