Leveraging Lotteries for School Value-Added: Testing and Estimation
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Author(s)
Angrist, Joshua
Hull, Peter Davenport
Pathak, Parag
Walters, Christopher Ross
Date Issued
February 2017
Journal
Quarterly Journal of Economics
Publisher
Oxford University Press (OUP)
Citation
Angrist, Joshua D. et al. “Leveraging Lotteries for School Value-Added: Testing and Estimation.” The Quarterly Journal of Economics 132, 2 (February 1, 2017): 871–919 © 2016 The Author(s)
Version
Original manuscript
Abstract
Conventional value-added models (VAMs) compare average test scores across schools after regression-adjusting for students' demographic characteristics and previous scores. This article tests for VAM bias using a procedure that asks whether VAM estimates accurately predict the achievement consequences of random assignment to specific schools. Test results from admissions lotteries in Boston suggest conventional VAM estimates are biased, a finding that motivates the development of a hierarchical model describing the joint distribution of school valueadded, bias, and lottery compliance. We use this model to assess the substantive importance of bias in conventional VAM estimates and to construct hybrid valueadded estimates that optimally combine ordinary least squares and lottery-based estimates of VAM parameters. The hybrid estimation strategy provides a general recipe for combining nonexperimental and quasi-experimental estimates. While still biased, hybrid school value-added estimates have lower mean squared error than conventional VAMestimates. Simulations calibrated to the Boston data show that, bias notwithstanding, policy decisions based on conventional VAMs that control for lagged achievement are likely to generate substantial achievement gains. Hybrid estimates that incorporate lotteries yield further gains.
MIT Department
Massachusetts Institute of Technology. Department of Economics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1093/QJE/QJX001
