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Optimizing the tie-breaker regression discontinuity design

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  • Art B. Owen
  • Hal Varian

Abstract

Motivated by customer loyalty plans and scholarship programs, we study tie-breaker designs which are hybrids of randomized controlled trials (RCTs) and regression discontinuity designs (RDDs). We quantify the statistical efficiency of a tie-breaker design in which a proportion $\Delta$ of observed subjects are in the RCT. In a two line regression, statistical efficiency increases monotonically with $\Delta$, so efficiency is maximized by an RCT. We point to additional advantages of tie-breakers versus RDD: for a nonparametric regression the boundary bias is much less severe and for quadratic regression, the variance is greatly reduced. For a two line model we can quantify the short term value of the treatment allocation and this comparison favors smaller $\Delta$ with the RDD being best. We solve for the optimal tradeoff between these exploration and exploitation goals. The usual tie-breaker design applies an RCT on the middle $\Delta$ subjects as ranked by the assignment variable. We quantify the efficiency of other designs such as experimenting only in the second decile from the top. We also show that in some general parametric models a Monte Carlo evaluation can be replaced by matrix algebra.

Suggested Citation

  • Art B. Owen & Hal Varian, 2018. "Optimizing the tie-breaker regression discontinuity design," Papers 1808.07563, arXiv.org, revised Jul 2020.
  • Handle: RePEc:arx:papers:1808.07563
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    References listed on IDEAS

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    1. David S. Lee & Thomas Lemieux, 2010. "Regression Discontinuity Designs in Economics," Journal of Economic Literature, American Economic Association, vol. 48(2), pages 281-355, June.
    2. Atila Abdulkadiroglu & Joshua D. Angrist & Yusuke Narita & Parag A. Pathak, 2017. "Impact Evaluation in Matching Markets with General Tie-Breaking," NBER Working Papers 24172, National Bureau of Economic Research, Inc.
    3. Wilbert Van Der Klaauw, 2008. "Regression–Discontinuity Analysis: A Survey of Recent Developments in Economics," LABOUR, CEIS, vol. 22(2), pages 219-245, June.
    4. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    5. Joshua Angrist & David Autor & Sally Hudson & Amanda Pallais, 2014. "Leveling Up: Early Results from a Randomized Evaluation of Post-Secondary Aid," NBER Working Papers 20800, National Bureau of Economic Research, Inc.
    6. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, October.
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    Cited by:

    1. Matias D. Cattaneo & Rocío Titiunik, 2022. "Regression Discontinuity Designs," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 821-851, August.
    2. Tim P. Morrison & Art B. Owen, 2022. "Multivariate Tie-breaker Designs," Papers 2202.10030, arXiv.org, revised Mar 2024.
    3. Harrison H. Li & Art B. Owen, 2022. "A general characterization of optimal tie-breaker designs," Papers 2202.12511, arXiv.org, revised Oct 2022.
    4. Dan M. Kluger & Art B. Owen, 2021. "Kernel regression analysis of tie-breaker designs," Papers 2101.09605, arXiv.org, revised Jan 2023.
    5. Harrison H. Li & Art B. Owen, 2023. "Double machine learning and design in batch adaptive experiments," Papers 2309.15297, arXiv.org.

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