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2020 Optimizing the tie-breaker regression discontinuity design
Art B. Owen, Hal Varian
Electron. J. Statist. 14(2): 4004-4027 (2020). DOI: 10.1214/20-EJS1765


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.


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Art B. Owen. Hal Varian. "Optimizing the tie-breaker regression discontinuity design." Electron. J. Statist. 14 (2) 4004 - 4027, 2020.


Received: 1 December 2019; Published: 2020
First available in Project Euclid: 28 October 2020

zbMATH: 07270284
MathSciNet: MR4167610
Digital Object Identifier: 10.1214/20-EJS1765

Primary: 62K99
Secondary: 62F99, 62J99


Vol.14 • No. 2 • 2020
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