Optimizing the tie-breaker regression discontinuity design
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Motivated by customer loyalty plans, 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 Δ of observed customers are in the RCT. In a two line regression, statistical efficiency increases monotonically with Δ, so efficiency is maximized by an RCT. That same regression model quantifies the short term value of the treatment allocation and this comparison favors smaller Δ with the RDD being best. We solve for the optimal tradeoff between these exploration and exploitation goals. The usual tie-breaker design experiments on the middle Δ subjects as ranked by the running variable. We quantify the efficiency of other designs such as experimenting only in the second decile from the top. We also consider more general models such as quadratic regressions.
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