# Optimizing the tie-breaker regression discontinuity design

arXiv: https://arxiv.org/abs/1808.07563 · HTML: https://mlsanity.com/paper/1808.07563/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2018.

## Built on by (most cited first, 1 of 1)

- [Learning treatment effects while treating those in need](https://mlsanity.com/paper/2407.07596/) (2024)

## Abstract (arXiv)

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.