Tie-breaker designs provide more efficient kernel estimates than regression discontinuity designs

Abstract

Tie-breaker experimental designs are hybrids of Randomized Controlled Trials (RCTs) and Regression Discontinuity Designs (RDDs) in which subjects with moderate scores are placed in an RCT while subjects with extreme scores are deterministically assigned to the treatment or control group. The tie-breaker design (TBD) has practical advantages over the RCT in settings where it is unfair or uneconomical to deny the treatment to the most deserving recipients. Meanwhile, the TBD has statistical benefits due to randomization over the RDD. In this paper we discuss and quantify the statistical benefits of the TBD compared to the RDD. If the goal is estimation of the average treatment effect or the treatment at more than one score value, the statistical benefits of using a TBD over an RDD are apparent. If the goal is estimation of the average treatment effect at merely one score value, which is typically done by fitting local linear regressions, about 2.8 times more subjects are needed for an RDD in order to achieve the same asymptotic mean squared error. We further demonstrate using both theoretical results and simulations from the Angrist and Lavy (1999) classroom size dataset, that larger experimental radii choices for the TBD lead to greater statistical efficiency.Comment: This version is quite different than version 1. We have added an analysis when the bandwidth is shrinking with the sample size. We have also added a discussion of other statistical advantages of a TBD compared to an RD