Adaptive Allocation for Enhancing Efficiency in Experiments with Noncompliance

• In Event: Innovations in Experimental Design

Abstract

In experimental social science, participant noncompliance is a significant challenge, especially in "encouragement designs" where treatment receipt cannot be guaranteed. This paper proposes an adaptive allocation strategy to enhance statistical efficiency amidst noncompliance. Existing adaptive designs in social sciences predominantly optimize outcomes, employing methods like the multi-armed bandit. These are essential where policy relevance is central, reallocating based on treatment efficacy. However, when the primary goal is not policy relevance, the efficiency of inference becomes more important. Research addressing the latter objective has not tackled experiments with significant noncompliance. Our framework seeks to allocate observations between the two assignment regimes in a way that, when the appropriate identification assumptions are met, enhances the efficiency of inference of the complier average treatment effect (CATE). We show that the oracle allocation, when applied to a two-batch setting similar to that in Blackwell et al. (2023), can improve efficiency. We also demonstrate the more general set-up where a gradient-descent algorithm iteratively explores and exploits allocations to reduce variance in the Horvitz-Thompson equivalent of the LATE estimator. We run simulations to confirm the performance of the algorithm.

Author

• Zikai Li, University of Chicago