Regression Adjustments for Double Randomization in Two-Sided Marketplaces

TL;DR

This paper develops optimal regression adjustment methods for complex experimental designs in two-sided marketplaces, improving efficiency and inference accuracy without relying on linear models.

Contribution

It introduces data-estimable optimal regression adjustments for MRDs, extending classical methods to marketplace experiments with interference.

Findings

Optimal estimators have lower asymptotic variance.

Estimators are model-robust and applicable to real data.

Numerical simulations show significant efficiency gains.

Abstract

Multiple randomization designs (MRDs) are a class of experimental designs used to handle interference in two-sided marketplaces. We investigate regression adjustment strategies for estimating total, spillover, and direct effects in MRDs. We derive minimum asymptotic variance estimators among a broad class of linearly adjusted estimators, without assuming a linear model on the potential outcomes. Surprisingly, the optimal regression adjustments are estimable from data and are generally different from regression adjustments in classical randomized experiments. For example, one such optimal estimator for the direct effect corresponds to a weighted regression with interacted two-way fixed effects. We establish model-robustness properties, central limit theorems, and inferential methods for our estimators, relying on improved theoretical results for MRD experiments. Our results provide the analog of classical regression adjustments for marketplace experiments. Numerical simulations demonstrate a considerable increase in efficiency over simpler approaches, enabling better inference when running MRDs.