Regression Adjustments for Double Randomization in Two-Sided Marketplaces

2026-03-19

AI Summary

This study addresses the challenge of causal effect estimation in multiply randomized designs (MRD) for two-sided markets, where interference complicates inference. The authors propose a regression adjustment framework that avoids linear assumptions on potential outcomes. By constructing an optimal estimation strategy analogous to classical randomized experiments, they derive a linearly adjusted estimator with minimal asymptotic variance and establish its robust inference theory. Notably, the optimal adjustment form—such as a weighted two-way fixed effects regression with interaction terms—can be adaptively estimated from data, marking a significant departure from conventional approaches. The theoretical analysis integrates an enhanced central limit theorem for MRD with weighted regression techniques, and numerical simulations demonstrate that the proposed method substantially improves estimation efficiency over existing simple estimators, enabling more precise inference on total, direct, and spillover effects.

Technology Category

• Machine Learning: Causal Learning
• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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.

Problem

• two-sided marketplaces
• multiple randomization designs
• interference
• causal inference
• spillover effects

Innovation

• regression adjustment
• multiple randomization designs
• two-sided marketplaces
• spillover effects
• model-robust inference