Regression Adjustments for Double Randomization in Two-Sided Marketplaces

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.

Figures (6)

• Figure 1: KDE estimate of sampling distributions for the direct effect estimators i) without adjustment, ii) with the ANCOVA adjustment, and iii) with the plug-in optimal adjustment.
• Figure 2: Sampling distributions for Unadjusted, ANCOVA, and Optimal Non-Interacted adjustments over 5000 Monte Carlo samples, on a fixed realization of the i.i.d. normal data generating process of \ref{['ex:iid_normal_superpop']} with parameters described in the text. The direct effect is the estimand. Monte Carlo randomizes over $W_i^\textsf{B}, W_j^\textsf{S}$. The three panels correspond to three scenarios for ratio $I_T/I = J_T/J$, $\lbrace 0.1,0.2,0.5 \rbrace.$ Legends show estimated standard deviations of each method.
• Figure 3: Coverage and CI length for Unadjusted, ANCOVA, and Optimal Non-Interacted adjustments averaged over 5000 Monte Carlo samples, on a fixed realization of the i.i.d. normal data generating process of \ref{['ex:iid_normal_superpop']} with parameters described in the text. The direct effect is the estimand. Parameters are described in the text. Monte Carlo randomizes over $W_i^\textsf{B}, W_j^\textsf{S}$. The three panels correspond to three scenarios for ratio $I_T/I = J_T/J$, $\lbrace 0.1,0.2,0.5 \rbrace.$
• Figure 4: Sampling distributions for Unadjusted, ANCOVA, and Optimal Non-Interacted adjustments over 5000 Monte Carlo samples, on a fixed realization of the marketplace data generating process of masoero2024multiple. The buyer spillover effect is the estimand. Parameters are described in the text.
• Figure 5: Coverage and CI length for Unadjusted, ANCOVA, and Optimal Non-Interacted adjustments averaged over 5000 Monte Carlo samples, on a fixed realization of the marketplace data generating process of masoero2024multiple. The buyer spillover effect is the estimand. Parameters are described in the text.

Theorems & Definitions (85)

• Definition 1.1: Local Interference Assumption
• Example 2.1: Direct Effect
• Example 2.2: Total Effect
• Example 2.3: Spillover Effects
• Theorem 3.1
• Proposition 3.1
• Proposition 3.2
• Theorem 3.2: Valid Conservative Inference
• Example 3.1: Inference for the Direct Effect
• Theorem 3.3