Open Access
2023 Design and analysis of bipartite experiments under a linear exposure-response model
Christopher Harshaw, Fredrik Sävje, David Eisenstat, Vahab Mirrokni, Jean Pouget-Abadie
Author Affiliations +
Electron. J. Statist. 17(1): 464-518 (2023). DOI: 10.1214/23-EJS2111


A bipartite experiment consists of one set of units being assigned treatments and another set of units for which we measure outcomes. The two sets of units are connected by a bipartite graph, governing how the treated units can affect the outcome units. In this paper, we consider estimation of the average total treatment effect in the bipartite experimental framework under a linear exposure-response model. We introduce the Exposure Reweighted Linear (ERL) estimator, and show that the estimator is unbiased, consistent and asymptotically normal, provided that the bipartite graph is sufficiently sparse. To facilitate inference, we introduce an unbiased and consistent estimator of the variance of the ERL point estimator. Finally, we introduce a cluster-based design, Exposure-Design, that uses heuristics to increase the precision of the ERL estimator by realizing a desirable exposure distribution.

Funding Statement

Christopher Harshaw gratefully acknowledges support from an NSF Graduate Research Fellowship (DGE1122492), NSF Grant CCF-1562041, ONR Award N00014-20-1-2335, as well as support from Google as a Summer Intern and a Student Researcher.


We thank P.M. Aronow, Kay Brodersen, Nick Doudchenko, Ramesh Johari, Khashayar Khosravi, Sebastien Lahaie, Vahan Nanumyan, Georgia Papadogeorgou, Lewis Rendell, Johan Ugander, and C. M. Zigler for stimulating discussions which helped shape this work.


Download Citation

Christopher Harshaw. Fredrik Sävje. David Eisenstat. Vahab Mirrokni. Jean Pouget-Abadie. "Design and analysis of bipartite experiments under a linear exposure-response model." Electron. J. Statist. 17 (1) 464 - 518, 2023.


Received: 1 July 2022; Published: 2023
First available in Project Euclid: 2 February 2023

arXiv: 2103.06392
MathSciNet: MR4543444
zbMATH: 07650533
Digital Object Identifier: 10.1214/23-EJS2111

Primary: 62D10 , 62K99
Secondary: 62G99

Keywords: bipartite experiments , Causal inference , cluster designs , potential outcomes , weighting estimators

Vol.17 • No. 1 • 2023
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