Average treatment effects for exchangeable random arrays

• Department of Economics

This seminar features a paper presentation by Bryan Graham (University of California, Berkeley).

We study large-sample properties of average treatment effect (ATE) estimators when outcomes are dyadic and can be embedded in a separately exchangeable array. Randomization designs include complete dyad-level assignment and multiple randomization designs built from agent-level latent variables. We compare an oracle benchmark with observable-potential-outcome contrasts, a reweighting estimator with known propensity, and a feasible inverse-probability-weighted (IPW) estimator with estimated propensity. Under standard moment and non-degeneracy conditions, and as the two network sides grow proportionally, all three estimators are asymptotically normal; under complete dyad-level randomization they are asymptotically equivalent. We characterize relative efficiency across designs and show how dyadic dependence creates redundancy that can offset missingness of potential outcomes. Notably, with complete dyad-level randomization and treatment probability possibly vanishing with sample size, feasible estimators can remain oracle-efficient provided treated mass grows sufficiently with network size. These results guide experimental design in large exchangeable networks.

Jointly with Michael Jansson (University of California, Berkeley) and Yassine Sbai Sassi (NYU).