Policy design in experiments with unknown interference

This paper proposes an experimental design for estimation and inference on welfare-maximizing policies in the presence of spillover effects. I consider a setting where units are organized into a finite number of large clusters and interact in unknown ways within each cluster. As a first contribution, I introduce a single-wave experiment which, by carefully varying the randomization across pairs of clusters, estimates the marginal effect of a change in treatment probabilities, taking spillover effects into account. Using the marginal effect, I propose a practical test for policy optimality. The idea is that researchers should report the marginal effect and test for policy optimality: the marginal effect indicates the direction for a welfare improvement, and the test provides evidence on whether it is worth conducting additional experiments to estimate a welfare-improving treatment allocation. As a second contribution, I design a multiple-wave experiment to estimate treatment assignment rules and maximize welfare. I derive strong small-sample guarantees on the difference between the maximum attainable welfare and the welfare evaluated at the estimated policy, which converges linearly in the number of clusters and iterations. Simulations calibrated to existing experiments on information diffusion and cash-transfer programs show welfare improvements up to fifty percentage points.