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 unobserved ways within each cluster. As a first contribution, I introduce a single-wave experiment to estimate the marginal effect of a change in the treatment probabilities taking spillovers into account and test for policy optimality. The design randomizes treatments independently within clusters and induces local perturbations to treatment probabilities within pairs of clusters. Using the estimated marginal effect, I construct a practical test for whether a given treatment allocation rule maximizes welfare, and I characterize its asymptotic properties. The idea is that researchers should report estimates of the marginal effect and test for welfare-maximizing policies: 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 small-sample guarantees on the difference between the maximum attainable welfare and the welfare evaluated at the estimated policy (regret). A corollary of such guarantees is that the regret converges to zero linearly in the number of iterations and clusters. Simulations calibrated to existing experiments on information diffusion and cash-transfer programs show that the method leads to significant welfare improvements.