Agnostic Characterization of Interference in Randomized Experiments

We give an approach for characterizing interference by lower bounding the number of units whose outcome depends on selected groups of treated individuals, such as depending on the treatment of others, or others who are at least a certain distance away. The approach is applicable to randomized experiments with binary-valued outcomes. Asymptotically conservative point estimates and one-sided confidence intervals may be constructed with no assumptions beyond the known randomization design, allowing the approach to be used when interference is poorly understood, or when an observed network might only be a crude proxy for the underlying social mechanisms. Point estimates are equal to H\'{a}jek-weighted comparisons of units with differing levels of treatment exposure. Empirically, we find that the width of our interval estimates is competitive with (and often smaller than) those of the EATE, an assumption-lean treatment effect, suggesting that the proposed estimands may be intrinsically easier to estimate than treatment effects.