Optimal Treatment Assignment Rules on Networked Populations

Abstract: I study the problem of optimally distributing treatments among individuals on a network in the presence of spillovers in the effect of treatment across linked individuals. In this paper, I consider the problem of a planner who needs to distribute a limited number of preventative treatments (e.g., vaccines) for a deadly infectious disease among individuals in a target village in order to maximize population welfare. Since the planner does not know the extent of spillovers or the heterogeneity in treatment effects, she uses data coming from an experiment conducted in a separate pilot village. By placing restrictions on how others’ treatments affect one’s outcome on the contact network, I derive theoretical limits on how the data from the experiment could be used to best allocate the treatments when the planner observes the contact network structure in both the target and pilot village. For this purpose, I extend the empirical welfare maximization (EWM) procedure to derive an optimal statistical treatment rule. Under restrictions on the shape of the contact network, I provide finite sample bounds for the uniform regret (a measure of the effectiveness of a treatment rule). The main takeaway is that the uniform regret associated with EWM, extended to account for spillovers, converges to 0 at the parametric rate as the size of the pilot experiment grows. I also show that no statistical treatment rule admits a faster rate of convergence for the uniform regret, suggesting that the EWM procedure is rate-optimal.

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