Policy Targeting under Network Interference

TL;DR

This work tackles policy design under network interference by leveraging quasi-experimental variation to account for spillovers without requiring full knowledge of the population network. It introduces Network Empirical Welfare Maximization (NEWM), a semi-parametric approach that builds a welfare estimator with known or estimated nuisance functions and solves the policy optimization via a mixed-integer linear program, yielding finite-sample regret guarantees. The method accommodates heterogeneity, policy constraints, and various network topologies, with regret bounds that depend on the maximum degree and overlap, and it includes extensions like trimming and higher-order interference. An empirical application using Cai et al. (2015) data demonstrates substantial out-of-sample welfare gains when accounting for network spillovers, even without observing the full network in the target population. The results offer a robust framework for targeting policies in networks, with practical implications for information campaigns, cash transfers, and related programs.

Abstract

This paper studies the problem of optimally allocating treatments in the presence of spillover effects, using information from a (quasi-)experiment. I introduce a method that maximizes the sample analog of average social welfare when spillovers occur. I construct semi-parametric welfare estimators with known and unknown propensity scores and cast the optimization problem into a mixed-integer linear program, which can be solved using off-the-shelf algorithms. I derive a strong set of guarantees on regret, i.e., the difference between the maximum attainable welfare and the welfare evaluated at the estimated policy. The proposed method presents attractive features for applications: (i) it does not require network information of the target population; (ii) it exploits heterogeneity in treatment effects for targeting individuals; (iii) it does not rely on the correct specification of a particular structural model; and (iv) it accommodates constraints on the policy function. An application for targeting information on social networks illustrates the advantages of the method.

Figures (3)

• Figure 1: Example of the experiment (left-hand-side figure) and policy targeting exercise in Section \ref{['sec:policy']} (right-hand-side figure). Green dots denote treated units, and pink dots denote untreated ones. In the first step, researchers run (or observe data from) an experiment on a (small) subset of individuals, here the black-tick unit. The treatment of such a unit and her friends is randomized with some positive probability, whereas the treatment of the other units can have arbitrary distributions (e.g., equal to the baseline value $D_i = 0$ almost surely if such units are not in the experiment). Researchers observe the vector of outcome, treatment, neighbors, treatments, and covariates of sampled units ($(Y_i, Z_i, Z_{\mathcal{N}_i}, D_i, D_{\mathcal{N}_i})R_i$), as well as the the identity of whom they sample ($R_i$). Researchers then design a treatment allocation $\pi(X_i)$ for the entire population using information $X_i$, a subset of $Z_i$.
• Figure 2: Example of the experiment (picture at the center) and policy targeting exercise when the sample is drawn from the target population as in Section \ref{['sec:policy']} (left-hand side) or the sample is not drawn from the target population (right-hand side). Green dots denote treated units, and pink dots denote untreated ones. The experiment runs as described in Section \ref{['sec:identification']}. Researchers observe the vector of outcome, treatment, neighbors, treatments, and covariates of sampled units ($(Y_i, Z_i, Z_{\mathcal{N}_i}, D_i, D_{\mathcal{N}_i})R_i$), as well as the the identity of whom they sample ($R_i$). When the experiment participants are drawn from the target population, researchers then design a treatment allocation $\pi(X_i)$ for the entire population using information $X_i$, a subset of $Z_i$ available to policymakers for all $n$ units. When instead the target population is different from the population from which the sample is drawn, policymakers only observe covariates $(X_i')_{i=1}^n$ from the target sample, and the experiment did not use a sample drawn from the target population.
• Figure 3: Design in cai2015social with household-level treatment randomization. Participants are assigned at random to first and second rounds, and within each round, to different information sessions. Simple session denotes the control arm, where researchers provided information about the insurance contract only. Intensive session is the main treatment arm, where individuals are also provided with information about the benefits of insurance. "More info" contains additional arms with information about purchase decisions, omitted in our analysis and cai2015social's main analysis. Purchase decisions were made at the end of each information session.

Theorems & Definitions (67)

• Example 2.1: Two-degree dependence
• Lemma 2.1: Identification
• proof : Proof of Lemma \ref{['prop:welfare']}
• Remark 1: Identification of the propensity score
• Remark 2: Non-reversible treatments
• Remark 3: Different populations
• Remark 4: Comparison with global treatment rules
• Remark 5: Additional extensions
• Example 2.2: Bounded degree
• Example 2.3: Unbounded degree