Spillover Effects under Network Interference When Neighbours' Treatment Effects Are Heterogeneous

Abstract

Optimizing budget-constrained network interventions requires evaluating not just who is connected, but predicting how strongly individual recipients will propagate the treatment's benefits. Existing models predict spillover from neighbors' treatments and attributes. We argue that spillover also depends on how strongly each neighbor responded to its own treatment. We prove that models summarizing neighbor treatments and attributes independently cannot capture this interaction, and we introduce SpilloverNet, a graph neural network designed to preserve neighbor-level response dynamics. Because a neighbor's response is unobserved, a natural approach is to estimate it from covariates and plug it in. However, we prove that any predictor relying solely on standard network data faces an irreducible error floor set by unobserved personal responsiveness. Empirically, the plug-in's error climbs to 51.9% as heterogeneity grows - worse than using no responsiveness estimate at all - while its overall correlation still looks acceptable. A per-unit estimate from a direct-response measurement, collected in a small pilot before spillover arrives, escapes this bound and recovers up to 14 percentage points of oracle-optimal welfare in a budgeted targeting problem. On two real social graphs, SpilloverNet reaches 7.7-8.4% error, outperforming standard GNNs as well as specialized causal-representation baselines.