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

Abstract

Optimising 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 neighbours' treatments and attributes. We argue that spillover also depends on how strongly each neighbour responded to its own treatment. We prove that no model in which neighbours' responsiveness enters separately from their treatments can capture this interaction, and we introduce \textsc{SpilloverNet}, a graph neural network designed to preserve neighbour-level response dynamics. Because a neighbour'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, at low heterogeneity the plug-in's correlation with the true response looks acceptable while its spillover error is already 24.5\% against an oracle 13.8\%; as heterogeneity grows its error climbs to 51.9\%, worse than using no responsiveness estimate at all. A per-unit estimate from a direct-response measurement, collected in a small pilot before spillover arrives, escapes this bound and cuts regret against oracle-$τ$ targeting by up to 14 percentage points in a budgeted targeting problem. On two real social graphs, \textsc{SpilloverNet} reaches 7.7--8.4\% error, outperforming standard GNNs as well as specialised causal-representation baselines.