Identifying Causal Effects in Experiments with Spillovers and Non-compliance

💡 Research Summary

This paper develops a rigorous identification and estimation strategy for causal effects in experiments that feature both spillovers (interference) and one‑sided non‑compliance. The authors focus on randomized saturation designs, in which groups are first assigned a saturation level (the fraction of members who will be offered treatment) and then, within each group, individuals receive treatment offers with a Bernoulli probability equal to the assigned saturation. Two sources of random variation—individual offers and group‑level saturation—provide the exogenous variation needed to separate direct (own‑treatment) effects from indirect (peer‑treatment) effects.

Four key assumptions underpin the analysis. First, partial interference: each individual belongs to a single, known group and spillovers occur only within that group. Second, anonymous interactions: a person’s potential outcome depends on the average treatment take‑up of peers, not on which specific peers are treated. Third, one‑sided non‑compliance: only those who receive an offer can take up treatment, creating a natural “complier/never‑taker” dichotomy. Fourth, individualized offer response (IOR): an individual’s decision to take up treatment depends only on her own offer and not on the offers received by peers. This assumption is plausible in many online or confidential settings and has testable implications; the authors find no evidence against it in their empirical application.

Under these assumptions the authors embed a random‑coefficients model for potential outcomes: \