🤖 AI Summary
This study addresses the challenge of identifying direct, indirect, and total effects in spatial interference experiments, where spillover effects—particularly under cluster randomization—render the level of the spillover kernel non-identifiable. The authors develop a unified causal framework that expresses estimands as linear functionals of the spillover kernel and introduce an “anchoring assumption” to resolve the level identification problem. By positing separability between the kernel’s shape and its level, they demonstrate that all estimators inherently depend on the choice of anchor and propose a “level leverage” measure to quantify sensitivity to the unidentifiable level. Integrating linear exposure mappings, bias decomposition, and design augmentation strategies, the framework leverages prior geometric structure to compute leakage terms and shape errors. The work further shows that conventional cluster-based analyses are special cases of implicit anchoring, thereby unifying existing approaches and offering principled criteria for deciding whether to augment the experimental design or select an anchor.
📝 Abstract
Interventions delivered in space generate effects that spill over between experimental units. We develop a framework for spatial experiments in which causal estimands, inclduing direct, indirect, total, and dose--response effects, are linear functionals of a spillover kernel. Under cluster randomisation with a fixed exposure set size, the data identify the shape of the kernel but not its level: the level is aliased with the intercept and direct effect, at any sample size and under any outcome model. Every estimator therefore rests on an anchoring assumption that fixes the level. We derive an exact decomposition of the bias of any anchored estimator into a level term, a shape error from kernel misspecification, and a leakage term absorbed by the realised geometry, each computable from the design before data collection. A single scalar, the level leverage, gives each estimand's exposure to the unidentified level, the exact level bias, and the variance cost of estimating the level instead. The conventional cluster-trial analysis is the special case of an implicit anchor, with contamination bias in closed form. Existing approaches, including identification through Bernoulli randomisation, elicited bounds on interference decay, and assumed compact support, are, within the linear exposure mapping, anchoring choices in this framework. We give a taxonomy of design augmentations that purchase the level and a criterion for when to augment and when to anchor.