Design-Based Inference for Spatial Experiments with Interference

Annals of Applied Statistics, 2025, with Cyrus Samii, Haoge Chang, and P Aronow.

Why this paper matters

Many policy experiments and field interventions, such as forest conservation programs, public health campaigns, and policing deployments, take place in geographic space. In these settings, treatment at one location can affect outcomes nearby, creating spatial interference that violates the stable unit treatment value assumption (SUTVA). Existing solutions to this problem typically require researchers to specify a parametric spatial model (e.g., spatial autoregression with a weight matrix) or an exposure mapping that summarizes all influences from neighboring units (e.g., the proportion of treated neighbors within 5 km). Yet the true interference structure—how one unit’s outcome responds to others’ treatments—is rarely known and often heterogeneous across units, making these assumptions fragile and impractical in applied work.

This paper introduces a fully design-based, model-agnostic framework for learning how interventions generate direct and indirect effects across space, without requiring researchers to specify how far spillovers reach or how they propagate.

What our approach contributes

We define a new estimand—the Average Marginalized Effect (AME)—which captures how switching a treatment on at one location influences outcomes at a given distance away, averaging over all possible treatment assignments elsewhere. Crucially, the AME at any distance d remains identifiable under randomized designs even when the interference structure is unknown. When spillover effects are additive, we show that the AME maps directly onto the underlying spatial effect function at distance d, making the estimand design-invariant.

Figure 1: Constructing circle averages as buffers around intervention nodes in Jayachandran et al. (2017)

Assuming only that the spatial reach of interference is finite, we show that AMEs can be consistently estimated using simple weighted regressions estimators with "circle averages"—the average outcome across neighbors that are roughly d units away from each intervention node—as the outcome. In Figure 1 above, we demonstrates how the circle averages can be constructed as buffers around treated and untreated villages when replicating the forest conservation experiment in Jayachandran et al. (2017). We show the estimator's asymptotic normality and prove that the Conley-type spatial HAC estimators provide robust inference in such settings. Across simulations and two real applications, AMEs reveal nuanced spillover patterns while avoiding the misspecification risks that undermine model-based spatial methods.

Figure 2: Replication results from Jayachandran et al. (2017)

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