Linear estimation of global average treatment effects

TL;DR

This paper analyzes the estimation of average treatment effects in the presence of spatial spillovers, deriving minimax rates and proposing estimators that adapt to different experimental designs and causal models.

Contribution

It introduces minimax rates for linear estimators under spatial spillovers and compares the performance of IPW and OLS estimators in various settings.

Findings

Inverse probability weighting achieves optimal rates with large clusters.

OLS estimator outperforms IPW with small clusters in linear models.

Application to a cash transfer experiment shows a 22% larger estimated effect.

Abstract

We study estimation of and inference for the average causal effect of treating every member of a population, as opposed to none, using an experiment that treats only some. Considering settings where spillovers can occur between any pair of units and decay slowly with distance, we derive the minimax rate over all linear estimators and experimental designs, which increases with the spatial rate of spillover decay. This rate of convergence can be achieved using an inverse probability weighting estimator when randomization clusters are large, but not otherwise. If the causal model is linear, however, an OLS-based estimator converges faster than IPW when clusters are small and is consistent even under unit-level randomization. We provide methods for radius selection and inference and apply these to the cash transfer experiment studied by Egger et al. (2022), obtaining a 22% larger estimated effect on consumption.