Estimating Heterogeneous Treatment Effects for Spatio-Temporal Causal Inference

TL;DR

This paper develops methods to estimate and test for heterogeneous treatment effects in high-frequency spatio-temporal data, accounting for spatial spillover and temporal carryover effects, with applications to conflict data.

Contribution

It introduces a novel estimator for conditional average treatment effects in spatio-temporal settings and provides asymptotic properties and a statistical test for heterogeneity.

Findings

The proposed estimator performs well in finite samples.

The test effectively detects heterogeneity in treatment effects.

Application reveals aid distribution moderates airstrike effects on insurgent violence.

Abstract

Scholars from diverse fields increasingly rely on high-frequency spatio-temporal data. Yet, causal inference with these data remains challenging due to spatial spillover and temporal carryover effects. We develop methods to estimate heterogeneous treatment effects by allowing for arbitrary spatial and temporal causal dependencies. We focus on common settings where the treatment and outcomes are time-varying spatial point patterns and where moderators are either spatial or spatio-temporal variables. We define causal estimands based on stochastic interventions where researchers specify counterfactual distributions of treatment events. We propose the Hajek-type estimator of the conditional average treatment effect (CATE) as a function of spatio-temporal moderator variables, and establish its asymptotic normality as the number of time periods increases. We then introduce a statistical test of no heterogeneous treatment effects. Through simulations, we evaluate the finite-sample performance of the proposed CATE estimator and its inferential properties. Our motivating application examines the heterogeneous effects of US airstrikes on insurgent violence in Iraq. Drawing on declassified spatio-temporal data, we examine how prior aid distributions moderate airstrike effects. Contrary to expectations from counterinsurgency theories, we find that prior aid distribution, along with greater amounts of aid per capita, is associated with increased insurgent attacks following airstrikes.