Estimating Heterogeneous Treatment Effects for Spatio-Temporal Causal Inference: How Economic Assistance Moderates the Effects of Airstrikes on Insurgent Violence

Scholars from diverse fields now increasingly rely on high-frequency spatio-temporal data. Yet, causal inference with these data remains challenging due to the twin threats of 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 in nature. 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.