Causal Inference with Spatio-temporal Data: Estimating the Effects of Airstrikes on Insurgent Violence in Iraq

TL;DR

This paper develops a novel causal inference framework for spatio-temporal point processes, enabling estimation of treatment effects such as airstrikes on insurgent violence, accounting for spillover and carryover effects.

Contribution

It extends the potential outcomes framework to spatio-temporal point processes and introduces estimators with proven consistency and asymptotic normality, including sensitivity analysis methods.

Findings

Increasing airstrikes may lead to more insurgent attacks.

Airstrikes can displace violence to locations up to 400 km away.

The proposed estimators perform well in finite samples.

Abstract

Many causal processes have spatial and temporal dimensions. Yet the classic causal inference framework is not directly applicable when the treatment and outcome variables are generated by spatio-temporal point processes. We extend the potential outcomes framework to these settings by formulating the treatment point process as a stochastic intervention. Our causal estimands include the expected number of outcome events in a specified area under a particular stochastic treatment assignment strategy. Our methodology allows for arbitrary patterns of spatial spillover and temporal carryover effects. Using martingale theory, we show that the proposed estimator is consistent and asymptotically normal as the number of time periods increases. We propose a sensitivity analysis for the possible existence of unmeasured confounders, and extend it to the Hajek estimator. Simulation studies are conducted to examine the estimators' finite sample performance. Finally, we illustrate the proposed methods by estimating the effects of American airstrikes on insurgent violence in Iraq from February 2007 to July 2008. Our analysis suggests that increasing the average number of daily airstrikes for up to one month may result in more insurgent attacks. We also find some evidence that airstrikes can displace attacks from Baghdad to new locations up to 400 kilometers away