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

Georgia Papadogeorgou, Kosuke Imai+2 more|arXiv (Cornell University)|Mar 30, 2020

Advanced Causal Inference Techniques42 references6 citations

TL;DR

This paper develops a causal inference framework for spatio-temporal point processes, modeling airstrikes as stochastic interventions to estimate their effects on insurgent violence in Iraq. Using martingale theory, the method ensures consistency and asymptotic normality, revealing that increased airstrikes may raise insurgent attacks and displace violence up to 400 km away.

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

Motivation & Objective

• To address the lack of causal inference methods for settings with continuous spatial and temporal treatment and outcome processes.
• To model complex, unstructured spillover and carryover effects in spatio-temporal data where traditional potential outcomes frameworks fail.
• To develop a stochastic intervention framework that allows for arbitrary treatment assignment strategies over infinite spatial and temporal domains.
• To enable sensitivity analysis for unmeasured confounders in point process settings, extending to the Hájek estimator.
• To apply the method to real-world data on U.S. airstrikes and insurgent violence in Iraq (2007–2008), assessing causal impacts with empirical validity.

Proposed method

• Formalizes treatment as a stochastic intervention over a point process, defining causal estimands as the expected number of outcome events under a given intervention strategy.
• Uses inverse probability weighting with estimated propensity score intensity functions to balance treatment assignment across space and time.
• Applies martingale theory to establish consistency and asymptotic normality of the estimator as the number of time periods increases.
• Develops a sensitivity analysis framework for unmeasured confounders, adapted to the Hájek estimator for improved robustness.
• Employs simulation studies to evaluate finite-sample performance under various spillover and carryover configurations.
• Extends the framework to adaptive interventions by modeling time-varying treatment intensities based on observed history, though full multi-period adaptation remains challenging.

Experimental results

Research questions

• RQ1 What is the causal effect of increasing the average number of daily airstrikes on the number of insurgent attacks in Iraq?
• RQ2 To what extent do airstrikes displace insurgent violence to new geographic locations, and how far can this displacement occur?
• RQ3 How do temporal carryover effects influence the relationship between airstrikes and subsequent insurgent violence?
• RQ4 What is the impact of spatial spillover effects when airstrikes are concentrated in specific regions?
• RQ5 How robust are the causal estimates to unmeasured confounding factors in the spatio-temporal point process setting?

Key findings

• Increasing the average number of daily airstrikes from 1 to 3 over 30 days is estimated to increase the number of insurgent attacks by 12.7 (95% CI: 0.4, 24.9) per month in Iraq.
• There is evidence that airstrikes displace insurgent attacks up to 400 kilometers away, particularly from Baghdad to surrounding regions.
• The estimated effect of increasing airstrikes from 1 to 5 per day shows a 1.2 (95% CI: -2.8, 5.3) increase in IED attacks, though this is not statistically significant.
• For SAF (suicide and other attacks), the estimated increase is 1.6 (95% CI: -1.2, 4.5) when airstrikes rise from 1 to 5 per day, also not statistically significant.
• The effect of increasing airstrikes from 1 to 3 per day in Baghdad results in a 3.6 (95% CI: -4.3, 11.4) increase in other attacks, with no strong evidence of effect.
• Adaptive interventions based on observed historical patterns yielded imprecise estimates, indicating challenges in evaluating time-dependent treatment strategies with current data.