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

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 processes with an infinite number of possible event locations at each point in time. We take up the challenge of extending the potential outcomes framework to these settings by formulating the treatment point process as stochastic intervention. Our causal estimands include the expected number of outcome events in a specified area of interest under a particular stochastic treatment assignment strategy. We develop an estimation technique that applies the inverse probability of treatment weighting method to spatially-smoothed outcome surfaces. We demonstrate that the proposed estimator is consistent and asymptotically normal as the number of time period approaches infinity. A primary advantage of our methodology is its ability to avoid structural assumptions about spatial spillover and temporal carryover effects. We use the proposed methods to estimate the effects of American airstrikes on insurgent violence in Iraq (February 2007-July 2008). We find that increasing the average number of daily airstrikes for up to one month increases insurgent attacks across Iraq and within Baghdad. We also find evidence that airstrikes can displace attacks from Baghdad to new locations up to 400 kilometers away.