Causal Inference with Spatio-temporal Data: Estimating the Effects of Airstrikes on Insurgent Violence in Iraq
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Although many causal processes have spatial and temporal dimensions, the classical causal inference framework is not directly applicable when the treatment and outcome variables are generated by spatio-temporal point processes. The methodological difficulty primarily arises from the existence of an infinite number of possible treatment and outcome event locations at each point in time. In this paper, we consider a setting where the spatial coordinates of the treatment and outcome events are observed at discrete time periods. We extend the potential outcomes framework by formulating the treatment point process as a stochastic intervention strategy. Our causal estimands include the expected number of outcome events that would occur in an area of interest under a particular stochastic treatment assignment strategy. We develop an estimation technique by applying the inverse probability of treatment weighting method to the spatially-smoothed outcome surfaces. We show that under a set of assumptions, the proposed estimator is consistent and asymptotically normal as the number of time periods goes to infinity. Our motivating application is the evaluation of the effects of American airstrikes on insurgent violence in Iraq from February 2007 to July 2008. We consider interventions that alter the intensity and target areas of airstrikes. We find that increasing the average number of airstrikes from 1 to 6 per day for seven consecutive days increases all types of insurgent violence.
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