利用时空数据的因果推断：评估空袭对伊拉克叛乱暴力的影响
Causal Inference with Spatio-temporal Data: Estimating the Effects of Airstrikes on Insurgent Violence in Iraq
摘要：
许多因果过程具有空间和时间维度。然而，经典的因果推断框架是不直接适用的治疗和结果变量产生的时空点过程。我们扩展了潜在的结果框架，这些设置制定治疗点过程作为一个随机干预。我们的因果被估量包括在特定的随机治疗分配策略下，在指定区域的预期结果事件数。我们的方法允许任意模式的空间溢出和时间结转效应。利用鞅理论，我们证明了所提出的估计是一致的，渐近正态的时间周期的数目增加。我们提出了一个敏感性分析的可能存在的不可测量的混杂因素，并将其扩展到Hajek估计。仿真研究进行检查估计的有限样本性能。最后，我们说明了所提出的方法，估计2007年2月至2008年7月在伊拉克的叛乱暴力美国空袭的影响。我们的分析表明，在长达一个月的时间内增加每日空袭的平均次数可能会导致更多的叛乱袭击。我们还发现一些证据表明，空袭可以将巴格达的袭击转移到400公里以外的新地点
英文摘要：
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
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