Yes, we needed economists to tell us this. A new working paper published by the National Bureau of Economic Research finds "strong evidence for a revenge effect" when examining the relationship between civilian casualties caused by the U.S.-led military coalition in Afghanistan and radicalization after such incidents occur. The paper even estimates of how many insurgent attacks to expect after each civilian death. Those findings, however intuitive, might resolve an internal military debate about the counter-productivity of civilian casualties – and possibly fuel calls for withdrawal.

"When ISAF units kill civilians," the research team finds, referring to the U.S.-led coalition in Afghanistan, "this increases the number of willing combatants, leading to an increase in insurgent attacks." According to their model, every innocent civilian killed by ISAF predicts an "additional 0.03 attacks per 1,000 population in the next 6-week period." In a district of 83,000 people, then, the average of two civilian casualties killed in ISAF-initiated military action leads to six additional insurgent attacks in the following six weeks.

The team doesn't examine the effect of CIA drone strikes in neighboring Pakistan, the subject of fierce debate concerning both the level of civilian deaths the strikes generate and their radicalizing effect.

A team of four economists – Stanford's Luke N. Condra and Joseph H. Felter, the London School of Economics' Radha K. Iyengar, and Princeton's Jacob N. Shapiro – used the International Security Assistance Force's own civilian-casualty data to reach their conclusions, breaking it down by district to examine further violence in the area in which civilians died. They examined the effect of over 4000 civilian deaths from January 2009 to March 2010 by looking at the sometimes-lagging indications of reprisal attacks in the same areas. To be clear, the team's research is inferential, creating a statistical model to examine spikes in violence following civilian-casualty incidents, rather than interviewing insurgents as to their specific motivations.

But in their study, the researchers found that there's a greater spike in violence after ISAF-caused civilian deaths than after insurgent-caused ones. "An incident which results in 10 civilian casualties will generate about 1 additional IED attack in the following 2 months," the researchers write. "The effect for insurgents is much weaker and not jointly significant."

In other words, even if the insurgents possess a "total disregard for human life and the Afghan people," as an ISAF press release reacting to this weekend's insurgent bombings in Herat put it, Afghans effectively would rather be killed by other Afghans than foreigners.

That's not all. The researchers found that ISAF-caused civilian casualties corollate with long-term radicalization in Afghanistan. Plotting reprisal incidents of violence in areas where civilians died at coalition hands, the data showed that "that the Coalition effect is enduring, peaking 16 weeks after the event. This confirms the intuition that civilian casualties by ISAF forces predict greater violence through a long-run effect." That's consistent with intuitions that civilian casualties "are affecting future violence through increased recruitment into insurgent groups," although they find no direct evidence for such a thing. Interestingly, the researchers found the opposite to be the case in Iraq: U.S.-caused civilian casualties are more likely to cause short-term retaliatory spikes than they are violence over the long term. (Yet.)

Repeated efforts to get in touch with the four researchers by email and phone were unsuccessful by publication time.

The relationship between civilian casualties and the creation of new enemies is no mere academic debate. As the paper notes, there can be "strategic military returns" for U.S. troops who incur greater risk to themselves in order to prevent civilian casualties if that stops Afghans from taking up arms against the U.S. in revenge. Some troops in Afghanistan bridled against General Stanley McChrystal's rules of engagement, considering them too restrictive against a violent insurgency. General David Petraeus' letter to his troops on Sunday indicates that he's trying to strike a balance between protecting the Afghan people and allowing troops to finish the battles they fight.

Additionally, some in the military consider a preoccupation with civilian casualties to be a media-driven phenomenon. Last December, the Air Force's intel chief, Lieutenant General David Deptula, told Danger Room's Noah Shachtman that "there appears to be an almost complete lack of indication to support the conventional wisdom, popularized in the media, that air attacks have been provoking deep hostility toward the U.S. and the Kabul government." Deptula was talking specifically about the air war, and the researchers found that only about six percent of civilian casualties caused by ISAF come through air strikes. (Of course, that's after McChrystal and his predecessor, General David McKiernan, scaled back ISAF's use of air strikes.) But after the study, Deptula might want to reconsider his contention that "there is little reason based on the admittedly limited data available in open source to expect that drastically reducing the civilian casualty issue would produce game changing results on the political battlefield."

The most recent United Nations quarterly study of political and security affairs in Afghanistan found that civilian casualties caused by the U.S. and its allies dropped from 33 percent to 30 percent of total civilian casualties, a dip the U.N. attributed to measures resulting from "a reiteration of the July 2009 tactical directive by the Commander of the International Security Assistance Force limiting the use of force." But the researchers suggest that Afghans aren't going say, "Those Americans are OK! They only cause one out of three dead innocent Afghans!" – especially if, as the U.N. also found, civilian casualties in the escalated war are on the rise overall.

After all, if the goal is just to stop U.S.-caused civilian casualties, then the policy implications are clear: stop the war. If it's to erode the influence of al-Qaeda's allies in Afghanistan while reducing civilian casualties to the "absolute minimum" Petraeus describes in his letter, then getting the balance between fighting insurgents and protecting civilians wrong risks making the Afghanistan war counterproductive for its stated purpose.

And while some recent academic research suggests that across the border in Pakistan, the CIA's drone strikes may not kill as many civilians as commonly believed – a very difficult thing to verify in any case – it's not as if the U.S. has much margin for error. At his sentencing last month, Faisal Shahzad testified that his failed attempt to detonate an SUV filled with explosives came as revenge for what he considered an avaricious U.S. foreign policy. "I am part of the answer to the U.S. terrorizing the Muslim nations and the Muslim people, and on behalf of that, I'm avenging the attacks," said Shahzad, a Pakistani-born U.S. citizen, "because only — like living in U.S., the Americans only care about their people, but they don't care about the people elsewhere in the world when they die."

Michael Leiter, the director of the National Counterterrorism Center, conceded the point made by the four researchers this weekend. He wouldn't argue, he said, "that some of our actions have not led to some people being radicalized," Leiter told an Aspen Institute security forum. "It doesn't mean you don't do it. It means you craft a fuller strategy to explain why you're doing it." Good luck with that. If the U.S. is killing innocent civilians – however accidentally, and however in pursuit of dangerous fanatics – what story can Washington tell to reassure the relatives of the innocent dead?

Credit: ISAF

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