John Quiggin has a post at Crooked Timber that asks us to think about opportunity costs when considering how allocate resources from the public purse. The title is, I think, not only needlessly provocative -- "Has the U.S. Defense Department Killed One Million Americans Since 2001?" -- but also clearly wrong. If anyone can be considered guilty of that offense it would be the Congress and Presidents Bush and Obama rather than DoD, but setting that aside he makes a valid point:



I’ve spent the day at a workshop on benefit-cost analysis where a lot of discussion is on valuing policies that reduce risks to life of various kinds. US policy, for better or worse, is focused on the idea of Value of a Statistical Life. Typically a policy that reduces risks of death will be approved if the cost per life saved is below $5million, and not otherwise. (There are similar numbers applied to publicly funded health care services, prescription drugs and so on, usually per year of life saved).

The numbers are quite striking. The ‘peacetime’ defense budget is around $500 billion a year, and the various wars of choice have cost around $250 billion a year for the last decade (very round numbers here). Allocated to domestic risk reduction, that money would save 150 000 American lives a year.



So, since 9/11, US defense spending has been chosen in preference to measures that would have saved 1.5 million American lives. That’s not a hypothetical number – it’s 1.5 million people who are now dead but who could have been saved. I think its fair to say that those people were killed by the Defense Department, or, more precisely, by the allocation of scarce life-saving resources to that Department.

US casualties in WWII were approximately half a million. Baseline assumption of planners, calibrated from the first half of the 20C, is that there is 40% chance of a conflict on that scale in any given decade.



So reducing that to a negligible chance saves ~200,000 US lives per decade, which is in the right order of magnitude. So by the time you account for the possibility of a worse (or just less successful) conflict, and the points mentioned above about the incidental benefits of defence spending, increasing marginal costs of other measures and so on, it starts to make sense on its own terms.

This is doing no justice to Slantchev's arguments, but to grossly oversimplify matters, he essentially argues that states can typically prevent war if they are willing to encourage sufficiently large costs.

However, as I demonstrate in a working paper (a new version of which I will be posting sometime next month), there might be reason to expect that the effect of military spending on the probability of war depends in part on the baseline distribution of capabilities. I identify results where the challenger risks war with the defender if and only if the defender engages in costly military buildups, yet the defender is nonetheless willing to adopt such a strategy. And for that matter, defense spending by would-be aggressors may similarly either embolden them or allow them to extract such large concessions even when playing it safe that the overall risk of war will go down. Put simply, I think there is very good reason to assume that the relationship between defense spending and the probability of war is non-monotonic.

As happens on the best of days at CT, many of the comments are well worth reading. Leigh Caldwell made a few good points: 1) the marginal cost curve is not only not flat, it likely slopes upwards pretty quickly (so theth life saved is much more expensive than theth life saved); 2) to the extent that defense spending represents a global public good at all it likely saves some lives, and perhaps quite a large number. 'soru' notes:Others referenced deterrence spending by India and Pakistan, and other scenarios whereby military spending may have conflict sufficiently costly that it does not occur when it otherwise might have. When we teach Poli 150 -- Intro to International Politics -- we generally say thatmilitary spending is inefficient in that it does not generate prosperity, but is nevertheless necessary to protect the prosperity that has been generated by other means. The implication is that, while military spending would be wasteful in a world with no threats, there exist threats and so some military spending is not wasteful. I think everyone involved in the discussion agrees that the US is currently spending too much on the military, but I also believe that cutting spending by something like 90% (or, as Quiggin mentions, 100%) would probably have some nasty knock-on effects.As soru says, we're talking in probabilities here, and the differences don't have to be all that large for large amounts of military spending to be rational on its own terms. Moreover, you want to over-insure against tail risks with extremely negative potential consequences. Obviously counterfactuals are hard, but it is pretty clearly the case that spending zero percent of national income on defense would embolden others to attack, and spending one hundred percent of national income on defense is not only overkill but defeats the whole point of defense spending. So there is a margin where spending more on defense will "save lives" via deterrence, and there is some margin where increased spending will have a very small or null effect, and could thus profitably be diverted to other uses. The question then should be: where is the relevant margin?I asked Phil Arena to write a post on what he thought were the best models addressing the question. He cited Slantchev (as I thought he might):Military preeminence is a stated intention of American military spending, at least partially for this reason. Phil also referenced some of his own work in progress:Which is precisely the relationship I described above. We're in Laffer-curve territory here, so it's no use belaboring the point. But it isn't difficult to see how a lot of US military spending -- perhaps even more than we now do -- could be cost-effective in the way that Quiggin describes if it were deployed with the intention of saving as many lives as possible. Tens of thousands of people die in horrible civil conflicts every year, most of which the US does not intervene in. Some of the US' interventions likely have saved many lives at relatively low cost (eg Kosovo and Libya) although the counterfactuals are, as always, very difficult.But as Phil notes, the goal of most military spending is not saving lives at cost-effective margins. (This gets back to where Quiggin's wrong to point the finger at DoD rather than the legislature and executive.) Thus, criticizing DoD for not maximizing lives-saved is like criticizing the Yankees for not winning the Super Bowl: the DoD is playing a different game. Hell, the legislative and executive branches are playing a different game.Quiggin should be criticizing the government for playing baseball rather than football. But if the government is guilty of massively misallocating resources in the same way over long time horizons then, as Phil hints, doesn't it make more sense to work towards reducing the ability of the government to misallocate resources rather than trying to force it to do something that it is clearly not well-constructed for? That's what I take away from Quiggin's post: shrink the government. If you don't, it'll spend the money on things that increases the capabilities of the government. I'm pretty sure this is not what Quiggin believes, but since this post isn't coupled with any theory of politics that allows the transference of military funds to other programs thatimprove public health, it's hard to take his post any other way.One last point: Phil notes that IR has a very poor understanding of the way that thework, as opposed to bilateral crisis bargaining. In other words, it isn't necessarily reasonable to infer from a model of a dyadic interaction to the broader system. I think this is especially true when talking about a superpower.