William Spaniel

I have a new chapter from my book project available. Here’s the abstract:

With complete information, rising states internalize declining states’ threats to launch preventive war. If that threat is credible, they do not pursue arms programs to avoid conflict. If that threat is incredible, declining states preemptively engage in bargaining to override the need to build those weapons, extracting the surplus in the process. Either way, no arms construction occurs. This paper investigates how negotiations work when that threat to intervene is uncertain. When rising states believe their rivals are strong, weak declining states can convince rising states not to build without offering any concessions by mimicking the strong type. When rising states are skeptical, inefficiency prevails. To keep the weak types honest, rising states sometimes attempt to build arms after receiving unencouraging signals. Weak types allow the power shift to transpire. Strong types respond with preventive war. The results indicate that many “preventive” wars are the result of information problems, \textit{not} commitment problems.

You can read the full chapter here. It has a number of important policy implications about Israeli behavior toward Iran’s nuclear program. I think I will write a post on those next week.

One thing I really like about large-n empirical papers is their ability to run robustness checks. Statistical models only produce the ideal results if the author captures the correct data generating process. For example, suppose a researcher theorizes that states with larger economies have higher chances of winning wars. If the size of economies and regime type are the only things that matter for winning a war, then you would want your model of war winning to just include economic size and regime type.

However, someone might object under the belief that industrial capacity matters as well. It might be difficult to know who is correct, but fortunately there is an easy solution: just run both models. If the size of the economy is positively correlated with winning wars in both cases, then the objection is irrelevant, the scholars can agree to disagree, and we can go back on focusing on the economy.

So despite only focusing on one model, empirical researchers usually include a few robustness checks within a paper and often include a much larger online appendix with yet more robustness checks. This should be applauded, as it gives us more confidence that the result is correct.

Yet formal theorists often fail to make such robustness checks–even though the problem is the same one empiricists face. Indeed, formal theorists tend to give us the result of one model. But that model is essentially a knife-edge case of a greater family of models, one in which the order of moves is reversed, players have additional moves, and information operates differently. And just like the empirical problem, it is very difficult for formal theorists to “know” that their version of the model is the correct game that real world actors play. Why, then, should we privilege the single version that the author presents? This is an especially important question given that authors have incentive to present the model with the most interesting results even if those results completely disappear if the author tweaks the assumptions slightly. (Note, again, that this is the empiricists have the same incentives.)

The answer, of course, is that we should not. We should expect formal theorists to think long and hard about the models they create and whether they actually represent a broad, robust finding.

For example, consider my work on nuclear nonproliferation agreements. I show that potential nuclear powers are always willing to accept nonproliferation settlements. That is an extremely broad and strong claim. And, dangerously, it comes from a very simple bargaining game. Why should you trust my results?

If that is all I presented to you, you probably should not. Observers of American/Iranian negotiations know that there are a lot of complexities to this type of bargaining. Consequently, I have received a large number of questions about how the results would change if I tweaked certain assumptions. I collected most of these in the back of my brain in case someone were to ask me those questions again.

But then my presentation at the annual Peace Science Society conference approached. For those unaware, Peace Science tends to slant very empirical. So as I was thinking about how to present the paper, I began considering how a strict empiricist would present the paper. She would probably start with a bit of theory, show the results of the main model, demonstrate robustness (or at least say “this is robust to…”), and then perhaps talk about a couple of cases if time permitted.

Theorists and empiricists may be different in many ways, but I think it is telling that the previous sentence could apply equally to both a theoretical and an empirical presentation. Yet theorists almost always completely skip the robustness step. This time, I did not. So instead of saying “bargaining works in the model I constructed,” I said “bargaining works in the model I constructed and in models with the following different assumptions.” I then showed a slide with the following:

• Prior investment in nuclear research
• Prestige
• Punishment for reneging
• Negative externalities
• Non-binary power shifts
• Nondeterministic proliferation
• Sanctions
• Bargaining over objects that influence future bargaining power
• Non-common discount factors
• Imperfect monitoring

This is much, much, much stronger than just saying “hey, bargaining works.” I think it won over a few people in the crowd, and I received many comments after the presentation about how it was a nice touch.

All of this is to say that we really should be making robustness checks of our formal models both in our papers and in our presentations. Why isn’t this commonplace already? There are two restricting factors. First, solving alternative model specifications is a time consuming task. An empiricist can just add a few robustness check variables, press a button, and be done. (This assumes that such data already exist. If not, they are in trouble.) Theorists often have to re-solve the entire model, which can take days.

Second, it is space consuming. I mentioned ten robustness checks above. The paper takes ten and a half pages addressing all of them. I can get away with this because I am writing a book; I would be in deep trouble if this were a journal article and I only had 10,000 words to work with.

Still, I don’t think either of these are particularly good excuses. Regarding time: yes, spending time doing these things is annoying. But it is an investment in getting your result right, and you should be willing to pay it. Moreover, if the central result you are finding is decent, then the logic should intuitively carry over in many of the cases. For example, Maya Sen and I have a working paper on judicial nominations that shows under certain conditions Senators randomly reject nominees despite not having any good reason to do so. We use a very simple model, yet (much to our surprise) the results immediately carry over to much more complicated setups, and we can explain why without having to do any more math.

Regarding space: this is a poor excuse. Empiricists solve the space problem by creating online appendices. When was the last time you ever saw an online appendix for a formal article that wasn’t just a proof of the model in the paper? There is no reason theorists can’t copy this solution.

Bottom line: empiricists and theorists face similar robustness challenges. We need our models to be robust, and the only way we can effectively communicate that in scholarly work is to conduct robustness checks. Empiricists do a good job here; theorists have a lot of room for improvement.

Here’s a story in poor timing. I’ve spent the last three years writing a dissertation on bargaining over nuclear weapons, often with Iran as substantive motivation and focus. On Saturday night, my best friend from high school was getting married. Also on Saturday night, the United States and Iran announced a preliminary agreement over Iran’s nuclear program. I didn’t even know until the next morning, and I have been playing catch up ever since.

That said, I have encountered a lot of discussion on social media about the deal. Having spent all those years analyzing the credibility of nuclear agreements, I wanted to make five quick comments about the Iranian deal and such deals in general:

1) Bargaining can work.
A common misconception about bargaining over weapons is that any deal is inherently incredible. The theory is as follows. To buy off a proliferator, the rival needs to offer concessions. But those concessions are hard to retract if the proliferator is not compliant. Thus, the proliferator can take the concessions and build weapons anyway. In turn, because offering concessions has no impact on the proliferator’s decision, the rival should not attempt a bargain.

Although I believed this intuition was true when I began my research project on bargaining over proliferation, it turns out this is wrong. Bargaining over nuclear weapons works. The reason is that a proliferator will ultimately receive some amount of concessions. The rival can just offer most of those concessions off the bat. At that point, the proliferator has no incentive to develop nuclear weapons–if it did, it wouldn’t get much more than it is already getting, but it will have to pay the costs. So bargaining can work.

2) Iran is getting an awful deal (so far).
Broadly, rivals can use one of two nonproliferation strategies. First, they can use “carrots” in the form of the concessions mentioned above. Second, they can use “sticks” like sanctions and preventive war.

Although the announced deal is only preliminary, Iran isn’t getting any carrots. The deal essentially places the United States and Iran at the status quo ex ante: the United States is lifting most of its sanctions (with some oil embargoes remaining), while Iran is agreeing to stricter weapons inspections. As the narrative goes, the “stick” has beaten Iran into submission.

If we are basically back where we started, what was the point of the last ten years of proliferation? One ad hoc story is that Iran is worried about preventive war. But why hasn’t Iran been worried about preventive war in the last ten years? Israel has consistently called for invasion, and Iran has persistently called its bluff. Meanwhile, despite Netanyahu’s desperate pleas, Obama has yet to campaign for a military option. If anything, American reluctance to intervene in Syria has signaled general war exhaustion. So preventive war does not seem to be the answer.

The other ad hoc story is that sanctions are crippling Iran’s economy. But this by itself is unsatisfying–policymakers in Iran must have foreseen that the United States would sanction Iran for noncompliance. Yet Tehran marched forward anyway–the regime must have calculated that the costs of nuclear weapons (both from sanctions and the R&D costs) were worth the end product. One way to resolve this is to assume that the United States had private information on the effectiveness of sanctions–Iran grossly underestimated the effectiveness of sanctions, while the U.S. knew they would work to perfection. If you think that sanctions were wildly more effective than anticipated, then you could reasonably expect the announced deal to be credible, and Iran will forgo proliferation so as to avoid more sanctions.

If you are skeptical that this is the case–and I am–then the United States will need to offer carrots to induce Iran’s compliance. In the absence of credible and effective “stick” options, nonproliferation agreements only work when potential proliferators receive good deals. The announced deal could not be much further from that, as Iran is getting nothing more than what it would have received had it not walked down this road at all. Perhaps these carrots will come in the second stages of negotiations. For now, however, if you think that the sanctions were not sufficiently effective, then this deal will not work until the United States gets out its checkbook.

3) Carrots must be permanent carrots.
If carrots are a part of some eventual grand bargain, they won’t come cheap. Washington won’t just be able to write Iran a one-time check for $10 billion in aid and expect the problem to go away. Rather, the U.S. will have to keep offering Iran that amount of aid year in and year out. In contrast, if concessions are a one-time gift, Iran has no incentive to maintain the deal going forward. That doesn’t mean that the United States shouldn’t pursue a deal. After all, deals are credible when structured correctly. Just don’t expect a comprehensive agreement to be on the cheap.

Along these same lines, the United States needs to make sure it will credibly give those carrots year in and year out. If Iran expects that a deal will suddenly stop at America’s whimsy–perhaps because of a new, hardline president–the deal will fail.

4) Inspections aren’t pointless.
Hardliners seem to have a mantra that inspections are useless since they can never be all-encompassing. They miss the point. Inspections aren’t always designed to create perfect information. Rather, inspections make it costlier to proliferate, since inspectors force proliferators to develop nuclear weapons via more inefficient means. Greater proliferation costs open up bargaining ranges, reducing the probability of preventive war or further investment in nuclear weapons.

Note, however, that inspections are only an intermediary step. Inspections don’t convince states to completely stop proliferation activities–that is what the carrots are for. Put bluntly, inspections without carrots won’t do much good.

5) War bargaining =/= arms bargaining.
From an IR theorist’s standpoint, it is tempting to use the bargaining model of war as a framework for nuclear negotiations. Yes, there are a number of similarities–bargaining, shadow of war, information issues, commitment problems. But nuclear weapons are not a bargaining object in themselves. No one in Tehran will look at the first Iranian nuclear weapon and think “SHINY!” Rather, nuclear weapons are an inefficient means to an end. Fearon 1995 is a good tool to start with, but we need a larger toolbox to really understand the dynamics of bargaining over proliferation.

Yes, that was a shameless plug for my dissertation.

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The bottom line here is that negotiations aren’t nearly over. The United States will likely have to make real concessions to Iran to induce Tehran to permanently end its program. Anything short of that will lead to more sanctions, preventive war, or nuclear proliferation.

I will be presenting a paper at the annual Peace Science Society meeting this weekend. The paper it is based on is from my dissertation. Here’s the abstract:

Why are some arms treaties broken while others remain stable over the long term? This paper argues that the changing credibility of launching preventive war is an important determinant of arms treaty stability. If preventive war is never an option, states can reach settlements that both prefer to costly arms construction. However, if preventive war is incredible today but will be credible in the future, a commitment problem results: the state considering investment must build the arms or it will not receive concessions later on. Thus, arms treaties fail under these conditions. The paper then applies the theoretical findings to the Soviet Union’s decision to build nuclear weapons in 1949 and Iran’s ongoing nuclear program today. In both instances, war exhaustion made preventive war incredible for the United States, but lingering concerns about future preventive war caused both states to pursue proliferation.

The presentation itself will cover the baseline bargaining-over-bombs model and use the war exhaustion extension to explain Soviet proliferation. If you can’t make the actual presentation (Friday, 10 am, Sequoya 3), check out a copy of the paper, look over the slides, or watch a video version of the presentation below. Comments are welcome!

Edit: I have since included a more detailed version of this post in my book Game Theory 101: Bargaining.

In the 24 hours since Congress reached a deal to reopen the United States Government, many reactions have been along the lines of “this shutdown was pointless–the deal they reached could have also been reached 16 days ago.” And while it is true that an identical deal could have been made 16 days ago and everyone would been better off, I think it is a huge leap to say that the shutdown was pointless. Rather, the shutdown conveyed information to moderate Republicans that they could not have received without the shutdown. This new information information made the deal palatable yesterday even though it was unpalatable two weeks ago.

I go into further detail in the video below, but here is the simple version. Neither Democrats nor moderate Republicans preferred a shutdown to some deal that kept the government going. However, based on the PR blitzes both parties went on during the shutdown, it seems reasonable that there were conflicting viewpoints on how the public would react. Republicans thought Democrats would shoulder most of the blame; Democrats thought Republicans would shoulder most of the blame. Consequently, both stood firm.

Sixteen days later, it became clear that the public was blaming the Republicans. Polling on this had been consistent for a solid two-week period. It would have been incredibly difficult for Republicans to stage a comeback at that point. And waiting any further risked a default, which would have been even more costly. So the Republicans agreed to the deal. The shutdown made this possible–the costly delay taught the Republicans that a shutdown was a losing battle, which in turn made them more amenable to a deal. From a welfare perspective, this sucks. But that is also the nature of bargaining under uncertainty.

Perhaps an analogy to war is useful. War is stupid–you could always take the result of the war, implement it without fighting, and leave everyone better off. But sometimes a weak party believes it is stronger than it really is. This makes it overly optimistic in bargaining, leading to a breakdown and war. However, the process of fighting reveals the weakness, in turn making the weak side willing to sit down at the bargaining table. The Republicans are the weak side. The Democrats are the strong side. The costs of war are the costs of the shutdown.

Overall, it is easy to blame the shutdown on partisan politics. And while extreme polarization makes the costs of bargaining breakdown appear smaller, partisanship alone gives a poor explanation for the shutdown. There needs to be some sort of bargaining friction, and I think uncertainty over who will receive the blame makes a convincing story.