Measuring Military Capabilities

There have been some interesting discussions about how to measure the position of the United States relative to China in the past few months (see here for an earlier take).

One point that has been made a few times, particularly by Beckley, is that we put too much weight on the sheer size of a country. If you took a middling power and added 50 million or so desperately poor, illiterate, starving people, both their GDP and CINC scores (available here, under the National Material Capabilities page of Available Data Sets) would increase dramatically. Yet none of us really believe that such a nation would grow appreciably stronger as a result. It's high time someone proposed a measure that is immune to this criticism.

I doubt it's perfect (in fact, I'm sure it's not), but I'd like to propose such a measure. It focuses exclusively on military components, and so I'm imaginatively calling it M.


Construction

This is a little messy. Math-phobes are going to want to skip this section. But for those who are interested in the details, here's how I constructed my measure.

Formally,
\begin{align*}
\mbox{M}= ln(\mbox{milper}_{i,t})\displaystyle\left(\frac{ln(\mbox{qual}_{it})}{\delta_t}\right),
\end{align*}
where \(\mbox{milper}_{i,t}\) is country \(i\)'s total military personnel in year \(t\), \(\mbox{qual}_{i,t}\) is \(i\)'s quality ratio (military expenditures per personnel) in year \(t\), and \(\delta_t\) is a time-varying discount factor that I constructed to adjust for changes in military technology.

Specifically,
\begin{align*}
\delta_t = 2.2^{\left((\mbox{year}-1700)/100\right)},
\end{align*}
which ensures that \(\delta\) takes on a value fairly close to the average quality ratio among the major powers in any given year, without exhibiting the fluctuations found in the actual average.

My goal was to account for the size of a military as well as it's sophistication. I also wanted a measure that didn't correlate so highly with time (as GDP does) nor require that the total of capabilities in the international system always sum to 1 (as CINC does). There are various other technical concerns I had in mind that I'm glad to discuss in the comments if anyone is interested.

But enough technical details. Let's look at some colorful graphs.

Validation

Here's a graph of the CINC scores for the United States, United Kingdom, Russia/Soviet Union, and China from 1945 to 2007 (the last year with available data).



And here's M for the same states over the same time period.



I don't know about you, but it looks to me like M has more face validity. According to CINC, China has already surpassed the United States. For all the debate between "alarmists" or "declinists" on the one hand, and "polyannas" on the other, no one seems to believe that the US has already ceased to be the dominant military power in the international system. We don't get that from M. CINC also tells us that the UK was a second rate power even in 1946, whereas M has the UK looking stronger even than the US in 1940 (not shown), soon to be eclipsed by their Atlantic ally during WWII, yet still quite formidable in 1946, though quickly dropping off from there. Finally, M makes the Soviet Union look like a real challenger to the US during the Cold War, whereas CINC suggests that the Soviet Union was far weaker than the US during the early decades of the Cold War. YMMV, but all of those things make me think that M does a better job of capturing the military might of these four powers.

That said, there are some patterns in M that stand out. China sees a big slump before the end of the Cold War and a smaller but still considerable one in the past few years. Do these reflect real changes in the relative military capabilities, or are they signs that something is wrong with the measure? I don't know enough about China to say.

Let's take a look at the European powers from 1816 to 1910.





Compared to CINC, M paints a picture of a much more evenly balanced continental system, particularly after 1850 or 1860. The CINC score points to a century of fairly pronounced British dominance that only begins to break down at the very end of the century. I think there are those who would argue that CINC gets it right here, but I don't know. Do we really believe that Germany was basically a nobody until 1890 or so? That Austria was never even one of the top 3 European powers? That France was never remotely close to as strong as the UK? If anyone is more familiar than I am with 19th century Europe, please feel free to chime in, but my sense is that M actually looks pretty good here too.

At any rate, this is all very preliminary, and only speaks to face validity. I'm excited enough about this measure that I just might decide to try to validate this measure in other ways. If it outperforms CINC in terms of explaining patterns of international conflict, both in terms of onset and outcome, I may start relying on it in my academic work. Maybe. For now, it's mostly just food for thought.

What M Is Not

Power is multi-faceted. It's also typically defined in a manner that's damn near tautological ("the ability to get others to do what you want them to do when they would otherwise not be inclined to do so"). I was careful above not to refer to M as a measure of "power", because I'm not at all sure that it is one. No more so, at any rate, than CINC is. It's a measure of military capabilities (as opposed to a broad basket of material capabilities that includes demographic and industrial components). One might argue that a measure based solely on nuclear or naval power might be more meaningful. Or one might argue that any debate about whether the future belongs to China should reflect measures of soft power and the growing dominance of the English language and American culture; the centrality of the United States in the global economy and the role of the dollar as the international system's reserve currency; or various other concerns. I have no principled argument to offer against such claims. All I set out to do was construct a measure of military might that would draw upon the same publicly available data that scholars of international relations are used to using but might be considered superior to CINC in certain respects. And I think I have done that...though if you ask me again in a month or so, my opinion may have changed.