## Tuesday, November 13, 2012

### Once More on Military Capabilities

I previously introduced a new measure of military capabilities, $$M$$, which is intended to capture the size and sophistication of a nation's military relative to prevailing standards of the day, here.  Some legitimate concerns were raised about how the scores were calculated, so I adjusted the measure.

The real question is how to normalize the raw military data to reflect prevailing standards of the day.  In my previous two attempts, I did this through the use of arbitrary constants.  This is unsatisfactory for a variety of reasons.  I've decided to instead base the $$M$$ scores on 5-year moving averages.

Construction

Formally the revised $$M$$ score for country $$i$$ in year $$t$$ is equal to,
\begin{align*}
\mbox{M}_{i,t}= \Pi_{i,t}q_{i,t},
\end{align*}
where $$\Pi_{i,t}$$ and $$q_{i,t}$$ are discounted measures of the military personnel and quality ratios (military expenditures per troop), respectively, of country $$i$$ in year $$t$$.

Specifically,
\begin{align*}
\Pi_{i,t} = \frac{\mbox{milper}_{i,t}}{\mbox{milper}_{i,t} + \delta^\Pi_t},
\end{align*}
where $$\mbox{milper}_{i,t}$$ is the military personnel for country $$i$$ in year $$t$$ (taken from the CINC data) and $$\delta^\Pi_t$$ is a 5-year moving average.  This is the big change from the previous version.

Specifically,
\begin{align*}
\delta^{\Pi}_{t} = \frac{\overline{\mbox{milper}}_{i,t-1} + \overline{\mbox{milper}}_{i,t-2} +... + \overline{\mbox{milper}}_{i,t-5}}{5}
\end{align*}
and $$\overline{\mbox{milper}}_{i,t}$$ is the global average military personnel in year $$t$$.

Similarly,
\begin{align*}
q_{i,t} = \frac{\mbox{qualrat}_{i,t}}{\mbox{qaulrat}_{i,t} + \delta^q_t},
\end{align*}
where $$\mbox{qualrat}_{i,t}$$ is the quality ratio for country $$i$$ in year $$t$$ (taken by dividing the military expenditures for that country by its military personnel, using the CINC data for both) and $$\delta^q_t$$ is a 5-year moving average of the average quality ratio.

As with each of the previous versions, my goal here is to account for the size of a military as well as it's sophistication. I also want a measure that doesn't correlate highly with time (as GDP does) nor require that the total of capabilities in the international system always sum to 1 (as CINC does). This new version of $$M$$, like the previous one, ranges from 0 to 1, with values nearer to 0 indicating that country $$i$$ has virtually none of the military might that could reasonably be possessed by a country in year $$t$$, while values closer to 1 indicate that country $$i$$ has achieved a level of military might that far exceeds the standards for that time period.

Validation

As before, let's look at $$M_{i,t}$$ for the United States, United Kingdom, Russia (Soviet Union), and China from 1945 (1950 for China, due to missing data) through 2007.

That looks a bit different from my previous attempt, but relatively similar to the first version. It tells us that the US came out of WWII with an unprecedented military advantage, quickly began cutting back, then climbed back to the top. We see that the Soviet Union and the US had roughly equal conventional military capabilities for much of the Cold War.  There's no longer evidence that the US fell behind the Soviet Union in the 70s though. There's also some interesting fluctuation in China's score that wasn't coming through before, and the UK looks quite a bit more capable under this version of the measure than it did previous versions.

I'm working on a paper introducing this measure.  Between now and then, I might change my mind about how to normalize things yet again, but I don't think so.   I wish I'd thought to use moving averages to begin with.  That makes the measure less arbitrary.  Once I have a draft ready, I'll post it on my website and link to it here.