We have been on a kick of government and power questions lately. In the field of international relations, power is often the cause or effect that we are most interested in. This makes measuring it appropriately very important, but the task is notoriously difficult.

Phil Arena recently suggested a new measure of military power:

Formally,

$M= ln(milper_{i,t}) ({ ln(qual_{i,t} \over \delta_t })$,

where $milper_{i,t}$ is country i's total military personnel in year t, $qual_{i,t}$ is i's quality ratio (military expenditures per personnel) in year t, and δt is a time-varying discount factor that I constructed to adjust for changes in military technology.

Specifically,

$\delta_t = 2.2^{(year-1700)/100}$,

which ensures that δ 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.

It is nice to see people thinking about how to resolve this issue. I recently replicated Benjamin Fordham's paper "Who Wants to be a Major Power?" and would be interested to see how the analysis changes (or stays the same) using Arena's M measure rather than the canonical Correlates of War index. Here is a plot (shamelessly stolen from Arena's blog) showing the European powers from 1816-1910 using M:

And of more contemporary interest: