Friday, February 24, 2012

Rational Military Spending

And by rational, I mean "of or relating to ratios." I raised this point in comments over at Tree of Mamre a few months ago, related to a Heritage Foundation graph. The topic came up again in the debate Wednesday, when Rick Santorum said this:
Some people have suggested that defense spending is the problem. When I was born, defense spending was 60 percent of the budget. It's now 17 percent. If you think defense spending is the problem, then you need a remedial math class to go back to. Defense spending will not be cut under my administration...
Rick Santorum was born in 1958, when "Major National Security" spending (PDF, page 69) was 61.4% of the federal budget, according to the Census Bureau's Statistical Abstract of the United States. So you can give Santorum credit for underestimating, at least. The 2012 edition (PDF) lists total federal spending in 2011 as $3,818.8 billion (page 4), and "National Defense" as $768.2 billion (page 5). Astute observers will note that 768.2/3818.8 = 20.1%, not 17%.* Nevertheless, 20.1% is less than a third of 1958's 61.4%. Is Santorum right?

This is where rationality comes into play, again referring to ratios. These percents are ratios, equal to defense spending divided by total spending. If you have a ratio q = a / b, there are two ways that q can get smaller. If either a gets smaller or b gets larger, while the other stays the same, q will shrink. What happens to q when both a and b move in the same direction? If both a and b increase, q will fall if b increases more than a, and q will rise if a increases more than b. (This may be elementary, but Santorum did suggest a remedial math class...)

In this case, a is defense spending and b is total spending, and Santorum's clear implication is that since q is falling, a cannot be too large. Both Santorum and the Heritage Foundation before him disregard the possibility that q is smaller only because b is larger. Santorum does so even though he had just finished saying he wanted to shrink b because it had grown too large!

According to the PDFs linked above, in 1958 total federal spending was a hair below $72 billion, while in 2011 it was about $3,819 billion. That's a 53-fold increase, although these numbers don't adjust for inflation. Military spending, on the other hand, increased from $44 billion in 1958 to $768 billion in 2011, a 17-and-a-half-fold increase, once again not adjusting for inflation. Military spending has increased, but total spending has increased far more.

Returning to the discussion of ratios, in the case of military spending since 1958, it is clear that b has increased more than a. It is true, as the Heritage Foundation and Santorum both said, that q is smaller now than it was when Santorum was born. That is emphatically not because a has fallen, by any means! The ratio of military spending to total spending has fallen solely because total spending has risen so dramatically!

What does the fall in the ratio of military spending to the total budget mean for actual military spending? Since the total budget has increased by such a vast amount, absolutely nothing! The ratio has zero mathematical significance, and is even misleading since military spending has actually increased since Santorum was born.

Is there some policy reason to prefer this measure of military spending to others, flawed and misleading as it may be? Not that I can think of, not unless your goal is to misrepresent the numbers to reach a predetermined outcome. Controlling for inflation with the GDP deflator, absolute military spending is about 3.17 times higher today than in 1958 in the middle of the Cold War. On a per capita (inflation-adjusted) basis, it's about 1.76 times higher today. As a percentage of GDP, military spending has fallen from about 9.4% in 1958 to 5.1% today, although once again, this is because the denominator, in this case GDP, has risen so much, not because military spending has fallen.

Could current military spending levels be appropriate, or even too low? Hey, anything is possible. But those who want to argue from that position at the very least need to get their numbers straight, and argue why more military spending is needed despite spending three times more than we were in the middle of the Cold War. Getting the numbers and fundamental math concepts wrong, then suggesting that the people who understand the math need a remedial math class, is not the way to make your case-- only Paul Krugman can get away with something like that. Rick Santorum should've known better.

*The ratio was 20.0% in 2010, 18.8% in 2009 and 20.7% in 2008. In fact, the ratio has been 18.8% or higher since 2003; it was 17.3% in 2002, but surely that wasn't what Santorum meant.

1 comment:

  1. Great analysis. If Santorum actually brought down b like he says we need to without cutting a like he says he won't, then by his percentage method of defense budget accounting the defense budget will grow enormously...

    Another point... if interest rate on the debt continues to take up a larger percentage of the budget (recent dip in treasury yields notwithstanding) then everything else will become a shrinking percentage of the budget, which could be used for an argument not to cut anything!