Does calculus matter?

I’m going to weigh in on a current political kerfuffle about federal spending levels, though I’m going to (try to) do so in an explicitly non-political manner. The point here isn’t to argue for or against some particular level of federal spending. Rather, it is to point out that the discussion of this matter all too often fails to maintain a distinction between the level of spending and the rate of change of the level of spending.

The kerfuffle is as follows. Romney says (on his website, at least as of Friday May 25, 2012), that “Since President Obama assumed office three years ago, federal spending has accelerated at a pace without precedent in recent history.” Rex Nutting writes a piece with the lede “Of all the falsehoods told about President Barack Obama, the biggest whopper is the one about his reckless spending spree.” Someone juxtaposes a picture of Romney with his quote and the first figure from the Nutting piece and it goes viral on facebook (and elsewhere).

First things first. Is Romney correct? No. The relevant data are available here, in Table 1.3. If we calculate the rate of increase in federal outlays, expressed in terms of the percentage change relative to the previous year, we get this:

Rate of change in federal outlays relative to previous year

As described elsewhere (e.g., here, here, here, and on facebook in various unlinkable places), Obama has presided over exceptionally low rates of growth. In fact, by my calculation, “growth” isn’t even the right word, since I get a 1.75% decrease in spending in 2010.

You could argue that the percentage change relative to the previous year isn’t the (only) appropriate quantity to look at (as I have, with respect to federal debt). For rates of change in spending, we get a similar picture if we look at percent of GDP:

Change in percent of GDP relative to previous year

Note the difference in the scale of the y-axis, but note, too, the same basic pattern: very big uptick in 2009 (W. Bush’s last budget), equally big reduction in 2010 and 2011 (Obama’s first two budgets).

Okay, so Romney was (and is, assuming the text on his website hasn’t changed) wrong. Obama has not presided over an unprecedented increase in federal spending.

But the rate of change in federal spending might not be the relevant quantity. If the federal government is spending at sufficiently unsustainable and detrimental levels, the rate of change hardly matters.

Suppose, for example, that the federal government’s outlays were 100% of GDP, and suppose that this year they were spending a full 25% less than they had last year. As desirable as such a large decrease would be, federal spending sitting at 75% of GDP would still be utterly absurd.

This example is chosen to be absurd and extreme. Clearly the federal government isn’t spending at 100% of GDP. But the basic point still stands. If you believe that spending at, or above, X% of GDP is too much, then the rate of change in spending is largely irrelevant if spending is above X% of GDP. Similarly in the other direction if you believe that spending should never dip below X% of GDP.

What do we see if we look at the level of spending rather than the rate of change in spending? The federal government is, in fact, spending massive amounts of money under Obama. Here’s a figure showing federal outlays as a percent of GDP:

Federal spending as a percent of GDP

And here’s a figure showing federal spending in current dollar terms:

Federal spending in current dollars

Obama’s budgets have given us very low rates of change in federal spending. But they’ve also given us very high levels of spending. Historically high, whether you express the numbers in terms of percent of GDP or billions of dollars (look at the y-axis there – it’s thousands of billions, i.e., trillions, of dollars – I initially thought that this had to be a mistake, but apparently it’s not).

To reiterate my non-political aims, I’m not arguing for or against any particular level of spending. My purpose is merely to point out how sloppy the discussions of this issue can be. If you follow the various links above, you’ll see that the discussion has focused pretty much exclusively on the rate of change of spending, which paints an incomplete picture at best, as I’ve been at pains to show.

But you’ll also see that the distinction between the rate of change of spending and the overall level of spending is sometimes lost on commentators. A particularly egregious example of this (by Rick Ungar, writing for Forbes) spurred me to write this post. Thankfully, most people writing about this aren’t as careless as Mr. Ungar.


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