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A Stack of Bills Reaching to the Moon: How to Quantify Our National Debt


Now that the U.S. national debt is in the headlines, the media is awash in astronomical numbers such as $14.3 trillion (the current debt). Everyone realizes that this number is incomprehensible. Even back in 1981, when the national debt was only about $1 trillion, the debt was still incomprehensible. Thus, speechwriters for Ronald Reagan created, or at least popularized, a widely used attempt to give it meaning. Speaking to Congress in February 1981, Reagan said:

A few weeks ago I called such a figure, a trillion dollars, incomprehensible, and I’ve been trying ever since to think of a way to illustrate how big a trillion really is. And the best I could come up with is that if you had a stack of thousand-dollar bills in your hand only 4 inches high, you’d be a millionaire. A trillion dollars would be a stack of thousand-dollar bills 67 miles high.

This comparison is often quoted as a stack of one-dollar bills 67,000 miles high (perhaps because thousand-dollar bills don’t exist). No matter which denomination you use, I give the explanation an A for effort, but an F for performance. For I have little idea of how far 67,000 miles is. I know it’s way too far to walk and even too far to fly (jumbo jets have a maximum range of around 7,000 miles). But is it large as a national debt? I have no idea. Perhaps a large national debt would reach all the way to Mars. The connection to a height has merely replaced one meaningless idea ($1 trillion) with another meaningless idea (a stack 67,000 miles high).
Recognizing this problem, many articles explaining the national debt attempt to give the distance meaning. Here is one example from a recent NPR article entitled “Any Way You Stack It, $14.3 Trillion Is A Mind-Bender”:

…here’s an astronomical analogy about today’s debt: If you stack up 14.3 trillion dollar bills, the pile would stretch to the moon and back twice.

My first reaction to such numbers is, perhaps like a lemming, to check whether they look reasonable. My quick check went as follows: if one trillion bills reach up to 67,000 miles, then 14.3 trillion bills reach up to 14.3*67,000 miles, or about one million miles. The moon is 250,000 miles away, making a roundtrip to the moon 500,000 miles. Thus, the stack is about two earth-moon roundtrips—as claimed.
However, I was a lemming because there was no point in checking the calculation. Even if it turns out correct, the moon comparison is as meaningless as the raw distance in miles. Thus, my second and healthier reaction is frustration. For I rarely (actually never) use the distance to the moon as a yardstick for national debts. Neither does the IMF, which tabulates national debt as a percentage of GDP (a dimensional confusion, but that is another story). Thus, I have no clue whether a national debt should be twice an earth-moon roundtrip, should be much closer, or should be much farther.
Offering another comparison, the article has us imagine laying bills flat on the ground. The national debt, laid out in one-dollar bills, would cover the whole state of Illinois. This time I restrained myself from checking the calculation, because I have even less idea about monetary areas than I have about monetary distances. Alas, at the end of the article, I am still ignorant about the size of the debt.
What is a better alternative? Give huge numbers meaning by converting them into human-sized quantities: for example, into per-capita amounts. Per-capita, the U.S. national debt is roughly $50,000 ($14.3 trillion divided among 300 million people). That number is graspable. Indeed, it is roughly the average per-capita annual income (the U.S. GDP divided by the population). Thus, if everyone in America spent his or her entire year working off the national debt, and on nothing else (including taxes or eating), the debt could be cleared in a year.
Is that amount of debt a lot? It partly depends on its origins. Imagine a household with an annual income of $100,000; a household is not a country, but the analogy is helpful. If the household has a debt of $100,000 from playing the horses, they are probably in trouble. Similarly, a $100,000 debt acquired to stockpile bazookas for war against the neighbors is also probably not a sound investment. However, if the household acquired the same debt to buy its home, it could be well worthwhile. That’s the reason for 30-year home mortgages: to make it possible to acquire and repay useful debts.
One commenter on the “Any Way You Stack It, $14.3 Trillion Is A Mind-Bender” article criticized it for providing unhelpful explanations of the size of the national debt. Instead, the commenter suggested that per-capita debt is a more useful number. Yes!
However, after dividing the debt among an estimated 200 million people in the workforce, the commenter arrived at a per-capita debt of $715,000. Due to the three significant figures, this number seems very reliable. (For more about this illusory reliability, see an earlier post of mine about the Gulf oil spill.) Yet the result seemed fishy. If it were right, then the U.S. per-capita income, which also involves dividing roughly $14.3 trillion among a few hundred million people, would also be around $715,000. Good news, everyone’s a millionaire! Indeed, in the comment the division had been done incorrectly: $715,000 is too large by a factor of 10. As Keynes is reputed to have said, but probably did not: It is better to be approximately right than exactly wrong.
As a final irony, I saw that the comment in question had been recommended by 11 others whereas other, nearby comments had garnered hardly any votes. Hoping for details on who had recommended the calculation, I clicked on the “Recommend (11)” link. Alas, my click increased the count to 12. This post is one way to atone for my sin!