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

(Photos.com)

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!

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  1. Ezzie says:

    If the debt is to acquire one home, sure, it’s not a bad investment. If however the debt is there but you’re going to keep buying homes every single year, then it’s not quite as wise.

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    • Soquel by the Creek says:

      In other periods of major debt increases, we did “invest” in a brighter future for America. The enormous cost of World War II helped defeat the Nazi and Japanese Imperial empires. The debt increases during the 80′s helped defeat the Soviet Empire.

      What exactly did we buy with the enormous debt of the Bush/Obama era?

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      • Ezzie says:

        Nothing. I’m reasonably moderately-conservative, and overall a Bush fan and not one of Obama. But Bush’s biggest failure was bailing out the banks rather than letting them fail, and Obama’s just compounded that – while adding to it with other initiatives yet to come.

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      • Brett Dunbar says:

        The bank bailout should turn a profit, the money is being lent at an interest rate greater than it is being borrowed. And the consequences of a collapse of the banking sector would be a lot worse than the consequences of a fairly short term increase in very cheap debt.

        A distinction needs to be drawn between big numbers and really big numbers, $800 billion is a big number but it is only $2,500 per American so isn’t a really big number. $14.3 trillion is a big number $14, 3000, 000 million/310 million is roughly $46,000 per American, roughly equal to annual income. If you have a mortgage about equal to earnings and at as low a rate as the US government can borrow that would be easily affordable.

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      • Brett Dunbar says:

        Addendum: The $14.3 trillion is the gross debt which includes debt that the federal government owes to itself. This is essentially an accounting fiction not actual debt. The net debt is about $13.6 trillion. $13,600,000 million/310 million is roughly $44,000

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      • Joshua Northey says:

        The outcome of WWII and the Cold War were decided long before we ran up the catastrophic debt. But believe our ridiculous a-historical narratives about American exceptionalism if you want.

        The outcome of WWII was decided by the Spring of 1942, most of the war from the US perspective was stopping the Russians from coming out the big winners in the post war reconciliation (not necessarily a bad thing, but definitely not the story we tell ourselves). It was an even fight before the largest and strategically invulnerable industrial power on the planet officially entered. After we entered it was simply a matter of playing out the “mate”.

        US military spending in the 80s might have sped the Soviet Union’s collapse, but it was in extremely rough shape without that. How long does it last with defense spending at 50% lower? An extra year, and extra 2 years? Maybe it even falls sooner if there is less paranoia from the hard liners? Or maybe Gorbachev successfully transitions it out of Communism without an indefinite interlude of kleptocracy and massive suffering?

        We ran up the debt because we could, and because the military and defense contractors are excellent at scare mongering. I don’t really see the Bush/Obama era as historically discontinuous with that of preceding administrations. The institutions in Washington are just slowly growing more and more “efficient”. Business lobbies the politicians, the politicians promise services but don’t ask the electorate to pay for them, and we take a few more steps towards eventually having a serious discontinuity.

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      • Merlinius says:

        lol. The cost of WW2 has nothing to do with current national debt. I don’t know what you learned in your history lessons but the US did not defeat the Soviet Union, especially not in the 80s, especially not with money. The debt originated from huge deficit spending by wasteful politicians and the wars in the middle-east from the 90s onward.

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  2. Soquel by the Creek says:

    Here are other potential ways to describe the size of the USA national debt.

    The USA is the world’s largest economy, with a GDP of $14.657 TRILLION (PPP). The size of the USA debt, at the moment, is some $14.3 TRILLION. In other words, we’re collectively in debt the equivalent of a full year’s salary.

    Measured in purchasing power parity (PPP), the world’s 2nd largest economy is China and the 3rd largest economy is Japan. The USA national debt is roughly equal to the entire economies of China and Japan COMBINED.

    The single largest economic block is the 27 countries in the European Union, with a combined GDP (PPP) of $15.1 TRILLION. The USA national debt is about $800 BILLION smaller than the entire economies of the European Union. For a point of reference, the US Stimulus Plan was over $800 BILLION.

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  3. Joshua Northey says:

    Here let me describe my yard to you.

    If my yard were a car it would be a 2005 Volvo Sedan traveling at 30 mph. What that is not helping? What if I tell you the Volvo is Navy. More clear now?

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  4. Andrew Collins says:

    Around the world 20 times.

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  5. James says:

    “Similarly, a $100,000 debt acquired to stockpile bazookas for war against the neighbors is also probably not a sound investment.”

    This depends entirely on the sort of neighbors you have. Although there are, almost certainly, more cost-effective choices of weaponry.

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  6. Ashley says:

    I looked into the debt a few weeks back and translated it into gold and diamonds as a mental exercise. http://sothatslike.blogspot.com/

    Spoiler: 287k tons of gold or 776 million carats of flawless diamonds.

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  7. james jones says:

    Just as a corrective note. $1,000 dollar bills DO exist, however the bill is no longer in production and its circulation is typically limited to collectors.

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  8. caleb b says:

    Putting it in terms of distance and size can be helpful, but they need to be in terms of practical life. Here is a great one for the solar system.

    If the sun were a basketball, the earth would be a marble 90’ away. Pluto would be the head of a pin a half mile away. I think that pretty much helps me understand. The solar system is really big.

    http://humealumni.org/solarsys.html

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    • JimFive says:

      Relating a non-human scale distance to a human scale distance makes sense.

      Relating a non-human scale amount of money to a human scale distance doesn’t make any sense. It is a bad analogy because it doesn’t tell you anything about that amount of money AS an amount of money.

      JimFive

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