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. Prashant Patel says:

    The article is great and spot-on. We need a way to make it make sense to us as individuals. I personally like the layout at http://usdebtclock.org/. However, there is still a glaring issue I see with your portrayal.

    If you have an income of $100,000 a year and you purchase say a $250,000 home on a 15 or 30 year mortgage (and say a down payment of 20%), most people would consider that within reason.

    If our government has an income of $14.5 trillion year and had say about $14.5 trillion in debt to fund its operations, most people would consider that well within reason (if your debts only total a year of your income, you could probably take on more debt and still be considered quite financially healthy).

    But therein lies the issue. The government does not take in $14.5 trillion a year. It only takes in $2.5 trillion a year. Our GDP is not the income of the government, it is the total product of our country as a whole. The comparable “debt” figure would be the total of public AND private debt, which, assuming arguendo the above website is correct, is $55 trillion dollars. Here are our true ratios then.

    Homeowner with $100,000 in annual income and a $200,000 home:
    Total Debt to Income Ratio: 2

    US Federal Government with $2.5 trillion in annual income and a $14.5 trillion debt:
    Total Debt to Income Ratio: 5.8

    United States with a $14.8 trillion GDP and a $55 trillion debt:
    Total Debt to “Income” Ratio: 3.7

    Now there is a small objection to my argument. A $200,000 home on a $100,000 income is probably not the likely case. Let’s up the ante then (and I do not have the necessary information on home prices and incomes of homeowners, so I am totally making this up; if you have such information, please reply with details). Let’s presume a $500,000 home with a 20% down payment. The ratio then is still only 4, just marginally above that of our GDP compared to total public and private debts. Of course a $100,000 household probably has two cars and other debts, but even then it is functioning with a smaller ratio than that of the federal government. And on top of that, the average household is probably not running an annual operating deficit of 50% or more of its annual income.

    Thus, the fact remains, no matter how we put it, our debt figure is big. Maybe even too big.

    Well-loved. Like or Dislike: Thumb up 17 Thumb down 1
  2. Eric M. Jones. says:

    Using distance correlates is IMHO ridiculous, since people have no sense of distance that correlates with money. A much better use of distance is to correlate it with time: Imagine 4.54 billion years (the age of the Earth) is laid out at 1000 years per mm (which is 1 million years per meter) distance. Then the dinosaurs existed a couple soccer-pitches ago. This makes long ages of evolution easy to understand.

    Here’s my proof that people don’t have a CLUE where or how distant the Moon is:

    If the Earth were represented by a basketball, the Moon would be a tennis ball over 22 feet away. This will win any bar-bet easily. Try it.

    The only way to imagine what a million-billion-trillion represents is to imagine what you can buy with the money. $800 billion dollars (what the Fed gave to Wall Street) would buy ONE HUNDRED Panama Canals built from scratch today.

    The same $800 billion would be the approximate cost of constructing a twin track 10,000 km maglev train system including 300 kph trains, tunnels, bridges and stations, between major US cities is about $800 billion. Average construction cost would be about $USD 50 million per kilometer. About 1200 maglev cars would be needed. The rolling stock would cost only US$20 billion.

    But we gave it to billionaires for bonuses. Hah!

    See my: http://www.periheliondesign.com/downloads/Zeros.pdf

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    • James says:

      “Imagine 4.54 billion years (the age of the Earth)…”

      The first problem here is that there are far too many people (including quite a few of those responsible for our budget mess) who’re firmly convinced that “The poor world’s only a bit over six thousand years old”. (Sorry, Will, but it has been a few centuries.)

      And then you have to explain “soccer pitch” to Americans. Soccer? Isn’t that where they kick the ball around?

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  3. D. Johnson says:

    I think Reagan’s comparison is great, actually. It’s a really effective ladder of relative concepts that are easily relatable to just about anyone. People may not all have a million dollars, but they can conceptualizize that amount relative to their own income (or savings, or whatever). That equates to a stack of thousand dollar bills 4 inches thick. The fact that very few people have ever seen a thousand dollar bill is irrelevant – what’s important is that he’s created a bridge between a million dollars and something else everyone can conceptualize: 4 inches (insert dick joke here, btw).

    The next step is to compare a million to a trillion, which seems easy but is hard to grasp in practice, but that’s where the 4 inches is relatable to 67 miles. When I saw that comparison, I thought “holy crap – is that right? That’s a huge difference!” In two steps, he’s made a trillion dollars understandable as a relative concept.

    The 67,000 miles concept is not nearly as effective. I’m with you on that one.

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  4. MB says:

    If your looking for a great comparison of the US debt try this link…

    http://www.wtfnoway.com/

    Scared the bejesus out of me and I’m not even an American.

    Good luck guys.. we need you to get this right. Just dont use it as an excuse to cut funding to those that need it.

    MB

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  5. Gates VP says:

    It seems to me that the easy way to pull this together is simply to use bigger building blocks. Measure debt in concrete things like skyscrapers or nuclear power plants.

    Your suggestion is to break it down into $ per capita, but I’m suggesting building it up from bigger blocks.

    Let’s say that a nuclear power plants costs $20Bn (rounding up). By that measure, $1 Trillion dollars is about the cost of building 50 nuclear power plants. The US currently has 104 nuclear power plants. Put differently, $1 Trillion dollars represents one nuclear power plant per state.

    A Trillion dollars in one year represents 50 nuclear power plants, assembled from scratch, in one 12 month period. We can then break that down into number of workers per power plant.

    This allows someone to scope a single power plant and then extrapolate that to 50 power plants and then say “hey that’s a trillion bucks”.

    A different Method: Football

    Imagine having to pay the salary of every NFL player for one year. That number is $3.25 Bn. A trillion dollars represents about 30 times that number.

    So a trillion dollars could pay every football player’s salary from here to 2041.

    Just my two cents on trying to measure large things.

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  6. Mike says:

    Isnt the comparison to help visualize the difference between a million and a trillion? Not the sense of the amount. Trillion is just becoming so every day

    Love the blog!

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  7. John B says:

    Remember that 14.3 Trillion figure isn’t static. It is growing every day by several billion $.

    The comparison I use is this:

    If Bill Gates, Warren Buffet and all the Waltons and their families had ALL of their money and assets taken away by the government (and the government could sell the assets at full value–quite unlikely), it would keep the national debt from increasing for between 2 and 3 months.

    Not reduce the debt–but just stop it from getting bigger for a short while. So even confiscation doesn’t work.

    Once this sinks in (and many people can’t comprehend this and still say that Gates, Buffet et al should pay higher taxes. I ask: higher taxes on what–everything was taken away), people then realize how bad it is.

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  8. Derek says:

    Per-capita figures are always easier to understand for anything related to government budgets. However, kids and homeless people are understood to get a free ride. Even better would be to scale it per $10000 of income tax. For example, if you paid $10000 in income tax last year, then $a went to fund the military, $b went to NASA, $c went to NPR, and $d was to pay interest on the national debt; if we had to pay of the entire national debt using one year of government revenue, it would take $x of that $10000. That gives you a very concrete feel for where your tax dollars go.

    By the way, most people have a poor idea of how far away the moon really is, since earth-moon diagrams are rarely drawn to scale. http://www.youtube.com/watch?v=Bz9D6xba9Og

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