# Is it now really mathematically impossible to pay off the US national debt? (No.)

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So if you google “impossible to pay off the US national debt” you’ll find an article that’s been circulating on many conservative blog sites that argues why the central banking + fractional reserve banking model is broken and that it is mathematically impossible for the US government to pay off its debt.  [1]

I actually stumbled on that article a long time ago and it seemed to pose a very interesting paradox, and it’s been turning around in my head for the last year or so because I couldn’t find any good resources online that give a direct refutation or clarification of the phenomenon it describes.  Finally today, after listening to an NPR Planet Money report on the debate between dollar bills and dollar coins and the key idea of seigniorage, I think I understand what’s going on.  It’s not terribly difficult, but I guess no one else thought it was interesting enough to write down (or Google didn’t care to list such rebuttals as high as the original article in the search results).

The (most basic version of the) paradox, in a nutshell, is that the US government as of March 2012 has about \$15.6 trillion in debt, while the money supply (let’s say M2) is roughly \$10 trillion.  (The exact numbers don’t really matter, just the fact that the outstanding debt is larger than the money supply.)  Ergo, it is mathematically impossible for the US government to pay off its debts, because even if it were to collect all of the money in circulation, it would not be enough to pay off the debt.  QED, right?

In fact one might even think that the situation is worse, since the M0 supply is only 1/10th of M2 (less than \$1 trillion), and only M0 consists of real currency issued by the Federal Reserve.  The rest of the money supply is either held as reserve balances at the Fed, or created by the money multiplier (because of fractional reserve banking).

The solution: the key point is that only money that is paid back to the Fed is removed from circulation.  Most of US government debt is owed to private creditors, both domestic and foreign, and payments made to those creditors remain in the economy and therefore can be collected by the US government again through taxes, and so used to pay debts again.  Namely, when the US gov’t pays debt to a private creditor, the money supply does not decrease.

In fact this point was noted in some versions of the paradox, but they dismiss it because they implicitly made the assumption that most US gov’t debt was owed to the Fed, and so when it is paid to the Fed that money is removed from circulation.  A quick look at the Fed’s balance sheet reveals that the amount of debt owed to the Fed is much smaller (roughly \$1.7 trillion as of April 19, 2012), and is easily covered say by M1.

Regarding the argument that “only M0 counts”, really what counts is M0 + MB, the amount of currency in circulation plus the amount of reserve balances held at the Fed.  While MB is not really in circulation, it is money issued by the Fed at some point, and so in theory it can be obtained by the US government (say if a commercial bank’s overall deposits drop and it withdraws some of its reserve balances, and uses some of its withdrawals to pay taxes).  It’s easy to see from the Fed balance sheets that it always holds that M0 + MB is larger than the US gov’t debt held by Fed.

There is in fact a subtler (but still resolvable) paradox lurking behind the basic one mentioned above.  To describe the paradox we need to describe in a little more detail how money comes into circulation.  The Fed “creates money out of thin air”, namely it is given the legal authority by the US government to create money out of nothing.  This money is then put into circulation when the Fed uses it to buy assets.  The Fed buys interest-accruing securities, most notably Treasury bonds.

Consider what happens when the Fed buys \$100 worth of US Treasury bonds, at an interest rate say of 2%.  This means that the US government now owes \$102 to the Fed.  But where does the US gov’t get the extra \$2 to pay back the Fed?  Since only the Fed has authority to create money, the US government has to issue more debt in order to obtain more dollars to fully pay off the original debt.  But now this new debt has additional interest, and so this creates a snowball effect.  Or does it?

The solution: there are two key points, one obvious, the other less so.  The first is that the US government pays its debts in installments, and pays off parts of its principal and interest in small pieces.  The second is that seigniorage occurs with the interest payments made by the US government to the Fed, and so this interest does not need to come out of further debt: while the Fed “uncreates” the money that constituted the principal of the original Treasury bond, the Fed does not “uncreate” the money that was paid as interest.  Rather, the Fed transfers this money to the US Treasury (and I believe also to its other shareholders, among them commercial banks), where that money then re-enters circulation.

Therefore, as the US gov’t is paying off its Fed-owned bonds, the interest is transferred to the Treasury and so even though the Treasury initially owed \$102 to the Fed, the \$2 interest is in fact incrementally given back to the Treasury out of the interest payments, and so there is no snowball effect.

#### Other issues and questions

While this shows that, at least in theory, it is mathematically possible for the government to pay off its debt, there are further practical and/or ethical issues in the way the central banking model fundamentally works. Two notable ones include:

• While there exists enough money in circulation for the government to pay off its debt, it seems undesirable for the government to collect all this money.  After all, the whole purpose of having money around is to provide liquidity in the economy.  Therefore some amount of government debt seems permanently necessary in order for there to remain enough money in the economy to provide liquidity.  It would be interesting to know how much debt is necessary to provide enough liquidity for a healthy economy.
• Seigniorage represents an implicit form of taxation.  When the Fed creates dollars and buys Treasury bonds in an OMO, interest that would have been paid to private investors is now paid to the Fed.  But since the Fed remits its profits to the US Treasury, this essentially means that the Treasury does not pay interest on bonds owned by the Fed, and so (in addition to depressing interest rates by buying Treasuries) having the Fed buy privately-held bonds saves the government on the interest payment that it would have paid to the private bond holders.

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1. [1] As far as I can tell the article is of unclear authorship and it is reposted without attribution across many different sites, so let me not link to any particular blog and rather suggest you go and find it yourself on Google.  If someone does know the authorship of this article please let me know and I’ll cite it appropriately.

1. Brian

This question warrants a book on the subject, but here is a quick first stab:

I am a fan of fiscal prudence, but it is emphatically NOT the case that repayment of the debt is a mathematical impossibility. The US Government is privileged in its ability to issue new currency and inflate away its debts. The US economy can also grow its way out of debt – the amount of money in the money supply (and the value of US dollar-denominated assets) is not fixed and typically increasing, even without inflation. But you nailed the biggest escape route: the same dollar can be collected as taxes more than once, and in most cases, that dollar is not then “retired” from the money supply. The amount of money in circulation is not the limit on debt – most assets at any given time are not liquid enough to count as part of the money supply, and most future earned income and capital gains income won’t be held as cash for long. But the government can still tax those things, even though they aren’t part of the money supply.

The focus on the money supply is a distraction from the real issue: the US government’s level of indebtedness is alarmingly high – so high, that creditors of the government are eventually going to insist on a higher rate of return (interest rates) on bonds because the probability that the US government will repay that debt is meaningfully less than 100%. This is what happened to Greece, Spain, Portugal and Ireland. Once the the dollar is no longer the de facto reserve currency for central banks around the world (already well underway – just look at China’s recent reserve holdings), the US Treasury will not be able to borrow ad infinitum at exceptionally low rates. As that cost of borrowing goes up, the size of the debt (which is already crushing on a per capita basis) will be a serious problem, because the cost of carrying that debt will be so high. Bond investors around the world know that there is a limit to how much taxation the US Treasury can squeeze out of its taxpayers.

Government projections on the deficit and debt are notoriously unhelpful because they do not take into effect likely changes in interest rates (borrowing costs) and dynamic response by economic actors to incentives (such as tax rates). Nor do they take into account the government’s ability to print money to devalue its debts. But I would argue that inflation is just stealing from people and institutions who are holding US dollar-denominated assets: mostly US taxpayers and foreign governments (and other bondholders) willing to finance our deficits by holding our debt. And when the US government inflates away those debts (or looks likely to do so), bondholders will wise up and stop buying those bonds unless interest rates go up. Our current fiscal path thus makes stagflation (high interest rates and high inflation – and low growth because interest rates are high) very likely in the not-so-distant future if Congress doesn’t get its fiscal house in order. We are spending too much, we are overestimating our ability to tax our future selves, and we are underestimating the severity and the swiftness of the economic collapse that will occur when the US no longer looks like the safe (remember the treasury bond rate referred to as the rate of risk-free return? Ha!) place for global investors to park their assets. I think the US (and the dollar) have been insulated a bit because it’s been a race to the bottom among many global currencies: the Euro has been even worse. Which is why we’ve observed a dramatic appreciation of assets that are independent of fiat currencies (such as gold and other precious metals and other commodities). Gold prices are at roughly triple the levels they were in 2007 and remain close to all-time highs. It does not auger well for the US Dollar – which of course, is a proxy for the US government and economy.

2. Brian

I am in good company: Bernanke sees it the same way, and of course, said it a lot better than I did…

3. The Random Oracle

Hey Brian, thanks for the comment! I definitely agree about the “race to the bottom” happening between Europe and the US (I’m sure Japan will join in at some point, its finances are even more catastrophic!) and it’s pretty scary. Do you think there are measures that can be taken to wean ourselves off of the government debt? It seems that Congress (and the other foreign governments stuck in similar situations) are unable to get their house in order because austerity is incredibly unpopular and, in the short term, not necessarily productive. At least in Europe the mood has started to shift and there are increasing calls for a relaxation in austerity, at least in places where it’s been in force for a few years and things have just gone from bad to worse. Of course, one corollary of that is that since those governments are already unable to pay their debts, the other countries with better finances will have to shoulder that burden.

In the US I guess the debate is different because the economy is not quite as bad as say in Greece or Spain, and there are already fiscal transfers across the various regions of the country. But do you think that the time has already come to cut back on government spending in general? Wouldn’t that hurt the current recovery? Is there perhaps a way to maintain short-term spending (e.g. with things like infrastructure, which require immediate investment but should be economically beneficial in the long run) without hurting the long-term debt outlook? It seems to me that theoretically this is possible, but the main obstacle is politics and a lack of a clear, rational discussion of what kinds of government spending should be prioritized.

One final point on a more theoretical note: if we take a step back and view the financial system as it truly is, which is a system of information and control that allocates productive resources in the economy, it seems that government austerity is really a half-measure. Namely, the point of austerity is to de-allocate labor and resources from the government, where it is presumably being employed inefficiently, and re-allocate it to other sectors where it would be more productive. But austerity only does half the job, namely the de-allocation part. It seems that there are very few “pro-active” re-allocation mechanisms that try to get people to work in more productive areas, and none of them seems to be particularly effective. I wonder, is there research or theoretical ideas on how to implement a more pro-active re-allocation policy, so that the workers laid off during austerity are not just sitting around idling?