For stability, is there a limit to the sovereign debt that a Government owes to itself against issued fiat currency?

Looking beyond the optical illusion of Governments owing debt to Central Banks, Governments effectively owe themselves the sovereign debt created against issued fiat currency.

By definition, there shouldn't be any limit to the debt that an entity owes itself.

Does this mean that Governments can continue to print a limited amount of fiat currency (say 5% of GDP) annually forever?

In other words, is there a problem even if this debt that the Government owes itself, grows to, say, 1000 times the GDP over centuries?

The national debt and currency are financial assets of the private sector and local governments. Since currency can be withdrawn on demand from the aggregate bank sector the ratio of national debt to fiat currency is determined as a portfolio choice of the private sector and local governments.

The central bank and/or commercial bank sector must use its balance sheet to allow the private sector and local governments to swap currency for other financial assets otherwise bank deposits would not keep par with currency. Some of these financial asset swaps are swaps of government securities for currency or currency for government securities.

FRED graph Federal Debt Held by Federal Reserve Banks:

https://fred.stlouisfed.org/series/FDHBFRBN

Notice the smooth increase up until Q3 2007 when Fed began to lend funds to the bank sector at the discount window, which adds reserves to the aggregate bank, and Fed sold Treasury securities to drain reserves so it could keep control over the federal funds rate. This strategy would not work in the long run because Fed would run out of Treasuries and then have no way to neutralize reserves added by discount window loans if the volume of lending became larger than Treasury assets.

FRED graph Currency in Circulation:

https://fred.stlouisfed.org/series/CURRCIR

If you convert these two graphs to the same time on the horizontal axis and the same units (millions or billions) on the vertical axis then it shows Fed holding Treasuries roughly equal to the currency in circulation up until Q3 2007 as discussed above. This means when the aggregate private sector and local governments would withdraw currency from the aggregate bank the Fed would go into the open market and purchase Treasuries to offset or "service" the currency drain. This was necessary when Fed kept the pool of bank reserves as small as possible to control the federal funds rate. Banks give reserves to Fed to buy vault cash (currency) and would not have any reserves if Fed did not provide those reserves while servicing the currency drain.

Banks must allow depositors to withdraw currency to keep checking deposits on par with currency since both currency and deposits are used to clear payment. Fed must service the currency drain during some operating conditions to retain control of the federal funds rate or also known as the monetary policy target rate. When Fed would buy Treasuries to service the currency drain this meant that the private sector and local governments had the option to hold either Treasury securities or currency in their portfolio of assets consisting of currency and Treasuries.

After Q3 2007 Fed sold and then purchased Treasuries without matching holdings to its currency liabilities so the currency holdings would be at the election of the private sector and local governments demand for currency via withdrawal from the aggregate bank. The distribution of Treasuries between Fed and the private sector and local governments would be in the discretion of Fed under efforts to manage monetary policy using its balance sheet.

So in general the amount of Treasury debt outside government, held by Fed, private sector, and local governments, equals the sum of net deficit spending over the history of the nation. The currency outside banks is determined by the portfolio choice of the private sector and local governments. The ratio of currency to Treasuries does not appear to be a factor correlated with inflation. Total deficit spending by households and firms is related to aggregate credit (loans). This combines with deficit spending by governments and a shortage of resources to drive inflation.

I published three papers on this subject matter which draw conclusions from research in the United States flow of funds and other sources.

Sources and Sinks of the M1 Money in a Four Sector Model of the U.S. Financial System.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2257270

Currency drain analysis from 1980-2011 is on pages 11-13 including Figures 4 and 5 which relate to the answer above.

• Thank you so much. The 2nd para is very enlightening! The fact that the Government cannot owe 100% of its debt to itself wasn't clear to me at all. Sir/Madam, If / when you have time, please do consider elaborating on your answer. Because I don't think I have seen this deeply insightful idea mentioned anywhere else. – Ritesh Singh Jan 11 at 2:36
• Could you please elaborate on "Since currency can be withdrawn on demand from the aggregate bank sector the ratio of national debt to fiat currency is determined as a portfolio choice of the private sector and local governments"? I think I didn't understand it completely. – Ritesh Singh Jan 11 at 13:41
• Sir/Madam, if/when free, please also consider answering this: economics.stackexchange.com/questions/42064/… – Ritesh Singh Jan 11 at 15:01
• Thank you for adding to the answer. It is a deeply insightful one and I will spend many hours on it, going through each idea to grasp the full implications. – Ritesh Singh Jan 11 at 18:06

Does this mean that Governments can continue to print a limited amount of fiat currency (say 5% of GDP) annually forever?

Yes government can 'print' (I use quotation marks because most money is created electronically nowadays) any amount of fiat currency it wants to.

In other words, is there a problem even if this debt that the Government owes itself, grows to, say, 1000 times the GDP?

Depends on your definition of a 'problem'. In terms of affecting probability of default it is not any problem at all. Central bank can scrap all the government debt it owns at a stroke of keyboard.

However, this being said, it is agreed by virtually all conventional economists that increasing amount of money (ceteris paribus) leads to inflation (see Mankiw Macroeconomics 8th ed.). So eventually if government would try to create arbitrary high amount of money it would eventually lead to inflation and at some point even hyperinflation. For this reason it is generally agreed by economists that governments can fund arbitrary amount of spending by creating new money (see this poll among the most prestigious policy economists). This being said there would be some scope for generating seigniorage revenue that way, so monetary financing might not be bad if it is done carefully, but having debt to GDP ratio of 1000:1, completely financed through central bank's high powered money, would likely lead to disastrously high inflation.

• Thank you for your answer. I understand how creating large amount of money in a short time could lead to loss of confidence and hyperinflation. Sorry for me being unclear. My main question was that what if this creation of money (the debt to GDP ratio of 1000:1) happens over centuries with, say, 5% of GDP being printed every year? Will that also lead to instability and significant possibility of loss of confidence? [I have added "over centuries" at the last of the question to make it clearer.] – Ritesh Singh Jan 11 at 2:30
• Special thanks for the poll link. It is very interesting and insightful 🙏🏼🙏🏼 – Ritesh Singh Jan 11 at 2:50
• Your insightful answer has led to another question: economics.stackexchange.com/questions/42055/… – Ritesh Singh Jan 11 at 3:21
• @RiteshSingh that depends on a state of economy, inflation is change in price level and that can be in a simplest models expressed as $P= MV/Y$ that means inflation price level increases in money supply and velocity of money but decreases in output. If it grows at 5% of GDP, average GDP growth is 2% and velocity does not change the average inflation will be just 3% per year. – 1muflon1 Jan 11 at 3:25
• @RiteshSingh no but only assuming all that debt is hold by central bank, this would not hold if that debt is hold by households or financial institutions etc. However, when central bank holds government debt it is really just really juggling money around (there are some reason why it is done that way, but in essence central bank holding government bond is almost equivalent of it just printing money and not holding that bond at all) – 1muflon1 Jan 11 at 3:39