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Thursday, October 12, 2017

Understanding Why Fiat Money Is A Liability Of The State

One of the topics I discussed in Abolish Money (From Economics)!  returned to Twitter today, and I just want to give a long form version of my arguments. The debate was with Eric Lonergan (web site) regarding where money should show up on the government's balance sheet. I discussed this topic in Chapter (Section?) 14 of Abolish Money -- "Money as Debt."

I am keeping the core of my argument short, since I am actually just applying boring mainstream logic to the question. As that section of the book noted, there's a lot of complicated questions that arise in this area. I am only interested in a narrow technical question.

The first thing to note is that all of the national accounting conventions that I am aware of treat money as a liability on the balance sheet of the issuing government. Note that we cannot use the terms "debt" and "liability" interchangeably: debts are undoubtedly liabilities, but not all liabilities can be classified as debts. For example, a corporation might have a liability that is an accounting provision for potential legal liabilities; such a provision does not meet the definition of debt according to almost any definition (legal, accounting). Instead, what I am interested in here is: how should we treat the monetary base from the perspective of economic analysis (the accounting conventions be damned).

Liability Definition Used Here

I am using a common definition of "liability" that would be used in financial analysis: does the instrument have a negative Net Present Value (NPV) from the perspective of the entity doing the NPV analysis. (Similarly, we define an asset as an instrument with positive NPV.) We must emphasise that this definition is always from a particular entity's perspective, and is not an absolute concept.

The next step is to define the Net Present Value. Our problem is that we are looking at this from an unusual perspective: nobody thinks about doing NPV analysis from the government's perspective, and I have never even seen an attempt to think about valuing money: it has a NPV equal to face value by most definitions! Therefore, we need to go back to basics.

We assume that we are in a country that has a "unit of account" legally defined, and that unit of account is equal to the unit of account used by the central bank. This unit of account typically extends through to the banking system, by design of the payments system. Since I am Canadian, we will call this unit of account Canadian dollars (conveniently denoted using the '$' symbol), but I want to underline that this exercise is hypothetical, and could be extended to similar countries with a change of the name of the unit.

Various entities (the Ministry of Finance, private banks) have accounts at the central bank. The state of an account is a number measured in the unit of account (Canadian dollars). The NPV of a set of instruments is also measured in this unit of account.

(An instrument for my purposes is something like a legal document that details payment obligations, a fixed amount of financial securities, or bearer instruments like notes and coin. They generally imply a set of "cash flows" on a certain schedule, where the cash flows are denominated in the unit of account.)

The Net Present Value of an instrument (that has no optionality) is equal to the sum of the discounted value of each of its cash flows. Since this article is only covering instruments that have cash flows in the current date, this is just equal to the current day's cash flows, and so I will skip over the argle-bargle regarding what discounting exactly means.

We rely on two properties of the NPV from mathematical finance.

  1. The NPV of a portfolio of instruments is equal to the sum of the NPV of the instruments in the portfolio.
  2. The NPV of a portfolio that has a zero cash flow for all dates has a NPV of zero.

Valuation of a $100 Deposit at the Central Bank

Assume an entity has a $100 tax bill due today, and a $100 deposit at the central bank. We know that the entity is able to exactly discharge its tax bill by this deposit. That is, the government must accept the central bank deposit at par for the purposes of discharging tax. (This is equivalent to saying that taxes are denominated in the unit of account.)

(This would not have to be case: we could imagine a situation where the government would only reduce the tax bill due by $90. This might occur where the taxpayer deposit was being held at a dodgy private bank.)

From the government's point of view, the tax bill (a receivable to the government) and the $100 deposit are both instruments, and form a portfolio. Since the two instruments cancel each other out, we know that the net cash flows are zero. We rely on the property listed above to assign a zero NPV to the portfolio.

Furthermore, we know that the tax bill receivable by the government today has a NPV of $100, by definition of the NPV. We can then apply the additivity property of the NPV to see that the NPV of the $100 deposit (to the government) is -$100.

It is trivial to generalise this example to see that the NPV of deposits at the central bank have a NPV that is equal to the negative of the amount on deposit.

(From the perspective of the taxpayer, the NPV values flip sign, since the tax bill is a cash flow payable, and hence has a negative NPV.)

Since the NPV of deposits at central banks are negative, they are a liability of the consolidated government.

Valuation of a $100 Bill

Observation: It is possible to exchange central bank deposits for currency, at a 1:1 par value (with only a nominal fee?).

Theorem: The NPV of a currency note to the government is the negative of the face value.
Proof: Left as an exercise to the reader. (Hint: use arbitrage arguments.)

Negative NPV Does Not Imply "Negative Value"

The fact that an instrument has a negative NPV to me does not imply that I think the instrument has a "negative value."

If I wrote a cheque that obligates me to pay the bearer $100 in one week, that instrument has a negative NPV to me. (The exact NPV depends upon what the discount rate is for a week, presumably over $99.)

However, if the bearer came to me on earlier date and offered to hand me back the cheque in exchange for a $50 bill (which allows me to legally rip the cheque up), I would almost certainly seize the offer, since my discounted value of $100 in one week is much greater than $50. (That is, I profit off of the transaction relative to the baseline of the cheque being cashed in a week for $100.) In other words, I still "value" the cheque.

(The bearer might make the offer if they either were desperate for cash, or thought my cheque would bounce.)

Concluding Remarks

This property of the monetary base should not be surprising. Any household that has paid off a bank loan by drawing on a deposit account at said bank has done a similar operation. The bank loan is an asset of the bank (positive NPV to the bank), while the bank deposit is a liability to the bank. From the customer's perspective, the deposit is an asset, and the bank loan a liability.

(c) Brian Romanchuk 2017


  1. "I am using a common definition of 'liability' that would be used in financial analysis: does the instrument have a negative Net Present Value (NPV)"

    That is NOT the common definition of 'liability' for accounting purposes! NPV is irrelevant for classifying assets or liabilities!

    Maybe you should start your reasoning with the IFRS definition (see IAS 37):

    “A liability is a present obligation of the enterprise arising from past events, the settlement of which is expected to result in an outflow from the enterprise of resources embodying economic benefits (IASB Framework).”

    Nonetheless, you would arrive at the same conclusion.

    “That is, the government must accept the central bank deposit at par for the purposes of discharging tax”

    So, what you are saying, is that the government is obligated to accept the central bank deposit for discharging tax. The currency is an obligation that the government has with the currency holder (to redeem taxes for the currency holder).

    1. I’m a (lapsed) mathematician. I can use whatever definition I want.

      If you go to accounting definitions, they already have money classified as a liability. I am addressing the possibility that the accountants are incorrect.

    2. "I can use whatever definition I want."

      Careful. The Sovereign Money crowd will be looking to hire you with an attitude like that ;-)

    3. In actual commerce cash flow rights and obligations are recognized via principles of law and accounting. Then NPV analysis can be done on the recognized cash flow rights and obligations. A problem I see is that many units can simply increase their liabilities to meet a current cash flow obligation - as Hyman Minsky observes - rather than pay stored up cash or sell an asset for cash to make a current payment. I'm not sure what this dynamic feature of the financial system has to do with NPV analysis?

      Peter Stella has a 3 page paper called Helicopter Bonds where he says future payment obligations have present discounted value on the liability side of the Sovereign balance sheet and future tax receipts have PDV on the asset side. The US government has a 23 page document: OMB Circular A-94: CIRCULAR A-94 GUIDELINES AND DISCOUNT RATES FOR BENEFIT-COST ANALYSIS OF FEDERAL PROGRAMS. This is an effort to estimate the NPV of a federal program for accounting purposes based on expected cash flows and assumed discount factors. However the discount rates change with monetary policy shifts in the future; and the government can renegotiate its cash flow obligations for so-called entitlement programs and other discretionary spending; and the tax law can be changed in the future. NPV calculations are an effort to make the government appear accountable like any other firm but are more like an exercise in futility since the Sovereign government has powers and duties unlike any other entity in society.

      I think Peter Stella gives the right framework for understanding that the federal government can make a credible commitment to spend more then it collects in taxes and other payments. This reduces the net worth on an NPV basis and predicts a future increase in the float of government liabilities to cover the gap between future receipts and outlays.

  2. "Understanding Why Fiat Money is a Liability of the State"

    Sorry, I am not convinced. I still believe that money is a product produced by the state. [The CB prints money, the Treasury arm of the government creates a debt instrument. The two branches of government trade products and the Treasury begins paying money for services.]

    Now let's talk about deposits at banks, including the CB. All deposits can be traced to owners who worked to acquire the money deposited UNLESS the deposit has been funded directly by a bank (as when a bank loan is made or the CB trades with Treasury).

    I can understand that government-as-a-bank has a liability to all those depositors whose money is on deposit. Government-as-a-bank has assumed an obligation to safeguard those deposits. But I don't think this is the liability of the state that you are explaining.

    I don't think I am grasping the macro-economic message you are trying to deliver.

    1. Deposits are created by making loans. Otherwise, the stock of deposits could not grow.

    2. "Sorry, I am not convinced. I still believe that money is a product produced by the state"

      Well, the fact that money is produced by the state doesn't rule out the accounting reasoning that Brian is making.

      I don't know if Brian is a "full MMTer" and believe that money is produced by the state. I think he is. But even if he is not, his reasoning seems very good.

      Currency can be though as an IOU that says "I, the issuing state, am obligated to discharge the holder's tax obligation on redemption".

      So currency is a obligation (liability) to the state and an asset to the holder...

    3. "Deposits are created by making loans"

      Brian, that seems Positive Money theory. Sometimes Bill Mitchell say it too, but I don't know why, because he for sure knows better.

      When the government pays the public servants' wages, it is usually done through banks as intermediaries.

      The Treasury transfers bank reserves to the private bank that has the public servants as its clients.

      After verifying that the reserves were successfully transferred, the private bank creates bank deposits for its clients (the public servants).

      As you can see, bank deposits were created without loans...

    4. "As you can see, bank deposits were created without loans..."

      Bank reserves *are* loans. They are forced loans to the central bank by the private bank at an interest rate determined by the central bank.

    5. Deposits are credited to current accounts which are promissory notes issued by the private bank when they gain assets to back that issue. Loans from the bank POV are assets that are promissory notes issued by the borrower (however the paperwork is actually performed). Similarly from the bank POV Reserves are promissory notes issued by the BoE, so yes reserves and loans create deposits.

    6. I finally get Neil's argument given my comment above. To finish here

      The private bank normally chooses via credit underwriting etc. whom to provide loans to, then it is as I just said above. In that case the bank is rewarded for its credit risk assessment and sets the cash flow on its asset etc.

      In the case of a CB account, the reserves is the "loan", it is not decided by nor credit analysed by the PB, of course the reserve is a risk-free asset to the PB. The bank is not rewarded for this credit risk, there is none. And yes they do not have a choice wrt charging interested and creating cash flow (pre-APF and now)

      Not sure if I quite agree with the use of "force" in Neil's description, but am willing to be convinced.


      No, they are not! Bank reserves are just the eletronic version of notes and coins. Are notes and coins some kind of loan? I don't think so...

      And they are not forced at all. They are a 100% voluntary.

    8. In the United States the central bank (Fed) generates reserves as borrowed reserves (bank borrowing from Fed) or non-borrowed reserves (Fed purchases something from a nonbank, it credits the bank with reserves, and the bank credits its nonbank customer with deposits). So technically only non-borrowed reserves also create net new deposits.

    9. You can put that way. "Non-borrowed reserves" create new deposits. But then you are acknowledging that "loans create deposits" is not the entire history.

      Also, usually banks do not lack reserves. Actually, it is the inverse. They have excess reserves, so they try to earn more interest - by buying bonds or thought repo operations.

      At some times, some banks may borrow reserves from the Fed, paying some kind of penalty rate. That's not the common situation.

    10. I wrote several papers on SSRN that attempt to clarify the roles and debit/credit operations of Fed, Treasury, Banks (depository institutions), and Nonbanks in the US financial sector. I use transaction accounts (TA) in the aggregate bank to show how the banking sector generates and destroys checking deposits via accounting transactions with the aggregate nonbank and with the Fed and with the Treasury - this is way beyond the catch-phrase "loans create deposits" which is true but not the whole story. I also show how Fed manages its balance sheet to provide the levels of reserve balances in the aggregate bank and to "service" the currency drain before the global financial crisis. Banks only usually have "excess reserves" for two reasons: (1) when money markets are functioning properly Fed provides banks with just enough nonborrowed reserves such that some banks are forced to borrow a small amount of reserves from the "discount window" at the end of the day, this helps Fed monitor the fed funds market and provide an interest rate channel; and (2) when markets are not functioning properly, as in the 2008 period of the financial crisis, Fed initially expanded liquidity programs (similar to the discount window) to provide a large amount of borrowed reserves, but this policy would have caused Fed to lose control of the Fed funds interest rate when it ran out of Treasuries to sell off its balance sheet, so Fed switched to providing nonborrowed reserves via Large-Scale Asset Purchases (LSAP) also known as quantitative easing (QE). So the phrase "loans create deposits" is indeed not a complete story for reasons that most people do not comprehend. Even though I can see the limits imposed by accounting customs I do not always recognize the policy rationale of Fed balance sheet operations until after the fact, and sometimes I must make an inference since experts are not describing Fed policy in terms of balance sheet operations.

    11. "Are notes and coins some kind of loan?"

      Yup. Hence the title of this piece.

      A note and coin is a receipt for a liability in the government sector, which is what makes it an asset. It's a 0% bearer bond.

      When you place a deposit in a bank you are loaning your money to the bank. It's the same when a bank has a deposit at the central bank. That's why you are 'in credit' - credit being the accounting term for a liability.

    12. "when money markets are functioning properly Fed provides banks with just enough nonborrowed reserves"

      Not any more. We have interest on reserves now. The mainstream realised that creating an artificial market served no purpose. Eventually they'll realise that bonds have the same effect.

    13. "Not any more." I did say Fed provides banks with non-borrowed reserves when executing the LSAP (QE) policy - but I did not mention interest on excess reserves (IOER) policy for brevity.

      If you are saying that the policy of forcing banks to lend and borrow federal funds (bank reserves) with each other has no public purpose (other than to make the Fed balance sheet appear smaller in a period without a money market crisis) then I would need to consider the arguments for or against having all banks do an overdraft with Fed and not deal with each other in fed funds. If I recall correctly Warren Mosler proposes government guarantee of all bank liabilities, unlimited bank overdraft at Fed, and strict regulation of banks on the asset side of the balance sheet to enforce "discipline". The main concern I have is with "agency problems" of executive pay packages in which an unlimited overdraft and unlimited deposit insurance makes it possible for an executive to grow the bank rapidly while shifting risk to the public sector. The regulators have so far shown a poor track record of fixing agency problems and are not likely to do better under such proposals.

    14. In the UK the notion of borrowed reserves versus non-borrowed reserves makes little sense, at least when it comes to payment by the Government Banking Service on behalf of its 700 odd government customers.

      Sterling is injected from the Consolidated Fund (rebalanced to zero every night through the Exchequer Pyramid) to the GBS and, given the Full Funding Rule that the Debt Management Office of the Treasury currently operates under, all the current account sterling in the CF is based on either reserves drained by tax, duties, excise,fees etc. or by Gilts and other Secs sales (via the National Loans Fund - part of the Exchequer Pyramid). Only when the GBS transfers the sterling to one of its 2 private bank partners, RBS or Citibank to pay for salaries, goods and services does this sterling become reserves in the private sector. The relevant balance sheets expand with an increase in reserves on the asset side and an increase in commercial bank money (as the BoE calls it) - bank credit - on the liability side. (Whether one wants to argue that the (drained) reserves are recycled or newly issued is not relevant to this argument here)

    15. Martin F,

      It is not clear to me that you understand what I mean by borrowed vs non-borrowed reserves. In the US there is always a positive level of bank reserve balances in the aggregate bank balance sheets. These reserves are provided by the central bank in accord with its monetary policy goals. Borrowed reserves are provided by lending directly to banks. Non-borrowed reserves are provided by purchasing government securities or government backed securities from banks or nonbanks. The mechanics in the UK should not be too different although the terms applied may not be the same. This 14 page paper discusses UK central bank monetary policy starting on page 7:

      To see what I mean by non-borrowed reserves look at Figure 3 on page 11. It shows how, under so-called Quantitative Easing, a pension fund sells government debt to the central bank. The pension fund shows a swap of government debt for deposits in its asset position. The central bank debits asset to increase its holding of government debt and credits reserves due to banks. The clearing bank(s) debit reserve assets and credit deposits both for an increase. This is what the term "non-borrowed" reserves means in the US.

    16. I dont think we are far off Joe. I was ignoring APF which is, you put it, non-borrowed reserves in the US.

      So are talking about "borrowed reserves" in the Exchequer pyramid? This is unclear and moot as far as I am concerned.

      The debate here (at least recently in the MMT UK group) has about whether those reserves are recycled (I imagine that is what you mean by borrowed?) - gilt sales by the DMO to fulfil its full funding rule mandate via the flow (on now non reserve sterling) into the NLF-> CF->GBS-> P Banks (reserves put back into PB system) or old reserves drained and new reserves injected? This is what I meant by my bracketed point in a previous post. IMV Either POV is plausible and makes no difference to the accounting Flow of Funds nor Balance Sheets.

      In the Uk there are no fractional requirements on M1. There was a bank volunteered maintenance reserve level over maintenance periods, not required given APF at the moment. So are you talking about the (umm lets call them) residual reserves in the system just needed to ensure the payment and settlement system functions?

      Of course the BoE has a variety of mechanisms to ensure sufficient reserves for settlement (SMF with Repos etc., Discount Window etc. etc.) and for temporary funding of Primary Dealers in Gilts auctions (Mosler's to do a reserve drain you need a reserve add) and they are by definition all borrowed reserves. However that is not the issue at hand as far as I can see, as that is all temporary?

      So after this analysis I am not sure what your concern is. We agree that APF/QE reserves are not relevant here but as I already stated from the POV to government purchased the origin of those reserves obtained by the DMO is irrelevant (in the sense that since the DMO use OMO and, must not buy off the APF, but from the Private sector only, otherwise the Full Funding Rule makes no sense).

    17. Brian et al

      Joe and I have taken this sub-conversation off to his google group.

      For myself having another argument to show that reserves are a government liability is all to the better.

  3. Far as I’m concerned, Warren Mosler nailed it. As he put it, central bank money is like points awarded by the umpire in a tennis match: both are assets as viewed by the recipients of the money / points. But they are not liabilities as viewed by the issuer of the money / points.

    You won’t get anything from government or CB in exchange for your $100 bill or £10 note. However, once government imposes a tax liability on you, your $100 bill becomes a government / CB liability of a sort in that that liability can be used to cancel out the tax liability.

    1. Sure, it has no inherent real value. I get thatit’s mind-bending. But we still have to balance balance sheets.

    2. Brian what is the left side entry on the govts balance sheet to offset this liability then? Seems like the asset entry is awarded to the non govt and this is where people start to lose it... normally you would need to enter the asset on the same entities balance sheet...

      Even Trump the other day was trying to assert the stock market gain offset the increase in govt debt... public reception of this was skeptical too...

    3. Depends on the accounting convention.

      Under non-consolidated accounting, the central bank has assets. In anglo countries now, normally government bonds, but it may be loans to banks (including loans collateralised by government bonds - “repos”).

      If we consolidate, the usual answer is that the government has almost no financial assets offsetting money if they do not hold bank loans. (The exception appears to be foreign currency reserves, but their level is not related to the size of the monetary base.)

      In the sfc_models framework, the usual situation is to have consolidated government with a massive negative net financial asset holding position.

      There are real assets on the government balance sheet, but their valuation is typically highly uncertain, and quite often meaningless.

    4. Matt, I am sure you know this but the stock market gain nets to zero when looking at the Flow of Funds accounting in a typical Godley 2/3 Sector framework. Whereas the asset/liability entries from Government to Non_Government cross that sectoral boundary, they don't net to zero within the sectors but still, of course, net to zero taking all sectors into consideration (but then there is no flow of funds and that is topic at hand, I think).

    5. Ralph Musgrave,


      Exactly! That's why money is a liability in the government balance sheet! I guess Brian said exactly this, but in his own particular way ("negative net present value"), I don't know...

    6. Matt also, as I understand it, in the UK Whole Government Accounts Financial Statement Total Assets = £1.7T, Total Liabilities = £3.7T, Net Financial Liabilities = ~£2T - this and mostly includes all Gilts but also all Reserves and currency in the non-government sector (and not the gov sector due to consolidation so no APF/QE gilts held at the BoE etc.). As an aside, I think Government Net Financial Liabilities is a more interesting measure than Government Debt (ie. all gilts etc. still outstanding) but relevant here one can also look at the statement to see the amount of financial assets (page 50 for summary).

      Dunno if there is equivalent USA account report or in Canada, would be useful see those but do not know what to search for.

    7. In United States the Central Bank (Fed) has small positive net worth as shown in balance sheet section on bottom of page 2:

      Whereas the federal government has negative net worth as shown in the balance sheet section on the bottom of pages 2-3:

      so the private sector, foreign sector, and local governments can hold a net financial asset position equal to the net liability position of the federal government. However the federal government also effectively insures liabilities issued by banks and other government sponsored enterprises. These are like off-balance sheet liabilities of the government that become evident in a money market crisis. Finally the Fed provides lender of last resort services to Primary Dealers and other financial dealers which helps put a "bid" under the stock market in the event that money markets are disrupted, and the Treasury can act like investor of last resort to support any industry in a cash flow crisis provided there is official authority to provide long term debt or equity subsidized by the public.

    8. Brian, Re your claim that "we have to balance balance sheets" I suggest what we actually "have to do" is recognize that double entry book-keeping is a brilliant device for some purposes, but some entries are plain silly. There's no harm in insisting on balance sheets that balance for the purposes of making sure one has done one's book-keeping correctly: one of the beauties of double entry is that it often alerts book-keepers to mistakes. But the idea that those entries are always an accurate portrayal of reality does not wash.

      E.g. the fact that Warren Mosler's tennis match analogy does not sit easily with double entry is not a defect in the analogy. Another example: equity / shares appear on the liability side of balance sheets and are entered as a specific number of dollars. But the idea that the relevant firm actually owes shareholders that specific number of dollars is of course nonsense.

    9. The only issue with Mosler's analogy is that people associate a real value with a nominal (e.g., dollar) amount. For the government, nominal values do not really matter, only real variables. In other words, the problem is not the accounting, just the people using the accounting.

      The fact that equity values are uncertain is hardly a controversial view. Almost all financial accounting textbooks discuss how to adjust balance sheets so that the adjusted numbers match reality better.

      Returning to the original topic, the belief that we have a hard time valuing the liability associated with the monetary base is extremely hard to support, and so it hardly needs to be a major topic for adjustment.

  4. Brian writes (in a comment) "In the sfc_models framework, the usual situation is to have consolidated government with a massive negative net financial asset holding position."

    Accounting is very exact, as is programming a computer. How is spontaneous wealth creation entered?

    I think we agree that [from a macro-economic perspective] money is created when banks make loans. This is a spontaneous creation of wealth [again, this is from the macro-economic perspective].

    Now, who has the asset and who the liability?

    Interestingly, we see both government and private borrowing from banks. In both cases borrowers agree to repay the loan. This is a liability to the borrower.

    In both cases, the asset (the money borrowed) is spent into the macro-economy. This is new money/new-wealth that will not disappear until the loans are repaid. We should be able to trace the successive owners of this asset as long as it continues to exist.


    Surely G&L and PK in general SFC models sometimes consolidate, sometimes don't, it depends on what is being modelled?

    I am confused in the UK the WGA has a massive negative net financial *liability* which matches the NG net financial *assets*

    1. (My previous reply disappeared?)

      In sfc_models, you can easily switch between consolidated/non-consolidated modelling convention. (There is no effect on the non-government part of the solution.) Working from memory, "Monetary Economics" by Godley and Lavoie only have the non-consolidated version, at least in the models where there is both money and government debt.

      For people developing the equations by hand, the decision to consolidate may be driven by tractability. sfc_models generates the equations for you, so you can do what you want.

    2. Just got your book Understanding Government Finance to see how things work in Canada without reserves at all.




