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 HereI 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.
- The NPV of a portfolio of instruments is equal to the sum of the NPV of the instruments in the portfolio.
- 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.)
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.