In my last post about public finance, I said that the public debt could also be called the "public liability side of nongovernment financial assets." I think, for a follow-up post, it may be worth exploring that point in greater detail, since that was probably way too jargony to make sense.
As implied by the title, this is mainly a discussion of the big three of accounting. Assets are more or less what you think they are, with the important addition that, for commercial banks, loans are assets. Liabilities are the weird one: your liability is someone else's claim against you. For you and I, the biggest liabilities we hold are loans. A somewhat trickier example is that, when you have money deposited at a bank, your deposits are your assets, and a liability on your bank. This is because, while your bank holds your cash, you have a claim against the bank in the amount of the deposit, in that you can always go to the bank and ask for your money back.
Trickier still is the fact that the so-called monetary base---paper and coins in circulation, as well as cash held by banks in reserve accounts (which are the accounts where they store your deposits while they hold them)---is a liability of the central bank. In principle, the reason for this is that our claim against the government (via cash) is the ability to pay taxes, perverse though that may sound. I'll make sure to make a post later about the infamous question of why money has value, which may clarify this point some, though for now it suffices to say that the monetary base in the US is a liability of the Federal Reserve. It's probably worth noting now that the asset side of the Federal Reserve is a little bit of foreign currency and a little bit of gold, and a whole ton of treasury bonds. This relationship is maintained by the fact that the Fed only issues money by purchasing securities (with new money) from investment banks.
So then there's what might well be the fundamental theorem of accounting: Assets = Liabilities + Equity, or else, Equity = Assets - Liabilities. For an ordinary person with a full-time job, your equity is your cash plus your 401k plus the market value of your house plus the market value of your car, minus the principals of your mortgage and auto loan.
So then, on to the point.
Every financial asset has a corresponding liability. Paper money in your wallet is your asset and the Fed's liability. A loan is a bank's asset and a customer's liability. A bank deposit is a customer's asset and a bank's liability. Bank reserves are a bank's asset and the Fed's liability. And treasury bonds are an investor's or bank's or the Fed's asset and the Treasury's liability.
Positive equity is the situation of having more assets than liabilities. However, since every asset is also a liability, the total value of all financial assets minus the total value of all financial liabilities across the entire economy must sum to zero. Thus, it's impossible for everyone to have positive equity simultaneously: if anyone has positive equity, at least one entity must have negative equity.
The big question is, who should have the negative equity? Or maybe more importantly, who can sustain negative equity in perpetuity? This question has been answered in the real world, and that answer is: Treasury. The negative equity---that enables positive equity---is the public debt.
There are a few other reasonable choices. But first, it should be obvious that having the private sector run perpetual negative equity is a bad plan, because private sector debt carries higher (which is to say, any) risk of default, and a highly leveraged private sector tends to cause financial crises.
The two other choices I'm aware of, besides public debt, are 1. having the Treasury not issue debt, and instead persistently overdraft its general account at the Fed (which is the account used for public spending), and 2. allowing the Fed to issue cash (into the Treasury's general account, most likely) without a corresponding purchase of securities, which is to say, having the Fed hold the negative equity.
Though there are other reasons to have a public debt than just the necessity of negative equity. The big one mentioned in the aforementioned last post is liquidity management, though the interbank lending rate can also be maintained by simply having the central bank pay interest at the policy rate (the target interbank rate) on excess reserves (such interest on excess reserves is called a "support rate"), so that's not a big deal. The more important one, that would require serious thought, is the public debt's role as a source of risk-free income for investors.
This last point makes me wary to suggest that we abolish the public debt; at the very least, though, it's safe to say that we should embrace the debt, rather than fantasizing about paying it off---and, in the process, paying off the private sector's ability to maintain system-wide positive equity.