I suppose that disputes about this will never end. But I am willing to die on the hill that says that fiat money is neither equity nor debt, that is, that units of it aren't "claims" of any sort.
This stand may seem bizarre because we're used to thinking of financial assets as claims to either real assets or other financial assets, and because accounting conventions, developed for the most part when there were no exceptions, don't allow them to be treated otherwise.
But fiat money _is_ an exception, because its a means for "final" payment. Other USD-denominated financial assets are claims to fiat Federal Reserve notes. But a Federal Reserve note itself isn't a claim to anything. The "buck" stops with it, so to speak.
Of course, you can trade Fed notes for goods, or pay parking tickets and taxes in them. But that doesn't make them "claims" to goods, or get out of jail cards. These are just things that Fed notes, being of course money, can _buy_.
When the Fed was established in 1914, its notes were genuine debt claims: IOUs to so much gold--not just money with which gold could be "bought" at some varying market price.
Today, those notes are still reckoned "liabilities" on the Fed's balance sheet. But they are no longer redeemable, fixed claims to any of the Fed's assets. Yet they aren't "equity," either: possessing them doesn't make you one of the Fed's shareholders.
Fed member banks do own stock in the Fed Reserve Banks, but their shares, which they must purchase o join, are proportional to their paid-up capital and surplus, not to their holdings of Federal Reserve notes or reserve credits. And the shares can't be sold or transferred.
So, the Fed is weird sort of business! And fiat money is a weird sort of financial asset. Just accept it.
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