Nick has a post on "alpha" and "beta" banks where he alights on one idea for what distinguishes a central bank from a non-central bank
Here's the answer. Commercial banks promise to redeem their monetary
liabilities for the monetary liabilities of the central bank at a fixed
(or at least pre-determined) rate. Central banks do not promise to
redeem their monetary liabilities for the monetary liabilities of the
commercial banks. This asymmetry of redeemability is what gives central
banks their power over commercial banks. But a bank with that power is
nevertheless not a true central bank unless it acts like one, and uses
I think this is an interesting question to ponder, but I don't come to the same conclusions that Nick does. When looking at existing central bank institutions, such as the US Federal Reserve for example, you don't see an "asymmetric redeem-ability" function like Nick postulates, and I'm sure Nick would agree that the Fed is a central bank.
So, given that central banks can and do exist without asymmetric redeem-ability, what is it precisely that they have which make them central?
Here's my take:
First and foremost, they need to act as a hub to handle payment settlements, and thus need to be able to operate at negative liquidity and capitalization levels which would put a regular bank out of business. To operate in this way they need an essentially different regulation scheme than commercial banks and are, by merit of this regulation scheme, an "extension" of the Government. There may be a better term than "extension" but I think it works for now.
In the real world this interbank interconnection is handled via reserve accounts, which are Fed liabilities and bank assets. Money circulating between banks as coordinated through the Fed so that checks do not bounce simply because of liquidity or solvency problems at a particular bank.
Another perspective is that the reserves circulating between banks via the Fed are the "inside money" counterpart to the deposits and loans circulating between the non-bank sector via the banks. The right hand and left hand sections of the balance sheets have to balance.
Note that this function is only necessary when there are multiple banks which need to have payments and transactions settle across them. If there was a single bank, in addition to the central bank, you would not need reserves to manage this process as everything would clear within the bank itself and you would not need a central clearing house capability.
Regardless, even in this scenario, you would still need/want a central bank to set interest rates. In the absence of a reserve system, it could introduce one and use requirements around that as an interest rate setting mechanism, but I think as a practical matter it would create a separate mechanism for this instead such as a modified discount window. I view the use of reserves, with their associated requirements, as a mechanism for setting interest rates as an artifact of the organic evolution of banking and not a sound, engineered solution for this function. And this then would be a second central bank characteristic, the ability and responsibility of setting rates through whatever mechanism is at hand. (And on that, note how the US Fed instigated IOR when needed--not a well engineered solution but expedient given what was on hand).
So, I do not find the story about asymmetric redeemability a compelling one given that nothing of the sort is observed in real life, and misses the key central bank function of supporting payment settlement. Instead, I would classify asymmetric redeemability as a theoretical model of something that could substitute for OMO today, but there are many such candidates and I don't think Nick was advocating this one as being particularly good.
I would also see this approach as a logical conclusion of lumping in reserves with deposits, thus conflating the liability side of the central bank along with the liability side of the commercial banking sector, and seeing those two as being fundamentally interchangeable. I think this is a source of all the errors and confusion that come from Monetarism as reserves and deposits are fundamentally different, they serve different functions, and they are not interchangeable the same way two fluids in a heat exchanger are not interchangeable nor do they intermingle. Reserves are best thought of an abstraction layer that lets independent commercial banks coordinate payments and settlements amongst depositors by having a separate reserve system act as the other part of the balance sheet at a higher level. This core function was then co-opted (again, not a great word choice) for setting interest rates.