I've had a few exchanges recently on the question of what gives the central bank the ability to set interest rates, including on Nick Rowe's most recent post.
The discussion prompted me to read Woodford's paper Monetary Policy in the Information Economy in which he discusses various possible implications of improvements in the efficiency of the use of monetary base. The paper includes an excellent analysis of the operation of a corridor system and the role of rates and quantities in such a system.
Woodford also considers how the central bank might set rates in a world where its liabilities had no useful function beyond any interest rate paid on them. Normally, central bank liabilities have other uses. Currency has a convenience value; reserves are used in clearing. Woodford wants us to think about what might happen if currency became obsolete and where clearing had became so efficient that reserves were no longer needed (assuming also that there are no mandatory reserve requirements).
He explains how this might work through an arrangement whereby there is a small aggregate positive balance held by commercial banks with the central bank. The central bank would decide what rate to pay on this balance and Woodford shows how this would then force all commercial banks to base their rates around this benchmark. The balances that commercial banks hold with the central bank in this system are functioning just like any other interbank balance. They have no longer have any special role in clearing.
"Why should the central bank play any special role in determining which of these outcomes should actually occur, if it does not possess any monopoly power as the unique supplier of some crucial service? The answer is that the unit of account in a purely fiat system is defined in terms of the liabilities of the central bank."
I don't actually like the idea that the dollar is defined by central bank liabilities. We can certainly make various observations about the relationship between liabilities of the central bank and those of commercial entities, including about the legal and commercial obligations over the rate at which liabilities get exchanged. But there isn't anything beyond that. There isn't anything additional to those relationships that constitutes defining the dollar (and I'm not sure those relationships themselves actually constitute defining the dollar), so I don't really like the introduction of this concept.
That said, Woodford goes on to specify one of the most important of such relationships. This is (from above) that "[a] financial contract that promises to deliver a certain number of U.S. dollars at a specified future date is promising payment in terms of Federal Reserve notes or clearing balances at the Fed...". The important points here are that, if another party (bank or non-bank) holds a balance at Bank A, a) it can require Bank A to deliver obligations of the Fed as settlement; and b) it is entitled to receive such obligations at par (dollar for dollar).
It is worth noting that as a commercial matter, banks also undertake to settle by delivery of claims on other banks. If I have money with Bank A, I can ask Bank A to pay into may account at Bank B. This is economically equivalent to Bank A depositing money with Bank B and then transferring title to that deposit to me. However, once Bank A has committed to delivering Fed obligations at par, it is no more onerous to also undertake to similarly deliver claims on other banks.
In order for the central bank to be able to set rates, is it sufficient that other banks commit to an either-way exchange of central bank liabilities for their own liabilities? In fact, whilst this is critical, slightly more is needed.
To see this we need to understand what the equivalent provision would mean if applied to the central bank. Let's imagine that everything is in equilibrium with interest rates at 5% and the central bank then decides to lower its deposit rate to 4%. At this point, anyone (bank or non-bank) holding deposits with the central bank would (if they could) require the central bank to settle that deposit by delivery of a claim on another bank (paying 5%). In Woodford's scenario, this would rapidly lead to all of the outstanding central bank liabilities being extinguished, whereupon the rate on them would be meaningless.
It is therefore critical that the central bank does not undertake to redeem its deposit liabilities by delivering claims on other banks. If a commercial bank wishes to reduce its balance with central bank, it must do so by lending the excess out. This is what forces the rates of all the other banks into line.
The fact that the central bank will not redeem its deposit liabilities in this way, when the commercial banks must do so is what Nick Rowe calls "asymmetric redeemability". In one form or another, it is essential to a central bank's ability to set interest rates. Normally, we do not notice it, because things like currency are by their very nature irredeemable and so it seems odd to even frame the question that way. In Woodford's hypothetical scenario, where balances with the central bank are otherwise no different from all other interbank balances, it's easier to see.