Thread by @GeorgeSelgin

Having asked this question, but not having gotten an answer, I will answer it myself, and invite criticisms. To anticipate: I conclude that, if one wants an "optimum quantity of money," a corridor system, not a floor system, is the way to go.

https://twitter.com/GeorgeSelgin/status/1408508766530813971

Let's start with the original Friedman-rule ideal: a rate of deflation sufficient to reduce the nominal interest rate on "bonds" to zero. Such deflation, Friedman argued, would eliminate the opportunity cost of money holding, thereby leading to "optimum" money holdings.

For those who consider deflation undesirable in itself, Friedman's solution is obviously unappealing. (I don't wish here to get into the merits of this view.) But there's an alternative that's theoretically equivalent: have money bear the same nominal interest rate as bonds.

Clearly, this alternative way of implementing the Friedman optimum solution can work for any chosen inflation-rate target.

But one thing has always troubled me about both versions of the Friedman rule, is that discussions of it generally assume two financial assets only: money and "bonds." But in the real world there are, besides non-i-bearing money, all sorts of other i-bearing financial assets.

The return on these assets varies according to the term to maturity and default risk (to simplify). Presumably, this would also be so in a world conforming to Friedman's ideal! Let's consider first the case of optimal deflation.

Presumably that deflation should not call for any negative rates. It seems reasonable to assume that it should reduce the nominal rate on the most liquid and risk-free asset to 0, with other rates rising above zero only to the extent that risk and term differences warrant it.

If we think further on this point, it is seen to imply that the deflation rate should be such that, with the nominal return on money itself--a 0 term, riskless asset--fixed at zero, other asset rates are reduced, but generally remain > 0.

Applying the same logic to the nominal interest-on-money alternative, we arrive at the conclusion that money, or rather the least-risky monetary liabilities, meaning Fed reserve balances and (ideally) currency, should bear interest, but less so than longer term or riskier assets.

Fed funds loans are not 0-maturity assets. They mature overnight. They are also unsecured and therefore not risk free. Overnight repos are secured. But they also are not as liquid as Fed liabilities. Nothing is.

It follows that, whether the Fed is targeting the fed funds rate or the SOFR (or any other overnight rate or rate index), if it wishes to implement a Friedman optimum, it must set IOR (and IOC, for currency--again, ideally) _below_ its overnight rate target.

Ergo: it must rely on a corridor rather than a floor operating system.

Q.E.D.

Counter-criticisms welcome.

Att'n: @dandolfa @DavidBeckworth @Frances_Coppola @TimDuy @greg_ip @PIrelandatBC @todd_keister @MacRoweNick @1954swilliamson