In 1969, Milton Friedman wrote an essay on "The Optimum Quantity of Money". Another way of framing this question is to ask: what is the optimum long run growth rate in the money supply, or the optimum long run inflation rate?
I want to suggest a different way of framing this same question: what is the optimum size of the central bank?
In the long run, the size of the central bank is negatively related to the rate of inflation.
If you want deflation, do you really want the central bank to get bigger? In the limit, if you want big enough deflation, do you really want the central bank to own everything? Are you a communist?
Suppose we had a very high long run growth rate in the stock of money supplied by the central bank, and a very high inflation rate. Since central bank currency does not pay interest, the desired velocity of circulation would be very high. People would want to get rid of their money very quickly, because it is depreciating rapidly. Nominal rates of return on other assets would be very high, and the nominal rate of return on money is zero, so the opportunity cost of holding money would be very high. So the stock of money held would be very small as a percentage of the total assets of the economy.
A simple picture of the central bank is a balance sheet with currency on the liability side, and an equal amount of assets on the other side. With high inflation, the central bank would be very small, relative to the size of the economy.
That was long run analysis. In the short run, the demand for money can fluctuate, and unless the central bank adjusts the supply of money to accommodate those fluctuations in demand, the result will be monetary disequilibrium with short run booms and recessions. So the central bank should expand and contract in the short run to accommodate those fluctuations in the demand for money. When it expands and contracts, both the liability and asset sides of its balance sheet will expand and contract. When it increases the supply of money it buys more assets; and when it decreases the supply of money it sells assets.
So in a world of high inflation, we will see a small central bank, relative to the size of the economy. The size of the central bank will fluctuate. In percentage terms those fluctuations may be large, but relative to the size of the economy they will be small.
As we reduce the long run money growth rate, and reduce the long run inflation rate, the cost of holding central bank money will fall, and the stock of central bank money held will increase as a percentage of the size of the economy. The central bank will get bigger. It will hold a larger percentage of the total assets of the economy. And even if the fluctuations in the demand for money stay the same size, percentage-wise, those fluctuations will be a bigger percentage of the total assets in the economy.
What happens as we push this process to the limit, and keep on reducing the long run inflation rate, down to zero, and then into deflation? The central bank keeps on getting bigger and bigger, and owns a larger and larger share of the total assets in the economy. It buys all the short-term government bonds, then all the long-term government bonds, then all the commercial bonds, then all the shares, then all the land, then all the houses....Because as the rate of inflation falls, falls to zero, and keeps on falling into negative territory, people will want to hold more and more of their wealth in the form of central bank money. And unless the central bank satisfies that demand, by selling them money and buying their other assets, the result will be an excess demand for money and recession.
Where does it end? Do we ever hit some absolute liquidity trap where people want to hold money rather than any other asset? Well, not really. Because the central bank has to keep on buying assets that people do not want to hold because they want to hold money instead.
It doesn't end in a liquidity trap. It ends when the central bank runs out of things to buy, because it already owns everything, right down to your house, furniture, and toothbrush, which it rents back to you. It ends in communism.
Those who wish for deflation should think through what it means.
If you don't want the central bank to get bigger permanently, you had better let it get bigger temporarily, so it can satisfy the temporary excess demand for money and prevent inflation falling into deflation.