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.
Worthwhile Canadian Initiative 
John Becker: “During the 19th century, there were many different types of banknotes in circulation, but these were not different types of money because all the banknotes represented claims on gold. There was only one true money and that was gold.”
People did not like that, though. At one point a bank in New Jersey issued some $600,000 in loans backed by 7 bits of a Spanish dollar (that’s $0.875) in the vault! In addition, the loss of money when the U. S. went off of a dual gold-silver standard to a gold standard in 1873 contributed to the Long Depression. That is why Bryan’s “Cross of Gold” speech remained popular for years. The gold standard also contributed to the Great Depression. When major economies went off of the gold standard, their economies rebounded. (That was not the only reason, OC.) The gold standard is oppressive.
Mike, If currency rises in value over the course of the year, what good is it as currency? I thought the whole point of currency was that its nominal price is fixed, otherwise it’s not very convenient. And even if the nominal value did rise over the course of the year, the interest rate on currency would still approach infinity as the date approached December 31st.
Nick,
When I say the central bank should do nothing, I really mean that they should close their doors, fire their employees, and dynamite the building. The second best thing they could do is cease all open market operations and only provide loans as a last resort to banks with liquidity and not capital constraints. Furthermore, these loans should come at a market rate based on the likelihood that the bank will survive to pay them back.
As far as money goes, I’d be in favor of a classical 19th century gold standard or the competing currencies idea put forward by Hayek. There are huge transaction costs to not having the same money throughout a fiscal area and, for that reason, one money will tend to predominate. If every bank could issue their currency, people would establish their preference for one very rapidly. The competition would force that currency to remain sound.
During the 19th century, there were many different types of banknotes in circulation, but these were not different types of money because all the banknotes represented claims on gold. There was only one true money and that was gold.
Nonsense.
Canada was one of the last countries to set up a central bank. We only did it in 1935. Before then there were Dominion Notes for $1 and bank notes drawn on chartered banks for everything else. Yes, the Canadian dollar was defined in gold but most transactions were conducted in chartered bank notes.
By 1930 there were 10 note-issuing banks.
This nicely competitive system did not save us from the Great Depression when then, as now, Canadian banks remained solvent by the Canadian economy still got squeezed by collapsing terms of trade. Canada went off the gold standard in 1933.
Actually Canadian experience goes against the Gold Standard or any fixed exchange standard. Any standard like that has to be defended and if it can’t be defended with infinite resources it will ultimately collapse. That’s why we let the Canadian Dollar float in 1950 in order to balance our trade accounts with the UK and the US. We always had large import/export flows for a country our size and the 1950’s were fine even with a floating currency. We eschewed Bretton Woods mostly. We went on a US dollar peg from 1962 to 1970 per Bretton Woods and then floated again thereafter.
Scott:
I don’t see how you arrive at infinite interest rates. I’m thinking of a world where a holder of $10 in paper can present them to the central bank on Dec 31 and get back $11. At the start of the year each dollar is worth 1 oz of silver. The dollar grows in value until it is worth 1.10 oz on dec 31, then the $1 interest is paid, and each dollar suddenly drops to 1 oz. It’s just like a stock that pays dividends in stock, and you don’t get infinite inflation in that case.
I agree about the convenience of a stable currency unit, but the fact is that old bills of exchange did grow in value over the year, thus effectively bearing interest even as they were used as money.
Besided, we presently use dollars that lose 3% of their value every year. I think I could deal with dollars that grew in value by 3%/year.
Darius: “Consider that in exactly the same sense that you’re using here, language is a natural monopoly.” “Let’s suppose that media of exchange are “sticky” and “contagious” in the same way that language is sticky and contagious,…”
I fully agree. I use that exact metaphor myself, sometimes. The only difference is that language is not a good, that somebody produces and prices. Microsoft Word is a better analogy in that respect.
Jon: I’m trying to think though what would happen if people used 100% reserve backed notes in the gold standard, and the equilibrium growth rate of the economy were high enough, relative to gold production and industrial demand for gold, that gold was appreciating at (say) 10% relative to the CPI. Who would want to hold any assets other than gold? Could that be an equilibrium?
Ralph: John and I above, in comments, were in effect talking about the Pigou effect.
Nick Ricc: But if helicopter money were big enough, you couldn’t have deflation.
Jon: I’m trying to think though what would happen if people used 100% reserve backed notes in the gold standard, and the equilibrium growth rate of the economy were high enough, relative to gold production and industrial demand for gold, that gold was appreciating at (say) 10% relative to the CPI. Who would want to hold any assets other than gold? Could that be an equilibrium?
In short, no. The economy would run into the constraint of the gold production rate. At that point there would be a choice: either suspend or modify the 100% gold backing standard, reduce the growth rate of the economy or accept deflation.
The latter choice is intellectually comfortable but entirely unrealistic. The economy can produce more goods and more real wealth but cannot because of an artificial money constraint. It’s nonsense and inhumane and that’s why most countries if faced with that choice modified their gold standard.
Deflation will mean a reduction in real growth anyway due to contracts which extend back through time. Deflation will mean default on nominal contracts.
Nick Ricc said: “What if the Fed simply prints and gives money away? If money is given away, instead of exchanged for assets — ultimately including toothbrushes and underwear — doesn’t the ‘deflation leads to communism’ argument evaportate?
Moreover, the mere prospect that sometime in the future money might be given away should serve to reign in the need for an ever expanding central bank.
Nick Ricc
Kyoto, Japan”
Let’s change that money to medium of exchange. Can “should serve to reign in the need for an ever expanding central bank.” be changed to “should serve to reign in the need for an ever expanding central bank on the asset side.”?
This seems to come down to what should a central bank have as assets, “nothing”, treasury debt, any type of debt, any type of asset.
Optimum size of the central bank:
IMO, liability side: the correct amount of medium of exchange
asset side: “nothing” (used loosely)
This is very funny, because I had recently exact copy of this discussion but for fiscal policy. If you have a government that promises budget surplus from now on forever, you also end in communism. That is a world run by Sovereign Funds who invest the money produced by surpluses and which own everything there is to be owned. It was very funny to watch that cognitive dissonance on the face of the “no deficit” believers trying to think it out in real time. In the end, the dogma prevails.
JV: Yep. That’s doubly funny, because I once did a paper with Vivek Dehejia (no downloadable version on the net) trying to figure out the optimum long run debt/GDP ratio if you assumed uncertainty and a deadweight cost of taxation function that gave you a Laffer curve. We “proved” that the government should run surpluses until the debt/GDP ratio went so negative that the government didn’t need any taxes at all. It could pay for all its spending from the interest on its negative debt.
I dunno. I distrust Friedman, because his arguments were based on such a partial analysis – and most especially, given his soapbox and his position as spokesperson for anti-government, he was intent on proving the non-existence of a liquidity trap.
If you have an argument that leads to an infinitely great central bank in a liquidity trap, then you have a problem: we ARE in a liquidity trap.
grandiosity. The funny thing is that Friedman never actually proposed monetary policy that would match with what he wrote in this paper. Even though this paper remains (roughly) undisputed as theoretically correct, while most/all other of Friedman’s writings have been disputed heavily. His actual proposals for monetary policy did not call for deflation at all.
“If you have an argument that leads to an infinitely great central bank in a liquidity trap, then you have a problem: we ARE in a liquidity trap.”
But that’s exactly my point. If we stay in a “liquidity trap”, because we have deflation (or at least the fear of deflation) we are going to have a very big central bank, relative to the size of the economy. Either the central bank grows to match the size of the economy at something roughly like “full employment”, or else the economy shrinks to match the size of the central bank.
There is one asset which central banks can not buy by definition. That is deposits at commercial banks. Central banks can choose a regulation to penalize such deposits but this decision is independent from the decision about the balance sheet size.
“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.”
J.V. Dubois said: “If you have a government that promises budget surplus from now on forever, you also end in communism.”
What is it called when the very few rich people continuously run surpluses (very high real earnings and real earnings growth) so they own all the “currency” and assets and want to rent them back to everyone else?
It seems to me that the problem is excess savers.
Nick Rowe: “But that’s exactly my point. If we stay in a “liquidity trap”, because we have deflation (or at least the fear of deflation) we are going to have a very big central bank, relative to the size of the economy. Either the central bank grows to match the size of the economy at something roughly like “full employment”, or else the economy shrinks to match the size of the central bank.”
Sorry to be the perennial skeptic, Nick, but that seems to me to be a false dichotomy. Perhaps there are some assumptions that need to be relaxed. 🙂
During the Long Depression in the U. S., banks, but not the central bank, because the U. S. did not have one, became larger, through usury and foreclosures. But that dynamic seems rather different from the one with a central bank. Can we say that deflation tends to make banks — central or not — larger relative to the economy?
Of course, financial repression is not optimal. In some way, the use of financial repression prove your point: to collect revenue from seignoriage, a state needs to use financial repression, otherwise it reaches rapidly the Laffer point where the balance sheet of the central bank shrinks too much to collect more revenue.