When I was in the UCLA Ph.D. program, one of the readings in my Monetary Theory course with Ben Klein, if I recall correctly, was Milton Friedman’s 1953 classic, “Commodity-Reserve Currency.” It was a chapter in his Essays in Positive Economics but originally appeared in the Journal of Political Economy in 1951.
It was that article, more than any other, that convinced me that a gold standard was too expensive. Friedman had shown that the annual cost of maintaining a gold standard would be 2.5 percent of GDP. That’s huge.
I now know that Friedman was wildly wrong. He greatly exaggerated the resource cost of a gold standard. I learned that in my Monetary Theory and Policy course, taught by Jeff Hummel at San Jose State University.
In his 1999 book, The Theory of Monetary Institutions, the main textbook for the course, Lawrence H. White goes through the math. The important point, though, before we get to the math, is that Friedman got his estimate by assuming that banks would hold 100 percent reserves of gold against demand deposits and time deposits. That assumption is wildly unrealistic and so his estimate of the resource cost of the gold standard is way too high.
Friedman gets his estimate as follows:
Delta G/Y = Delta G/Delta M * Delta M/M * M/Y
where Delta G is the dollar value of the annual change in the stock of gold,
Y is annual national income,
M is the size of the money stock M2, and
Delta M is the annual change in M2.
For M/Y Friedman took M2/NNP (where NNP is net national product). That was 0.625, which White says is roughly right today.
What is Delta M/M? White and Friedman assume that the purchasing power of gold remains constant as money demand grows. So the money stock must grow to maintain a constant price level (zero inflation).
Using the dynamic equation of exchange (which I used to call the “quantity equation” until Jeff said the “equation of exchange” is more precise),
Delta M/M + Delta V/V = Delta P/P + Delta y/y,
Where V is velocity,
P is price level, and
y is real income.
Friedman estimated Delta V/V to be -1% annually and Delta y/y, the growth rate of real income, to be 3% annually.
With a zero inflation rate, therefore, Delta M/M =4% annually (0 + 3 -(-1))
With Friedman’s earlier mentioned 100 percent reserve requirement, Delta G/Delta M = 1.
So now plug into: Delta G/Y = Delta G/Delta M * Delta M/M * M/Y
Delta G/Y = 1(0.04)(0.625)
= 0.025.
In short, the annual cost of maintaining a gold standard is a whopping 2.5% of GDP.
But White considers the actual history of reserves against deposits under the gold standard and gets a very different answer for the ratio of gold to money, G/M.
G/M = (R + Cp)/M,
where R = bank reserves,
Cp is gold coins held by the public, and
M is M2.
(R + Cp)/M can be rewritten as
R/(N +D) * (N + D)/M + Cp/M.
R/(N + D) is the ratio banks maintain between their gold reserves and their demand liabilities, which are N (currency notes) and D (demand deposits.)
In 19th century Scotland, which had a gold-based banking system and no legal reserve requirements, R/(N +D), was 2% or 0.02.
(N +D)/M is the ratio of M1 to M2.
Coins in 1999 United States were 8 percent of currency, currency was about 51% of M1, and M1 was about 32% of M2.
So Cp/M = 0.08 * 0.51* 0.32 = 0.013
Since M1 is 32% of M2, and coins (Cp) are 1.3% of M2, currency notes and demand deposits must equal 32% – 1.3% = 30.7% of M2
Therefore, R/(N +D) * (N + D)/M = 0.02 * 0.307 = 0.00614
So (R + Cp)/M = 0.00614 + 0.013 = 0.01914.
The ratio of gold to the money stock is therefore about 2%, which is 1/50th of Friedman’s estimate.
So the annual resource cost of the gold standard, as a fraction of GDP, equals: 0.02 * 0.04 * 0.625 = 0.0005.
So that’s 0.05 percent of GDP. QED.
READER COMMENTS
KevinDC
Apr 19 2021 at 8:22pm
To add an unsolicited postscript – according to Mark Skousen’s book Chicago & Vienna: Friends or Foes?, Friedman was later persuaded by Roger Garrison’s rebuttal to his “cost of resources” argument, and he and Anna Schwartz abandoned this particular criticism of the gold standard. White’s book is also citied in that particular chapter – Skousen’s book was a fascinating bit of intellectual history.
David Henderson
Apr 19 2021 at 11:40pm
Thanks. I hadn’t known that, or, if I had, I’d forgotten it.
Rob Rawlings
Apr 19 2021 at 9:34pm
Very informative article!
I’m not quite getting why it would reasonable be assume “Delta V/V to be -1%”. Why would velocity be falling by 1% each year ? Is it because real income is assume to be increasing by 3% per year and desire to hold money increases as income increases ?
David Henderson
Apr 19 2021 at 11:43pm
Thanks, Rob.
White says that it’s historical evidence. And I’m pretty sure your reasoning is correct. Money is a normal good.
Thomas Lee Hutcheson
Apr 20 2021 at 6:44am
Interesting, but what if the optimal rate of inflation, both over time and during periods of positive and negative real and nominal shocks, is not zero? The issue ultimately comes down to how well the central bank of a fiat standard reacts to events (and avoids itself becoming and “event, like the 1929 Fed) given non-monetary features of the economy like stickiness of prices, ability to write inflation/deflation adjusted contracts.
David Henderson
Apr 20 2021 at 11:40am
You wrote:
Actually, Thomas, you now have the tools to answer your own question. Plug in what you think is the optimal rate of inflation. Plug it into Friedman’s equation and into White’s equation. Then solve. What you will see, I predict, is that the resource of a gold standard is much, much smaller than Friedman claimed.
Thomas Lee Hutcheson
Apr 21 2021 at 6:18am
Quite possibly. I meant that the optimal rate of inflation will influence the choice between a metallic standard and a fiat standard. The resource cost of a metallic standard is only one consideration.
Matthias
Apr 25 2021 at 12:56am
Historically, the long running rate of inflation under a gold standard was often negative.
See Selgin’s book Less Than Zero on this topic.
Alan Goldhammer
Apr 20 2021 at 8:38am
While interesting, doesn’t this still beg the question of whether a reserve currency is better/worse than fiat money? Would the Fed have sufficient control if the US were to move back to a Gold Standard? Doesn’t the history of the 19th and early 20th century argue against this?
David Henderson
Apr 20 2021 at 10:33am
No, it doesn’t beg that question.
To look at big issues, the way that makes sense is to look at them piece by piece. As I wrote in the post, it was Friedman’s resource cost estimate that, in 1973, talked me out of the gold standard. Now I know that that’s a bad argument.
That doesn’t mean that there are no good arguments against the gold standard.
Matthias
Apr 25 2021 at 1:03am
The idea would be that there’s no need for anything like a Fed to have control.
Contract law, courts and the behaviour of individual profit maximising banks and their customers would regulate the money supply.
Andrew_FL
Apr 20 2021 at 9:22am
In other words, Friedman’s argument is a valid criticism of 100% Reserve Gold-that is, some of the old Chicago proposals and Rothbard’s proposal-but not of a Gold Standard with a reasonably free fractional reserve banking system.
David Henderson
Apr 20 2021 at 10:31am
Correct.
Knut P. Heen
Apr 20 2021 at 12:21pm
The problem with the gold standard is not the cost in gold, but rather that it is an attempt to commit to something the government is not able to commit to. Every single time there was a war, the government of any country went off the gold standard and printed money like mad.
Sticking to the gold standard through thick and thin is simply not a sub-game perfect equilibrium. Once you know the government will go off the gold standard as soon as there is a minor crises, you don’t trust it, and the gold standard is dead.
It is the same story with the constitution. A living constitution is a dead constitution. The point of the constitution is to stick to it even if it is rational to change it because it is a commitment device. A constitution carved in stone is great ex ante, but unbearable ex post; hence, it becomes living and thus dead.
It is difficult to create renegotiation proof contracts.
robc
Apr 20 2021 at 12:27pm
The answer to that is to get government out of the money business. Free market banking is the answer. Lets bank print their own money and back it with what they want to back it with (or nothing). I think the equilibrium you reach is something very similar to a fraction-reserve gold standard. There might be some oddball silver or paladium backed currencies floating around, but I think gold standard would be the standard standard.
And that solves the problem of the government going off the gold standard during wars. The government wouldn’t be in charge of money, so wouldn’t have the option.
David Henderson
Apr 20 2021 at 2:01pm
Well said, Knut P. Heen, and well answered, robc.
Matthias
Apr 25 2021 at 1:05am
Yes, though what is perhaps more remarkable than governments going off the gold standard in times of war, were their repeated and often painful attempts of getting back _on_ the gold standard.
Eg Britain after the Napoleonic wars.
Peter Watt
Apr 20 2021 at 3:12pm
So, Bitcoin is the answer if governments can’t control it? But I guess they can?
Fazal Majid
Apr 23 2021 at 4:22am
Except gold is mostly useless, apart from its use to plate electronic connectors, so digging it up, refining/smelting it then putting it into underground storage vaults has little opportunity costs or externalities unlike the pollution caused by Bitcoin, and thus this is literally the same thing as Keynes’ much derided thought experiment of burying money and charging people for the privilege of digging it up.
Matthias
Apr 25 2021 at 1:07am
Mining gold has lots of bad effects. Yes, not using the gold for anything but storage isn’t much of an opportunity cost, but digging it up and separating it from the soil are very polluting activities.
The article actually provides the solution to this challenge: fractional reserve banking drops the amount of gold needed to run a gold standard by orders of magnitude.
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