Suppose the French wanted to double the size of the Sun. They hacksaw the rod in two, throw one half away, et voila! The diameter of the Sun, measured in metres, is now doubled.

There is a metal rod in Paris that defines the length of the metre. (Actually, Wikipedia tells me that isn't true now, and was never exactly true, but never mind, because it makes a good metaphor). I think you could call that a "stipulative" definition of the metre. "See the length of that metal rod over there? That's a metre."

How do the French control the size of the Sun? How does the Fed control the size of the US economy? More importantly, how are those two questions related?

Someone who asked how a hacksaw in Paris could reach all the way to the Sun, and who enquired about the causal chain connecting the two, would be making something like a Category Mistake. The only causal chain worth enquiring about is the one between the rod in Paris and scientists' minds. Would scientists accept the new definition of the metre? The causal chain isn't physical; it's, um, metaphysical? It's perhaps a question of the Sociology of Knowledge.

You might say that the French control only the nominal size of the Sun, measured in metres, and not the real size of the Sun. And what the French have really done is halved the real size of the metre, not doubled the real size of the Sun. OK.

If you accept the analogy, you would say the Fed controls the definition of the US Dollar just as the French (in my story) control the definition of the metre. And you would say that the Fed controls only the nominal size of the US economy, not the real size of the US economy. The Fed, for example, controls nominal GDP but not real GDP. The Fed can double GDP measured in dollars by halving the real value of the dollar.

Some economists do believe something very close to that. But most of us believe that when the Fed changes the nominal size of the US economy it will also affect the real size of the US economy too, at least in the short run. And what is puzzling, for us, is not that the Fed can change the nominal size of the US economy; the puzzle is that doing so can affect the real size of the US economy too, at least in the short run. And we think it's got something to do with sticky prices and expectations. When the Fed changes the definition of the dollar, it takes time for that new definition to spread out across people's minds, and so changing the definition will have real effects in the interim. If lumber was sold in old metres, while architects worked in new metres, the French hacksaw might cause real effects in the housing market too.

If you will forgive the anachronism (the Fed wasn't around in David Hume's day), both Hume and Patinkin agree that the Fed controls the nominal size of the US economy in the long run, and can affect the real size of the US economy in the short run. But I think there's a big difference between the two.

I think that Hume would basically accept my metre analogy, and Patinkin wouldn't.

Hume's own analogy, between money and a system of counting, is similar to my metre analogy.

"It was a shrewd observation of ANACHARSIS the SCYTHIAN, who had never seen money in his own country, that gold and silver seemed to him of no use to the GREEKS, but to assist them in numeration and arithmetic. It is indeed evident, that money is nothing but the representation of labour and commodities, and serves only as a method of rating or estimating them. Where coin is in greater plenty; as a greater quantity of it is required to represent the same quantity of goods; it can have no effect, either good or bad, taking a nation within itself; any more than it would make an alteration on a merchant's books, if, instead of the ARABIAN method of notation, which requires few characters, he should make use of the ROMAN, which requires a great many. Nay, the greater quantity of money, like the ROMAN characters, is rather inconvenient, and requires greater trouble both to keep and transport it."

Hume discusses the causal chain between the quantity of money and the level of prices only in the context of discussing why a change in the quantity of money can have real effects in the short run.

"To account, then, for this phenomenon, we must consider, that though the high price of commodities be a necessary consequence of the encrease of gold and silver, yet it follows not immediately upon that encrease; but some time is required before the money circulates through the whole state, and makes its effect be felt on all ranks of people. At first, no alteration is perceived; by degrees the price rises, first of one commodity, then of another; till the whole at last reaches a just proportion with the new quantity of specie which is in the kingdom. In my opinion, it is only in this interval or intermediate situation, between the acquisition of money and rise of prices, that the encreasing quantity of gold and silver is favourable to industry. When any quantity of money is imported into a nation, it is not at first dispersed into many hands; but is confined to the coffers of a few persons, who immediately seek to employ it to advantage. Here are a set of manufacturers or merchants, we shall suppose, who have received returns of gold and silver for goods which they sent to CADIZ. They are thereby enabled to employ more workmen than formerly, who never dream of demanding higher wages, but are glad of employment from such good paymasters. If workmen become scarce, the manufacturer gives higher wages, but at first requires an encrease of labour; and this is willingly submitted to by the artisan, who can now eat and drink better, to compensate his additional toil and fatigue. He carries his money to market, where he, finds every thing at the same price as formerly, but returns with greater quantity and of better kinds, for the use of his family. The farmer and gardener, finding, that all their commodities are taken off, apply themselves with alacrity to the raising more; and at the same time can afford to take better and more cloths from their tradesmen, whose price is the same as formerly, and their industry only whetted by so much new gain. It is easy to trace the money in its progress through the whole commonwealth; where we shall find, that it must first quicken the diligence of every individual, before it encrease the price of labour."

To Hume, it is self-evident that the French control the nominal size of the Sun. What needs explaining is how the French can influence the real size of the Sun.

Don Patinkin's "Money Interest and Prices" is the opposite. The whole point is to explain how the French control the nominal size of the Sun. He deliberately rigs his example (by assuming flexible prices, that new money is distributed to individuals in proportion to their existing holdings of money, etc.) so that there will be no real effects. Starting in one equilibrium, a doubling of each individual's stock of money creates an excess supply of money, and by the logic of Walras' Law, that means an equal excess demand for non-money goods at the previous equilibrium price vector. And that excess supply of money/excess demand for non-money goods is what causes the price level to rise.

Patinkin thought that a reduced form equation like MV=PY or M=kPY wasn't good enought to explain why a doubling of the supply of money caused a doubling of the price level. And just to make sure people got the point, he repeated it in the form of a "stability experiment", by asking what would happen if all prices hypothetically halved, while holding the nominal stock of money (and everything else) constant. He said it would create an excess supply of money/excess demand for non-money goods which would cause all prices to double back up again, to the original equilibrium.

Money Interest and Prices was a book of its time. At that time (the 1950s and 1960s), there was no expectations-augmented Phillips Curve. Prices rose because of an excess demand for goods. So Patinkin explained why an increase in the supply of money would create an excess demand for goods.

There are many specific criticisms one can make of Patinkin's theory. To my mind the most important comes from Clower's observations that: money is not really needed as a medium of exchange in Patinkin's Walrasian economy; if we ask what would happen at a disequilibrium price vector we must allow that agents will be quantity-constrained; and if we put these two observations together we realise that Walras' Law makes no sense in a monetary exchange economy. But there's a more general criticism I want to make here.

There is more than one way to define the metre. You can define it relative to a metal rod in Paris, relative to the circumference of the Earth, relative to the wavelength of krypton-86, or relative to the distance light travels in one second, etc. Similarly, there is more than one way to define a value for the dollar. You can define it relative to gold, or relative to silver, or relative to the CPI basket of goods (which is roughly what modern central banks do now). Or you can define it by fixing the quantity of dollars, which is what Patinkin assumed.

Once you have grasped the idea that the French can double the nominal size of the Sun by cutting the metre rod in half, and redefining the metre, it doesn't matter how the metre is defined, and who defines it. You can translate the same basic idea into the new dictionary. Similarly, once you have grasped David Hume's idea, it doesn't matter how the dollar is defined, and who defines it. You can translate the same basic idea into the new dictionary.

If the dollar is defined by fixing the quantity of dollars, then doubling the quantity of dollars halves the value of each dollar in terms of all goods, which means the prices of all goods double. If instead the dollar is defined by fixing the price of gold, then doubling the price of gold halves the value of each dollar, doubles the quantity of dollars, and doubles all prices. And so on. The Quantity Theory of Money does not need to take the quantity of money as the exogenous variable and the prices of all other goods as the endogenous variables. The same idea is equally valid if the price of gold, or some basket of goods, is the exogenous variable. The Quantity Theory of Money is a theory about units. It says the units don't matter, at least in the long run.

If Patinkin had written a third edition of Money Interest and Prices, in which the dollar price of gold was the exogenous variable, it would be a complete re-write. How would a doubling of the price of gold in terms of dollars cause all other prices to double and the stock of money to double too? That's quite a different question. And inflation targeting, or NGDP level-path targeting, would be complete re-writes again.

All of which makes me wonder: did Patinkin really fill a massive gap in monetary theory by explaining how a change in the quantity of money causes a change in the price level? Or, at the other extreme, is the magisterial Money Interest and Prices just one big Category Mistake?

Patinkin (or the reader) might object that I am confusing money as the medium of exchange with money as the medium of account. Changing the length of the metre is like changing the value of the unit of account, which is a question more like the Sociology of Knowledge, where we ask who decides what units will mean, and how those meanings get propagated into the population. But that still leaves open the question of the value of the good which serves as medium of exchange in terms of other goods, which was Patinkin's question. Patinkin was very careful to make that distinction; Hume didn't.

But I don't think I'm making that mistake here.

The Quantity Theory of Money would not work if we used cows as money. Patinkin could not put M/P in the utility function if M stood for "Cows", because a doubling of the number of cows plus a doubling of all prices in terms of cows would not leave us indifferent. We would be drinking more milk, for one thing.

If we used gold bars as money I could define the physical quantity of money independently of its value in terms of the medium of account. Because I can measure the quantity of gold in kilograms, as well as in dollars. A 2 kilogram bar of gold will be worth twice a 1 kilogram bar of gold, because it's got twice as much gold. A $20 bill isn't worth twice a $10 bill because it's got twice as much paper. It's only worth twice as much because the central bank will exchange them two for one.

The history of money is like the story of the Cheshire Cat, which slowly disappears leaving only its smile. The usefulness of a unit of a good that is used purely as a medium of exchange (and not to produce milk as a byproduct) depends only on its exchange value. Except for the slight difficulties in counting the notes, and fitting them all in our pockets, there is no economic difference between multiplying the number of notes tenfold and adding a zero to each of the existing notes.

David Hume's idea works for a (pure) medium of exchange, even if it isn't the medium of account.