The Equation of Exchange and the Metaphysics of Commerce

"The Balance of trade is the metaphysics of commerce, which few understand and which serves no other purpose than to disturb the imagination" - Thomas Fitzsimmons, 1785

*****

What would you all think if I wrote "By definition Y=C+I+G, so if you increase G you increase Y". You probably wouldn't take me very seriously. Even when I make a case for fiscal policy, it's never that case. Freshmen learn what's wrong with that argument. Would it improve things at all if instead I said "By definition Y=C+I+G, so if you increase G holding everything else constant you increase Y"? This version is at least logically coherent, but would your opinion of me change all that much? Probably not. Let me put it this way - I should hope you would still think I was talking nonsense. It's true that Y=C+I+G; that is trivially true. But when you change government spending, you can't expect other things in the equation to stay the same. So the first, unqualified statement that I made is logically wrong because nothing constrains C and I to stay the same, allowing me to conclude that we can increase G ad infinitum to achieve permanent growth. The second version of my statement was logically sound, but meaningless and demonstrative of a very poor understanding of economics. The lack of understanding is evident not in my manipulation of the equation itself, but in my understanding of the meaning and use of the equation.

Unfortunately, Don Boudreaux recently made precisely the same mistake with another famous economic law, the equation of exchange, MV=PQ. Don writes:

"In today’s Wall Street Journal, U.S Treasury Secretary Timothy Geithner, Singapore Finance Minister Tharman Shanmugaratnam, and Australia Treasurer Wayne Swan worry aloud that, in emerging economies, “rapid growth” increases “the risk of domestic inflation.” Baloney. Inflation is the result of too much money chasing too few goods. So by increasing the flow of goods (and services) produced in an economy, rapid growth decreases the risk of domestic inflation. That the finance ministers of three major world governments do not understand this fundamental fact is appalling." (emphasis is mine)

Don is quite wrong here, and the various finance ministers he cites are correct*. The key to understanding how to think about the quantity theory is that it's simply a balancing of the books. Alone, it tells you nothing about the causal relationship between any of these variables. I want to emphasize that because a lot of people from all sides of the aisle treat it like it's a causal law (Exhibit A being the regular testimony in the banking committee of the politician that every libertarian wants to pretend isn't just another politician).

Don is discussing the role that rapid growth (and increase in Q) plays in inflation. Taking the naive view of the equation of exchange, he reasons that since P = MV/Q, when Q increases P (the general price level) must decrease. He doesn't even say "holding everything else constant", and so his claim is logically wrong. But even if he had said "holding everything else constant", that just begs the question - why would you ever claim to hold everything else constant? Don certainly wouldn't let me get away with "holding everything else constant" in the national income identity. So how does Q grow in Don's example? Well for the answer to that question we have to turn to some method of determining output - Q. For this, of course, economists traditionally turn to supply and demand. Profit maximizers and utility maximizers come together in a market and set their respective marginal benefits and marginal costs equal to each other and come to agreement on a Q and a P**. So that gives us two of the four variables in the quantity theory - not bad. How does Q and P change in a supply and demand model? Well, the supply schedule can shift, the demand schedule can shift, or both can shift simultaneously. These supply and demand curves, unlike the equation of exchange, are actual behavioral claims made by economists. If you have a given set of preferences, and you have certain rational and informational prerequisites, and you face a particular suite of prices you will purchase Q goods for P dollars each in the market. This is claimed to be causal and it does describe behavioral relationships. It is not an accounting identity like MV=PQ or Y=C+I+G. So what happens if demand for goods and services increases? We would expect to see Q and P both increase. What happens if the supply schedule shifts to the right? We would expect to see Q increase and P decrease.

Now, to make another trivially true statement, we can say that if M and V are held fixed, these supply and demand dynamics will be reflected in observed values. On this point alone - even at this "trivially true"/"ceteris paribus" stage in the game, and after adding one supply curve and one demand curve to give some actual behavioral traction to our equation of exchange, Don is clearly wrong. Output growth can occur for at least two reasons - a supply shift (i.e. - increased productivity) or a demand shift, and a shift in demand will cause prices to increase at the same time that quantity increases***.

But presumably we aren't satisfied with a "trivially true" refuation of Don's point. When supply or demand shift, things happen to M and V too. When demand for goods and services increases, more transactions occur and people increase the rate at which they spend a given stock of money. In other words, the velocity of money, V, increases. Another way of saying this is that the desire to hold on to cash decreases if your demand for goods and services increases and your income stays the same. That cash did not circulate before, and now it is put into circulation. This is a standard impact of an increase in demand, and its inverse is why Keynesians associate low demand with an increase in the desire to hold cash or other liquid, idle assets. So if we have demand-lead growth, we would expect V to go up as well (which is another reason why when Q goes up in the equation of exchange you can't simply assume P goes down - that increase in Q may be a part of a process that simultaneously increases V).

What happens with the money stock? Well, of course that depends on how you define money. If you're thinking in terms of a very narrow definition of money, you can safely assume that that stays fixed and the explanation provided above of P, Q, and V gives you what you need. I don't know too much about this end of the theory, but clearly there are definitions of M with varying breadth. Nominal credit creation in response to an increase in demand can also be said to increase the money supply, and would also create inflationary pressure. Would you have nominal credit creation in response to a productivity (i.e. - supply schedule) increase? I don't really see why you would expect that. People need less exchange media to conduct the same amount of commerce, so it's probably less sensitive to supply-lead growth. Then again, if the aggregate demand schedule is highly elastic, maybe you would need more. These are the kinds of issues you have to think through - the equation of exchange doesn't provide you the answer to any of these relationships.

So be careful when you use these. Don't get caught saying "when we print more money it creates inflation" or "when output grows, it lowers prices". These are abuses of the quantity theory.

*George Selgin has some comments in the comment section of this post that are worth reviewing. I think Selgin is basically right and understands precisely what I'm saying here. Unfortunately he was clearly indulging Don's misunderstanding of the issue when he was taking issue with my comments, and trying to paper over a pretty egregious Cafe Hayek post.

**You could of course raise some market process objections to this story, but the basic supply and demand relationship has been experimentally verified (by other George Mason professors, in fact), so whatever non-auctioneer market process is going on is clearly giving us about the same results, which should not be surprising to anyone.

***In the article that Don discusses, the authors mainly point to demand-lead growth in emerging economies as the inflation risk for emerging economies only. They specifically cite demand for exports, growing domestic demand, and rising commodity prices (which have been demand-driven, not supply-driven).

*****

Quantity theory links:

- I started a thread on this issue in Jonathan's forum here.

- This recent post by Brad DeLong doesn't explicitly mention the quantity theory, but he does bring up the problems with a Monetarist approach to the crisis. His critique is based on the interpretation of Monetarism as a misuse of the quantity theory... or at least a misuse given the very special circumstances we're going through now.

- Stephen Williamson replies to Mark Thoma and writes: "This is why I'm not an old-fashioned quantity theorist. What has to be going on here is a large increase in the world demand for US currency during the financial crisis. All the more reason to be worried about inflation, as the crisis-driven demand [for US currency] goes away." I'm not sure if Williamson is saying that "old-fashioned quantity theorists" misuse the equation of exchange, but this doesn't seem quite right as a critique of the quantity theory itself. If there is an increase in world demand for US currency that you expect to be temporary, then that's the same as saying there is a decrease in V that you expect to be temporary. If you expect it to be temporary, then you'd expect an increase in V in the future. If, following the processes I outlined above, you think that increase in V is going to be paired with an increase in demand and thus P and Q, then Williamson's worry about inflation in the future is perfectly justified and perfectly consistent with the quantity theory. It's simply not on the top of my list of things to worry about right now. When we actually see that inflation, it means we're probably out of the slump.

- Bill Mitchell, of the Modern Monetary Theory school, has a weekly quiz. The second question of a recent quiz is on the quantity theory. Mitchell sets up a straw man of what quantity theorists believe (essentially attributing Don Boudreaux-type views to them), and then credits Keynes with fixing all that. This is a little much - many users of the quantity theory long before Keynes used the quantity theory without making these mistakes, and Keynes certainly embraced the quantity theory - and he used it correctly and to great effect. So Mitchell's analysis here is correct - but his history is a little self-serving.

- Jonathan reposts some thoughts by Richard Ebeling on Hayek and the quantity theory here.

- And of course, a lot of this emerges from our discussion of Hayek's Prices and Production. You'll find my post on the first lecture, in which I deal with some of these questions, here. I think Hayek does much the same thing that Mitchell does with his treatment - he provides a reasonably accurate analysis of the quantity theory, but a fairly self-serving history of the idea. He also has a weird "this isn't important and in fact it's misleading" reaction to it by the end.

- Keynes has a suberb discussion of the use and misuse of the quantity theory in the Tract on Monetary Reform (it actually is the same discussion where he says "in the long run we're all dead"). I'll hopefully get a chance to quote it at length this weekend, but if I don't please look it up yourselves