### Monday, August 31, 2009

## Another Scott Sumner Money Illusion

I pick on monetary maverick Scott Sumner a lot, but only because I care. (In fact, Scott himself gets this; see the opening paragraph of this post.)

So it is merely in the spirit of loving correction that I bring to your attention a recent profundity from Scott. The context is (a very interesting) discussion of the difference between the quantity theory of money and the equation of exchange, which are often conflated.

The equation of exchange is the familiar MV = PQ, which is just the accounting tautology that the total money stock times the "velocity of circulation" must equal the "average price level" times the quantity of real output. Some people use different letters, and people like Rothbard get mad over the nonsense placeholders like "V" which only serve to complete the equation. But if we put aside such complaints, the equation is an identity and so has to be true.

In contrast, the quantity

So finally we can review Scott's illustration of the problem:

By the same token, assuming central planning could work, then Lange whupped Mises in the socialist calculation debate.

So it is merely in the spirit of loving correction that I bring to your attention a recent profundity from Scott. The context is (a very interesting) discussion of the difference between the quantity theory of money and the equation of exchange, which are often conflated.

The equation of exchange is the familiar MV = PQ, which is just the accounting tautology that the total money stock times the "velocity of circulation" must equal the "average price level" times the quantity of real output. Some people use different letters, and people like Rothbard get mad over the nonsense placeholders like "V" which only serve to complete the equation. But if we put aside such complaints, the equation is an identity and so has to be true.

In contrast, the quantity

*theory*of money is just that, a theory, and so could be falsified in principle. Scott says that different people mean different things by the theory, and he lists four popular contenders:Does everyone see the difference? Just to give you an example, when Friedman famously said that price "inflation is always and everywhere a monetary phenomenon," he wasn't just relying on the equation of exchange. Yes, MV = PQ must always be true--it's an identity--but it doesn't mean that increases in M correspond to increases in P, or that a big jump in P must be due to a big increase in M. (For example, many economists right now believe that a big jump in M would cause a big jump in Q--this would also keep the equation in balance.)1. The ratio of P and M is relatively stable.

2. The ratio of P*Y and M is relatively stable.

3. An exogenous, one time, permanent increase in M causes a proportional rise in P*Y

4. In the long run an exogenous, one time, permanent increase in M causes a proportional increase in P.

So finally we can review Scott's illustration of the problem:

I think Scott has here performed the classic economist trick of assuming his conclusion, but doing it in a such a jargon-laden way that few can see where the rabbit gets put into the hat. The easiest way for me to demonstrate is a physics analogy. So suppose a physicist at Bentley College started a blog called The Gassy Illusion and wrote:But I also think the quantity equation can get in the way of clear thinking. For instance, people worried that current Fed policy will lead to much higher future inflation sometimes cite the quantity theory. But this is a misuse of the theory. It does not imply that any increase in the money supply is inflationary, but rather that permanent, exogenous increases are inflationary. For instance, suppose the Fed adopted a policy of targeting the expected inflation rate at 2%. Assuming their policy was efficient, i.e. the errors were unforecastable, then there should be zero correlation between the money supply and inflation. Of course the Fed doesnâ€™t have a precise 2% inflation target, but they certainly have some inflation target in mind. If so, then changes in the money supply are partly endogenous, and the [quantity theory] does not predict much correlation between the money supply and inflation.

So yes, Scott is right that if the Fed could commit itself to 2% inflation, and could do so without systematic errors, then...we would get on average 2% inflation, regardless of what happened to the money supply. But does that really help us? Note that Scott is NOT merely saying, "If the Fed commits to 2% inflation, then we'll get it." Because the Fed could commit and then be horribly wrong, year after year. So the real rabbit is where Scott innocently says, "Assuming their policy was efficient..."We're all familiar with Boyle's law of gases, which states that for a gas at a fixed temperature, Pressure and Volume are inversely proportional. Now many people assume that if we started shrinking the size of this airtight room, that the air pressure inside would increase. However, what if Ben Bernanke could perfectly anticipate the rate at which the room's volume were decreasing, and cooled the room accordingly? Why, then there would be no observed correlation at all between Pressure and Volume. So people worried about the shrinking room need to be more careful when invoking Boyle's law.

By the same token, assuming central planning could work, then Lange whupped Mises in the socialist calculation debate.

Comments:

MV = PQ?

I'd say :

M - D = PQ

where D is the demand for cash holdings, which would mean that the price-level is dependant not on some arbitrary "velocity", which seems to be about as moronic as the Keynesian multiplier, but rather

- The productive output

- The amount of money _in circulation_

I'd say :

M - D = PQ

where D is the demand for cash holdings, which would mean that the price-level is dependant not on some arbitrary "velocity", which seems to be about as moronic as the Keynesian multiplier, but rather

- The productive output

- The amount of money _in circulation_

Savecapitalism,

I think you're in trouble if you try to separate money "in circulation" from money being held in cash balances. At any given time, all money is held in cash balances. If you try to focus on money that is being spent as opposed to "hoarded," then you're back with the concept of velocity, which you are saying is arbitrary.

I think you're in trouble if you try to separate money "in circulation" from money being held in cash balances. At any given time, all money is held in cash balances. If you try to focus on money that is being spent as opposed to "hoarded," then you're back with the concept of velocity, which you are saying is arbitrary.

Sorry I'm late to the party, but I do have a response. My point isn't that they can't miss, or even that they can't miss badly, rather it is that you should not be able to predict their misses by looking at the money supply. If you predict when the Fed would miss its target merely by looking at the money supply, then the Fed wouldn't be very good at what it does. And since the market also forcasts low inflation, they would also have to be bad forecasters. Yes, the Fed hasn't been very effective recently, but I'd still like to think they wouldn't make that particular elementary error. Time will tell.

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