The Quantity Theory of Money seems straightforward, but a little thought about it brings up many questions. Different economists have taken different approaches to it, so we have several Quantity Theories rather than one distinct Quantity Theory. In his many books Ludvig Von Mises discusses these theories extensively. He criticises some of them on various counts, for being too mechanical, for example. That doesn’t mean, though, that Mises doesn’t believe in any sort of Quantity Theory; he praises the general idea, saying that there’s a “core truth” in it. Mises rejected certain aspects of other Quantity Theories and embraced other aspects; he had his own Quantity Theory.
Anthony Evans and I have taken up this subject in a paper, we compare Mises version of the Quantity Theory to some others. Expectations of the future are closely related since they drive decisions to hold more or less money. We examine what Mises has to say about expectations and how this relates to his version of Quantity Theory. This puts the financial crisis of 2008 and it’s aftermath in a different light, something we discuss briefly.
The Theory of Money and Credit (1912) is a seminal book in the development of the Austrian school approach to monetary theory. We argue that Mises’ understanding of the quantity theory is distinct from both the Fisherian and Cambridge versions, and warrants recognition as a third, separate version. After supporting this claim we demonstrate how it can be utilised to make expectations the central channel of a quantity theory with microfoundations.
The draft paper is here:
Comments are welcome.
One reason I tend to focus on Y, rather than T, is because, I think, Y has more to do with employment.
During a recession, for example, people begin buying used goods where they would otherwise buy new. Bringing together buyers and sellers of used goods is a productive service, but purchasing, for example, a used car, does not provide income to car manufacturers. The sale might be $10,000, but only a fraction of that — the cut taken by the car salesman — provides employment. (It’s important to stress, in this example, that the new car would have been bought in monetary equilibrium.)
Y is not perfect either, but it comes closer to counting expenditures on newly produced goods and services, i.e. spending that provides income from present employment.
I wonder how Mises would have felt about measuring the temperature of water in a boiling kettle. Obviously, the temperature is not uniform. Perhaps we might measure the temperature in different places or at different times, but our measurement will always be some average temperature (or an aggregate of the total energy in the water). Should be methodological atomists, and only describe the behaviour of individual water molecules?
When talking in averages and aggregates, it is important not to lose sight of the fact that we are really talking about the interactions of many individuals. Therefore, when arguing in averages and aggregates, we make implicit assumptions about how all or most of those individuals respond to different circumstances. Critics of such arguments need to explain why those implicit assumptions are false, not just that they might be false because “aggregates don’t act upon each other.” Methodological individualism (or praxeology) is a good way to check these assumptions for consistency; it should not be used as a strategy to reject arguments without consideration.
Aggregates of some kind or other are implicit in the explanation of supply and demand. They are used in all economics. The difference is in how they’re used. I prefer to tackle that issue on a case-by-case basis.
It’s easy to criticise some of the arguments that say “aggregates don’t act upon each other”. But I think some are quite valid. Let’s suppose that a claim has been made about a connection between two aggregate quantities. There are two possible ways to substantiate that claim. The first is through empirical evidence, and in most cases this is very difficult because of the difficulty of getting accurate data over significant periods of time and because the identification problem admits of so many different interpretations of it. The second, which nearly all schools of economics take if they’re been honest, is to create a logic argument built from microeconomics reasoning and microeconomic evidence for the link.
Going back to the Quantity Theory. What you’re saying is that measures of income or output are most important for economic performance. That’s a difficult point and I don’t completely agree. But, for the sake of this argument I will here, let’s say Y transactions are important and transactions of assets and second hand goods are not. Does this mean that we should use MV=PY? I don’t think so.
Using MV=PY cuts of a major part of the picture, the side containing assets, second-hand goods, inventory and most taxes. Those things may not contribute to output, but they still factor in decisions about money holding. That means they still affect what agents do. Cutting them out of the equation doesn’t cut them out of what happens.
If we have the total quantity equation:
Then the V here is “velocity”, it is the average number of times that a unit of money is exchanged during a period. This means that any reason an individual may have to raise or lower the stock of money that they keep can be reasoned about using the equation. If I want to hold a larger money balance and the supply of money is fixed then PT must fall.
But, in the equation:
Here the V doesn’t have anything like an obvious interpretation. It isn’t the average time a unit of money is exchanged during a period because only GDP is being included. The salesman’s commission that you pay for a second hand car is included, but the price of the car isn’t. The problem here is that some actions contribute to this “income velocity”, such as buying consumer goods, but other actions that are very similar at the agent’s level don’t, such as buying second hand goods. So the V here isn’t really a velocity, it’s an arbitrary parameter, a fudge-factor. When we give reasons for secondary recessions we talk about an increase in the demand for money, but what does the fraction of the price of the car’s price paid to the salesman have to do with the demand for money? It doesn’t really have anything to do with it. The logic works because the V in MV=PY is closely related to the V in MV=PT, not because they’re the same thing or proportional. The same, of course, is true of P. The P in MV=PT is the price vector of all prices, the P in MV=PY is that of all output. The prices of output and prices of all goods are closely linked by substitution, because for many goods there are new and used substitutes and for many there is only new output.
I don’t think it is ever valid, logically, to criticise an argument because it is expressed in terms of averages or aggregates. Such averages and aggregates do limit the range of logically compatible microeconomic particulars. Like you suggest, two good criticisms might be empirical evidence that such particulars do not, in fact, exist, or praxeological-like reasoning about the actions of individuals that suggests such particulars are unlikely or impossible. However, even if one of these avenues of criticism turns out to be fruitful, it does not follow arguments like “aggregates don’t act upon each other” were good to begin with.
In any case, to clarify my other comment. I was not suggesting that Y is categorically better or preferable to T. However, these discussions often take place in the context of low nominal expenditures and high unemployment. To the extent that satisfying or reducing money demand boosts nominal expenditure, if the spending mostly when on non-GDP stuff, then it would do little to alleviate unemployment. But I don’t think that is a realistic situation. I also don’t think V becomes a fudge-factor, it just has to mean something like: “the average number of times a unit of money is exchanged for newly produced goods and services.”
You do, however, bring out some subtle distinctions that normally go unnoticed in these equations. I seem to remember being involved in a discussion with you a long time ago about this very issue. I commend your persistence and progress with the matter.
There’s a difference between an argument that’s expressed in terms of aggregates or averages and one that depends only on them.
As you know, I could make a case for various forms of the quantity theory from a marginalist starting point. Then I could turn to aggregate equations and express the idea that way.
But, my logic isn’t sound if I start with aggregates. That can only be valid it’s backed up by empirical evidence.
But, those who say things like this are making the case that I described. The phrase you are using comes from page 4 of “Price and Production”. In the discussion on p.4-5 of that book Hayek makes pretty much the case I made.
I agree that this sort of discussion occurs when nominal expenditures are low. But, in this situation discussing MV=PT is only marginally more difficult to discussing MV=PY. Because the factors that govern V are closely linked in both cases I don’t think there is much advantage in simple presentation for MV=PY.
You’re right that spending money on things that aren’t GDP constituents doesn’t directly increase employment. That’s part of the problem I’m trying to point to here. Monetary equilibrium in MV=PT isn’t the same thing as an NGDP target policy using MV=PY.
Let’s start with P and T in MV=PT. Those are a vector of prices and one of transacted assets. Now, a sub-vector of each of these is the P and Y in MV=PY. If those sub-vectors rise and fall with the overall vectors then V in both equations is the same. But, if they don’t then it isn’t. In that case there is a different money supply that meets demand to the money supply that keeps NGDP meeting some target.
For example, suppose that the demand for GDP goods falls and that for asset rises. That means that an GDP targeting system would increase the money supply. But, in terms of MV=PT that may not be appropriate, in MV=PT V may have remained constant. So, in this situation in MV=PT terms the creation of money will raise prices overall. We have the opposite situation if the demand for GDP good rises and that for assets falls. So, the situation where the state of money supply-and-demand isn’t affecting intertemporal is different from the situation where we have a constant NGPD or a constant NGDP trend. Of course this may not be important in practice, but we need to consider what it means.
Yes, that’s what it means. I suppose you’re right about this, and it’s pretty subjective anyway what a “fudge factor” is.
As I said earlier, I think the problem with the caveat about newly produced goods and services is that it prevents a clear link back to money demand. As we say in the paper money holding must be planned by individuals without taking into consideration the difference between GDP output and other goods and assets.
Thanks. I have been talking about this for years. Lots of the progress in the paper compared to my internet discussions came from Anthony Evans. I won’t bore everyone with it for years to come though, except when it’s relevant.
Are you presuming here that the aggregate explanation in question has already passed an empirical test? In that case, sure, the aggregate theory has value.
Or are we comparing different explanations? Theories that could pass an empirical test is one could be created? In this case isn’t the aggregate theory only one of many? In that case surely we should look to the more carefully constructed explanations first.
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