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Tuesday, August 31, 2021

Primer: Quantity Theory Of Money

Note: This is an unedited excerpt from my inflation primer manuscript.

Even if we put aside the atypical argument that an increase in the money supply is how to define inflation, there is a widespread belief that increasing the money supply causes inflation (as normally defined). These beliefs can be traced back to what is termed the Quantity Theory of Money, which has a long history in economic thinking.

I am extremely allergic to the Quantity Theory of Money. That said, my plan within this book is to stay away from theoretical controversies, and so will attempt to offer as neutral as possible description without inflicting too much pain on myself.

Although I refer to this as The Quantity Theory of Money, there are a few variants, with a long history. My impression is that the most reputable version of the theory is the “equation of exchange” variant. As I discuss below, this variant is not obviously wrong, rather it has the problem that it says very little in practice. As for the other variants, I mainly see various phrasings in popular discussion that have obvious defects, which are not tied to modern economic theory (at best, some garbled version of some dubious assertions made in mainstream Economics 101 textbooks).

Variants

I see three variants of the Quantity Theory of Money appearing in modern discourse. If we order the variants in increasing reputability, they are as follows.

  1.  Loose Definition. An increase in the money supply causes prices to rise. A mathematical relationship is not specified. The usual logic behind this are vague invocations of “basic economics” such as “the law of supply and demand.” A typical phrasing might include “too much money chasing too few goods.” The vagueness of this variant allows it to fit any number of observations made by people over the years, such as people who argued that gold imports from North America caused inflation in Spain.

  2. Formal Definition. A stronger version of the previous that says that increasing the money supply will cause prices to increase proportionally. My feeling – which many might not agree with – is that this is the only variant that matches the name of the theory.

  3. Equation of Exchange. The final variant is based on the equation of exchange: MV = PQ (I give the equation variables below). My argument is that this formulation does not really count as a Quantity Theory of Money, but I have been contradicted by others on that point.

I will discuss these variants in turn.

Loose Definition

The problem with the loose definition of theory – an increase of the money supply increases prices – is that it is probably too loose to qualify as a theory. A theory should give us a way to explain observed phenomena. But if your “theory” is too loose, it is not really explaining anything.

If we look at the post-World War II experience in the developed countries, we can see that the usual situation was that both the price index and the money supply grow each year (the next section will examine some of the data). Based on this experience, it would be reasonable to observe that they move in the same direction. However, this leaves open two major theoretical issues.

  1. There is nothing in this variant of the theory to suggest how much inflation is associated with money supply growth. Will it be 1%, or 10%? Although I am not too impressed with the power of mathematical models in economics, we should at least have something to work with.

  2. The absence of quantitative predictions means that we cannot really be sure that money supply growth causes price increases, since we do not know price increase is allegedly implied by a particular increase in the money supply.

If someone insists that increasing the money supply causes prices to increase without offering any further details, there is nothing much to say. We know that prices generally increase over time – as do a great many other economic variables. Since they are all increasing, we cannot look at them and say that one “causes” the other. In summary, this variant of the “theory” says too little to be considered a true theory.

Formal Definition

We can create a theory that can be tested by offering a quantitative rule – or at least what appears to be a quantitative rule. The simplest way of phrasing this would be as follows, which matches earlier thinking on the subject (I give a more modern textbook version later).

A percentage increase in the money supply will cause the price level to rise by the same percentage, assuming that all else is equal, over the short/long/medium term (depending upon the beliefs of the person making the argument).

The textbook Economics: Private and Public Choice by James D. Gwartney and Richard L. Stroup gives an abbreviated summary that is consistent with my version but missing some of qualifiers. (This text is a conventional “Economics 101” textbook, which I assume is representative of others that are used.) They write (page 330): “Nearly a hundred years ago, the great classical economists, Englishman Alfred Marshall and American Irving Fisher formalized a theory in support of this view [that rapid money growth caused inflation]. According to this early quantity theory of money [emphasis in original] an increase in the supply of money will lead to a proportional increase in the price level.” That textbook does not dwell on this version, instead moving to the equation of exchange version.

In popular commentary, the person making the argument rarely writes out their thesis, instead relying on looser arguments that appear to be consistent with y definition.

  1. They show a graph of the growth rates of some measure of the money supply versus the inflation rate and suggest that inflation will catch up to the growth rate of the money supply. (They only show these graphs when money supply growth is rapid. It is extremely rare for money bugs to discuss the prospect of falling inflation.)

  2. Similarly, they show graphs of the level of the money supply against some other variable of interest.

  3. In text, they quote percentage increases in the money supply over some historical period and use this to imply that this means that prices are going to go up a lot.

In most cases, the proponents accept a certain amount of fuzziness in the linkage between money growth and inflation, so we could not apply the same quantitative standards that physicists (for example) are used to. For example, the observed deviations between Newtonian laws of physics and Special Relativity are generally very hard to detect, but even that was enough to prefer Special Relativity. Nevertheless, if money growth is 20% per year, it would be hard to square with an inflation rate of 2%.

The definition I give above captures the usual sources of uncertainty.

  • I wrote “all else equal” – the Latin version of which (ceteris paribus) economists drop into “casual” speech. The equality of growth rates assumes that nothing else changes in the economy. Since things are always changing in the economy, this condition is never true – and allows believers in the Quantity Theory of Money to explain away its failures.

  • The time frame over which it holds is vaguely defined. A typical phrasing would be “long term”: which is how many days exactly? (Some of the more aggressive proponents will say the law holds in the medium or even short term, but once again, how long these “terms” are is unknown. This is another method to explain away failures: the inflation they predicted just has not happened yet.

  • I did not specify which measure of the money supply to use. There are multiple definitions of the money supply, often labelled M1, M2, M3, etc. The final way to explain away failures of the Quantity Theory of Money is to keep developing new measures of the money supply – which are carefully crafted to fit historical data. (And once that definition of money makes flawed predictions, create a new money supply definition.)

It should be noted that my phrasing above has obvious empirical problems (as I discuss below). This does not bother many of the market commentators who invoke the theory. However, more serious economists tend to dislike being mocked for proposing obviously incorrect theories, so they use variants that can avoid problems. In most cases, this involves using the equation of exchange (which I discuss next), or retreating into more abstract theory. An example of the latter is found in Section 6.1 of Macroeconomic Theory by Stephen McCafferty (page 191):

In long-run equilibrium, growth in the money supply in excess of the growth of money demand will show up as inflation. While the above equation does not hold precisely on a day-to-day or even a year-to-year basis, over longer time periods the quantity theory of money provides a good accounting of the most important determinants of the rate of inflation.

(The previous statement follows a compact mathematical model. For someone with a mathematical background it is straightforward – at least compared to the modern mainstream literature. However, it would be too complicated to explain for what is largely an aside within this text. This textbook is somewhat old and does not represent the state of the art, but I just picked it as an example on the basis that I had a copy of the text on the bookshelf next to my desk.)

The first thing one notes is that McCafferty makes clear that he does not expect annual inflation rates to immediately track the changes in the money stock. However, in the “long run,” it “provides a good accounting.” Nevertheless, there is a fudge factor that is within the text – money demand. The reality is that we do not have any good idea what “money demand” is.

If we had to estimate “money demand,” the only way is to look at the equations of a model that assumes the Quantity Theory of Money is true, then use it to back out an implied money demand function. In other words, the model only works because we infer a hidden variable that is estimated based on assuming that the model is true.

To spell out the problem more concretely, imagine that the money supply grew “quickly” for a few years. Any of the following could happen.

  • If inflation rises, that “proves” that money growth in excess of “money demand” causes inflation.

  • If the inflation rate is unchanged, that means that “money demand” grew just as quickly as money growth.

  • If the inflation rate fell, well, that means that money demand got really, really high. (Although that sounds silly, I have seen claims that recessions are the result of excessive money demand, so spikes in money demand allegedly happen.)

In summary, every possible outcome is “explained” by the theory.

Equation of Exchange

The equation of exchange is an equation that links nominal GDP to the stock of money. The equation is:

Nominal GDP = PY = MV.

The variables in the equation are:

  • P is the price level,

  • Y is real GDP (often replaced by Q for quantity of goods, making the equation PQ = MV),

  • M is the money stock,

  • V is the velocity of money.

Since we usually think of these variables in terms of growth rates, the above equation implies the following approximation:

(Growth of real GDP) + (Rate of inflation) = (Growth rate of the money supply) + (Growth rate of velocity).

(Multiplicative compounding means that there is a small error term with higher growth rate differentials.) If the velocity factor is constant, then the growth rate of the money supply will equal the growth rate of nominal GDP. This means that the price level would not increase proportionately with the money stock, rather price growth would be reduced by the growth of real output. Instead, the price level grows in line with the ratio of the money stock to real GDP.

However, as conceded by the text Economics: Private and Public Choice, the equation of exchange is a tautology. This is the fancy way of saying that it is a statement that is true by definition – which implies it does not say anything. The reason is that money velocity is not a well-defined value (like the speed of light). Instead, velocity is only found via using the equation of exchange itself:

V = PY/M.

This means that velocity is just the number you multiply the money stock by to get nominal GDP. The problem is that we can always find a number to multiply practically anything that is strictly positive to equal nominal GDP, since that is just how multiplication works. As I (sarcastically) pointed out in Abolish Money (From Economics)!, Canadian mink production does a comparable job explaining U.S. nominal GDP as does the monetary base in the Unites States in the 1980-2015 period. Economics: Private and Public Choice explains, we need some extra content to turn this equation into something that justifies being a theory (page 331).

The quantity theory of money, though, postulates that Y and V are determined by factors other than the amount of money in circulation. Classical economists believed that real output Y was determined by such factors as technology, the size of the economy’s resource base, and the skill of the labor force. These factors were thought to be insensitive to the changes in the money supply.

Similarly, classical economics thought the velocity of money was determined primarily by institutional factors, such as the organization of banking and credit, the frequency of income payments, the rapidity of transportation, and the communication system. These factors would change quite slowly. Thus, classical economists thought that, for all practical purposes, the velocity, or turnover rate, of money in the short term was constant.

Note that velocity does not have to be constant, but we need it to somewhat predictable for it to be useful. In the next section, we will see how useful a concept it is.

More Advanced Theories?

My concern here is mainly looking at what is commonly encountered in popular discussions. I cited what was in an Economics 101 textbook, as well as an older senior textbook. These sources would be more reliable than almost everything one encounters in market and economic commentary. Nevertheless, they do not represent the cutting edge of mainstream economic research. (I am discussing mainstream research here since most post-Keynesian authors are not fans of the Quantity Theory of Money.) My argument is that this modern research really does not fit with the Quantity Theory of Money as it is usually invoked in popular discussions.

As previously discussed, to get at the Quantity Theory of Money, we need stable money velocity. In modern mainstream models (dynamic stochastic general equilibrium or DSGE models), money velocity will not be particularly stable except in the cases where the author forces it into the model.

An immediate objection to my previous statement is that many of these models might exhibit the property that the model velocity will tend towards a constant if the model enters a steady state. (In a steady state, the model variables either grow at a constant rate or are in fact constant.) Although that might be true, the reality is that we would not see such a steady state – all manner of things are jumping around in the real world as well as in the model. (In the model, there are random disturbances hitting it.) As such, we might never see that “steady state velocity” in the model – just like in the real world. To the extent the velocity is constant within a model’s trajectories, the model is badly matching reality.

OK, Does It Work?

Having run through the variants of the Quantity Theory of Money, we then need to ask the important question – does it work? I turn to that in the next section. (As a spoiler, the answer is “not really.”)

References and Further Reading

  • McCafferty, Stephen. Macroeconomic Theory. Harper & Row, Publishers, Inc., 1990. ISBN: 0-06-044324-3

  • James D. Gwartney and Richard L. Stroup Economics: Private and Public Choice (8th Edition), The Dryden Press, 1997. ISBN: 0-03-019269-2

  • Brian Romanchuk, Abolish Money (From Economics)! BondEconomics, 2017. ISBN: 978-0-994748-8-9

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(c) Brian Romanchuk 2021

2 comments:

  1. It would be wise to describe someplace in your book that an increase in the money supply is a macroeconomic measurement of microeconomic actions.

    What do I mean? Well, to have an increase in the money supply, you need to first define how money is measured. Let's just measure the amount of money in private bank accounts as a starter. If that number rises, either the private sector has taken more loans from banks or government has paid the private sector more without increasing the tax rate.

    Both pathways increase the amount of spendable wealth available.

    With more spendable wealth available, it is reasonable to predict that the demand patterns for everything should shift toward the patterns seen in the more wealthy sector of the economy.

    ReplyDelete
    Replies
    1. I will discuss the money definition elsewhere.

      The book discusses inflation. What you wrote does not really fit the analysis of inflation.

      Delete

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