Tag Archives: money multiplier

Money, the Money Multiplier, and Monetary Theory

John Williams recently gave a speech on teaching about monetary theory and policy after the financial crisis. Here is the basic thesis:

When I was an undergraduate at Berkeley in the early 1980s, much of the monetary economics that I learned was based on theories from the 1950s or even earlier. These included the quantity theory of money, Keynes’s LM curve, Milton Friedman’s monetarism, and the Baumol-Tobin theory of money demand, to name a few examples. Now, there’s no question that Keynes, Friedman, and Tobin were among the greatest monetary theorists of all time. Their theories are elegant statements of fundamental economic principles. As such, they deserve to be taught for a long time to come. But viewing them as definitive in today’s world is like thinking that rock and roll stopped with Elvis Presley. The evolution of money and banking since the 1950s is at least as dramatic as what’s happened with popular music—not that I want to compare the Fed with Lady Gaga. The theories of that era need to be adapted to the brave new world in which we now live.

I am not sure what this means, however, given the remainder of the speech. Despite the fact that Williams claims that the work of Friedman, Tobin, and Keynes represent “elegant statements of fundamental economic principles”, he subsequently goes on in the speech to largely disparage this work; in particular, the quantity theory of money and the Baumol-Tobin inventory-theoretic model of money demand. While I share Williams view that we need to understand modern innovations in economic thinking, I also think that it is important to understand and appreciate contributions of the likes of Friedman, Tobin, Keynes, and others. There is much that we can learn from the history of economic thought and, in this respect, it is important to read primary sources of the literature and not second-hand accounts (note: this is a general statement, not a knock against Williams). Thus, while I share Williams’ view that we need to appreciate recent contributions, I think that it is important to give fair treatment to earlier important contributions as well. I will elucidate this point below.

Williams seems to disparage the quantity theory of money by pointing to a fairly standard objection:

There have been a number of attempts to find a broader measure of “money” that has a stable relationship with nominal spending — that is, a constant velocity.

He then proceeds to detail differences in different monetary aggregates and their growth rates during the crisis. Differing growth rates and changes in velocity over the past few decades are then cited as evidence that using using the money supply to forecast nominal spending or inflation is a fool’s errand. This reasoning is flawed for two reasons. First, constant velocity is a straw man as Thomas Sowell details in On Classical Economics:

The idea that the price level is rigidly linked to the quantity of money by a velocity of circulation which remains constant through all transitional adjustment processes cannot be found in any classical, neoclassical, or modern proponent of the quantity theory of money. Changes in the velocity of circulation — short run and/or long run — were analyzed by David Hume, Adam Smith, Henry Thornton, T.R. Malthus, David Ricardo, Nassau Senior, John Stuart Mill, Alfred Marshall, Knut Wicksell, Irving Fisher, and Milton Friedman.

As I have illustrated before, velocity is not constant, but appears to be a stable function of the interest rate. (See Allan Meltzer’s graph.)

The second flaw in the analysis is that Williams is relying on simple sum aggregates, which are theoretically flawed and often produce puzzling empirical results. The question surrounding the quantity theory of money is essentially whether or not money can forecast inflation and nominal income growth and the answer is yes especially using longer time horizons and low frequency data.

Williams similarly caricatures analysis of the money multiplier:

The breakdown of the standard money multiplier has been especially pronounced during the crisis and recession. Banks typically have a very large incentive to put excess reserves to work by lending them out.

I assume that what Williams means by “the standard money multiplier” is the framework put forward in Phillips’ (1920) Bank Credit in which the money multiplier is a parameter. This view of the multiplier might be taught in principles, but I don’t think that it is used beyond that point. Even in Mishkin’s Money and Banking text, which does include analysis of the multiplier, there are explicit references to changes in the underlying factors that determine such a multiplier. Indeed, the literature on monetary theory has long recognized that the money multiplier could not be viewed as fixed coefficient. In the post-war era, this view was recognized by Gurley and Shaw (1960) and Tobin (1963). In addition, Brunner and Meltzer (e.g. JPE, 1968; JPE, 1972) explicitly modeled the money multiplier as a function of interest rates.

Jurg Niehans (1978: 274) elaborates on the points above:

While this fixed-coefficient approach, though perhaps pedestrian, is often useful and , for certain purposed, illuminating, it is also subject to serious limitations. Taken at face value it seems to say that money is very different from other things, inasmuch as demand has no influence on the quantity available; the quantity seems to be purely supply-determined. However, this is a superficial impression. It is well recognized that the coefficients appearing in the multiplier are not, in fact, technological constants, but depend, in turn, on interest rates (Brunner and Meltzer, 1968).

In addition, as Niehans (1978: 274) details, the general equilibrium approach in which interest rates are jointly determined with the money supply was developed by Tobin (1963), but actually has “its long ancestry in the pre-Phillips tradition of money supply theory.” Those who have used the money multiplier in discussions of the crisis have, by and large, recognized these points as well.

Like Williams, I agree that the financial crisis and the broader recession pose important questions for monetary theorists and teachers. However, I believe that there is much to be learned in both the present literature and the past literature on issues of monetary analysis and central banking (see Perry Mehrling’s The New Lombard Street, for example). And I wish that Tobin and Friedman would have received fairer treatment from Williams.

Inflation is a Monetary Phenomenon, But This Isn’t Inflation

There has been much talk recently about the potential inflation on the horizon given the unprecedented movement of the Federal Reserve of increasing the monetary base through quantitative easing. The talk has predominantly surrounded the substantial increase in the monetary base. However, increases in the monetary base are not sufficient to cause inflation. Like discussion of other markets, we must consider both supply and demand conditions.

Milton Friedman famously quipped, “inflation is always and everywhere a monetary phenomenon.” Friedman was undoubtedly correct. However, recently a few seem to have taken this claim to mean something different entirely. Namely, that any increase in the money supply necessarily causes inflation. This is something that Friedman himself did not believe.

In his restatement of the quantity theory of money, Friedman pointed out that the quantity theory is primarily a theory of money demand. Specifically, quantity theorists view the level of real money balances as more important than the nominal quantity of money. Thus, if at any point in time people have chosen to hold some level of real money balances that they deem optimal, an increase in the nominal money supply will leave these individuals with a larger level of real money balances than they wish to hold. These individuals will then necessarily try to reduce their holdings of nominal money balances such that their real money balances fall back to their optimal level (perhaps by increasing spending). Unfortunately, as a group, they will not be able to do so because every person’s spending is another person’s receipt (or income). Initially output will increase and gradually prices will rise until the level of real balances falls back to the optimal level.

Given this discussion, it should not be difficult to understand why I prefer a monetary equilibrium framework. What’s more, it should be apparent that what causes inflation is not an increase in the money supply, but rather an excess supply of money.

Ultimately, the question at hand is whether the current increases in the monetary base imply that there is an excess supply for money. If so, inflation is on the horizon. If not, we need not fear inflation.

Personally, I do not believe that the recent increases in base money imply that there is an excess supply of money. There are a couple reasons for this belief. First, it has been well-known — at least among monetarists — since Clark Warburton’s influential work that the peaks in the time series variables important for quantity theorists follow this order: (1) money, (2) output, and (3) velocity. The implication here is that declines in velocity (increases in the demand for money) are an accentuating feature of the business cycle. In other words, after output begins to fall, the demand for money increases. As our previous discussion of monetary equilibrium implies, this creates an excess demand for money, which results in falling output and prices — thereby exacerbating the previous decline in output.

Second, the money multiplier has declined drastically. In fact, the money multiplier for M1 remains below 1. This means that for every increase of $1 in base money, the money supply (as measured by M1) increases by less than $1. In order to determine the cause of the decline in the M1 multiplier, we should first discuss its components. The money multiplier for M1 consists of the currency-to-deposit ratio, the required reserve-to-deposit ratio, and the excess reserve-to-deposit ratio. An increase in any of these ratios implies that the money multiplier will fall. The required reserve ratio is set by the Federal Reserve and has not changed. Thus, the decline in the M1 multiplier must be the result of changes in the currency-to-deposit ratio and the excess reserve ratio. As previously mentioned, the demand for money often increases during the downturn in the business cycle. What’s more, financial crises often induce a flight to quality in which individuals abandon risky investments for safe investments such as bonds or cash. The increase in cash balances increases the currency-to-deposit ratio.

The largest cause of the decline in the money multiplier, however, is the result of the increase in the level of excess reserves. What’s more, this increase in excess reserves can be directly attributed to the fact that the Federal Reserve started paying interest on excess reserves late last year. In doing so, the Fed essentially reduced the opportunity cost of holding excess reserves thereby giving banks the incentive to hold more reserves on their balance sheets. This is why our friend Scott Sumner not only supports eliminating the interest payments on excess reserves, but prefers that the Fed impose a penalty on those who hold reserves above the required level.

Ultimately, the money multiplier (M1) has fallen from around 1.6 prior to the recession to .93 as of June 17. At the beginning of January 2008, the monetary base was roughly $848 billion. Given that money multiplier, this would suggest that M1 was around $1.356 trillion. Thus, given the current money multiplier, this would suggest that the monetary base would have to be about $1.458 trillion today to maintain the same money supply — an increase of roughly 72%. Given that we are currently in a recession, this suggests that the Fed wants to increase the money supply rather than simply maintain the earlier level. Given that the monetary base is about 90% higher than it was at this time last year, this would suggest that the Fed is expansionary, but hardly over-expansionary given the circumstances surrounding money demand.

With that being said, the Fed must be careful and begin pulling money out of the economy when this demand for base money subsides and the money multiplier begins to rise again. A failure to do so would result in a substantial period of inflation. However, at the current time, the evidence suggests that the massive increase in the monetary base is justified by the increase in the demand for base money. Thus, the increase is in the monetary base doesn’t suggest that massive inflation is on the horizon … yet.

(In the future, I hope to post on how the Fed can prevent finding itself in such a precarious situation in the future, but this is clearly enough for now.)