Chapter 21: The Demand for Money

Chapter 21 begins the last section of your textbook, which deals with monetary theory. Monetary theory develops the link between money supply and other macroeconomic variables, including the price level and output (GDP). In this chapter we begin with competing theories of money demand and some empirical evidence about the behavior of money demand.

I.  The Quantity Theory of Money

This theory, developed by the classical economists over 100 years ago, related the amount of money in the economy to nominal income. Economist Irving Fisher is given credit for the development of this theory. It begins with an identity known as the equation of exchange:


Where M is the quantity of money, P is the price level, and Y is aggregate output (and aggregate income). V is velocity, which serves as the link between money and output. Velocity is the number of times in a year that a dollar is used to purchased goods and services.

The equation of exchange is an identity because it must be true that the quantity of money, times how many times it is used to buy goods equals the amount of goods times their price.

To move towards the quantity theory of money, Fisher makes two key assumptions:

  1. Fisher viewed velocity as constant in the short run. This is because he felt that velocity is affected by institutions and technology that change slowly over time.
  2. Fisher, like all classical economists, believed that flexible wages and prices guaranteed output, Y, to be at its full-employment level, so it was also constant in the short run.
Putting these two assumptions together lets look again at the equation of exchange:


If both V and Y are constant, then changes in M must cause changes in P to preserve the equality between MV and PY. This is the quantity theory of money: a change in the money supply, M, results in an equal percentage change in the price level P.

We can further modify this relationship by dividing both sides by V:

M = (1/V) x PY

Since V is constant we can replace (1/V) with some constant, k, and when the money market is in equilibrium, Md = M. So our equation becomes

Md = k x PY

So under the quantity theory of money, money demand is a function of income and does not depend on interest rates.

Is Velocity Constant?
A constant V is key to the quantity theory of money. For Fisher, the assumption was a leap of faith since data on GDP and the money supply did not exist in 1911. However, looking at that data in Figure 1, page 542, we see very clearly that velocity is not constant, even in the short run. In particular, velocity drops significantly during recessions.

With the problems of the Great Depression, economists began to look for factors other than income that influence money demand.

II.  Keynes Liquidity Preference Theory

In 1936, economist John M. Keynes wrote a very famous and influential book, The General Theory of Employment, Interest Rates, and Money. In this book he developed his theory of money demand, known at the liquidity preference theory. His ideas formed the basis for the liquidity preference framework discussed in chapter 5.

Keynes believed there were 3 motives to holding money:

Keynes also modeled money demand as the demand for the REAL quantity of money (real balances) or M/P. In other words, if prices double, you must hold twice the amount of M to buy the same amount of stuff, but your real balances stay the same. So people chose a certain amount of real balances based on the interest rate, and income:

M/P = f(i, Y)

The importance of interest rates in the Keynesian approach is the big difference between Keynes and Fisher. With this difference also comes different implications about the behavior of velocity. Consider the two equations:

M/P = f (i, Y)

so M = PY/V in the first equation. Substituting in the second equation:

Y/V = f(i, Y) or V = Y/(f(i,Y)).

This means that under Keynes' theory, velocity fluctuates with the interest rate. Since interest rates fluctuate quite a bit, then velocity must too. In fact, velocity and interest rates will move in the same direction. Both are procyclical, rising with expansions and falling during recessions.

Further Developments to the Keynesian Approach
After World War II, Keynes economic theories became very influential and other economists further refined his motives for holding money. One of these economists, James Tobin, later won a Nobel Prize for his contributions.

Tobin (and another economist Baumol) both developed theories and how the transactions demand for money is also related to the interest rate. As interest rates rise, the opportunity cost of holding cash for transactions will also rise, so the transactions part of money demand is also negatively related to the interest rate. Similarly, people will hold fewer precautionary balances when interest rates are high.

One problem with Keynes' speculative demand is that his theory predicted that people would hold wealth as either money or bonds, but not both at once. That is not realistic. Tobin avoided this problem by observing that the return to money is much less risky than the return to bonds, so that people will still hold some money as a store of wealth even when interest rates are high. This diversification is attractive because is reduces risk.

Still one problem with money demand remains. There are other low risk interest bearing assets: money market mutual funds, U.S. Treasury Bills, and others. So why would anyone hold money (M1) as a store of wealth? Economist today still try to develop models of investor behavior to solve this "rate of return dominance" puzzle.

III.  Friedman's Modern Quantity Theory of Money

Milton Friedman (another Nobel Prize winner) developed a model for money demand based on the general theory of asset demand. Money demand, like the demand for any other asset, should be a function of wealth and the returns of other assets relative to money. His money demand function is as follows:

where Yp = permanent income (the expected long-run average of current and future income)
rb = the expected return on bonds
rm = the expected return on money
re = the expected return on stocks
pi(e) = the expected inflation rate (the expected return on goods, since inflation is the increase in the price (value) of goods)

Money demand is positively related to permanent income. However, permanent income, since it is a long-run average, is more stable than current income, so this will not be the source of a lot of fluctuation in money demand

The other terms in Friedman's money demand function are the expected returns on bonds, stocks and goods RELATIVE the expected return on money. These items are negatively related to money demand: the higher the returns of bonds, equity and goods relative the return on money, the lower the quantity of money demanded. Friedman did not assume the return on money to be zero. The return on money depended on the services provided on bank deposits (check cashing, bill paying, etc) and the interest on some checkable deposits.

Friedman vs. Keynes

When comparing the money demand frameworks of Friedman and Keynes, several differences arise

Friedman's money demand function is much more stable than Keynes'. Why? Consider the terms in Friedman's money demand function:

If the terms affecting money demand are stable, then money demand itself will be stable. Also, velocity will be fairly predictable.

IV.  Empirical Evidence on Money Demand

So who is right? Well, the chief differences between Keynes and Friedman lie in the sensitivity of money demand to interest rates and the stability of the money demand function over time. Looking at the data on these two features will yield some answers about the best theory of money demand.

Tobin did some of the earliest research on the relationship between interest rates and money demand and concluded that money demand IS sensitive to interest rates. Later research in the 1950s and 1960s backed up his findings. Furthermore, the sensitivity did not change over time. Many researchers looked at this question and their findings are remarkably consistent (which in economics is somewhat miraculous :)).

Now for the stability of the money demand function. Up until the mid-1970s, researchers found the money demand function to be remarkably stable. In other words, money demand functions estimated in the 1930s, worked just as well predicting money demand in the 1950s or 1960s. The relationship between money demand, income and interest rates did not change over time.

However, starting in 1974, the stability of the money demand function (M1) began to breakdown. Existing money demand functions were overpredicting money demand (i.e. actual money demand was lower than what old money demand functions were predicting). This case of the "missing money" was a problem for policy makers that relied on these functions to predict the effects of monetary policy. What caused this breakdown? It is likely that financial innovations in the 1970s (money market accounts, NOW accounts, electronic funds transfers) changed the working definitions of money even though our official definitions did not change. This problem grew worse in the 1980s.

With the problems in the M1 money demand functions, policy makers turned to M2 money demand. However, the stability of M2 money demand functions also broke down in the 1990s. This cause the Federal Reserve to stop setting targets for M2 in 1992 after abandoning M1 targets in 1987.

FYI: Related Links

Milton Friedman Read more about the 1976 Nobel Prize winner and one of the most influential living economists

John M. Keynes A web page by economist Brad DeLong on John M. Keynes, definitely one of the 100 most influential thinkers of the 20th century (or so says Time Magazine)