The Demand for Money

Theories and Evidence

The Demand for Money• So far we have considered the money supply

and how a central bank goes about changing it.

• Where does money demand come from?

• Understanding the demand for money will allow us to examine the links between monetary policy, inflation, and unemployment.

• The quantity of money circulating around the economy and the interest rate at which it circulates are determined by both money supply and money demand.

The Quantity Theory of Money

• How much money would you need to purchase the economy’s annual output of goods and services?– Suppose GDP (P*Y) was $14 trillion. – Would you need a money supply of $14 trillion to buy all this

output over the course of a year?– No! Each dollar is used multiple times. You would need

considerably less M than P*Y.

• Velocity is defined as the number of times a dollar bill changes hands over the course of a year in an economy.– It tells us the turnover rate for money in the economy.

• Equation of Exchange: M*V ≡ P*Y– The total money supply multiplied by the number of times this

money changes hands must be equal to nominal income (or nominal GDP)

– Total expenditure (M*V) = Total production (P*Y)– Everything produced is consumed

The Quantity Theory of Money

• When the money market is in equilibrium, Md = Ms = M.

• The quantity theory of money can be re-written as:– Md = (1/V)*PY– Md = k*PY (k = 1/V = constant if V is a constant)

• The demand for money is solely a function of nominal GDP

• Money demand is not directly affected by interest rates.

Is Velocity Constant?

The Liquidity Preference Theory of Money

• As seen, velocity cannot be accurately treated as a constant.– If velocity can change, then the link between prices and money

is muddled.

• J.M. Keynes postulated that individuals hold money for three reasons:– Transactions Motive You need money to buy things– Precautionary Motive You might need money on hand for an

unexpected purchase– Speculative Motive You hold your wealth as money (as

opposed to bonds) to store value

• The biggest innovation was to identify a link between money and interest rates (an inverse relationship.)

The Liquidity Preference Function

• What people really care about is the purchasing power of their money– If prices rise, then the real value of money falls. – Want to look at the demand for real money balances

• Md/P = f(i,Y)– Real money demand is a decreasing function of nominal interest

rates– Real money demand is an increasing function of real income.

• Recall that M*V ≡ P*Y– V = P*Y/M– P/Md = 1/f(i,Y)– V = Y/f(i,Y) when the market for money is in equilibrium.

– As i↑, f(i,Y)↓, and V↑ Velocity is not constant!

The Transactions Motive for Holding Money• Suppose you earn $3000 per month and consume $100 per day.

– We’ll assume 30 day months and a constant rate of consumption over this period.

• Case 1: You hold the entire $3000 in cash to carry out your transactions.– You have $3000 at the beginning of the month and $0 at the end.– Your average cash balance is $1500.– Your annual income (P*Y) $36,000 and your holdings of money (M)

average $1500.– V = PY/M = 36,000/1500 = 24

• Case 2: You hold $1500 in cash and buy $1500 in bonds at the beginning of each month– After 15 days, you sell your bonds and use the principal ($1500) to

make your purchases, keeping any earned interest for yourself.– Your average cash balance is now $750 (1500 at day 1, 0 at day 15,

1500 at day 16, 0 at day 30: (1500+0+1500+0)/4 = 750.– V = PY/M = 36,000/750 = 48– If i = 1% per month, you also earned (i/2)*1500 = .005*1500 = $7.50

Two Cases

Time

Cash on Hand

Time

Cash on Hand

0 1 2

3000

1500

½

1500

750

0 ½ 1 1.5 2¼

The Transactions Motive for Holding Money• Case 3: Now suppose you hold $500 in cash and buy $2500 in

bonds. – Every 5 days (1/6th month) you run out of cash and have to sell $500

worth of bonds to make your purchases.– Your average cash holdings over the course of the month is M = $250.– V = 36,000/250 = 144– At 1% monthly interest, you earn (1/6*1%*$2500)+(1/6*1%*$2000)+…

+(1/6*1%*500) = $12.50

• As your average cash balance shrinks, both velocity and the interest earned on bonds increases.

• So why not hold the smallest amount of cash possible?• Transactions costs of bonds!

– Brokerage fees– Time costs

• As interest rates rise, people want to hold smaller average cash balances, causing money demand to fall and velocity to rise.

• As transactions costs of bonds rise, people want to hold more money at any given point, causing money demand to rise and velocity to fall.

The Speculative Motive• A weakness of Keynes’ original analysis of the

speculative motive is that it has a knife edge solution– If the return on bonds is higher, then all speculation is in bonds.

If the return on money is higher, then all speculation is in money.– Only when the two assets have identical returns (an uncommon

occurrence) will people hold money and bonds for speculative purposes.

• James Tobin offered a refinement in 1958 by arguing that people care about both expected returns and risk.– Money has a certain nominal return: zero– Bonds have more volatile returns that may in fact be negative.– Through carrying a diversified portfolio of money and bonds, the

overall risk of the portfolio may be minimized relative to expected returns.

• However, it is not clear that money offers any greater diversification benefits than near risk-free bonds such as U.S. treasury bills.– No speculative motive for holding money?

Friedman’s Modern Quantity Theory of Money

• Milton Friedman built upon Keynes’ idea and introduced his own model of the demand for money:

• Real money demand is a function of…– Permanent income (YP), expected average income over the

course of one’s life. (+)– The excess return on bonds over money (-)– The excess return on equities over money (-)– The rate at which money loses purchasing power. Can also be

thought of as the excess return on goods over money. (-)

)()()()(

,,, me

membP

d

rrrrrYfP

M

Conclusions of Friedman’s Refinement

• Includes alternative assets to money

• Views money and goods as substitutes

• While the expected return on money is not a constant, the excess return on bonds (rb – rm) is assumed to be a constant.– Thus, interest rates (because they cause the returns on all

assets to rise by the same proportion) will not affect money demand.

• Therefore, the demand for money is predictable a direct function of permanent income.– Thus, Velocity is predictable and stable!– MV = PY Money is the primary determinant of aggregate

spending.

Empirical Evidence

• Money and Interest Rates– Money demand does appear to be sensitive to interest rates– In the extreme case, money demand is so sensitive to interest

rates that it is a flat curve at the current rate.• Known as a liquidity trap, since monetary policy cannot affect

interest rates in this case.– Very little evidence that money demand hits a liquidity trap at

interest rates above zero.– When nominal interest rates approach zero, we can fall into such

a trap (see Japan).

• The Money Demand function is variable and unpredictable in Keynes’ model, but stable in Friedman’s model– Before 1970, Md was fairly stable.– Since 1970, Md has been much less stable due to the rapid pace

of financial innovation.– Greater instability in Md makes monetary policy harder to control

and less predictable.