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320.326: Monetary Economics and the

European Union

Lecture 2

Instructor: Prof Robert Hill

Keynes’s Theory of Liquidity Preference,

Hicks and ISLM

Mishkin – Chapters 19-21

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1. Keynes’s Liquidity Preference Theory

Keynes (1936) abandoned the classical view that velocity is

constant and developed a theory that emphasizes the importance

of interest rates. He postulated that there are three reasons for

holding money.

(i) Transactions motive

People hold money since it is a medium of exchange that can be

used to make transactions. Keynes, like the classicals, assumed

the transactions demand is proportional to income.

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(ii) Precautionary motive

People hold money as a cushion against unexpected need (e.g. a

sale or car repair). He assumed that the precautionary demand is

also proportional to income.

(iii) Speculative motive

People hold money as a store of wealth. To simplify matters, he

assumes there are only two types of wealth (assets), money and

bonds, and that money does not pay any interest.

People want to hold whichever asset has the higher expected

return.

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Expected return on an asset = interest + expected capital gain

The expected return on money is zero.

Bonds pay interest. Hence the expected return on money can only

exceed that on bonds when people expect a capital loss on bonds

(i.e., they expect the price of bonds to fall).

The price (PB) of a zero-coupon bond with face value F that

matures next period is related to the interest rate (i) as follows:

i = (F – PB)/PB = F/PB – 1.

Hence, bond prices are expected to fall when the interest rate is

expected to rise.

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Like the classicals, Keynes believed that the interest rate

gravitates to some normal value. If the interest rate is below this

level, people expect it to rise (and hence bond prices to fall).

In this situation, people are more likely to hold their wealth in the

form of money rather than bonds.

When the interest rate is above its normal level, people expect

bond prices to rise and hence are more likely to hold bonds.

It follows that the speculative demand for money is negatively

related to the level of the interest rate.

Keynes also believed that for a given interest rate, the speculative

demand increases with income.

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Combining the three motives, we obtain the following money

demand equation:

Md/P = f(i,Y)

(-)(+)

where Md denotes nominal money demand, P the price level and

Md/P real money demand.

The equation states that real money demand is an increasing

function of income and a decreasing function of the interest rate.

See Blanchard (2006), Figure 4.1.

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(iv) Equilibrium in the money market

In equilibrium, money supply (Ms) = money demand (Md) = M

Let’s suppose that f(i,Y) = Y × f(i)

Then in equilibrium: M/P = Y × f(i), or M = PY × f(i)

See Blanchard (2006), Figure 4.2

The interest rate adjusts to equate the supply and demand for

money.

The impact of changes in nominal income (PY) and the money

supply (M) on the interest rate (i) are shown in Blanchard (2006),

Figures 4.3 and 4.4 (note Y in Blanchard denotes nominal income

rather than real income as it does here).

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How well does the demand for money equation Md/P = f(i,Y)

hold up empirically?

(a) It implies velocity rises as the interest rate rises.

V = PY/M = Y/f(i,Y) - assuming Ms = Md = M

If we again assume that M/P = Y × f(i), then it follows that

V = 1/f(i).

This is consistent with the empirical finding that velocity

increases in booms and falls in recessions, since interest rates are

procyclical.

(b) Changes in V due to other causes can confuse the empirical

relationship between V and i. See Figure 1 in Blanchard (2006).

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Figure 1 in Blanchard compares changes in (Md/P)/Y and i over time.

Given that (Md/P)/Y = 1/V, it follows that (Md/P)/Y should rise when i

falls, and vice versa.

In Blanchard’s Figure 1, (Md/P)/Y fell dramatically from 1960

to 1980 as i rose. But when i fell significantly between 1980 and

1994, there was only a slight increase in (Md/P)/Y.

The weakish correspondence between 1/V=(Md/P)/Y and i in Figure 1

after 1980 can be attributed at least partly to the widespread adoption

of credit cards. This has caused a big increase in V and a

corresponding fall in (Md/P)/Y.

In other words, although V rises in booms and falls in recessions, there

are other events that can also change V (e.g., technological innovations

in financial markets).

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2. The Baumol/Tobin Model of Transactions Demand

A problem with Keynes’s speculative demand theory is that it implies

that, for speculative purposes, people will hold either bonds or money

but not both (except in the special case where the expected return on

bonds is zero). In practice, people are risk averse, and hence tend to

spread their wealth across different asset classes.

Baumol (1952) and Tobin (1956) showed anyway that we do not need

speculative demand to generate Keynes’s money demand equation.

Transactions demand will also be sensitive to changes in the interest

rate.

Suppose you sell $1000 of bonds each month to spend on transactions

and that these transactions occur at a constant rate during the month. It

follows that your average transactions money holding per month is

$500.

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You incur an opportunity cost on this money holding in terms of

forgone interest.

Suppose now instead you sell $500 of bonds twice per month to

spend on transactions. Now your average transactions money

holding is $250.

If the interest rate is 1 percent per month, you earn an additional

0.01 × $250 = $2.5 of interest by selling bonds twice a month

rather than just once a month to pay for transactions.

See Mishkin (2006), Chapter 19 - Figure 2.

The act of selling bonds incurs a transaction cost, which must be

traded off against the forgone interest. For any given interest

rate there will be an optimal frequency to sell bonds to provide

money for transactions.

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As the interest rate rises, the optimal frequency for converting

bonds to money will rise, thus reducing the transactions demand

for money.

Implication: the transactions demand for money (like the

speculative demand) is a decreasing function of the interest rate.

Mathematically, the Baumol-Tobin model proceeds as follows:

Suppose you want to spend an amount W on transactions in a

month. During this month, you earn interest i on bond holdings,

but zero interest on money holdings. Also, let c denote the cost of

selling bonds (we assume c is independent of the dollar value

sold).

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The foregone interest of your money holding = i W/(2N),

where N denotes the number of times in the month you sell

bonds, and W/(2N) is your average money holding during the

month.

The transaction costs of selling bonds = cN

In equilibrium: iW/(2N) = cN.

Hence: N = [iW/(2c)]1/2

The optimal average money holding = W/(2N) = [cW/(2i)]1/2

A rise in i causes the optimal average money holding to fall.

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Similar arguments apply to the precautionary motive for holding

money. The gains of holding precautionary money need to be

weighed against the opportunity cost of the forgone interest.

Hence precautionary money holdings should also decrease as

the interest rate rises.

These findings reinforce Keynes’s argument that the demand for

money responds to changes in the interest rate (as well as income).

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3. The ISLM Model

The ISLM model was developed by Hicks (1937).

Hicks’s key insight is that the equilibrium interest rate i in the

money market depends on real output Y, and that equilibrium

real output Y in the goods market depends on the interest rate i.

The IS curve models equilibrium in the goods market:Y=f(i).

The LM curve models equilibrium in the money market: i=f(Y).

To have an overall equilibrium both the goods and money market

must be simultaneously in equilibrium. Such an equilibrium exists

at the point of intersection of the IS and LM curves.

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Derivation of the IS curve in Y-i space

The goods market is in equilibrium when Y = AD.

AD = C + I(i) + G + NX

An increase in i reduces I and hence AD. When AD falls, firms

sell less output. They respond by cutting production. This in

turn reduces the level of Y. Hence the IS curve in Y-i space is

downward sloping.

See Mishkin (2006), Chapter 20 - Figure 7.

The IS curve shifts when AD and Y change due to something

other than a change in i.

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y

Y

AD = Y AD

AD0 [i =15%]

AD1 [i =10%]

AD2 [i = 5%]

i

Y0 Y1 Y2

5%

15%

10%

I-S

Excess demand

for goods

Excess supply

of goods

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For example, an increase in G, a fall in T, or an appreciation of the

home currency (which increases net exports NX) all shift the IS

curve to the right.

See Mishkin (2006), Chapter 21 – Figure 1

Derivation of the LM curve in Y-i space

Hicks derived the LM curve from the Keynesian premise that

Md/P = f(i,Y)

The demand for money curve in M/P-i space is downward

sloping. An increase in Y shifts the money demand curve to the

right.

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By plotting combinations of Y and i in Y-i space we obtain the

LM curve, which represents equilibrium points in the money

market.

See Mishkin (2006), Chapter 20 - Figure 8.

Combining the IS and LM curves we obtain the equilibrium

interest rate i and equilibrium output Y.

See Mishkin (2006), Chapter 20 - Figure 9.

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4. Monetary and Fiscal Policy in the ISLM Model

(i) The impact of a change in fiscal policy

(e.g., G or T) on the interest rate and output

An expansionary fiscal policy shifts the IS curve to the

right. This increases the interest rate i and output Y.

See Mishkin (2006), Chapter 21 – Figures 1 and 5.

(ii) The impact of changes in the money supply on the

interest rate and output

An expansionary monetary policy shifts the LM curve to the

right. This reduces the interest rate i and increases output Y.

See Mishkin (2006), Chapter 21 - Figures 2 and 4

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(iii) Special cases

(a) The demand for money is interest inelastic

This is the case assumed by the classical quantity theory of

money, i.e., Md/P = f(Y)

The Md/P curve is vertical. It follows that the LM

curve is also vertical, since there will be only one level of real

income Y at which the money market is in equilibrium (i.e.,

Md = Ms).

Fiscal policy in ineffective.

Monetary policy is effective.

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The Md curve shifts to the right as Y rises. There will be one

specific level of Y at which the Md and Ms curves coincide,

which pins down the location of the LM curve.

Changes in the interest rate have no impact on either Md or Ms,

and hence the LM curve is vertical.

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Fiscal policy is ineffective Monetary policy is effective

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(b) The liquidity trap

In this case, the Md and LM curves are horizontal. This can

happen if everyone expects the interest rate to rise. In the

context of Keynes’s speculative demand for money, when the

money supply rises no-one switches any of their wealth to

bonds, so interest rates do not change.

When the nominal interest rate falls to zero, the economy is

also effectively in a liquidity trap.

Now monetary policy is ineffective, while fiscal policy is

effective.

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An increase in Y shifts the Md curve to the right. However,

since it is already horizontal, the Md stays where it is. Hence

a change in Y does not affect i, and the LM curve is horizontal.

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Fiscal policy is effective Monetary policy is ineffective

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Fiscal policy is effective Monetary policy is ineffective

An alternative version of the liquidity trap arises when the

nominal interest rate falls to zero.

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(c) Investment is interest inelastic

If investment does not respond to changes in the interest

rate, then the IS curve is vertical.

Again monetary policy is ineffective, while fiscal policy is

effective.

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Fiscal policy is effective Monetary policy is ineffective

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(iv) Money supply versus interest rate targets:

When the IS curve is unstable, a money supply target will tend to

produce smaller fluctuations in output.

See Mishkin (2006), Chapter 21 – Figure 7

When the LM curve is unstable, an interest rate target will tend to

produce smaller fluctuations in output.

See Mishkin (2006), Chapter 21 – Figure 8

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(v) The ISLM model in the long run

In the long run, if output is above (below) its natural level Yn, the

price level rises (falls). The LM curve adjusts so that it intersects

the IS curve at Yn.

Hence an expansionary monetary policy will only raise output in

the short run. In the long run monetary policy is neutral.

See Mishkin (2006), Chapter 21 – Figure 9(a).

An expansionary fiscal policy likewise will only increase output

in the short run.

See Mishkin (2006), Chapter 21 – Figure 9(b).

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