2 2 The IS LM Model

Aggregate Demand
The IS-LM Model
Macro Theory and Policy 2013-14

Tommaso Trani

1

(2) Demand Side: IS-LM

Outline


IS-LM model
• Investment and goods market
• Construction of IS curve
• Construction of LM curve



• Equilibrium

Policy in the IS-LM model
• Fiscal and monetary policy shocks
• Policy mix
• Liquidity trap/Zero-Lower-Bound

2

(2) Demand Side: IS-LM

The Goods Market and Investment Spending


We already know that, in the short run, the demand for goods and services
is driven by planned expenditures

Y  PE

PE  C YD  I  G




However, this is based on a simplified characterization of investment
Firms and households need to ask for loans or use their own savings to
invest, so it is reasonable to think that they will invest more when they find
it less costly for them

3

(2) Demand Side: IS-LM

The Investment Function


Thus, investment is inversely related to the interest rate, considered as a
measure of the opportunity cost for the use of funds

I  I r 



I
with  I' r   0
r

Example: A baker needs to buy a new oven that costs €1000 and yields
€100 worth of bread per week
Baker needs to borrow: it will invest only if r ≤ 10% (cost of borrowing)
Baker has sufficient funds: it will invest only if r ≤ 10% (cost of using internal funds)

1.
2.

4

(2) Demand Side: IS-LM

The Investment
Function: Graphically

Remarks:

r

I

5

(2) Demand Side: IS-LM

•

Economic theory directly
assumes that the relevant
driver of investments is
the real interest rate,
regardless of whether
prices are fixed or flexible

•

As in other cases, we are
making the simplifying
assumption that only one
interest rate matter
(neglecting aspects such
as maturity, credit risk and
taxation)

The IS Curve


Definition: the IS curve is given by all of the combinations (Y,r) for which
the market for goods and services is in equilibrium
Y  C YD  I r   G

• Since I is inversely related to r, there is an inverse relationship between Y and r

 To increase GDP by 1%, the rate of interest should fall as much as needed to induce firms to

invest in line with the percentage increase in investment; and viceversa



If we assume a linear functional form not only for consumption, but also for
investment, the IS schedule is
1
b
I  I r   I  br Y 
C  G  I  cT 
r
1 
1 c
c 

 





driven by PE

6

(2) Demand Side: IS-LM

driven by
cost of funds

The IS Curve: Graphically
If r ↓

PE

• I↑
• Autonomous PE ↑
• Y ↑ (the increase in output takes place

through various rounds because of the

multiplier effect acting through
consumption)

r

Y1

Y

Y2

r1

IS

r2

Y1
7

(2) Demand Side: IS-LM

Y2

Y

The IS Curve and the Loanable Funds
 G  I r 
Y  C  I  G Y
C 
YD


PE

S

The higher demand for investment can be
satisfied by an increase in savings because
people tend to save more when GDP is higher

r

S1

r

S2

r1

r1

r2

r2

8

I(r)

S, I

Y1

Y

Y2

IS
Y1

(2) Demand Side: IS-LM

Y2

Y

The LM Curve


Money demand is driven by transaction and liquidity motives, so – taking
the supply of money by the CB as given – the money market equilibrium is

MS MD M

  Lr ,Y 
P
P
P

• Since the real money supply is a constant, the relationship between Y and r is positive
 An increase in GDP spurs the demand for money, so r needs to increase to bring the market

back to equilibrium
 Note: substitution between money held for liquidity and money held for transactions



Definition: The LM curve is given by all of the combinations (Y,r) for which
the money market is in equilibrium
9

(2) Demand Side: IS-LM

The LM Curve: Derivation with Linear Functions


Linear form for the money demand function:



Under this functional form, the LM schedule is

Lr ,Y   kY  hr

with k , h  0

MS MD

P
P
M P
k
r Y
h
h

10

(2) Demand Side: IS-LM

LM Curve: Graphically
(a) The market for

(b) The LM curve

real money balances

r

r

r2

r2

r1

r1
M/P

11

Y1
(2) Demand Side: IS-LM

Y2

Y

The IS-LM Model


The IS-LM model describes the conditions for the simultaneous equilibrium
in the goods market and in the money market
• The macroeconomic equilibrium is a unique combination of production and interest rate

for which both markets are in equilibrium


The model is suitable to study
• How (exogenous) policy measures affect the economy
• How policy-unrelated shocks affect the economy and how policymakers can respond
 Policy-unrelated IS shocks



Changes in consumer confidence
Changes in investors’ sentiments (animal spirits; optimism, pessimism)

 Policy-unrelated LM shock
 Any types of exogenous changes in money demand (e.g., new regulation on the use of credit cards)

12

(2) Demand Side: IS-LM

The IS-LM Model: A Formal Definition


Y  C YD  I r   G

The model
IS :
LM :

M
 Lr ,Y 
P

• IS: inverse relationship between Y and r; LM: positive relationship between Y and r
• 2 equations and 2 endogenous variables, Y and r: unique solution (Y*,r*)







With linear consumption, investment and money demand, the solution is

M
k
1c
 
C  I  G  cT 
r* 
h1  c   kb
h1  c   kb  P 


M
h
b
Y * 
 
C  I  G  cT 
P





h
1

c

kb
h
1

c

kb
 




13



(2) Demand Side: IS-LM

The IS-LM Model: Graphically
r
PE
b

r*

1  c  b

k/h

Y

Y*

14

M P
h
(2) Demand Side: IS-LM

The IS-LM Model: Interpretation


Equilibrium
• There are two key determinants: the autonomous components of the demand for goods

and services and the real money supply
• The effect of these two determinants on GDP and interest rate depend on the
parameters of consumption, investment and money demand functions


GDP
• Positive function of both determinants



Interest rate
• Increases with the autonomous demand for goods but decreases with money supply

• In equilibrium, it is affected by the IS multiplier (of fiscal policy shocks)

15

(2) Demand Side: IS-LM

Fiscal Policy Shock


r
LM
C

r2
r1

B
A

Y1 Y2 YIS

16

Y

Expansionary fiscal policy (G ↑)
has a smaller effect in the
macroeconomic equilibrium than in
the goods market alone
1. A-B: the initial tendency for GDP
is to increase by 1/(1 – c) times
the increase in G
2. B-C: the upward pressure on the
demand for money requires an
increase in r and a partial
contraction in Y

(2) Demand Side: IS-LM

Fiscal Policy Shock: “Crowding Out”


The difference between macroeconomic and partial equilibrium is the
double interaction between goods and money markets
• As soon as r falls, the money market has a second-round effect on planned

expenditures: investment falls (crowding out effect of public expenditures)




Formally:

Y *
h

G h1  c   bk

h
1
1


with
k
h1  c   bk 1  c  b
1
c

h partial
equilibrium

A fiscal stimulus originating from a cut in taxes has similar crowding out
consequences, but the effect on expenditures is indirect

17

(2) Demand Side: IS-LM

Example (Other IS Shocks)




Using the IS-LM model, analyze the effects of a housing market crash that
reduces consumers’ confidence
Indicate
• What happens to consumption and investment
• How the economy adjusts to the new equilibrium (curve shifts / movements along the

curve)
• What are the effects on GDP and rate of interest

18

(2) Demand Side: IS-LM

Example (Other IS Shocks): Solution


The IS curve shifts to the left
• C falls because of lower wealth and

r

lower income
• I rises because of lower interest rate
• (Leftward) Movement along the LM

LM

 Less money is held for transactions

 More money is held for liquidity motives

 The two effects counterbalance (money

r2

supply is held constant)

IS
Y2

19

Y



Both r and Y fall

(2) Demand Side: IS-LM

Monetary Policy Shock


r

A

r1
r2

C
B

IS

Y1 Y2

20

Y

Expansionary monetary policy (M
↑) has a smaller effect in the
macroeconomic equilibrium than in
the money market equilibrium
alone
1. A-B: initially r falls by 1/h times
the increase in M in order to
encourage the money demand
2. B-C: GDP should now expand
because the fall in r has
encouraged investment as well
 r increases a little bit
(2) Demand Side: IS-LM

Monetary Policy Shock: Policy Transmission


We have again a double interaction between money market and goods
market
• The increase in GDP has a second round effect on the demand for money, which calls

for a higher rate of interest




Formally:

r *
1c

M / P h1  c   kb

1c
1
1


with
h1  c   kb h  kb
h

1  c partial
equilibrium

Monetary policy gets transmitted to (real variables in) the goods market,
as investment reacts to the change in money supply

21

(2) Demand Side: IS-LM

Example (Other LM Shocks)




Using the IS-LM model, analyze the effects of a more frequent use of cash
in transactions in response to an increase in identity thefts on online credit
card transactions
Indicate
• What happens to consumption and investment
• How the economy adjusts to the new equilibrium (curve shifts / movements along the

curve)
• What are the effects on GDP and rate of interest

22

(2) Demand Side: IS-LM

Example (Other LM Shocks): Solution


The LM curve shifts to the left
• Less money is held for transactions
• Less money is held for liquidity motives

r

• (Leftward) Movement along the IS

LM

 C falls because of lower income

 I falls because of higher interest rate

r2
r1

 The combined fall in C and I equate the

fall in Y



IS
Y2 Y1
23

Y falls while r rises

Y

(2) Demand Side: IS-LM

Policy Interdependence






Fiscal and monetary policy mix are important combinations of policy
measures that authorities put in place to deal with a given historical
situation
Depending on the economic conditions, fiscal and monetary authorities
may need to move in the same direction or in opposite directions
US 1979-1981
• In 1979 the Fed opts for a contractionary monetary policy to combat the inflation created

by the oil shocks of previous years
• In 1981 the Congress expand its defense spending and cuts taxes to restart the
economy (the recession had been hightened)
24

(2) Demand Side: IS-LM

Policy Interdependence: Further History


US 1990s
• Clinton adopted a fiscal consolidation, cutting expenditures and increasing taxes, in

order to slim down the federal budget deficit
• The fiscal contraction was accompanied by a monetary expansion to avoid a recession


US 2000-2001: see later



US and EU 2007-2010
• Fiscal authorities of the western world expanded their stances to avoid a too large fall in

the aggregate demand
• Fed, ECB and Bank of England adopted expansionary policies too, as they fought
against a systemic bankruptcy of their financial sector

25

(2) Demand Side: IS-LM

Example of Policy
Interdependence (a)
Recession

T leads to Y because of a
fall in disposable income for
consumption
Tendency for L(Y,r) to fall
because of lower number of
transactions
•

•

Source: Mankiw “Macroeconomics” (Eighth Edition), Figure 12.4a

26

(2) Demand Side: IS-LM

r because money supply
has been kept constant
and thus money market
equilibrium should be
preserved
I, which attenuates ∆T

Example of Policy
Interdependence (b)
Deeper Recession
…
•

Source: Mankiw “Macroeconomics” (Eighth Edition), Figure 12.4b

27

(2) Demand Side: IS-LM

MS because the Fed,
aiming at keeping r
constant, moves MS in
line with L(Y,r)

Example of Policy
Interdependence (c)
No Recession
…
•

•

Source: Mankiw “Macroeconomics” (Eighth Edition), Figure 12.4c

28

(2) Demand Side: IS-LM

MS because the Fed
wants to avoid a
recession
r to a great extent to
keep L(Y,r) constant

•

I is stimulated so much
that it compensates ∆T

•

Yet, the composition of
PE has been totally
modified: C has been
exactly replaced by I

Example: The 2001 US Recession


In 2001, the following shocks reduced consumers and investors’ spending:
• Stock market crashed in August 2000
• NY and DC went through a terrorist attack in September 2001
• The Dot-Com bubble bursted in 2001



Policy Responses
• US Congress

 Tax cuts in 2001 and 2003

 Government support to NY (“Ground Zero”) and the airline companies

• US Fed

 the 3-month T-bill rate falls from 6.4% (November 2000) to 3.3% (August 2001) to 0.9% (after

September 2001)

29

(2) Demand Side: IS-LM

Example: The 2001 US Recession (Interest Rates)
7
6

Percent

5
4
3
2
1
0

Fed Funds Rate

3-month T-bill Rate

Source: FRED, Fed of St. Louis; monthly frequency, NSA

30

(2) Demand Side: IS-LM

Monetary Policy in “Normal” Times


Since the 1950s, monetary policy has increasingly been about inflation
targeting, with the CB intervening on the nominal interest rate



Note: the CB can affect both the supply of money and the rate of interest



Yet: money supply is not fully under central bankers’ control
• Exogenous money demand shocks are more frequent than exogenous IS shocks
• In fact, money = cash + demand deposits: CB controls the amount of cash (monetary

base), but this is usually multiplied by financial intermediation (lending deposits)
 Policy committee achieves

whatever interest rate target with the required

open market operations
31

(2) Demand Side: IS-LM

Zero-Lower-Bound (ZLB)


r

LM

An economy falls in a “liquidity
trap” when GDP and interest rates
are both very low:
• 2007-2009 Crisis (credit crunch and

monetary easing)

 Fed Funds rate fell from 5.25%

(September 2007) to almost 0%
(December 2008)
• Formally: i = 0 (zero-lower-bound)

Y

-E

IS
32

(2) Demand Side: IS-LM

Zero-Lower-Bound (ZLB) & Policy


r

An economy falls in a “liquidity
trap” when GDP and interest rates
are both very low:
• 2007-2009 Crisis (credit crunch and

monetary easing)

 Fed Funds rate fell from 5.25%

(September 2007) to almost 0%
(December 2008)
• Formally: i = 0 (zero-lower-bound)

Y

-E



Which policy response?
• Monetary policy is ineffective
• Fiscal policy is fully effective (no

crowding out)
33

(2) Demand Side: IS-LM

Monetary Policy @ the Zero-Lower-Bound (ZLB)


One possibility is to convince private agents that inflation will rise in the
future because of higher money supply
• The real interest rate falls spurring investment



An alternative is that the CB buys various types of securities, included
mortgage debt and corporate bonds to “clean up” the balance sheets of
banks (quantitative easing)
• The effect this time is on long-term interest rate




Currently, CBs are promising to keep i = 0 until economic growth picks up
and unemployment falls (forward guidance)
Another important case of liquidity trap: The Great Depression in the 1930s
34

(2) Demand Side: IS-LM

How to Derive the IS, LM, IS-LM?

35

(2) Demand Side: IS-LM

IS Curve: Formal Derivation - Steps
Impose the equilibrium Y = PE
2. Use the behavioural equations
3. If consumption and investment are linear, express Y as a function of r
4. Figure out what determines
1.

•

The intercept (affecting the position of the curve)
The slope (affecting the steepness of the curve)

•

36

(2) Demand Side: IS-LM

LM Curve: Formal Derivation - Steps
Impose the equilibrium MS /P= MD/P
2. Use the behavioural equations
3. If money demand is linear, express r as a function of Y
4. Figure out what determines
1.

•

The intercept (affecting the position of the curve)
The slope (affecting the steepness of the curve)

•

37

(2) Demand Side: IS-LM

IS-LM Model: Formal Derivation - Steps
Impose the IS and the LM equilibrium conditions
2. Use the behavioural equations in both equilibrium conditions
3. Write down the system formed by the IS and the LM
4. Solve this system by substitution, finding the common (Y,r)
1.

38

(2) Demand Side: IS-LM