2 2 The IS LM Model

Aggregate Demand

The IS-LM Model

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

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

 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

 

YD I G

C PE

PE Y

  

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

 Example: A baker needs to buy a new oven that costs €1000 and yields

€100 worth of bread per week

1. Baker needs to borrow: it will invest only if r ≤ 10% (cost of borrowing)

2. Baker has sufficient funds: it will invest only if r ≤ 10% (cost of using internal funds)

 

 '

 

0



 I r

r I r

I

The Investment

Function: Graphically

Remarks:

• 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)

r

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

• 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

The IS Curve: Graphically

If r ↓

• I ↑

• Autonomous PE ↑

• Y ↑ (the increase in output takes place through various rounds because of the multiplier effect acting through

consumption)

Y Y

Y₂

Y₁ Y

PE

r

Y r₁

The IS Curve and the Loanable Funds

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

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

• 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

 

r Y L

P M

P M

P

MS D

,

 

The LM Curve: Derivation with Linear Functions

 Linear form for the money demand function:

 Under this functional form, the LM schedule is

 

r,Y  kY hr k,h 0

L _with

h P M Y

h k r

P M

P

MS D

 

LM Curve: Graphically

M/P

r

r₁ r₂

r

Y

Y₁ r₁

r₂

Y₂

(a) The market for

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

The IS-LM Model: A Formal Definition

 The model

• 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

The IS-LM Model: Graphically

Y

r

P M 

k/h

Y*

 

₁c b

b PE

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

Fiscal Policy Shock

 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

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:

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

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)

Example (Other IS Shocks): Solution

 The IS curve shifts to the left

• C falls because of lower wealth and lower income

• I rises because of lower interest rate

• (Leftward) Movement along the LM  Less money is held for transactions  More money is held for liquidity motives  The two effects counterbalance (money

supply is held constant)

 Both r _and Y _fall

IS

Y

r

LM

Monetary Policy Shock

 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

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:

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

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)

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

• (Leftward) Movement along the IS  C falls because of lower income  I falls because of higher interest rate  The combined fall in C and I equate the

fall in Y

 Y _{falls while} r _rises

IS

Y

r

LM

r₁

Y₁ Y₂

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

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

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

• 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

…

• MS _{because the Fed,} aiming at keeping r

constant, moves MS _in line with L(Y,r)

Example of Policy Interdependence (c)

No Recession

…

• 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

Example: The 2001 US Recession (Interest Rates)

0 1 2 3 4 5 6 7

P

er

ce

nt

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)

Zero-Lower-Bound (ZLB)

 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

r

LM

-E

Zero-Lower-Bound (ZLB) & Policy

 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)

 Which policy response?

• Monetary policy is ineffective

• Fiscal policy is fully effective (no crowding out)

Y

r

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}

IS Curve: Formal Derivation

-

Steps

1. 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

• The intercept (affecting the position of the curve)

LM Curve: Formal Derivation

-

Steps

1. 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

• The intercept (affecting the position of the curve)

IS-LM Model: Formal Derivation

-

Steps

1. 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