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EC201 Intermediate Macroeconomics
EC201 Intermediate Macroeconomics

Lecture 9: Extensions to the IS-LM Model
Lecture Outline:
- shocks and fluctuations in the IS-LM model;
- the credit crunch and the IS-LM model
- the IS-LM model with a Taylor Rule
Essential reading:
Mankiw: Ch
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However, we can use the IS-LM
model to explain why income fluctuates over time
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We have seen that economic policies can
shift the IS and the LM curve up and down
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For example, it is unlikely
that a government wants to create a recession by decreasing government expenditure
or by restricting money supply
...
This means that short-run fluctuations, booms and
recessions, have some random component that makes them not completely
predictable
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Exogenous shocks are economic events that cannot be
completely anticipated by the people
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However, this change is exogenous because it cannot be explained by our ISLM model in the way we have developed it
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Those shocks have the effect to shift the IS and the LM
curve over time and those shifts cause the real income to fluctuate
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The reason is that being in a recession can have
1

This section is adapted from William Poole (1970) “Optimal Choice of Monetary Policy Instruments
in a Simple Stochastic Macro Model” Quarterly Journal of Economics vol
...
2 pp
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important economic costs that we would like to avoid
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For example if the boom lasts for a long period, it means that demand is very
high
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In
particular we will see how monetary policy can be used to stabilise the economic
fluctuations
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Over we do not know with certainty where the IS will end up
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We know that the IS will shift but we do not know where it will end up
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The initial equilibrium is r0, Y0
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We need to control the LM curve
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To keep constant the interest rate we must move the LM
curve to LM1 if the shock moves the IS to ISU
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As we can notice by doing that, the real income in equilibrium can be
YL if the shock moves the IS to ISL, or YU if the shock moves the IS to ISU
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Suppose you do option b)
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Conclusion: when there is a real shock, to stabilise the level of income it is better to
keep constant the money supply while the interest rate is free to change
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In this case
moving the IS curve is still a bad option since we may increase the variability of
income
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If the LM shifts to LMU, we can decrease the money supply to bring
back the system to the original LM
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By doing this, the interest rate will be stabilised and the income
fluctuation will be reduced to zero
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The IS-LM model and the Credit Crunch
In the Autumn 2008 the world economy entered the deepest recession since the Great
Depression
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The “sub-prime” market is a relatively small part of the
mortgage market intended for borrowers with a relatively high probability of not
being able to repay their loan
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Implicitly we have the banks in
the IS-LM since the interest rate is also the price of credit
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Banks are financial intermediaries, they
collect money from savers and lend it to borrowers
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The balance sheet of a commercial bank is given
by:
Assets
Loans
Other assets

Liabilities
Capital
Deposits

The value of the bank’s assets is mostly the value of the loans it has made to
households and firms (although the bank may own other assets, such as the buildings
it uses or financial assets such as bonds
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Leverage: when you buy an asset (financial or real like a house) the leverage is the
ratio between how much you borrow and how much your own capital you put up to
buy the asset
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As the expression below
shows, the smaller the amount of equity for any given value of the asset you buy, the
higher the leverage
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This implies that if there is a loss for the bank (for example some customers decide to
withdraw the money from the bank, like for the case of Northern Rock), then the bank
is in trouble because it may not have enough capital to absorb the loss and it can
become insolvent
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2 %)

In order to introduce the banking sector in the IS-LM model we need to see the
following: when firms want to make investments they will do so by borrowing some
money from commercial banks
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The rate borrowers have to pay, i
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the cost of a loan
from the bank, ρ, is usually equal to the rate savers receive (i) plus a spread, x:
ρ=i+x
Here we use i for the interest rate but you should remember that i = r in the IS-LM
model
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Investment demand therefore depends on the cost of
bank loans (and not simply on the interest rate ) and can be expressed as:
I = I (ρ)

What determines the spread x between the lending rate ( ρ ) and the deposit rate ( i )?
1) The Banks’ capital: K B
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The first reaction of the banks is therefore to reduce their assets,
meaning they stop to lend
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2) The firms’ capital: K F
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Suppose the firm has a level of capital K F
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If the firm fails to repay the
loan then bank can get K F
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Therefore anything that makes the Banks’ capital and/or the Firms’ capital to
decrease will increase the lending rate and therefore it will reduce the Firms’
investments
...
The LM equation is the usual one:
M
= L(Y , i )
P
Now suppose that for any reason, the capital of the banks decreases
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The leverage of the bank increases and so the bank becomes
riskier
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We know
that when the capital of the bank is reduced the spread x increases and so the cost of
borrowing for the firms increases and investment decreases
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Also this effect will increase the spread x and this will reduce investment
even further
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Notice that the
nominal interest rate is reduced after the shift of the IS curve, however this is not very
helpful since for firms is now relevant the lending rate that is the nominal interest rate

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plus the spread x
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This
shows how a change in the level of capital of commercial banks and firms can have
indeed an effect in the equilibrium level of real output
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This is what many governments have done during the crisis by putting
money into the system to nationalise some of the troubled institutions;
2) The central bank can increase money supply and try to shift the LM to the
right
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Graphically we can have the following situation:

The IS shifts to the left because of the decrease in the capital of Banks and firms
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By increasing government expenditure,
the IS can shift to the right, for example to IS’’
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However, as we can see from the graph, we may have the case in
which there is not a positive interest rate consistent with the previous equilibrium of Y
(Y*), and we may be stuck to Y’’ that is much lower
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How long are we going to be
stuck to the low equilibrium? This depends on how effective are the policies used
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A Note on the Monetary Policy instrument
We considered monetary policy as a change in money supply
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In fact, central banks tend to target the overnight interest rate – the
interest rate banks charge one another on overnight loans
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In the US that interest rate is called the federal funds rate
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Until the 1980s most central banks used a
monetary policy known as Monetary Targeting
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In this case the LM curve that is derived for an exogenous money supply
makes sense in describing such a policy
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Inflation targeting is now becoming more popular
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In this case money supply is
endogenous since it depends on the interest rate chosen by the central bank
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Why do central banks set interest rates instead of the money supply?
1)

They are easier to measure than the money supply
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If so, then targeting the interest rate stabilizes income better than targeting the
money supply
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The monetary transmission mechanism explains how monetary policy, in this case
changing the short-run interest rate affects economic activity and so inflation
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As you may guess there are many interest rates in the economy that are
relevant (interest rates that banks charge borrowing firms, interest rate on mortgages,
etc
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The central bank controls directly only one interest rate (the interest rate at
which it lends to other banks overnight)
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Because interest rates tend to move together
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The IS-LM model with the Taylor Rule
As we noted above, monetary policy is done by setting the interest rate and so money
supply becomes endogenous and not exogenous as we have assumed in deriving the
LM curve
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What a central bank should
do is to do monetary policy to achieve low and stable inflation and to avoid causing
fluctuations in output and employment
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This is a rule proposed by John Taylor (economist at
Stanford) in 1993 that appeared to be consistent with the actual behaviour of the
Federal Reserve (and also of other central bank institutions)
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Suppose that the
Central Bank wants to achieve an inflation rate of 2%
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Then the typical Taylor Rule is:
Y −Y 
i = π + 2 + 0
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5
 Y 



where 100 x

Y −Y
= GDP gap = = percent by which real GDP is below its natural
Y

rate (denoted by Y )
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For each one-point increase in π, monetary policy is
automatically tightened to raise the interest rate by 1
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For each one percentage point
that GDP falls below its natural rate, monetary policy automatically eases to reduce
the interest rate by 0
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In the graph below we see how the interest rate implied by the
Taylor Rule matches the interest rate set by the Federal Reserve in US (the federal
funds rate)
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Therefore, it is like the FED was implicitly behaving according to the
Taylor Rule
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Consider the following version of the Taylor Rule:

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i = i + α (π − π ) + β (Y − Y )

1)

Equation 1) looks slightly different than the empirical version of the Taylor Rule
described above but it is exactly the same thing
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The coefficients α and β are positive and denotes the
responsiveness of monetary policy to deviations of inflation from the target and of
output from the target respectively
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This tells us that the central bank raises the
interest rate whenever output is above the natural level and it decreases the interest
rate whenever output is below the target
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The TR schedule is positively sloped in the (i, Y)-space since β > 0 , like the
LM curve
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However, the central bank in reality
does control directly the nominal interest rate (not the real)
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Assume for simplicity that the IS and
the TR schedules intersect at the natural level of output
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e
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Suppose an increase in
public expenditure so that the IS curve shifts to the right to IS’
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Notice
the slight difference with the IS-LM model
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Here, the increase in the interest rate is
due to the fact that the central bank is following a Taylor Rule
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What happens here in the money market?
Still an increase in public expenditure increases the money demand
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Then we can ask the following: will the result we had
be equal to one we would obtain with an LM curve? Or another way to say: is the TR
schedule the same as the LM curve? The answer is generally no
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The
new interest rate in the money market, if money supply remains fixed, should be ia,
that is higher than the interest rate set by according to the Taylor Rule
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So depending on how the money demand reacts to changes in output we may have
a different response in terms of the interest rate depending if we use the IS-LM or the
IS-TR model (obviously we can have also the case where the TR schedule is steeper
than the LM curve)
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How do we model a change in monetary policy
in the IS-TR model? For example the central bank may change the natural interest
rate
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Another possibility is that central bank may
change the way it responds to deviation of output from the natural level
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This will rotate the TR schedule
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What is different is the
mechanism behind those results (for example, we still have the crowding out effect,
but here the way it arises is different from the way it arises in the classical IS-LM
model)
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In the IS-LM model, by setting
the level of money supply, the central bank can decide to increase money supply in
order to increase output (expansionary monetary policy)
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This seems to be consistent with what central banks tend to
do in normal times, that is caring about price stability without trying to affect too
much economic output
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