IS-LM Extensions
Readings: 24.2-24.3
Application from last lecture:
Example: Suppose that there are real shocks that affect the IS curve. If we know that the IS will
shift but we do not know where it will end up, what policy can minimize the variation in income
and interest rates due to this shock?
In this case, we cannot control the IS curve.
The best response is to control the LM curve. We can do two things:
a) Move LM to keep the interest rate constant
b) Keep the money supply constant without moving LM
Suppose we do option a). To keep the interest rate constant we must move the LM
curve to LM1 if the shock moves the IS to ISU. Or we move the LM to LM2 if the IS
moves to ISL. 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. Now the
variability of income is very large: from Y0 to YL or from Y0 to YU.
Suppose you do option b). In this case the LM does not move, and now the variability
of real income is much less than before: from Y0 to Y1 or from Y0 to Y2.
Another application: the IS-LM model and the credit crunch
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In Autumn 2008 the world economy entered the deepest recession since the Great
Depression. The origin of the crisis was the financial crisis in US in 2007, in the so called
“sub-prime” market. 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.
How can it be possible that problems in such a small market can create such a big
recession? Furthermore, can we study the current recession using the IS-LM model?
To study the credit crunch using the IS-LM model, we need to introduce the role of
banks in the model.
Implicitly, we have the banks in the IS-LM since the interest rate is also the price of
credit. However, we need to introduce the role of banks more explicitly.
Recall that banks are financial intermediaries; they collect money from savers and lend
it to borrowers. Here we consider a commercial bank and not an investment bank. The
balance sheet of a commercial bank is given by:
Assets
Loans
Other assets
Liabilities
Capital
Deposits
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The value of the bank’s assets is mostly the value of the loans it has made to households
and firms
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Capital, which appears on the right side, is the difference between the value of the
assets and the value of the liabilities since Assets = Capital + Deposits is the accounting
identity for a commercial bank
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. However, when a firm borrows money from a bank it must pay an interest rate that is
normally different (higher) from the interest rate that savers receive from deposits. The rate
borrowers have to pay, i.e. the cost of a loan
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from the bank, ρ, is usually equal to the rate savers receive (i) plus a spread, x:
Here we use i for the interest rate but you should remember that i = r in the IS-LM model.
Therefore, when a firm has to decide whether to buy a machine, ρ is the interest rate she has to
look at. Investment demand therefore depends on the cost of bank loans (and not simply on
the interest rate) and can be expressed as:
What determines the spread x between the lending rate (ρ) and the deposit rate ( i )?
1) The Banks’ capital: KB .
2) The firms’ capital: KF .
Given this information we can write the IS equation as:
where x(KB , KF ) means that the spread x depends on the banks’ capital and firms’ capital as
outlined above. The LM curve is the usual one.
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Now suppose that for any reason, the capital of the banks decreases. For example,
suppose that some borrowers do not repay their loans and so the bank needs to use its
capital to cover for that. The bank then can look for new capital, but this takes time and
it may be difficult, or can reduce their assets for example by stopping to lend money.
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.
Now suppose that for any reason, the capital of firms also decreases, for example
because the stock market is going down. Also this effect will increase the spread x and
this will reduce investment even further. Graphically, a reduction in investment shifts
the IS curve to the left:
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.
From a policy point of view, what can we do?
1) We can try to increases government expenditure and try to shift the IS to the right. This
is what many governments have done during the crisis by putting money into the
system to nationalize some of the troubled institutions
2) The central bank can increase money supply and try to shift the LM to the right. This is
indeed what happened during the crisis.
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The IS shifts to the left because of the decrease in the capital of Banks and firms.
The new IS curve is IS’ and the equilibrium is E’. By increasing government expenditure,
the IS can shift to the right, for example to IS’’. By increasing money supply the LM shifts
to the right.
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.
This is exactly a situation consistent with the liquidity trap studied previously.
How long are we going to be stuck to the low equilibrium?
Empirical investigation: Is the general price level really fixed in the short run?
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The analysis done so far is based on the assumption that the general price level is fixed.
Does this hold in reality?
Bernanke and Gertler (1995)1 estimate a VAR (Vector Autoregression) and they check if
after a positive shock in the interest rate (change in monetary policy) whether the
general price level will change.
Observations:
Bils and Klenow (2004)2 checks the frequency of price changes for 350 consumption goods
(covers 70% of consumer spending). On average, a price remains fixed for 5.5 months or less
The IS/MP model (Investment Savings/ Monetary Policy)
1
Bernanke and Gertler (1995), Inside the Black Box: The Credit Channel of Monetary Policy Transmission, Journal of
Economic Perspectives, Vol. 9, No. 4. (Autumn, 1995), pp. 27-48.
2
Bils and Klenow (2004), Some Evidence on the Importance of Sticky Prices, Journal of Political Economy, Vol. 112,
947-985.
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The LM curve is the more traditional way to characterize the asset equilibrium
relationship. It describes the condition leading the quantity of money demanded to
equal the quantity of money supplied. The upward sloping collection of (Y,r) pairs
that describe this equilibrium is the LM curve.
The LM analysis was developed to describe a financial system in which the central
bank follows a policy of choosing a target level (or growth rate) for the money
supply. The short term interest rate adjusts in order to balance money demand with
the quantity that the central bank chooses to supply.
Most modern central banks no longer set monetary policy according to money
supply or money growth rate targets. Now, policies target a specific short-term
interest rate and allow the money supply to adjust to whatever level achieves
balances asset markets at the desired interest rate target. (The IS/MP model is a
more natural way to describe monetary policy in this case.)
The MP curve and the Taylor rule
Monetary policy is best described as a rule for setting interest rates in response to important
macroeconomic goal variables:
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Output
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Inflation
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Financial market stability
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The exchange rate
Some believe the Fed has used a Taylor rule type of policy (Taylor, 1993)3
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3
The Taylor Rule provides a good way of characterizing the way monetary policy actually
behaves in any country that implements policy through interest rates.
John Taylor (1993), Discretion versus policy rules in practice, Carnegie-Rochester Conference Series on Public
Policy 39, 194-214.
A simple way to write this monetary policy rule is:
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where * denotes the levels for r, Y and π that are desired by the central bank
fy and fπ are parameters in the monetary policy function
In Taylor’s Rule these parameters each are equal to .5 (i.e. ½)
This rule clearly ties the interest rate to goals for Y and π
The goal for r is actually related to financial market stability and to exchange rate
stability, but you can’t see that yet
The interest rate implied by the Taylor rule with Taylor rule parameters = 0.5 and inflation
target = 2% yields the following graph:
Deriving the MP curve
If we use the Fisher equation
and assume that expected inflation equals the inflation target
we can write the Taylor Rule as:
So this policy rule says that:
 When Y and π are at their desired levels, the central bank should set r at it’s desired
level
 If Y exceeds Y* , Y exceeds its desired level, the central bank should raise r relative to it’s
desired level
 If π exceeds π*, π exceeds its desired level, the central bank should raise r relative to it’s
desired level
Another way to write this equation is:
Factors that will shift the MP curve upward (to the left) are:
•
An increase in r*
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A decrease in Y*
•
An increase in π
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A decrease in π*
Each of the above events increases f0 which shifts the MP Curve upward. The opposite
movement of these 4 factors will shift the MP curve downward
Note most of the factors which shift the LM curve have no effect on the MP Curve
 This is because the non-policy money supply factors and the money demand factors that
shift the LM Curve have no effect on the interest rate choice of the central bank
Why does the Fed care about inflation?
Costs of inflation:
(1) Shoe-leather costs
(2) Tax distortions
(3) Money illusion
(4) Menu costs
(5) Inflation variability
Shoe Leather costs
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Resources, time and real expenditures, are used up when you manage your finances and
make sure that you have enough money to make the purchases you make.
Higher inflation causes people to reduce their holdings of money
Inflation acts like a tax on money holdings because a dollar of money loses real purchasing
power when the price level rises
Even the types of money that pay interest lose value because the return on these assets
typically will not keep up with inflation
therefore people will spend more of their resources economizing on the amount of money
they hold.
Tax distortions
• As a result, inflation can raise the real cost of tax payments.
Eg. Taxation of capital gains are typically based on the change in the price in dollars of the asset
between the time it was purchased and the time it sold. This implies that the higher the rate of
inflation, the higher the tax:
The higher the rate of inflation, the higher the tax
• This was more of a problem in the days when personal income tax brackets were fixed in
nominal terms.
– If your nominal income increased at the same rate as inflation, there is no change in your
real income and yet you could find yourself in a new tax bracket with a higher marginal
tax rate.
– In that case, you would be paying a larger fraction of your real income in taxes even
though your real income stays the same, and so inflation would have a real cost in terms
of reduced real disposable income for households.
– The higher the inflation rate the larger the number of people who get pushed into the
higher brackets, thus the real cost of inflation rises with the inflation rate
• While this particular problem has been eliminated, all taxes are not fully indexed to π
Money illusion
People often do not keep track of the difference between the real interest rate and the nominal
interest rate and make systematic mistakes in assessing nominal versus real changes in income.
This leads people and firms to make incorrect decisions.
Menu costs
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cost of changing prices
Printing new price lists
Deciding on what the new price has costs associated with data collection and analysis
Potential loss of customers – this might induce customers to shop around and find a store
they like better
As π gets higher, prices will, on average, change more frequently, and so these menu costs
will increase
Inflation Variability
Higher inflation is typically associated with more variable inflation. This makes financial assets
such as bonds riskier.
Costs of unanticipated inflation
Definition:
• The higher inflation is at a given time, the more likely we are to be surprised by a large
change in future inflation
– surprises can be positive, π higher than expected, or negative, π lower than
expected
• Therefore as π gets higher, the chances of a large unanticipated change in π will increase.
• As the rate of inflation rises, and the probability of a larger unanticipated change in
inflation increases, the costs of unanticipated inflation rise.
• Thus, firms and some individuals will spend more time and expenditures trying to:
– forecast future inflation
– reduce the risks of inflation
• one way to reduce risks of inflation is by using futures, options, or other
financial contracts to “hedge”, which means essentially to try to protect
yourself or your company’s return from unforecastable changes in prices
that could be very costly if they were to occur
• This is not costless – insurance is never free:
• One must design a sound hedging strategy and pay any
costs associated with buying and selling financial assets
• Another cost of unexpected inflation: distributional consequences regarding the return
on savings and investments
– the ex ante real rate:
• The expected return is what we base savings and investment decisions on
– the ex post real rate is equal to:
•
This is the real return we actually get from an asset
– But what if the expected inflation and actual inflation are different?
• the ex post real rate is less than the ex ante real rate when π > π e
– In this case, borrowers are pleasantly surprised by the unexpectedly low real rate
they end up paying while lenders are not happy to be surprised that the real rate
turns out to be lower than they expected it would be.
• The cost to the economy:
• the ex post real rate is greater than the ex ante real rate when π < π e,
– In this case it is borrowers who are unhappy with the high real rate they end up
paying ex post while lenders are pleasantly surprised by the higher return the
get, compared to what was expected
• The cost to the economy:
 Another cost of unexpected inflation: Prices become less informative.
- This is because when the rate of inflation increases, there is wider variation in relative
prices in an economy. This means people must expend greater effort trying to
determine if they have found the best price or even if they simply want to know if they
are getting a good price.
The IS-MP Analysis
• Combines the IS Curve that we derived before with this new MP curve
– The LM curve in the traditional IS-LM model is replaced by the MP Curve
• Because the MP slopes up it appears similar to the upward sloping LM, but it is a
fundamentally different relationship.
– Specifically, the MP Curve is:
• Determined by the Fed’s choice of targets for the various goal variables
of monetary policy
• Only shifted by the 4 factors mentioned previously
• Is not shifted by most of the factors that shift the LM Curve
A shift in the IS curve
Scenario: Suppose the government decides that it wants to reduce its budget deficit. How
might it do so and what will this policy do in our model?
• An increase in the tax on firms reduces Id while an increase in the tax on consumers
reduces Cd. We saw that each of these changes shifts the IS Curve to the left (ignoring
Ricardian Equivalence)
• When the IS Curve shifts left it is because desired spending has fallen, and therefore
income (Y) will fall. The central bank does not like output to fall, and so it lowers the real
interest rate (r).
– This monetary policy response causes output to fall by less than it would have if
the Fed kept the real rate constant at some initial level.
• The same basic effect occurs for any of the following:
– A decline in Cd (Except when caused by a change in Y or r)
– A decline in Id (Except when caused by a change in Y or r)
– A decline in G
– A decline in NXd (Except when caused by a change in Y or r) - later
– Of course, increases in these 4 cases will do the opposite
A shift in the MP curve
• Suppose the central bank decides to lower its target for inflation
• What will this do in our model?
• The central bank raises r to slow the economy, and the rise in r reduces desired spending
(e.g. when r rises, the user cost of capital rises and so Id must fall) and this causes Y to
fall
• The same basic graph applies if the Fed decides to raise interest rates for any of the
reasons that cause the MP Curve to shift up:
• an increase in r*
• a decrease in Y*
• an increase in π
• a decrease in π*
– In all of these cases the MP curve shifts up, resulting in higher r and lower Y
• If these factors move in the opposite direction, then the MP curve shifts downward, and r
falls while Y rises in the IS-MP model
Policy Coordination
• Suppose fiscal policy is stimulative
– This yields a RIGHT shift of the IS Curve (from IS0 to IS1)
• Depending what monetary policy does, the effects of this fiscal policy on the
macroeconomy can be very different
– We know that r and Y RISE, if MP curve doesn’t shift (MP0)
• The MP Curve doesn’t shift when
– the Central Bank’s monetary policy (i.e. its desired levels for y, r
and π) has not changed
– and also, that inflation has not changed, which is a good
assumption for the short-run.
– However, central banks have sometimes changed policy in response to a change
in fiscal policy
• If the Fed shifts MP to the right, such that r is not permitted to rise,
monetary policy is working with fiscal policy to stimulate the output of
the economy (MPC)
• Alternatively, the Fed might not wish to let output rise, in which case
they would shift MP to the LEFT enough so that IS and MP intersect at the
same level of Y, and a higher r (MPA)