# IS-LM

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```					Macro modeling 1

January 15, 2009
Macro models

A macro model is a mathematical structure that describes the economy

A good macro model has six features
1. It should include the variables we want to predict
2. It should capture the most important factors whose effects we want
to determine
3. Its equations should be consistent with how the variables are
defined and measured
4. Its equations should be easily defended
5. It should make predictions that are qualitatively in line with the real
world
6. It should be easy to use

January 15, 2009                   IS-LM                              Page 2
Variables we would like to predict

We would like to predict:
 GDP
 Unemployment
 Inflation
 Interest rates
 Exchange rates

But,
 GDP and unemployment move in opposite directions, so we only
model one of them
 We will model the price level (value of CPI) instead of inflation
(growth rate of CPI)

January 15, 2009                  IS-LM                               Page 3
Today

Today we begin constructing a model that eventually explains the
following variables and also has the six features of a good model
 GDP
 Interest rates
 Price level
 Exchange rates

Today we will only get to the first two of these variables
 Next session adds price level
 Session after that adds exchange rates

January 15, 2009                    IS-LM                         Page 4
The model

Remember that a model is a set of equations that relate the different
macro variables to each other

Here is today’s model, known as the IS-LM model

Y=C+I+G+X
C = a + b(Y – T)
I = e – dR
M/P = hY – kR

January 15, 2009                  IS-LM                            Page 5
The model

The IS-LM model

Y=C+I+G+X
C = a + b(Y – T)
I = e – dR
M/P = hY – kR

We   will
1.   Figure out what each equation means
2.   Defend the assumptions embodied in the equations
3.   Put all the equations together
4.   Be able to talk about the economy at the end

January 15, 2009                 IS-LM                  Page 6
IS-LM: The first equation

The first equation is
Y=C+I+G+X
where
Y = GDP = output = income = spending
C = consumption
I = investment
G = government spending
X = net exports

Why is it true?
 It is true because GDP can, by construction, be separated into the
four spending components

January 15, 2009                   IS-LM                           Page 7
IS-LM: The second equation

The second equation is
C = a + b(Y – T)
where
C = consumption
Y = income
T = taxes
a and b are parameters, both positive, b < 1

The quantity Y – T is after-tax income, also known as disposable income

The equation says that when the average household gets an additional
dollar of disposable income, it spends an additional \$b on newly
produced goods and services, and saves the rest

January 15, 2009                       IS-LM                      Page 8
IS-LM: The third equation

The third equation is
I = e - dR
where
I = investment
R = interest rate
e and d are parameters, both positive

The equation says that when interest rates rise, investment falls
 Recall that investment is spending by businesses and spending on
new housing
 Tends to be financed through borrowing
 Higher interest rates make borrowing more expensive
 When interest rates rise, firms borrow less and investment falls

January 15, 2009                    IS-LM                       Page 9
IS-LM: The fourth equation

The fourth equation is
M/P = hY – kR
where
M is money supply
P is the price level
Y is income
R is the interest rate
h and k are parameters, both positive

The left-hand side is real money supply, the right-hand side is money
demand

The equation says that money supply = money demand

January 15, 2009                    IS-LM                         Page 10
Money demand

Recall that money is the sum of currency and checking account
balances
 Neither of these pay interest

When income rises, people want to buy more
 To buy more, they need more money
Money demand increases when income rises

When interest rates rise, people would like to take advantage of the
higher interest rates
 Reallocate their financial portfolio to move more assets into interest-
bearing accounts
 Reduce currency holdings and checking account balances
Money demand falls when interest rates rise

January 15, 2009                   IS-LM                           Page 11
The IS-LM model
The IS-LM model
Y=C+I+G+X
Using the model:
C = a + b(Y – T)
See how the
I = e – dR               endogenous
M/P = hY – kR              variables shift
when the
Endogenous variables (determined by the system)       exogenous
variables change
Y = GDP                    C = consumption
R = interest rate           I = investment

Exogenous variables (determined outside the system)
X = net exports            P = price level

Exogenous policy variables
G = government spending     T = taxes      M = money supply

January 15, 2009                IS-LM                           Page 12
Examples of what we want to do

GDP is currently too low
 How will a tax cut affect GDP and interest rates?
 How will a spending package impact GDP and interest rates?
 What about a tax cut financed through a spending cut?
 How will monetary policy affect GDP and interest rates?
 How does the nature of the recession matter?

When we expand the model next week, we can look at the same issues,
but get the impacts on inflation and exchange rates

The model forces us to take the politics out of the questions
 Some people might want tax cuts to be the answer to everything
 Some people might want spending increases to solve all
problems

January 15, 2009                 IS-LM                         Page 13

The chapter tells how to turn the four equations into two, and the two
into a graph

The graph has two lines

The IS curve has combinations of GDP and interest rates that make
income equal spending
 Used for fiscal policy – changes in government spending or taxes

The LM curve has combinations of GDP and interest rates that make
money demand equal money supply
 Used for monetary policy – the Fed changes money supply (Federal
funds rate)

January 15, 2009                  IS-LM                           Page 14
IS-LM analysis

The economy operates where the IS
curve and the LM curve intersect.
R
To use the graph we must know how
LM
the curves shift

R                             IS shifts right when:
 Gov’t spending increases
 Taxes decrease
IS           Net exports increase
Y
Y
LM shifts right when:
 Money supply increases
 Price level falls

January 15, 2009                IS-LM                            Page 15
A fiscal stimulus package

A fiscal stimulus is either
 A gov’t spending increase
R
 A tax cut
LM
Either one shifts IS to the right
R’                                     GDP increases
R                                     Interest rates increase
IS’
IS            We also know how the components of
GDP are affected
Y         GDP increase causes consumption to
Y   Y’
rise
 Interest rate increase causes
investment to fall

January 15, 2009                       IS-LM                                  Page 16
A monetary stimulus package

A monetary stimulus is an increase in
money supply
R                                   Reported as the Fed cutting interest
rates
LM
LM’      LM shifts to the right
R                                     GDP increases
R’                                    Interest rates decrease

IS            We also know how the components of
Y        GDP are affected
Y   Y’
 GDP increase causes consumption to
rise
 Interest rate decrease causes
investment to rise

January 15, 2009                       IS-LM                               Page 17
Cutting taxes and spending together

What happens if we cut taxes and cut
spending by the same amount?
R                          Budget-neutral tax cut

LM
The tax cut tends to shift IS to the
right, but the spending cut tends to
R                             shift IS to the left

Which effect is bigger?
IS
Y
Y

January 15, 2009                IS-LM                              Page 18
Cutting taxes and spending together
Which effect is bigger, the tax cut or
the spending cut?

R                             Look back at the IS equations:
Y=C+I+G+X
LM
C = a + b(Y – T)
I = e – dR
R
R’                                The tax cut causes C to increase
The spending cut causes G to decrease
IS
IS’
Y      Which changes more?
Y’ Y

Answer: G falls more than C rises
 Net effect is leftward shift of IS
 Spending cut has bigger effect
 Economy contracts

January 15, 2009                    IS-LM                                Page 19
Cutting taxes and spending together

Which effect is bigger, the tax cut or
the spending cut?
R
Answer: G falls more than C rises
LM
 Spending cut has bigger effect
 Economy contracts
R
R’                                Why?
 The tax cut increases disposable
IS          income
IS’
Y       People only consume a fraction of
Y’ Y                     their additional disposable income
 So only some of the tax cut turns
into consumption, and therefore GDP
 All of the government spending
turns into GDP

January 15, 2009                    IS-LM                                Page 20
Temporary vs. permanent tax cuts

The model says that tax cuts cause the
IS curve to shift to the right
R
How far it shifts right is determined by
LM            the coefficient b in the equation

R’                                                C = a + b(Y – T)
R
IS’      b is the amount an individual spends
out of a \$1 increase in disposable
IS            income
 (1 – b) is the amount an individual
Y
Y   Y’                 saves out of the additional dollar of
disposable income

Which generates more spending, a
permanent income increase or a
temporary income increase?

January 15, 2009                       IS-LM                               Page 21
Temporary vs. permanent tax cuts

Which generates more spending, a
permanent income increase or a
R                                    temporary income increase?

LM
This is an empirical question.

R                                        The data tell us that a permanent
ISperm      income increase has a much larger
IStemp               impact on consumption than a
IS                     temporary income increase

Y
Y                          So, one-time tax cuts have little impact
on the economy, while permanent tax
cuts have large impacts on the
economy

January 15, 2009                           IS-LM                               Page 22
Intentionally left blank

January 15, 2009   IS-LM   Page 23
What now?

Where we are:

   IS-LM model
   Useful for predicting GDP and interest rate changes
   Useful for evaluating fiscal and monetary policy

What’s missing
 Inflation
 Exchange rates
 Dynamics

Next time we add time and inflation to the model
 Get a model of business cycles

January 15, 2009                   IS-LM                  Page 24
Macro modeling 1

January 15, 2009

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