Chapter 11 - IS Curve

Intermediate Macroeconomics (Chapter 11 - IS Curve)

1. Chapter 11: The IS Curve
Ryan W. Herzog
Spring 2020
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2. 1
Introduction
2
Setting up the Economy
3
Deriving the IS Curve
4
Using the IS Curve
5
Microfoundations of the IS Curve
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3. Introduction
Learning Objectives
The rst building block of our short-run model: the IS curve describes
the eect of changes in the real interest rate on output in the short
run.
How shocks to consumption, investment, government purchases, or
net exports (i.e. aggregate demand shocks) can shift the IS curve.
A theory of consumption called the life-cycle/permanent-income
hypothesis.
That investment is the key channel through which changes in real
interest rates aect GDP in the short run.
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4. Introduction
The Federal Reserve exerts a substantial inuence on the level of
economic activity in the short run by setting the rate at which people
borrow and lend in nancial markets
The basic story is this:
"interest rate)#investment)#output (1)
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5. Introduction
The IS curve
The IS curve captures the relationship between interest rates and
output in the short run.
There is a negative relationship between the interest rate and
short-run output.
An increase in the interest rate will decrease investment, which will
decrease output.
IS stands for \investment equals savings"
(YTC)
|{z}
private saving
+ (TG)
|{z}
government saving
+ (IMEX)
|{z}
foreign saving
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6. Introduction
The IS Curve
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7. Setting up the Economy
The national income accounting identity
Implies that the total resources available to the economy equal total
uses
One equation with six unknowns
Yt=Ct+It+Gt+EXtIMt (2)
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8. Setting up the Economy
Key Equations
We need ve additional equations to solve the model:
Ct=acYt (3)
Gt=agYt (4)
EXt=aexYt (5)
IMt=aimYt (6)
It
Yt
=aib(Rtr) (7)
Level of potential output is given exogenously.
ConsumptionC, government purchasesG, exportsEX, and imports
IMdepend on the economy's potential output.
Each of these components of GDP is a constant fraction of potential
output.
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9. Setting up the Economy
Potential Output
Potential output is smoother than actual GDP.
A shock to actual GDP will leave potential output unchanged
The equation depends on potential output.
Shocks to income areOsmoothedO to keep consumption steady.
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10. Setting up the Economy
Investment Equation
It
Yt
=aib(Rtr)
where,aiis the share of potential output that goes to investment.
bis a term weighting the dierence between the real interest rate and
the MPK.
Rtis the real interest rate
ris the marginal product of capital (K)
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11. Setting up the Economy
Marginal Product of Capital
The MPK is an exogenous parameter and is time invariant
If the MPK is low relative to the real interest rate rms should save
money and not invest in capital
If the MPK is high relative to the real interest rate rms should
borrow and invest in capital
In the short run, the MPK and the real interest rate can be dierent.
Installing capital to equate the two takes time
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12. Setting up the Economy
The IS Curve Model
The model has six endogenous variables (Yt;Ct;It;Gt;EXt;IMt)
The model has six equations:
National income identity:Yt=Ct+It+Gt+EXtIMt Consumption:Ct=acYt Government:Gt=agYt Exports:EXt=aexYt Imports:IMt=aimYt Investment:
It
Yt
=aib(Rtr)
Exogenous parameters:Yt;ac;ai;ag;ag;aex;aim;b;r;Rt
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13. Deriving the IS Curve
Deriving the IS Curve
Divide the national income accounting identity by potential output.
Yt
Yt
=
Ct
Yt
+
It
Yt
+
Gt
Yt
+
EXt
Yt

IMt
Yt
(8)
Substitute the ve equations into this equation.
Yt
Yt
=ac+aib(Rtr) +ag+aexaim (9)
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14. Deriving the IS Curve
Recall the denition of short-run output. Simplies the equation for
the IS curve:
~
Yt=
YtYt
Yt
(10)
Subtract one from both sides:
Yt
Yt
1
|{z}
~
Yt
=ac+ai+ag+aexaim1
| {z }
a
b(Rtr) (11)
Rewriting
~Yt=ab(Rtr) (12)
whereac+ai+ag+aexaim1 =a
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15. Deriving the IS Curve
The gap between the real interest rate and the MPK is what matters
for output uctuations.
Firms can always earn the MPK on new investments.
The parametera:
Isa=ac+ai+ag+aexaim1
Is called the aggregate demand shock
Will equal zero when potential output is equal to actual output
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16. Using the IS Curve
The Basic IS Curve
When the demand shock parameter equals zero, the IS curve has a
short-run output of 0 where the real interest rate is equal to the long-run
value of the MPK.
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17. Using the IS Curve
Basis IS Curve
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18. Using the IS Curve
Interest Rate Change
When the real interest rate changes, the economy will move along the
IS curve.
An increase in the interest rate
causes the economy to move up the IS curve
Causes short-run output to decline
The higher interest rate
raises borrowing costs
reduces demand for investment
reduces output below potential
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19. Using the IS Curve
An Increase in the Interest Rate
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20. Using the IS Curve
Sensitivity Parameter
If the sensitivity to the interest rate were higher
The IS curve would be atter
Any change in the interest rate would be associated with larger
changes in output
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21. Using the IS Curve
Example
IS Curve:
~
Yt=ab(Rtr) (13)
Supposea= 0,b= 2,R=r= 5%, andR1= 6%
Initially the economy has no output gap~Yt= 02(0) = 0.
If interest rates increase to 6% then:~Yt= 02(65) =2%
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22. Using the IS Curve
An Aggregate Demand Shock
Suppose that information technology improvements create an
investment boom.
The aggregate demand shock parameter will increase.
Output is higher at every interest rate and the IS curve shifts right.
For any given real interest rateRt, output is higher whenais higher.
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23. Using the IS Curve
Shift in the IS Curve
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24. Using the IS Curve
Movement or Shift?
A change inRshows up as a movement along the IS curve. The IS
curve is a graph ofRversus short-run output.
Any other change in the parameters of the short-run model causes the
IS curve to shift.
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25. Using the IS Curve
Shock to Potential Output
Shocks to potential output change actual output by the same amount
in our setup
Do not change short-run output
Some shocks to potential output may change other parameters.
Earthquake, for example:
Reduces actual and potential output by the same amount
Leads to an increase in short-run output because it also increases the
MPK
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26. Microfoundations of the IS Curve
Microfoundations
The underlying microeconomic behavior that establishes the demands for
C,I,G,EX, andIM.
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27. Microfoundations of the IS Curve
Consumption
People prefer a smooth path for consumption compared to a path
that involves large movements.
The permanent-income hypothesis: People will base their
consumption on an average of their income over time rather than on
their current income.
The life-cycle model of consumption: Suggests that consumption is
based on average lifetime income rather than on income at any given
age.
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28. Microfoundations of the IS Curve
The Life-Cycle Model of Consumption
Young people borrow to consume more than their income.
As income rises over a person
~
Os life consumption rises more slowly
and individuals save more
During retirement, individuals live o their accumulated savings.
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29. Microfoundations of the IS Curve
Life Cycle / Permanent Income Hypothesis
Implies that people smooth their consumption relative to their income
This is why we set consumption proportional to potential output
rather than actual output.
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30. Microfoundations of the IS Curve
Life Cycle Model of Consumption
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31. Microfoundations of the IS Curve
Multiplier Eects
We can modify the consumption equation to include a term that is
proportional to short-run output.
Ct
Yt
=ac+x~Yt (14)
Solving for the IS curve:
~
Yt=
1
1x
|{z}
multiplier
(ab(Rtr))
| {z }
original IS curve
(15)
Now includes a multiplier on the aggregate demand shock and
interest rate terms:
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32. Microfoundations of the IS Curve
With a multiplier:
Aggregate demand shocks will increase short-run output by more than
one-for-one.
A shock willOmultiplyO through the economy and will result in a
larger eect.
If short-run output falls with a multiplier
Consumption falls
Which leads to short-run output falling
Consumption falls again
\Virtuous circle" or \vicious circle"
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33. Microfoundations of the IS Curve
Investment
At the rm level, investment is determined by the gap between the
real interest rate and MPK.
In a simple model the return on capital is the MPK minus
depreciation.
The richer framework includes:
Corporate income taxes
Investment tax credits
Depreciation allowances
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34. Microfoundations of the IS Curve
Investment cont.
A second determinant of investment is the rm~Os cash ow or the
amount of internal resources the company has on hand after paying
its expenses
Agency problems occur when one party in a transaction has more
information than the other party
It is more expensive to borrow to nance investment because of this.
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35. Microfoundations of the IS Curve
Asymmetric Information
Adverse selection
If a rm knows it is particularly vulnerable
It will want to borrow because if the rm does well it can pay back the
loans.
If it fails, the rm cannot pay back the loan but will instead declare
bankruptcy.
Moral hazard
A rm that borrows a large sum of money may undertake riskier
investments
if it does well, it can repay.
if it fails, it can declare bankruptcy.
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36. Microfoundations of the IS Curve
Investment Equation
The potential output term in the investment equation incorporates
cash ows.
It=aiYtb(Rtr)Yt (16)
Captures cash ow.
If we wish to add short-run output, it would provide additional
justication for a multiplier
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37. Microfoundations of the IS Curve
Government Purchases
Government purchases can be
A source of short-run uctuation
An instrument to reduce uctuations
Discretionary scal policy
Includes purchases of additional goods in addition to the use of tax
rates
For example, the government can use the investment tax credit to
encourage investment
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38. Microfoundations of the IS Curve
Transfer spending often increases when an economy enters into a
recession.
Automatic stabilizers
Programs where additional spending occurs automatically to help
stabilize the economy
Welfare programs and Medicaid are two such stabilizer programs. They
receive additional funding when the economy weakens
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39. Microfoundations of the IS Curve
Fiscal policy~Os impact depends on two things:
1
The problem of timing
discretionary changes are often put into place with signicant delay.
2
The no-free-lunch principle
implies that higher spending today must be paid for today or some
point in the future.
such taxes may oset the impact of the discretionary spending
adjustment.
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40. Microfoundations of the IS Curve
Consumption
What matters for consumption today?
The permanent-income hypothesis says what matters is the present
discounted value of your lifetime income, after taxes.
Ricardian equivalence says what matters is the present value of what
the government takes from the consumers rather than the specic
timing of the taxes.
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41. Microfoundations of the IS Curve
Government Policy
An increase in government purchases nanced by taxes today
Will have a modest positive impact on the IS curve
Will raise output by a small amount in the short run
An increase in spending today nanced by taxes in the future
Will shift the IS curve out by a moderate amount
Perhaps by 75 cents to $1 for each dollar
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42. Microfoundations of the IS Curve
Case Study: ARRA
Economists had a wide range of opinions about the eectiveness and
costs of the stimulus.
Congressional Budget Oce (CBO) gave estimates of unemployment
with and without a stimulus.
Estimated 9 percent peak without a stimulus
Actual unemployment rate with stimulus was above this.
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43. Microfoundations of the IS Curve
Great Recession
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44. Microfoundations of the IS Curve
Net Exports
If the trade balance is a decit (surplus) the economy imports more
(less) than it exports
If Americans demand more imports the IS curve shifts left and
reduces short-run output
If foreigners demand more American exports the IS curve shifts right
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45. Microfoundations of the IS Curve
A Reduction in Interest Rates
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46. Microfoundations of the IS Curve
Decline in Consumer Condence
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47. Microfoundations of the IS Curve
Improvements in Info Technology
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