Transcript Stimulus

Keynesian Economics, Multipliers,
Ricardian Equivalence, PIP, etc.
In the classical model, the business decision maker compared the interest
rate to the current marginal productivity of capital:
dY
r
dK
Keynes reminds us of the long life and income stream available from capital,
and compares the interest rate to the present value of the future profit stream
of the capital. He does this by finding the discount factor d that makes the
price of the capital equal to the future stream of income:
n
PK  
i
i

1

d

i j
He then compares d to the interest rate. If d > r, then investment is profitable.
The variable d is called the marginal efficiency of capital.
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1. The MEC is contructed.
2. The Money market yields r.
3. The decisionmaker confronts the MEC with r, and makes the investment
decision.
4. The resulting investment changes Y and S = S(Y) is determined.
Therefore, investment is a function of the supply price of capital, the rate of
interest, and long-term expectations. A decline may occur as a result of
an increase in PK, an increase in r, or if the MEC collapses as a result of
negative expectations about the future.
During periods of grossly negative expectations about the future (like the
great depression), the investment decision becomes dominated by the
expectations term and unresponsive to interest rate changes. The
investment schedule becomes quite interest inelastic, so nearly vertical
in (I,r)-space.
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The MEC is essentially the modern finance concept
called the internal rate of return.
The businessperson’s formation of expectations about
the future profit stream is pure speculation, and tends to
make investment erratic.
Although this is a more sophisticated look at investment
than the classicals, still we have that investment
depends upon interest rates (and expectations). I = I(r)
Note that I  I(Y) and I  I(Yd)
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Aggregate planned expenditure
(trillions of 1992 dollars/year)
o
45 line
Real GDP exceeds
planned expenditure
10.0
Total Expenditure
C+I+G
8.0
f
6.0
b
4.0
c
a
Equilibrium
expenditure
Planned
expenditure
exceeds
real GDP
C0
G
I
0
e
d
2
4
6
8
10
Real GDP (trillions of 1992 dollars per year)
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Aggregate planned expenditure
(trillions of 1992 dollars/year)
Stability of the Equilibrium
o
45 line
10.0
Total Expenditure
C+I+G
8.0
f
Increase Output,
increase Employment
6.0
e
d
Reduce Output,
Reduce Employment
c
b
4.0
a
0
2
4
6
8
10
Real GDP (trillions of 1992 dollars per year)
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Y=C+I+G
but C = C0 + c(Y-T), so
Y = C0 + c(Y-T) + I + G
Y = C0 + cY – cT + I + G
Y – cY = C0 + I + G – cT
Y(1-c) = C0 + I + G – cT
Y* 
1
C0  I  G  cT 
1 c
But this means that
1
Y 
G
1 c
1
Y 
I
1 c
1
Y 
C
1 c
but
c
Y 
T
1 c
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
Thus 1/(1-c) is called the aggregate expenditure
multiplier or autonomous expenditure multiplier.
◦ It is positive.
◦ An increase in autonomous spending has a amplified impact on
GDP.
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But –c/(1-c) is the tax multiplier.
◦ It is negative.
◦ An increase in taxes reduces GDP.
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This implies that deficit spending can have a powerful
effect for stimulating the economy.
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Clearly taxes slow an economy, having a negative effect
on GDP and therefore employment.
Note that if G= T, a balanced budget :
1
c
G 
G
1 c
1 c
1 c
Y 
G
1 c
Y  G
Y 

Thus the balanced budget multiplier is 1.
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As an example, if the mpc = 0.9, then
1/(1 – 0.9) = 1/(0.1) = 10 !
For every $1 increase in government spending,
GDP will increase by $10 !
But also for every $1 that taxes are increased,
GDP falls by $9 !
With a balanced budget (G=T), every $1
increase in G will increase GDP by only $1.
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Planned
Expenditures
E1
E0
G
Y0
Yf
Y
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The demand for imports is
Z = Z0 + zY, Z0>0, 0<z<1
Little “z” is the marginal propensity to import.
Exports are thought to be exogenously
determined—they don’t depend on conditions in
our economy, but rather the conditions in the
economy of the buyer nation.
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Now we have some new components to the multipliers:
1
C0  I  G  X  Z0 
Y
1 c  z
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Note that we leave out taxes for the moment.
Because the marginal propensity to import is greater
than one, the multiplier is now smaller.
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1.
2.
Agents are rational and farsighted.
Agents either live forever, or care about their progeny as much as
they care about themselves.

3.
4.
5.
6.
7.
8.
This implies that agents are linked to the past and the future (by
immortality or bequests), and have an infinite time horizon.
The belief that current budget deficits imply future taxes is correct.
Taxes are lump sum.
The availability of the deficit spending does not alter the political
process.
No distributional effects. Households are homogeneous, so that a
representative agent model can be used.
No liquidity constraints.
Capital markets are perfect.
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Question: Does it matter whether government
finances current spending through taxes or debt?
Assume the gov’t decreases lump-sum taxes in
the current period and finances the change with
debt:
 T  B
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The New Classical Economists argue that
agents are not fooled. They recognize that:
◦ In future periods, gov’t will have to pay interest on the
additional debt, and
◦ Gov’t will eventually have to repay the debt (assuming
it does not have an infinite maturity).
◦ For a given level of gov’t expenditures, the gov’t will
have to increase future taxes to pay the debt service
and repay the debt.
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Therefore, households will not view the bonds as
an increase in net wealth.
They will subtract the present value of the future
taxes from it.
For simplicity, let’s consider a bond of infinite
duration:
Tt  r  B; t  1, ..., 
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If the bonds and other assets are perfect substitutes, then the
subjective discount factor (for time preference in the PV) is equal to
the interest rate, and the present value of the tax burden is:


Tt
r  B
T0  

 B
t
t
t 1 (1  r )
t 1 (1  r )


It turns out that the present value of the additional taxes is equal to
the debt.
Hence there is no difference between tax and debt finance in terms
of the effect on the economy. Gov’t borrowing is not perceived as an
increase in private wealth, and consumption demand is not
stimulated.
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Agents increase saving in anticipation of future
tax increases.
This causes a reduction in private sector
spending that is exactly equal to the increase in
government spending.
Deficit spending is not stimulative. It has no
effect whatsoever. Thus fiscal policy is useless
at best. Activist policy cannot work!
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In his later work, Barro makes it clear that he
views the “equivalence result” as a benchmark—
an extreme case that makes it clear that the
effects of deficit spending are not as clear-cut nor
as large as Keynesians had suggested.
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How expectations are treated in macro models
fundamentally affects the results.
Under rational expectations (endogenous
expectations), real output and employment are
uneffected by systematic or predictable
changes in aggregate demand policy.
If policy changes are systematic, therefore
predictable, then agents will not make
systematic mistakes in their forecasts.
Unanticipated policy changes will have a shortrun impact.
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inflation
LRPC
2
5
4
SRPC(2)
1
3
2
SRPC(1)
1
U1
U*
Unemployment
SRPC(0)
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If a shock to the economy could be anticipated, and if it
were to persist, then unanticipated aggregate demand
policy could be used to offset its effects.
◦ But if the shock could be anticipated by policymakers, then it
could also be anticipated by all agents, and the policy response
would also be anticipated and would therefore be ineffective.
◦ Shocks don’t persist (aren’t guaranteed to persist).
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Hence there is no role for stabilization policy.
Systematic money supply policy would avoid
expectational errors that would likely move the economy
temporarily away from full employment.
◦ Therefore, adopt a constant growth rate rule for the money supply.
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Kydland and Prescott (1977). “Rules Rather
than Discretion: the Inconsistency of Optimal
Plans,” JPE.
Because of endogenously formed expectations,
optimal policies will not be optimal in practice.
A result of the linear optimal control structure?
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