macroeconomics chapter 81 an equilibrium business-cycle model c h a p t e r 8
TRANSCRIPT
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Macroeconomics Chapter 8 1
An Equilibrium Business-Cycle Model
C h a p t e r 8
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Macroeconomics Chapter 8 2
Cyclical Behavior of Real GDP—Recessions and Booms
Real GDP = trend real GDP + cyclical part of real GDP
Cyclical part of real GDP Coming from the business cycle Short-term economic fluctuations.
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Macroeconomics Chapter 8 3
Cyclical Behavior of Real GDP—Recessions and Booms
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Macroeconomics Chapter 8 4
Cyclical Behavior of Real GDP—Recessions and Booms
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Macroeconomics Chapter 8 5
Cyclical Behavior of Real GDP—Recessions and Booms
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Macroeconomics Chapter 8 6
An Equilibrium Business-Cycle Model
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Macroeconomics Chapter 8 7
An Equilibrium Business-Cycle Model
Conceptual Issues Assuming that these fluctuations reflect
shocks to the economy. Change in level of technology
Y= A· F( K, L) An increase in A means that the economy
is more productive. A decrease in A means that the economy
is less productive.
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Macroeconomics Chapter 8 8
An Equilibrium Business-Cycle Model
Uses equilibrium conditions to determine how the shocks affect real GDP, Y, and other macroeconomic variables, such as consumption, C, investment, I, and the quantity of labor input, L.
RBC model Finn Kydland & Edward Prescott
( 2004 Nobel Laureates )
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Macroeconomics Chapter 8 9
An Equilibrium Business-Cycle Model
The Model Y= A· F( K, L)
the capital stock, K, as fixed in the short run,
the labor input, L, is fixed. Changes in Y will reflect only changes
in A. When A rises, Y rises, When A falls, Y falls.
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Macroeconomics Chapter 8 10
An Equilibrium Business-Cycle Model
The Model The marginal product of labor and the
real wage rate An increase in the technology level, A,
raises the marginal product of labor, MPL, for given inputs of capital, K, and labor, L.
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Macroeconomics Chapter 8 11
An Equilibrium Business-Cycle Model
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Macroeconomics Chapter 8 12
An Equilibrium Business-Cycle Model
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Macroeconomics Chapter 8 13
An Equilibrium Business-Cycle Model
The Model Marginal product of capital, real rental
price, and the interest rate An increase in the technology level, A,
raises the marginal product of capital, MPK, for given inputs of capital, K, and labor, L
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Macroeconomics Chapter 8 14
An Equilibrium Business-Cycle Model
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Macroeconomics Chapter 8 15
An Equilibrium Business-Cycle Model
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Macroeconomics Chapter 8 16
An Equilibrium Business-Cycle Model
Marginal product of capital, real rental price, and the interest rate
i = R/P − δ i = MPK(evaluated at given K and L) − δ
The model predicts that an economic boom will have a relatively high interest rate, whereas a recession will have a relatively low interest rate.
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Macroeconomics Chapter 8 17
An Equilibrium Business-Cycle Model
Consumption, saving, and investment Aggregate household budget constraint
Given the markets for bonds, labor, and capital services clear:
C + ∆K = Y − δ K
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Macroeconomics Chapter 8 18
An Equilibrium Business-Cycle Model
C+ ∆K = A · F( K, L) −δ K depreciation, δK, is fixed in the short
run, An increase in A raises real GDP for
given K and L, we see that a rise in A raises overall real income.
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Macroeconomics Chapter 8 19
An Equilibrium Business-Cycle Model
Consumption, saving, and investment income effect : The increase in real income motivates households to raise current consumption and future consumption. Intertemporal-substitution effect : The increase in the interest rate tends to reduce current consumption.
The net change depends on whether the income effect is stronger or weaker than the intertemporal-substitution effect.
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Macroeconomics Chapter 8 20
An Equilibrium Business-Cycle Model
Consumption, saving, and investment Assume that the change in A is permanent.
the increases in real income tend also to be permanent.
The propensity to consume out of higher income would be close to one.
When the increase in A is permanent, current consumption will rise. However, as long as the intertemporal-substitution operates at all, the increase in current consumption will be less than the increase in real GDP.
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Macroeconomics Chapter 8 21
An Equilibrium Business-Cycle Model
Consumption, saving, and investment
Since current consumption, C, rises, but by less than the increase in real GDP, Y. Therefore, net investment, ∆K, must increase - the increase in real GDP shows up partly as more C and partly as more K.
Since net investment, ∆K, equals real saving, this result is consistent with our finding that real saving increased.
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Macroeconomics Chapter 8 22
Matching the Theory with the Facts
Consumption and Investment When a variable fluctuates in the same
direction as real GDP that variable is procyclical.
A procyclical variable moves in the same direction as the business cycle—it tends to be high relative to its trend in a boom and low relative to its trend in a recession.
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Macroeconomics Chapter 8 23
Matching the Theory with the Facts
Consumption and Investment A variable that fluctuates in the
opposite direction from real GDP is countercyclical.
One that has little tendency to move in a particular direction during a business cycle is acyclical.
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Macroeconomics Chapter 8 24
Matching the Theory with the Facts
相关系数0.88
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Macroeconomics Chapter 8 25
Matching the Theory with the Facts
相关系数0.92
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Macroeconomics Chapter 8 26
Matching the Theory with the Facts
消费和投资都是顺周期变量。
实际消费的波动幅度大于实际 GDP 的波动;而投资的波动比 GDP 的大很多。
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Macroeconomics Chapter 8 27
Matching the Theory with the Facts
The Real Wage Rate The model predicts that the real wage
rate, w/P, will be relatively high in booms and relatively low in recessions.
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Macroeconomics Chapter 8 28
Matching the Theory with the Facts
相关系数0.58
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Macroeconomics Chapter 8 29
Matching the Theory with the Facts
The Real Rental Price The model predicts that the real rental
price of capital, R/P, will be relatively high in booms and relatively low in recessions.
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Macroeconomics Chapter 8 30
Matching the Theory with the Facts
相关系数0.52
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Macroeconomics Chapter 8 31
Matching the Theory with the Facts
The Interest Rate The model predicts that booms will
have a high interest rate, i, whereas recessions will have a low interest rate.
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Macroeconomics Chapter 8 32
Temporary Changes in the Technology Level
A decrease in A due to a harvest failure or a general strike would be temporary.
To allow for these cases, we now assume that the change in A is temporary.
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Macroeconomics Chapter 8 33
Temporary Changes in the Technology Level If A increases temporarily, real GDP, A · F
(K, L), still rises for fixed values of K and L.
The marginal product of capital, MPK, and the interest rate, i, also rise as before.
The intertemporal-substitution effect from the higher i still motivates households to reduce current consumption, C, and raise current real saving.
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Macroeconomics Chapter 8 34
Temporary Changes in the Technology Level
The model therefore predicts that economic boom would feature high real GDP and investment. Consumption would rise by a small amount.
A recession would have low real GDP and investment. Consumption would decline by a modest amount.
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Macroeconomics Chapter 8 35
Variations in Labor Input
Labor Supply More labor supplied means less leisure
time for the family. Assume that households also like more
leisure time. As with consumption and saving, the
choice of Ls involves substitution and income effects.
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Macroeconomics Chapter 8 36
Variations in Labor Input
tc ,
max ,1
. .t
t t tl
t t t
u u c l
s t c w l
wlLS
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Macroeconomics Chapter 8 37
Variations in Labor Input
C
1-L
?
?
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Macroeconomics Chapter 8 38
Variations in Labor Input
The substitution effect for leisure and consumption
A higher real wage rate, w/P, raises the quantity of labor supplied, Ls
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Macroeconomics Chapter 8 39
Variations in Labor Input
Income effects on labor supply A higher w/P means higher real wage
income, (w/P)· Ls Household spends the extra income on
consumption and leisure time. A higher w/P leads to a smaller quantity
of labor supplied, Ls.
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Macroeconomics Chapter 8 40
Variations in Labor Input
Income effects on labor supply Resolve the ambiguity by considering
whether the income effect is strong or weak
C1 + C2/(1+i1) + C3/[( 1+i1)·(1+i2) ] + · · ·
= (1 + i0)·(B0/P+K0) +
(w/P)1·Ls1+(w/P)2·Ls
2/(1+i1) +
(w/P)3·Ls3 /[(1+i1)·(1+i2)]+ · · ·
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Macroeconomics Chapter 8 41
Variations in Labor Input
Income effects on labor supply A permanent increase in real wage
rates results in a large income effect. If the change in year 1’s real wage rate,
(w/P)1, is temporary, the income effect is small.
The income effect will be weaker than the substitution effect.
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Macroeconomics Chapter 8 42
Variations in Labor Input
Intertemporal-substitution effects on labor supply
C1 + C2/(1+i1) + C3/[( 1+i1)·(1+i2) ] + · · ·
= ( 1 + i0)·(B0/P+K0) +
(w/P)1·Ls1+(w/P)2·Ls
2/(1+i1) +
(w/P)3·Ls3 /[(1+i1)·(1+i2)]
+ · · ·
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Macroeconomics Chapter 8 43
Variations in Labor Input
Intertemporal-substitution effects on labor supply. If i1 rises, a unit of year2’s real wage
income, (w/P)2·Ls2, becomes less valuable
as a present value compared to a unit of year1’s real wage income, (w/P)1·Ls
1.
The household would increase Ls1 and
decrease Ls2 as the interest rate
increases.
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Macroeconomics Chapter 8 44
Variations in Labor Input
用数字说话:劳动供给的跨期替代效应的实证
Alogoskoufis(1987b)
Mulligan (1995) 的两个“自然实验”
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Macroeconomics Chapter 8 45
Variations in Labor Input
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Macroeconomics Chapter 8 46
Variations in Labor Input
The cyclical behavior of labor input: theory Increase in A will lead to:
The real wage rate increases Labor inputs increase.
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Macroeconomics Chapter 8 47
Variations in Labor Input
Fluctuations in Labor Input Measures of labor input are procyclical:
they move in the same direction as real GDP during booms and recessions.
Employment Total hours worked
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Macroeconomics Chapter 8 48
Variations in Labor Input
相关系数0.81
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Macroeconomics Chapter 8 49
Variations in Labor Input
相关系数0.88
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Macroeconomics Chapter 8 50
Variations in Labor Input
The cyclical behavior of labor productivity Measures of labor productivity,
Y/L, is real GDP per worker, Real GDP per worker-hour.
Labor productivity turns out to be procyclical in both cases.
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Macroeconomics Chapter 8 51
Extra : labor supply model
For simplicity: the household has only one member and he lives only for one period and has no initial wealth.
FOC:
ttt
tttl
lwcts
blbcut
..
01lnlnmax,c t
cwllbcL 1lnln
01
c
01
wl
b
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Macroeconomics Chapter 8 52
Extra : labor supply model
Intuition: In one period, the income and substitution
effects of a change in the wage offset each other.
bl
1
1*
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Macroeconomics Chapter 8 53
Extra : labor supply model
212211
2211
1
1
1
1
1lnln1
11lnln
cr
clwr
lw
lbclbcL
01)1(
10
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rcc
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)1)(1(0
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wrl
bw
l
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Two periods:
FOC:
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Macroeconomics Chapter 8 54
Extra : labor supply model
1
2
1 2
2 1
1,
1
1 1
1 1
c
c r
l w
l r w
Intuition: intertemporal substitution in labor supply