MACROECONOMICS I March 14 th, 2014 Class 4. Class 4. The Solow-Swan Model (Cont.)
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Transcript of MACROECONOMICS I March 14 th, 2014 Class 4. Class 4. The Solow-Swan Model (Cont.)
![Page 1: MACROECONOMICS I March 14 th, 2014 Class 4. Class 4. The Solow-Swan Model (Cont.)](https://reader030.fdocuments.net/reader030/viewer/2022032707/56649e0c5503460f94af41b1/html5/thumbnails/1.jpg)
MACROECONOMICS I
March 14th, 2014
Class 4. The Solow-Swan Model (Cont.)
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0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 4800
5
10
15
20
25
k
y
y k
0.3i k
0.05k k
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The Solow-Swan Model: Population Growth
• Labor force is growing at a constant rate n:
Lt+1=(1+ n)Lt
( , )t t tY F K L
( )k sy n k
What happens to Capital/Labor ratio (k)?
It is affect by investment (+), depreciation (-), and population growth (-)
Law of motion for k?
kt+1= sf(kt)+(1- - n)kẟ t
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0 26 52 78 1041301561822082342602863123383643904164424684940
5
10
15
20
25
k
y
Solow-Swan Model: Population Growth (Cont.)
y k
( )n k
i s k
*k
*y
( )newn k
*newk
*newy
Economies with high rates of population growth will have lower GDP per capita
Government policy response?
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Population Growth: Summary
Steady state:
• Population growth increases Y and K (level effects)
N!B! Both Y and K grow in the steady state at the rate n, but k* and y* are
constant
• Population growth reduces k* and y*
Population growth consists of natural population increases + migration
2*
2( )
( )
ss k n k k
n
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Population Growth Rates, 1985-1995
Source: The World Bank
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The Role of Technological Progress
• Technological change, increase in factor productivity
Larger output for given quantities of capital and labor
( , )Y F K A L Effective labor
( , , )Y F K L A
How does technological progress translates into larger output?
• State of technology (A)
Labor-augmenting technological progress
• A as labor efficiency
• TP reduced number of workers needed to produce the same output
• TP increases output using the same number of workers
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The Solow-Swan Model with Technological Progress
• Technology is improving every year at the exogenous rate (g)
Production function: GDP per effective labor
( ) ( ) ( )( , , )Y F K L A
1t t
t
A Ag
A
( , )
t t
t t t t
Y F K A L
Y KF
A L A L
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The Solow-Swan Model with Technological Progress (Cont.)
• From GDP per effective labor to the GDP per capita?
' '
( , )
( )
t t
t t t t
t t
Y F K A L
Y KF
A L A L
y f k
'( )t tt t t
t t t
Y Ky A F A f k
L A L
GDP per effective labor
Capital per effective labor
• We are interested in GDP per capita
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0 30 60 90 1201501802102402703003303603904204504800
5
10
15
20
25
k’
y’
' 'y k
( )n g k
' 'i s k
'*k
'*y
Steady state: Constant levels of capital and output per effective worker
The Solow-Swan Model with Technological Progress (Cont.)
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The Solow-Swan Model: Technological Progress (Cont.)
• Capital and output per effective worker are constant in steady state
• What about per capita variables?
GDP per capita grows at the rate of technological progress (sustainable growth)
Balanced growth path: growth of variables at the same rate
•Per capita variables (capital, output and consumption) grow at a constant rate g
• Per effective labor variables are not growing in the steady state
* '*( )ty A f k
N!B! Solow model explains 60 % of cross-country variation of the GDP per capita
by differences in savings rate and population growth
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Growth Accounting
Real GDP per capita growth rate for Czech Republic in 2011 was 1.7 %
Real GDP per capita growth rate for the USA in 2012 was 2.2 %
How much of this growth is due to the factors’ accumulation and/or technology?
( , , )Y F A K L
Y A K L
Growth accounting: breakdown of observed growth of GDP into changes in
inputs and technology
A Y K L
Contribution of technology as a residual
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Growth Accounting (Cont.)
• Capital (K) increases by 1 unit
What is the effect on output Y?
Marginal product of capita (MPK)
TE Capital stock increased by 10 units and MPK =0.1. What is the impact on
GDP?
unit
( , 1, ) ( , , )F A K L F A K L
( , , )Y F A K L
0.1 10 1Y
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Growth Accounting (Cont.)
• Labor (L) increases by 1 unit
What is the effect on output Y?
Marginal product of labor (MPL)
TE Labor force increases by 10 units and MPK =0.3.
units
( , , 1) ( , , )F A K L F A K L
( , , )Y F A K L
0.3 10 3Y
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Accounting for the increase in all components
How to account for the technological change?
Solow Residual: the left-over growth of output when growth attributed to the
changes in labor and capital is subtracted
( , , )
A K L
Y F A K L
Y MP A MP K MP L
Solow Residual
A K LMP A Y MP K MP L
Calculate it as a residual
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Solow Residual (Cont.)
Where do we get marginal products of capital and labor?
L
L
Y
LF
K
K
Y
KFg
Y
Y Lk
A K LY MP A MP K MP L
Mathematical manipulations
• Transforming changes to growth rates
A K L
Y A K LMP MP MP
Y Y Y Y
GDP growth rate
Unobservable technological change (g)
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Solow Residual (Cont.)
L
L
Y
LMP
K
K
Y
KMPg
Y
Y LK
Share of capital in output
Share of labor in output
K L
Y K Lg MP MP
Y Y Y
N!B! Key assumption: Factors of production are paid their marginal
product
• Wages and rental rate of capital reflect productivity of factorsY K Lg
Y K L
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Historical Factor Shares
Labor (2/3)
Capital (1/3)
Source: Acemoglu, 2009
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Source: Mankiw, 2009
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The Asian Growth Miracle?
A. Young (1995) QJE
Exceptional growth due to changes in TFP or factor accumulation?
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The Asian Growth Miracle?
Exceptional growth due to the factors accumulation? Conclusion?
The miracle was bound to stop
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1981
1984
1987
1990
1993
1996
1999
2002
2005
2008
2011
-0.1
-0.05
0
0.05
0.1
0.15
Hong Kong SAR
Korea
Singapore
Taiwan
Asian Tigers: Performance After 1990s
Source: IMF World Economic Outlook Database
Real GDP growth rate
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Country Average growth rate 1990-2012 (%)
Hong Kong 3.9Singapore 5.9
South Korea 5Taiwan 4.8
Asian Tigers: Performance After 1990s
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Global Slowdown in Economic Growth
GDP per capita growth rate (% per year)
Country 1948-1972 1972-1995 1995-2010
Canada 2.9 1.8 1.6
France 4.3 1.6 1.1
Germany 5.7 2 1.3
Italy 4.9 2.3 0.6
Japan 8.2 2.6 0.6
UK 2.4 1.8 1.7
USA 2.2 1.5 1.5
Source: Mankiw (2013)
What are the reasons?
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Theories Explaining Disparities in Development
Fundamental causes
Geography: geographical concentration of poverty and prosperity
Tropical climate: lazy people, diseases, and poor agricultural lands
Counter examples: Botswana, Nogales
Culture: beliefs, values, ethics, trust, cooperation
Counter examples: North and South Korea
Ignorance of policy makers: poor policies
Transfer of resources to a small powerful group
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The Institutional Hypothesis
• Countries differ in economic success because of different institutions (rules)
Laws, regulations, enforcement of property rights and social norms
Extractive institutions: concentration of power in the hands of elite
Inclusive institutions: inclusive markets and opportunities
Free choice of occupation, education, constrained and broadly distributed
power
Institutions => Incentives to acquire education, start a business and innovate
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Nogales
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African Growth Miracle
GDP per capita
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Next class: Business cycles
N!B! Homework is due next week before the class