cee economic growth & development - cerge-eihome.cerge-ei.cz/dragana/l71.pdf · cee economic...
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CEE Economic Growth & Development
Fall Semester, 2014
Lecture 7. Economic Growth:
The Role of Technological Progress
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• The Solow model: Deriving steady state
• The Solow model and technological progress
• Growth accounting
Class Outline
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The Vicious Circle of Poverty
GDP
Low savings
Scarce investment
capital
Scarce jobs,
Poor capital
Low output and
income
POVERTY
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Breaking the Cycle
GDP
Better
institutions
Investment
capital
Better jobs,
Technology
Higher output
ECONOMIC
GROWTH
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Solow-Swan Model of Economic Growth(1956)
Overview
Production function
• Diminishing returns to factor inputs
GDP per capita
( ) ( )( , )Y F K L
,1
( )
t t t
t t
t t
Y K KF F
L L L
y f k
y k
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Diminishing Returns to Factor Inputs
( )y f k k
Implication: Countries
with small capital stock
are more productive =>
grow faster
Output per capita
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Economic Growth and Capital Accumulation
Increase in capital stock (K)
Investments of firms
Savings of households provide investment funds to firms
s - exogenous savings rate
New additions
to the capital stock
Replacement of the
worn-out capital
(depreciation)
1
1
(1 )
(1 )
t t t
t t t
K I K
K sY K
Net investment = Total savings – Replacement of the depreciated capital
K sY K
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Economic Growth and Capital Accumulation (Cont.)
Increase in capital stock (K)
Investments of firms
New additions
to the capital stock
Replacement of the
worn-out capital
(depreciation)
K sY K
• If capital stock is growing
• If capital stock is shrinking
• Break-even investment
sY K
sY K
sY K
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0
5
10
15
20
25
0 100 200 300 400 500
y
k
y k
i s k
k
Steady State Level of Capital
0 0I K K k
The economy would grow as long as
*k
*y
( )sf k k
Steady state capital (k*)
and output (y*) per capita
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The Solow-Swan Model: Steady State
Steady state: the long-run equilibrium of the economy
•Savings are just sufficient to cover the depreciation of the capital stock
N!B! Savings rate is a fraction of wage, thus is bounded by the interval [0, 1]
In the long run, capital per worker reaches its steady state for an exogenous s
Increase in s leads to higher capital per worker and higher output per capita
Output grows only during the transition to a new steady state (not sustainable)
Economy will remain in the steady state (no further growth)
Economy which is not in the steady state will go there => Convergence
Government policy response?
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The Solow-Swan Model: Numerical Example
0.5 0.5( , )Y F K L K L
0.5 0.5 0.5
0.5
;
Y K L K
L L L
K Yk y
L L
Production function
Production function in per capita terms
GDP per capita:
Savings rate:
Depreciation rate:
Initial stock of capital per worker:
y k
30%s
10%
0 4k
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Year k y i c δk Δk
1 4
2
…
Consumption: C = (1-s)Y
Consumption per capita C/Y = c
Steady state capital/labor ration:
2*
2
ss k k k
The Solow-Swan Model: Numerical Example (Cont.)
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The Solow-Swan Model: Convergence to Steady State
N!B! Regardless of , if two economies have the same s, δ, N, they will
reach the same steady state
0k
• If countries have the same steady state, poorest countries grow faster
•Not much convergence worldwide
Different countries have different institutions and policies
• Conditional convergence: comparison of countries with similar savings rates
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0
5
10
15
20
25
0 100 200 300 400 500
y
k
y
i
k
Solow Model: Convergence to Steady State
Convergence to steady state
*k
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Solow Model: Increase in Savings Rate
0
5
10
15
20
25
0 100 200 300 400 500
y
k
• Savings rate increases from 30 % to 40 %
• Economy moves to a new steady state => Higher capital and output per capita
y
k
i
newi
*k*
newk
*y
*
newy
What effect would
have increase in δ on
the steady state?
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Source: Mankiw (2009)
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Log income per capita in 1960 (100=1996)
World Wide Convergence
Changes
in Log
income
per capita
in 1960 -
1990
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The Golden Rule Level of Capital
Increasing savings rate means less present consumption
What is the optimal savings rate?
* * * maxc k k
N!B! Optimal savings
rate maximizes
consumption per capita
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The Solow-Swan Model: Population Growth
Labor force is growing at a constant rate n =10%
( , )t t tY F K L
( )k sy n k
• Per capita capital stock is affect by investment, depreciation, and population growth
2*
2( )
( )
ss k n k k
n
Steady state:
• Population growth increases Y (level effect)
• Population growth reduces k* and y*
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0
5
10
15
20
25
0 100 200 300 400 500
y
k
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?
N!B! Sustainable
economic growth
still remains
unexplained
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The Role of Technological Progress
• Technological change, increase in factor productivity
Larger output with 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
5
10
15
20
25
0 100 200 300 400 500
y’
k’
' '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 marginal product
• Wages and rental rate of capital reflect productivity of factors
Y 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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