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Long-term economic growthGrowth and factors of production
Lecture 2Nicolas Coeurdacier
Understanding the World Economy
Master in Economics and Business
1. The neoclassical growth model
2. Do countries catch with economic leaders?
3. The Asian growth miracle?
Lecture 2 : Long-term economic growth
Growth and factors of production
0
5,000
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15,000
20,000
25,00019
50
1953
1956
1959
1962
1965
1968
1971
1974
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1980
1983
1986
1989
1992
1995
1998
2001
What makes countries rich ?
A Tale of Two Countries
The average income on a Japanese person
The average income on a Ghanaian person
Output per capita
(constant USD)
By 1996, Japan had 19 times the income of Ghana
• Three-quarters of Ghanaians have no access to health
care; all Japanese do.
• Forty percent of all Ghanaians do not have clean
drinking water; all Japanese do.
• Half of all Ghanaian women cannot read; all Japanese
women can.
• Ghanaian mothers are 91 times more likely to die in
childbirth than Japanese mothers.
What are the engines of economic growth?
• The full picture is complicated and involves many
different aspects. Next two lectures build up a
complete picture.
• Focus first on just one factor - capital accumulation.
Increases in the stock of physical capital (buildings and
machinery).
• Stress many other things important – not least how
efficiently this capital stock is used. Capital is just a
starting point.
Production function
OutputproducedOutput
produced
Buildings andmachinery
Buildings andmachinery
Labourinput
Labourinput
Technicalknowledge and
efficiency
Technicalknowledge and
efficiency
This lecture focuses on first input – capital accumulation
• How does increasing the capital stock lead to higher output?
The marginal product of capital (MPK) is the increase in output
that comes from increasing the capital stock leaving everything
else unchanged
• The MPK can be :
• decreasing (Solow neoclassical model) – each new machine
adds less than the last
• constant (Endogenous Growth I – AK) – each new machines
adds the same as the last
• increasing (Endogenous Growth II – Poverty Trap) – each new
machine adds more than the last
How does capital accumulation work?
THE RETURN ON CAPITAL
Diminishing Marginal Product of Capital
Capital �
Return on Capital
(MPK)
0 < � < 1
� = �(�)�( )���
��� =��
��= �A( /�)���
THE RETURN ON CAPITAL
Constant Marginal Product of Capital
Capital �
Return on Capital
(MPK)
� = 1
� = �K
��� =��
��= A
THE RETURN ON CAPITAL
Diminishing Marginal Product of Capital
Capital �
Return on Capital
(MPK)
� > 1
� = �(�)�( )�
��� =��
��= �A(�)���( )�
• Assumptions about MPK purely technological – no economics
involved.
• Different assumptions may be needed for different technologies.
• We stick on decreasing returns - neoclassical production function
with 0 < � < 1 and k =�
�= capital per capita:
��� =��
��= �A(�)���
Remark: Different assumptions lead to dramatically different
implications. What would cross country growth patterns look like if
MPK were initially increasing and then became decreasing?
The neoclassical MPK
} 1y∆
2} y∆
{k∆
{k∆
∆ > ∆1 2y y
Capital per worker �
Output per worker y
� = ���
The neoclassical production function
Will countries which invest more grow faster?
• Ultimately - No
• Short Term - Yes
• In long-run, investment affects only level not
growth of output.
• To show this we need to add some economics
to our technology assumption – need to
introduce investment.
Production: � = � (� )�( )
���
Capital accumulation:
� = (1 − ")� ��+$
"= depreciation rate; $ = investment
$ =Savings = constant fraction s of income:
$ = s� = &� (� )�( )
���
Thus, capital obeys to:
� = (1 − ")� ��+&� (� )�( )
���
The Solow growth model
� = (1 − ")� ��+&� (� )�( )
���
Assuming for now constant and � .
In per capita terms:
� = 1 − " � �� + &�(� )�
Steady-state is defined as: � = � �� = �∗
"�∗ = &�(�∗)�
Steady-state capital and output per worker:
�∗ = (()
*)�/(���); �∗ = �(�∗)�
The Solow growth model: steady state
Steady-state capital stock per worker
Capital per worker �
+ = &���
�∗
+ = "�Steady state
investment
per worker
� When capital stock is low:
Each new machine leads to a big increase in gross output
The amount of output needed to replace machines that have worn out is
low
As a result net output increases with the capital stock
� When capital stock is (too) high:
Each new machine leads to a small increase in gross output
Every period a substantial part of output is needed to replace machines
that have worn out
Eventually net output decreases with capital stock
� Key to these results is decreasing marginal return on capital.
Convergence to the steady state
Higher savings increase the steady-state capital stock
Steady state
investment
per worker
Capital per worker �
+ = &���
�∗
+ = "�
�∗∗
Higher &
Source: PWT
Investment Rate and Level of Per Capita Real GDP
5
6
7
8
9
10
11
12
0 5 10 15 20 25 30 35 40 45 50
Log(GDP per capita) in 2008
Average Investment Rate 1950-2008
Savings or Investment?
• We are using investment and savings interchangeably
• If a country cannot borrow from overseas then its savings has
to equal investment.
• Most countries do not borrow much from overseas (as a % of
GDP) so savings and investment closely linked.
• When country borrows I > S but then it has to repay funds so
S>I. Therefore on average I = S
• When country can borrow abroad (I > S , convergence towards
steady-state can happen faster.
Higher TFP increases the steady-state capital stock
Capital per worker �
$ = &���
�∗
$ = "�
�∗∗
Higher �
Steady state
investment
per worker
� A high savings rate leads to high income but low consumption
� A low savings rate leads to low income but high consumption
Consumption per worker in the steady-state:
,∗ = (1 − &)�(�∗)� = (1 − &)(&�
")�/(���)
The “Golden rule” - level of savings that maximizes consumption
in the steady state. Simple calculations suggest that optimal rate
around 30-35% of GDP
Optimal consumption and welfare
- +
Savings rate (% of GDP) Selected countries, average 1998-2008.
Source: PWT
0
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d S
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Ca
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Afr
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Me
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Au
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Fra
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Ita
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Po
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Mo
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Ge
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Ind
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Cze
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itze
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Jap
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Ma
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Ko
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, R
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Ch
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Sin
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Steady-state: �∗ = (()
*)�/(���)
Dynamics: � = 1 − " � �� + &�(� )�
� = -(� ��)with�∗= -(�∗)
Convergence: � converges to �∗.
As � approaches �∗, the growth rate of � (and
output � ) decreases.
The further away from �∗ a country is, the faster
it grows.
The Solow growth model: dynamics
German GDP and capital growth 1936-1955
-50
-40
-30
-20
-10
0
10
20
3019
36
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
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1953
1954
1955
GDP Growth
Change in Capital Stock
Implications of the neoclassical growth model
1. Countries always eventually reach their steady state
2. In the steady state/long run growth only comes from TFP.
Countries at their steady state no longer grow from capital
accumulation. Think of the OECD economies as those at their
steady state.
3. Richer countries should grow slower than poorer ones:
Higher returns on investment in poorer countries. Emerging
markets are moving towards a steady state and growing fast.
According to this story we would expect countries to “catch
up” with economically most advanced nations
Catch up amongst Europe’s big 4
Source: Maddison, GGDC and DataStream
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11.018
6118
6618
7118
7618
8118
8618
9118
9619
0119
0619
1119
1619
2119
2619
3119
3619
4119
4619
5119
5619
6119
6619
7119
7619
8119
8619
9119
9620
0120
06
France
Germany
Italy
UK
Log output per capita (US $ 1990)
1. The neoclassical growth model
2. Do countries catch up with economic leaders?
3. The Asian growth miracle?
Lecture 2 : Long-term economic growth
Growth and factors of production
Output per worker growth (/0) dynamics
/0
� �∗�.
Everything else equal, countries starting
further away from their steady-state capital
stock are growing at at a faster pace.
Zero growth
from capital
accumlation
Do countries converge?
• According to the Solow neoclassical growth model,
poorer countries (in terms of capital stock per worker
should) grow faster.
• Does it hold in the data?
• Investigate link between future growth and initial
income per capita.
Do countries converge ?
The Evidence - Round I: The World
-2
0
2
4
6
8
10
12
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
GDP per Capita 1970, USD
Ave
rage
GD
P g
row
th r
ates
197
0-20
02
If economies converge then expect negative correlation : countries with high GDP in
1970 should grow more slowly as capital earns a low return.
Source: PWT
The “Iron Law of Convergence”
• On average 2% of the gap between poor and rich
countries that are similar vanishes in a year.
• Very slow - takes 35 years to eliminate half of the
initial output gap.
Reconciling the evidence
•When we look at all economies no evidence of convergence.
• When we examine very similar countries strong evidence of
convergence.
• How can we explain this mixed evidence concerning
convergence?
- take into account that steady states can differ across
countries!
Conditional convergence
• Neoclassical Solow model does not predict convergence
unconditionally.
• Everything else equal, countries with lower capital stock
should grow faster.
• Countries with same steady-state should converge =
conditional convergence
• In particular, countries with lower TFP (or lower savings)
should not catch-up.
• Importance for growth is distance from steady-state which
can be different across countries.
Conditional convergence: an illustration
Which country should grow faster?
Capital per worker �
&�12��= &�345464��
�784564 �345464
Steady state
investment
per worker
�12
&�784564��
Initial conditions:
�784564 < �12 = �345464
�784564 < �345464 < �12
$ = "�
•Only when countries share the same steady state should we
see convergence. Explains why only see evidence for
convergence amongst similar countries.
• Explains why many African countries do not catch up with
Europe/U.S.
• Suggests that wealthier economies will persistently stay
wealthier, but within wealthier economies should see evidence
of catch up.
• The big question is what determines a countries steady state?
Conditional convergence
Convergence implies that growth increases with distance form steady-state:
GDP Growth = b (log(YSS)-log(Y(0))), b>0
Don’t have data on YSS but assume
log(YSS )= a1 x Education + a2 x Health + a3 x Investment…
And can estimate for a cross-section of countries:
GDP growth = b x (a1 x Education) + b x (a2 x health) +
b x (a3 x Investment) – b Y(0)
• If b> 0 then have support for convergence (conditionally on SS determinants)
• Can estimate if a1, a2, a3 are significantly different from zero and matter for
steady state
•Typical ‘cross-country’ growth regressions (initiated by Barro)
Estimating the steady state
Source: Barro (1991)
Dependent variable: real GDP per capita growth (1960-1990), 100 countries.
(in 1960)
‘I JUST RAN TWO MILLION REGRESSIONS’
(Salah-i-Martin (1997))
Always significant Frequently significant Often significant Sometimes significant
Education – Primary school Enrolment
Regional dummies (Latin America, Sub Saharan Africa, Negative)
Exchange Rate
Overvaluation (Negative)
Government Consumption (Negative)
Investment Rule of Law Black market premiums (Negative)
Financial Sophistication
Health – Life Expectancy Political Rights Primary Products (% exports – Negative)
Inflation (Negative)
Religious dummies (confucian, Muslim, Protestant)
Ethnic Diversity (Negative)
Openness Civil Liberties
Degree of Capitalism Revolutions, Coups, Wars (Negative)
Religious dummies (Buddhism, Catholic)
Public Investment
1. The neoclassical growth model
2. Do countries catch with economic leaders?
3. The Asian growth miracle?
Lecture 2 : Long-term economic growth
Growth and factors of production
�Since the post-war period we have witnessed astonishing levels
of growth in the “Asian Tigers”.
� The press and political commentators:
� Bad for the West: Take our jobs
� Western leaders and CEO’s should look at the Tigers and
learn how to improve efficiency.
� Economists: No growth miracle. Just accumulation of inputs.
Asian Tigers: growth miracle?
Average Growth GDP per capita 1966-2009
Source : Penn WT 6.3 and DataStream.
0% 1% 2% 3% 4% 5% 6% 7%
Germany
Mexico
US
Canada
France
Brazil
Italy
Chile
Japan
Singapore
HongKong
China
Korea
Taiwan
Investment rates
0
10
20
30
40
50
60
7019
60
1963
1966
1969
1972
1975
1978
1981
1984
1987
1990
1993
1996
1999
2002
2005
Source : Penn World Table 6.3
% of GDP
Singapore
Hong Kong
China
Large amount of compulsory savings in Singapore
0
10
20
30
40
50
60
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991
Employee
Employers
% of Wages
Source : Young 1995, Barro and Sala-I-Martin 1991
CPF Contributions
Growth Accounting 1966-90 for Asian DragonsEmployment
18%
Capital42%
TFP40%
Employment18%
Capital42%
TFP40%
Employment38%
Capital62%
TFP-4%
Employment38%
Capital62%
TFP-4%
Employment17%
Capital59%
TFP23%
Employment17%
Capital59%
TFP23% Employment
19%
Capital53%
TFP28%
Employment19%
Capital53%
TFP28%
Source : Young 1995, Barroand Sala-I-Martin 1991
Hong Kong
Singapore
Korea
Taiwan
� Some differences in the sources of growth. BUT: Increased capital stock MOST important factor for all of them.
� Krugman: “Perspiration rather than inspiration”!
� Too rapid development? No gains from the learning curve? Incorrect balance between innovation and experience?
� Does it matter?
� No: They got much richer anyway
� Yes: Some have paid for it - those that were young early on in the process: Low income, high savings
� Future? Need to shift from extensive to intensive margin
Asian Tigers: growth miracle?
• Countries show enormous differences in their standard of living. Further
some poor countries have shown rapid growth while others have
remained poor.
• The neoclassical (Solow) growth model focuses on explaining these
differences through capital accumulation, assuming diminishing marginal
product of capital. This assumption implies convergence. Countries with
high investment rates have a high steady state and are rich. At the steady
state all countries grow at the rate of technological progress.
• The neoclassical model relies on conditional convergence – conditional on
countries sharing the same steady state then poorer countries will grow
faster than rich ones.
• The steady state depends on many factors. Strong roles are found for
education, health and rate of investment but many other additional
variables are also found important. The analysis suggests that making a
country rich will involve a broad package of economic, social and political
policies – don’t look for magic ingredient X.
Summary