Growth and factors of productionecon.sciences-po.fr/sites/default/files/file/UWE_2_2017...Long-term...

Long-term economic growthGrowth and factors of production

Lecture 2Nicolas Coeurdacier

[email protected]

Understanding the World Economy

Master in Economics and Business

0

5,000

10,000

15,000

20,000

25,00019

50

1953

1956

1959

1962

1965

1968

1971

1974

1977

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 2000, Japan had more than 20 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.

1. The Solow 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

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

Output ��(at date t) is produced using inputs (capital ��and labour ��) more or less efficiently.

�� = ��(�� , ��)

Output �� increasing in the quantity of inputs, �� and ��.

Output �� increasing in the ‘efficiency’ of inputs ��(think

‘technology’). Also called ‘Total Factor Productivity’ (TFP).

Production function

�� = ��(��)�(��)

��

Constant returns to scale with respect to both inputs.

Double �� and ��, double ��.

Decreasing returns to scale to each input (0 < � < 1):

each additional unit of input brings less and less output.

Output per capita (with �� =��

��=capital per capita):

��/�� = �� = ��(��/��)� = ��(��)

�

Example: neoclassical production function

Higher capital stock per capita increases output per capita

Output per worker y

Capital per worker �

� = ��

Higher TFP increases output per capita

� = ��


Output per worker y

• 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(�/�) ��


Constant Marginal Product of Capital

Capital �

Return on Capital

(MPK)

� = 1

� = �K

�� = �

�= A


Increasing 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


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 defined as: ��$ = �� = �∗

&�∗ = *�(�∗)�

Steady-state capital and output per worker:

�∗ = (,-

.) /( ��); �∗ = �(�∗)�

The Solow growth model: steady state

Steady-state capital stock 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


/ = *��

�∗

/ = &�

�∗∗

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


/ = *��

�∗

/ = &�

�∗∗

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:

0∗ = (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

- +

0∗ = (1 − *)�(�∗)� = 1 − * �(*�

&)�/( ��)

Optimal consumption and welfare

100%0%

0∗

*�

Saving rates (% of GDP) Selected countries, average 2010-2015.

Source: World Bank

0

10

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30

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60M

oza

mb

iqu

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Se

ne

ga

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Rw

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d K

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d S

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Ita

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Ind

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itze

rla

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Ch

ina

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ga

po

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Wo

rld

Steady-state: �∗ = (,-

.) /( ��)

Dynamics: ��$ = 1 − & �� + *�(��)�

��$ = 1(��)with�∗= 1(�∗)

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

Dynamics of the capital stock per worker

��$

��

��$ = 1(��)

�∗

��$ = ��

�∗

�2

45°

Implications of the Solow 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

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10 000

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France Germany Italy UK

5000

2500

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GDP per capita (log-scale, USD)

Output per worker growth (34) dynamics

34

��∗�2

Everything else equal, countries starting

further away from their steady-state capital

stock are growing at at a faster pace.

Zero growth

from capital

accumulation

Do countries converge?

• According to the Solow 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

If economies converge then expect negative correlation : countries with high GDP in

1960 should grow more slowly as capital earns a low return.

Source: PWT

Do economies converge?

The evidence - Round II: OECD

Evidence for convergence is much stronger

Do economies converge? The evidence

Round III: The States


The evidence - Round IV: Japanese Prefectures


The evidence - Round V: European Regions


The evidence - Round VI: canadian provinces

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

• The 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?


*�56��= *�7898:8��

�;<89:8 �7898:8

Steady state

investment

per worker

�56

*�;<89:8��

Initial conditions:

�;<89:8 < �56 = �7898:8

�;<89:8 < �7898:8 < �56

( = &�

•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 from 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 log(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

�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

0

10

20

30

40

50

601

96

2

19

64

19

66

19

68

19

70

19

72

19

74

19

76

19

78

19

80

19

82

19

84

19

86

19

88

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90

19

92

19

94

19

96

19

98

20

00

20

02

20

04

20

06

20

08

20

10

20

12

20

14

Singapore

China

South Korea

Hong Kong

Source: World Bank

Saving rates (% of GDP)

�� = ��(��)�(��)

��

Take log- of both sides and first time difference:

log ��@A��

= log -�@A-�

+� log ��@A��

+(1 − �) log ��@A��

3� = 3- + �3� +(1 − �)3�

Output growth 3� comes from TFP growth 3- and

growth in inputs 3� and 3� .

Output per capita:�� = ��(��)�

34 = 3- + �3C

Growth Accounting

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 standards 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 decreasing marginal

product of capital. This assumption should imply 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 Solow 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

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