EconomicGrowth&Convergence

1Economics of LDCs

Lecture 2: Economic Growth and Convergence

Economics of Least Developed Countries

Week 2: Theory of Economic Growth and Convergence

2Economics of LDCs


Introduction

„The consequences for human welfare involved in questions like these

(economic growth) are simply staggering: Once one starts to think about

them, it is hard to think about anything else.“ Lucas

� Small percentage change in rate of growth => huge difference for standard of

living

– Example: country growing 1% double income in 70 years vs 3% doubles in 23

years

– Rule of thumb for period necessary for doubling income (70/g)

– Great appeal to find determinants of economic growth

� Growth as very recent phenomena

3Economics of LDCs


Neoclassical models

Harrod-Domar model

Sollow model

Convergence?

Unconditional

Conditional

Why catching-up may not take place?

Endogeneity of variables

Human capital

Complementarities

4Economics of LDCs


� Economic growth results from abstention from current consumption in the form of savings

� Macroeconomic balance (savings = investments)

� All that is needed for production is physical capital => constant capital-output ratio

� Saving rate: proportion of income saved

� Economic growth is positive when investments (I) exceed depreciation (delta)

– Total:

– Per capita:

Harrod-Domar model (I): Capital fundamentalism

)(/)( tYtSs =

θ/)()( tKtY =

)()()1()1( tItKtK +−=+ δ

)(*/)()1()1( tkstkntk θδ +−−=+

5Economics of LDCs


Harrod-Domar model (II): Results

� Influential Harrod-Domar equation:

� Determinants of growth: ability to save and invest (s), ability to convert

capital into output (teta), depreciation rate and population growth (n)

nsg −−≅ δθ/

k

(n+d)k

s*y=s* θ/k

y= θ/k

6Economics of LDCs


Harrod-Domar model (III): Implications and Beyond

� Policy implications

– To ensure growth stimulate savings and reduce population growth

– Foreign capital can substitute domestic

– Case: India and Soviet Union: pushing up savings in CP, not very successful

� Beyond Harrod-Domar model

– How are savings and population growth determined?

– Constant returns to physical capital is not very plausible assumption => Solow

model

– Is physical capital the only important factor of growth? Labor? Technology? Other?

7Economics of LDCs


Solow model (I): Diminishing returns

� Adds to H-D model law of diminishing returns to individual factors of

production (capital and labor)

– In very poor countries returns to capital are very high due to abundance of labor

and available technology

– In richer countries the capital has lower returns (marginal product)

� Model

– Production function with diminishing returns:

– Per capita capital accumulation

• Figure fresh investment sf(k) are eaten by depreciation and population growth

)(kfy =

)()()1()1( tsytkntk +−−=+ δ

8Economics of LDCs


Solow model (II): Results

� Results

– If k is low => returns are high (abundance of labor) => capital accumulation

– If k is high => returns are low (lack of labor) => capital decreases

– k* is staedy state: from any initial level of income the economies should converge

k k*

sf(k)

(n+d)k

f(k)

9Economics of LDCs


Solow model (III): Implications

� Savings and capital accumulation are not capable to ensure long-term growth

of per capita income, their effect eventually dies out

– Level effect (savings, population, depreciation) vs. growth effect (outside of this

model)

– Need to study technological progress (not specifically part of this course)

� Hypothesis of international convergence irrespective of its historic starting

point

– very important feature!

– Poor countries should grow faster than rich countries and eventually catch up

10Economics of LDCs


Neoclassical models

Harrod-Domar model

Sollow model

Convergence?

Unconditional

Conditional



Human capital

Complementarities

11Economics of LDCs


Convergence? Intuition

� Technology is a global public good – can spread among countries and can be

easily adopted once invented

� Falling marginal returns to capital (Solow model)

� Change from agriculture to industry has a higher pace in poor countries

� Learning from mistakes of more developed countries

12Economics of LDCs


Unconditional Convergence

� Unconditional convergence

– In long-run technical progress, saving rate, population growth and capital

depreciation are the same in all countries => the countries will converge to

the same staedy state

– Predicts strong negative relationship between growth rates and initial

value of per capita income

time

(log) per

capita

income B

A

C

D

F

E

13Economics of LDCs


Unconditional Convergence? Evidence (I)

� Methodology

– Regress: g = a + b log yt0 + e

– Interpretation:

• If b < 0 poor countries grow faster => indicating unconditional converge

• If b > 0 rich countries grow faster => divergence

� Baumol (1986)

– Examined 16 richest countries at that time and plotted their 1870 per capita

income and average growth rate in in period 1870-1979

– Finds unconditional convergence

– BUT: selection bias: these countries are not selected randomly, only success

stories included into the sample (Japan vs. Argentina)

14Economics of LDCs


Unconditional Convergence? Evidence (II)

� De Long (1988)

– adds 8 countries that (seen with the eyes of 1870) should have caught up (e.g.

Argentina, Ireland, Spain)

– unconditional converge does not hold

� Cross-country comparison over short time

– 102 countries included into the sample over period 1960-85

– In scatterplots of average growth versus initial income we do not see convergence

– again poorer do not grow faster

� Conclusion:

– Unconditional convergence does not hold!

– Forces that go against convergence may be powerful

15Economics of LDCs


Conditional Convergence?

� Saving rate and population growth may differ among countries in long run =>

Each country converges towards its own steady state = conditional

convergence

� Difficult to test empirically, but there is some empirical support for conditional

convergence

time

(log) per

capita

income

C

B

A

D A’

B’

E

F

16Economics of LDCs


Critical questions

� Why saving rate and population growth remain systematically different

different across countries?

– Endogeneity of critical parameters (so far treated as exogenous)

– Persisting cultural and social norms („The proper woman has a lot of children.“)

� Are physical capital, labor and technology the only major factors of growth?

– Human capital: education and health

– Institutions and Politics

� Does technollogical progress costlessly diffuses?

– Complementarities

– Ability to absorb: human capital

17Economics of LDCs


Neoclassical models

Harrod-Domar model

Sollow model

Convergence?

Unconditional

Conditional



Human capital

Complementarities

18Economics of LDCs


Endogeneity of Savings and Income

� Mutual relationship between savings and income

– Imagine someone close to subsistance level of income => saving rate is very low

– As an economy gets richer people save more => saving rate increases

� Poverty trap may appear: poor people cannot save, and therefore remain poor

(n+d)k

sf(k)

f(k)

k k*poor country kthreshold k*rich country

19Economics of LDCs


Human capital and Convergence (I)

� Human capital (~quality of labor)

– Represents education, health, nutrition, knowledge, experience, etc

– Can be accumulated through investments e.g. in education

– Additional factor of production besides technology, labor and physical capital,

� Human capital, returns to physical capital and convergence

– In poor country is high return to physical capital due to abundance of unskilled

labor and available technology => convergence (argument from Sollow)

– But: In poor country labor is unskilled which decreases the return to physical

capital => lack of human capital hinders convergence

– Total: competing effects on marginal product => due to lack of human capital not

necessarily higher investments in poorer countries => convergence weakened

20Economics of LDCs


Human Capital and Convergence (II)

� Human capital as new factor of production => flatter production function (in

extreme can be even constant) because returns to physical capital diminish

less rapidly

k

sf(k)

(n+d)k

f(k)

k*

21Economics of LDCs


Human Capital and Convergence: Implications and Evidence

� Poor countries will convergence to rich countries only if they will invest

enough into the human capital (!)

� Examples:

– Germany after WWII, Japan in 1960, Korea and Taiwan later: low stock of physical

capital and relatively high stock of human capital → phenomenal growth,

– Sub-Saharan Africa in 1960: school enrolments were relatively low relative to their

per capita GDP → slow growth

� Barro (1991): Evidence for convergence conditional on level of human capital

– by conditioning on the level of human capital, poor countries tend to grow faster

than rich countries

22Economics of LDCs


Technological progress and Complementarities (I)

� Technological progress

– A) Deliberate diversion of resources from current productive activity into R&D

– B) Diffusion of technology (transfer of technical knowledge)

� Many investments complementary with the decisions of other firms

� Example of complementarity

– Two possible states: Only agriculture vs. Railways, coal, steel

– Consider undertaking separate investments:

• Railway alone – who will use it?

• Coal alone: who will buy it? How to transport it?

• Steel alone: no coal, no freight, no engineers

– These investments are complementary: All of them are needed and at once and

depend on the believes of the investments in the other ”complementary” sectors

23Economics of LDCs


Technological progress and Complementarities (II)

Individual

investment

rate

45

s1 s2

Anticipated investment

rates in an economy (sa)

� Model: Individual investment rates (s) as a function of projected average economy-wide

rates (sa)

� If the firm believes the investments in the economy sa will be high → it will invest big

proportion s

24Economics of LDCs


Technological Progress and Complementarities: Implications

� Possibility of two investment equilibriums

– s1: individual firms have pessimistic expectations about investments of the others

in an economy => low investments

– s2: positive forecasts, stable climate (important in poorest countries), optimistic

expectations => high investments

� Two identical copies of the same economy may grow at different rates

depending on expectations and history

25Economics of LDCs


Summary

� Sollow model:

– Difference from Harrod-Domar model

– logic and its implications for growth and convergence of countries

� Unconditional and conditional convergence: intuition and evidence

� Why countries may not catch-up?

26Economics of LDCs


Readings for Week 2

Primer readings

� Debray Ray (1998): Development Economics, ch.3 and 4

� Barro and Sala-i-Martin (2004): Economic Growth, Introduction

Recommended readings

� Todaro and Smith (2003): Economic Development, ch. 4 and 5

� Barro and Sala-i-Martin (2004): Economic Growth, Selected parts of ch.1

(Solow model) and 5 (Human capital)

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