Economics of Least Developed Countries Week 2: Theory of Economic Growth and Convergence
Economics of LDCs Lecture 2: Economic Growth and Convergence
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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
Economics of LDCs Lecture 2: Economic Growth and Convergence
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Neoclassical models Harrod-Domar model Sollow model
Convergence? Unconditional Conditional
Why catching-up may not take place? Endogeneity of variables Human capital Complementarities
Economics of LDCs Lecture 2: Economic Growth and Convergence
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Harrod-Domar model (I): Capital fundamentalism
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
Y (t ) = K (t ) / θ
s = S (t ) / Y (t )
Saving rate: proportion of income saved
Economic growth is positive when investments (I) exceed depreciation (delta) – Total:
K (t + 1) = (1 − δ ) K (t ) + I (t )
– Per capita:
k (t + 1) = (1 − δ − n) k (t ) + s / θ * k (t )
Economics of LDCs Lecture 2: Economic Growth and Convergence
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Harrod-Domar model (II): Results g ≅ s /θ − δ − n
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)
y= k / θ s*y=s* k / θ (n+d)k
k Economics of LDCs Lecture 2: Economic Growth and Convergence
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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?
Economics of LDCs Lecture 2: Economic Growth and Convergence
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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:
y = f (k )
– Per capita capital accumulation k (t + 1) = (1 − δ − n) k (t ) + sy (t ) • Figure fresh investment sf(k) are eaten by depreciation and population growth
Economics of LDCs Lecture 2: Economic Growth and Convergence
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Solow model (II): Results f(k) (n+d)k sf(k)
Results
k*
k
– 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
Economics of LDCs Lecture 2: Economic Growth and Convergence
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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
Economics of LDCs Lecture 2: Economic Growth and Convergence
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Neoclassical models Harrod-Domar model Sollow model
Convergence? Unconditional Conditional
Why catching-up may not take place? Endogeneity of variables Human capital Complementarities
Economics of LDCs Lecture 2: Economic Growth and Convergence
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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
Economics of LDCs Lecture 2: Economic Growth and Convergence
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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 (log) per capita income
F
B D
E
A C
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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)
Economics of LDCs Lecture 2: Economic Growth and Convergence
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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
Economics of LDCs Lecture 2: Economic Growth and Convergence
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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
(log) per capita income
B’ F A’ E
D B
C A
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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
Economics of LDCs Lecture 2: Economic Growth and Convergence
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Neoclassical models Harrod-Domar model Sollow model
Convergence? Unconditional Conditional
Why catching-up may not take place? Endogeneity of variables Human capital Complementarities
Economics of LDCs Lecture 2: Economic Growth and Convergence
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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
f(k) (n+d)k sf(k)
k*poor country
kthreshold
Economics of LDCs Lecture 2: Economic Growth and Convergence
k*rich country
k 18
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
Economics of LDCs Lecture 2: Economic Growth and Convergence
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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
f(k) (n+d)k sf(k)
k*
Economics of LDCs Lecture 2: Economic Growth and Convergence
k
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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
Economics of LDCs Lecture 2: Economic Growth and Convergence
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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
Economics of LDCs Lecture 2: Economic Growth and Convergence
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Technological progress and Complementarities (II)
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
Individual investment rate
45 s1
Economics of LDCs Lecture 2: Economic Growth and Convergence
s2 Anticipated investment rates in an economy (sa) 23
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
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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?
Economics of LDCs Lecture 2: Economic Growth and Convergence
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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)
Economics of LDCs Lecture 2: Economic Growth and Convergence
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