Conditional Convergence and Long-Run Economic Growth

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C h a p t e r 5
Conditional Convergence and Long-Run Economic
Growth
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Conditional Convergence in Practice

• Growth rate of capital per worker, ?k/k
• ?k/k ? k(0) , k
• (-) ()
• y A f(k)
• Growth rate of real GDP per worker is a function
  of initial and steady-state real GDP per worker
• ? y/y ? y(0) , y
• (-) ()

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Conditional Convergence in Practice
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Conditional Convergence in Practice

• Variables that influence y that are held
  constant.
• A measure of the saving rate
• The fertility rate
• Subjective measures of maintenance of the rule of
  law and democracy
• The size of government
• The extent of international openness, measured by
  the volume of exports and imports
• Changes in the terms of trade
• Measures of investment in education and health
• The average rate of inflation

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Conditional Convergence in Practice

• Japan and Germany after 2nd world war.
• East Asia countries
• African Countries

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Long-Run Economic Growth

• Solow model, the growth rate of capital per
  worker, k, is given by
• ?k/k s (y/k) - sd - n

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Long-Run Economic Growth

• A case in which capital broadly defined to
  include human and infrastructure capital is the
  only factor input to production.
• AK model
• y Ak

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Long-Run Economic Growth

• k capital per worker
• y/k A
• ?k/k sA- sd - n

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Long-Run Economic Growth
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Long-Run Economic Growth

• Conclusions
• The long-run growth rate of capital per worker,
  ?k/k, is greater than zero and equal to sA- sd -
  n
• Growth rates of capital and real GDP per worker,
  ?k/k and ?y/y, do not change as capital and real
  GDP per worker, k and y, rise.
• poor economies with low k and y do not tend to
  grow faster than rich economies

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Long-Run Economic Growth

• The regular process of improvement in technology
  is called technological progress.
• exogenous technological progress - the
  improvements in technology were not explained
  within the model.
• ?A/A g

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Long-Run Economic Growth

• Exogenous Technological Progress
• ?Y/Y ?A/Aa(?K/K)(1-a)(?L/ L)
• Using ?A/A g and and ?L/L n
• ?Y/Y g a(?K/ K) (1-a) n
• ?y/y ?Y/Y- ?L/L ?Y/Y- n

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Long-Run Economic Growth

• Exogenous Technological Progress
• ?y/y ga(?K/K)(1-a)n - n
• ga(?K/K - n)
• ? k/k ? K/K - ?L/L ?K/K - n
• ?y/y ga(?k/k)

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Long-Run Economic Growth

• Exogenous Technological Progress
• ?k/k - in the Solow model
• ?k/k sAf(k)/k- sd - n
• Growth rate of real GDP per worker with technical
  progress
• ?y/y ga sA f(k)/k- sd-n

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Long-Run Economic Growth

• Steady state all variables grow at constant
  rates.
• ?k/k is constant
• ?k/k s(y/k)- sd - n
• y/k is constant

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Long-Run Economic Growth

• Exogenous Technological Progress
• (?y/y) (?k/k)
• (?y/y) g a(?k/k)
• (?y/y) g a(?y/y)
• (?y/y) - a(?y/y) g
• (1-a)(?y/y) g

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Long-Run Economic Growth

• Exogenous Technological Progress
• Steady-state growth rate with technological
  progress
• (?y/y) g/(1 - a)
• Since 0 lt a lt 1 the steady-state growth rate of
  real GDP per worker, (?y/y), is greater than the
  rate of technological progress, g.

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Long-Run Economic Growth

• Exogenous Technological Progress
• (?k/k) (?y/y)
• (?k/k) g/(1-a)
• Exogenous technological progress at the rate
  ?A/A g leads to long-term growth in real GDP and
  capital per worker, k and y, at the rate g/(1-a)

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Long-Run Economic Growth

• Exogenous Technological Progress
• ?k/k s(y/k) - sd - n
• (?k/k) g/(1 - a)
• g/(1-a) s(y/ k) - sd - n
• s(y/k)-d ng/(1-a)
• (y/k) d(1/s)ng/(1-a)
• For Cobb-Douglas function

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Long-Run Economic Growth
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Long-Run Economic Growth
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Long-Run Economic Growth
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Endogenous Growth Theory

• Extend the model to explain why technological
  progress occurs.
• Most endogenous growth models focus on
  investments in research and development (RD)

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Endogenous Growth Theory

• The essential feature of knowledge or technology
  
• non-rival good ? MC is zero
• Production function of A ?A f(A,K,L)
• Is the marginal product of A decreasing,
  increasing,
• or constant?
• Human capital

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Endogenous Growth Theory

• The determinants of the allocation of resources
  to RD
• Support for basic scientific research
• Private incentives for RD and innovation
• Alternative opportunities for talented
  individuals rent-seeking
• Learning-by-doing

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Endogenous Growth Theory

• Optimal intellectual property rights
• The Diffusion of Technology
• The imitation and adaptation of one countrys
  technology by another country.
• The rate of technological diffusion to a
  developing country is high when the country
  trades a lot with rich countries, has high
  education levels, and has well functioning legal
  and political systems.

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Endogenous Growth Theory
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The basic RD model

• Assumptions
• The labor force is the single production factor
• Generalized Cobb-Douglas function without capital

3. The fraction of the labor force is exogenous
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The basic RD model

• The evolution function of labor

where

• The evolution function of knowledge

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The basic RD model

• The dynamic of knowledge accumulation

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The basic RD model

• Case 1

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The basic RD model

• Case 1

• Interpretation
• endogenous long run growth rate
• positive link with population growth

has a level effect but not a growth effect
2.
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The basic RD model

• Case 2

ever-increasing growth
has a growth effect
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The basic RD model

• Case 3

linear growth model
has a growth effect