EMEA7: New Growth Models

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EMEA7 New Growth Models

• Romers model
• Learning by doing
• Competitive markets
• Human capital
• Applications?
• Greenhouse gas emission reduction, technology,
  and cost-effectiveness

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Nobelity

• No one won a Nobel Prize for consumer or producer
  theory, as the main architects were long dead in
  1948
• Leontief got one for input-output models
• Arrow and Debreu for general equilibrium
• Solow for growth theory, and Koopmans too
• No one got a Nobel Prize for new growth theory,
  because there are four contending models (three
  shown here), while it is not clear which will
  become the new standard

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New Growth Models

• We looked at models in which economic growth was
  driven by exogenous investments and technology
  (Solow-Swan)
• We looked at models in which economic growth was
  driven by endogenous investments and exogenous
  technology (Ramsey-Cass-Koopmans)
• These models cannot explain income differences,
  and only 25 of long-term growth
• Today, we endogenise technology change

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Romers Model

• Output follows from
• That is, part of the capital and labour inputs
  are used for technological development

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Romers Model -2

• Forget about capital for a while
• The growth rate of knowledge
• Which is zero if
• Note a faster growing population implies faster
  economic growth

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Romers Model with Capital

• Reintroduce capital
• The growth rate of knowledge
• This economy always converges if ß?lt1, always
  diverges if ß?gt1
• (This is because labour growth is given)

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Learning by Doing

• Knowledge depends on capital
• The dynamics of capital follow
• This is structurally similar to
• We looked at this model before. The dynamics are
  quite the same, regardless of physical or human
  capital.

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Endogenous Technology and Competitive Markets

• Above, we tacitly assume that markets are
  perfect, one of the implications of which is that
  capital earns its marginal productivity
• This assumption cannot be maintained when looking
  at endogenous technology
• Suppose that a firm invest 10,000 hours to design
  a 20 MB drive, and then produces 20 trillion MB
  with a 10 million factory and 100 workers
• If it doubles capital and labour, 4 trillion MB
  worth of disk space is produced

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Endogenous Technology and Competitive Markets -2

• If the firm invests 20,000 hours, it designs a 30
  MB drive, and with 20 million factory and 200
  workers, 60 trillion MB is produced, more than
  twice the original amount
• This is because the design of the disk drive is
  non-rival it can be used in unlimited quantities
• More formally,

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Endogenous Technology and Competitive Markets -3

• This implies that
• And that
• So, if the firm sells at marginal costs, paying
  the marginal costs of labour and capital, it
  would make a loss as there is no money left for
  the technology investment
• Perfectly competitive markets do not innovate

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Human Capital

• The above models do not account for observed
  income differences one needs to assume that
  technologies are very different, and diffusion is
  very slow
• This problem can be overcome by distinguishing
  two types of capital physical and human
• Because of non-linearities in the production and
  accumulation functions, allowing for two capital
  stocks makes the growth rate more sensitive to
  changes in savings

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Human Capital -2

• Output follows from
• Assume the usual about capital and labour
• Knowledge grows exogenously, but human capital
  requires investment

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Human Capital -3

• Per effective labour (AL)
• Physical capital dynamics are given by
• Human capital dynamics follow
• The economy converges to a steady state

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Steady States

• One reason why it is interesting to know whether
  a model has a steady state, or balanced growth
  path, is that one needs not be overly concerned
  with disequilibrium dynamics particularly not
  if the rate of convergence is rapid
• Disequilibrium is just noise
• Note that convergence rates are much slower in
  natural systems

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Human Capital -4

• On the balanced growth path
• Taking logs and solving for lnk and lnh
• Recall that

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Human Capital -5

• This leads to
• Suppose that a0.35 and ß0.40, then the
  elasticity of output to investments in physical
  and human capital is 1.4 and 1.6, respectively,
  but only 0.54 in the Solow model

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Applications

• New growth theory, as its name suggests, is
  relatively new
• There are only a few applications to
  environmental issues so far
• Those applications are not very insightful, for
  various reasons
• First, the nature of technological development
  only matters in the long run (for all issues
  except the short term policy portfolio)

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Applications -2

• Those applications are not very insightful, for
  various reasons
• Second, the role of technology in the short term
  policy portfolio is qualitatively clear. More
  serious problems, and problems with a longer time
  horizon require substantial technological
  progress. Stimulating technology requires
  continuous pressure (taxes, evolving standards),
  RD subsidies or niche markets. The government
  should only interfere with basic research.

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Applications -3

• Those applications are not very insightful, for
  various reasons
• Third, serious applications require a solid
  empirical foundation. Unfortunately, technology
  is hard to measure. As a consequence,
  technological progress is even harder to measure,
  let alone changes in the rate of technological
  progress as a result of policy interventions in
  the economy or in research and development.

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New Growth and Climate

• New growth theory did contribute something to
  climate change
• In 1994, Enting et al. (IPCC WG1) published a set
  of emission scenarios that would lead to
  atmospheric stabilisation
• In 1996, Wigley et al. (IPCC WG3) countered with
  a set that would reduce the same targets at much
  lower cost
• This is a cost-effectiveness analysis How to
  reach a given target at minimum cost

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Efficacy and Efficiency

• In a cost-effectiveness analysis, the question is
  how to reach a given target at minimum cost
• In a cost-benefit analysis, the question is how
  to set and reach the target so as to maximise
  welfare, or rather how to reach economic
  efficiency
• (Some people use the word cost-efficiency, but
  thats not English)

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WGI v WRE

• WRE argued that it is better to decelerate
  emission reduction in the short run, accelerate
  in the medium run, because
• Later emissions contribute more to climate change
• One should replace capital at the end of its
  lifetime
• The discount rate makes future emission reduction
  costs less important
• Technological change will make future emission
  reduction easier and cheaper
• Counterargument Action now to stimulate
  technological development

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Goulder and Mathai

• GM investigate two alternative models
• Emission reduction costs fall if the stock of
  knowledge grows
• GM1 The knowledge stock grows with investment
• GM2 The knowledge stock grows with experience
• As the models are quite different, also from the
  model with exogenous technology, calibration is
  very tricky

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Goulder and Mathai -2

• If the mechanism is research and development,
  then initial abatement falls but abatement rises
  more steeply
• If future emission reduction is cheaper, one
  would want to do more later as the target is
  the same, one starts lower
• Investing in technology has a higher payoff in
  earlier periods than in later ones
• In earlier periods, there is a trade-off between
  investing in RD and abatement

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Goulder and Mathai -3

• If the mechanism is learning by doing, then one
  cannot say whether initial abatement falls and
  rises, and ditto for later times
• The reason is that early abatement makes later
  abatement cheaper and this is a reason to
  increase early abatement
• As a result, later abatement gets cheaper and
  this is a reason to reduce early abatement
• The data are not there to tell which of the two
  effects is stronger
• (Note RD is data independent)

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New Growth Theory

• New growth theory endogenises technological
  progress and so one of the key drivers of
  long-term growth and income differences
• Unfortunately, there is no model (yet) that can
  do both
• Lack of data hinder the application of new growth
  theory, but it can be used to look at trade-offs
  between action now and preparing for action later