EMEA5: Recursive Dynamic CGEs

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EMEA5 Recursive Dynamic CGEs

• The Solow-Swan model of economic growth
• Matches and mismatches with observations
• Solow-Swan models with many sectors and regions
• Carbon leakage

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Where are we?

• Yesterday, we looked computable general
  equilibrium models, that is, models of the
  economy with many goods, consumers and producers
• In a way, CGEs merge partial equilibrium models
  and input-output models
• We considered static CGEs only, that is, time was
  absent, or rather investment was
• This morning, well introduce investment in an
  ad-hoc way
• This afternoon, well make investment part of
  utility and profit maximisation

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The Solow-Swan Model

• Output (total production) Y is a function of
  capital K, labour L and the effectiveness of
  labour A
• Technological progress only enters in labour, not
  in capital technology is labour-augmenting or
  Harrod-neutral
• If not, the model does not have a steady state
  (unless Cobb-Douglas)
• This is an example of rigour over realism

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The Solow-Swan Model -2

• The production function is homogenous of degree 1
  (constant returns to scale)
• That is, (1) the economy is big enough that the
  advantages of specialisation have been exhausted
  (2) other inputs (e.g., land) than capital,
  labour and knowledge are relatively unimportant
• Constant returns to scale implies

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The Solow-Swan Model -3

• We have the intensive-form production function
  yf(k), which states that output per unit of
  effective labour is a function of capital per
  unit of effective labour
• Assume a Cobb-Douglas function

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The Solow-Swan Model -4

• Assume that labour and knowledge grow at constant
  rates
• Output is divided over consumption and investment
• Capital grows with the difference between
  investment and depreciation

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The Solow-Swan Model -5
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The Solow-Swan Model -6

• So, we have that
• The rate of change of the capital stock per unit
  of effective labour is the difference between the
  actual investment per unit of effective labour
  and the break-even investment
• Break-even investment is the investment needed to
  keep the relative capital at the same level. It
  equals depreciation plus the growth of labour and
  knowledge

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The Solow-Swan Model -7

• What are the convergence properties?
• So, k converges to k this is known as the
  steady state or the balanced growth path
• Capital grows at rate ng and, because of
  constant returns to scale, so does output
• Output per worker grows at rate g

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The Solow-Swan Model -8

• Effective labour AL grows at rate ng
• Capital KALk grows at rate ng
• Constant returns to scale Output grows at rate
  ng
• One of the key predictions of the Solow-Swan
  model is that k is constant, that is, the ratio
  of capital to output is constant
• Output grows faster than labour (by g)
• These corresponds to observations

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The Solow-Swan Model -9

• What is the sensitivity to savings?
• In a competitive market, the share of revenue
  paid to input is its marginal productivity that
  is kf(k) this is about 1/3 of output
• The output elasticity to savings is thus 0.5
• 1 more saving implies 0.5 more growth
• A tenfold difference in output, require a
  thousand-fold difference in capital

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The Solow-Swan Model -10

• What is the rate of convergence?

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The Solow-Swan Model -11

• The Solow-Swan model leaves much to be desired.
  Particularly, it cannot account for the fact that
  there are large income differences between
  countries.
• Nonetheless, Solow-Swan (type) models are
  frequently used in computable general equilibrium
  models
• That is, recursive-dynamic CGEs assume an
  exogenous savings rate, just like Solow-Swan.

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Recursive-Dynamic CGEs

• Savings are not based on optimisation, or
  forward-looking behaviour, but either exogenously
  given or based on some current and past
  indicators
• Thus, the future is determined by the past and
  present, not by the future itself
• That is why these models are recursive-dynamic,
  or (time-wise) simulation models
• Adaptive expectations are a special form

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Recursive-Dynamic CGEs -2

• So, we know total savings and thus total
  investments
• How are these investments allocated over sectors?
• We assume that the capital market is perfect, so
  that investments flow to the highest marginal
  pay-off
• Typically, one would need to stop to much money
  flowing to developing countries

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Leakage

• Suppose the countries of the OECD reduce their
  emissions of carbon dioxide but the rest of the
  world does not
• (This is not entirely hypothetical. It is, e.g.,
  in the Kyoto Protocol.)
• Is the OECD able to realise this goal, or would
  the rest of the world increase its emissions?
• The share of the emission reduction that is
  replaced is known as the leakage rate

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Estimated Leakage Rates
Ratio of additional emissions in the rest of
the world to the emission reduction in the OECD
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Leakage -2

• Estimates diverge quite a bit. How come?
• Let us first look at the static effects.
• Carbon dioxide emission reduction implies a lower
  consumption of coal, perhaps oil, and a higher
  consumption of gas
• Reduced oil consumption in the OECD implies a
  lower price on the world market, and thus higher
  consumption and higher emissions in the ROW

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Leakage -3

• Reduced coal consumption in the OECD has little
  effect on the world market, as the coal market is
  highly fragmented shipping coal is expensive,
  building coal-fired power plants is
  time-consuming and unattractive commercially and
  environmentally
• Emission reduction implies that energy-intensive
  products become more expensive. Imported
  energy-intensive products become relatively
  cheaper and emissions in the ROW go up

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Leakage -4

• Reduced oil imports may lead to a depreciation of
  the own valuta, which would lead to higher
  imports and thus to higher emissions abroad
• Summary static effects
• Coal Oil Gas Other Exchange Total
• ? ?
  
• What about the dynamic effects, that is, how
  would emission reduction affect investment and
  growth?

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Leakage -5

• Reduced oil imports may lead to a depreciation of
  the own valuta, which would lead to a higher
  inflow of capital (or rather, a lower outflow)
  and thus to lower emissions abroad
• Reduced growth in the OECD would lead to reduced
  imports and thus to lower growth and lower
  emissions abroad
• So, the overall tendency is negative, but there
  are changing patterns too

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Leakage -6

• Higher energy prices in the OECD imply that
  investing in energy-intensive industries in the
  ROW become relatively more attractive the energy
  extensification of the OECD economy is
  accompanied by an energy intensification of the
  ROW economy
• Summary of dynamic effects
• Exchange Growth Structure Total
• - -
  ?

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Leakage -7

• So, from a static point of view, leakage may be a
  real problem
• From a dynamic point to view, leakage is
  ambiguous
• The story turns around the relative strengths of
  the arguments, that is, price elasticities, the
  exchange rate, international capital mobility
  and, obviously, the extent and costs of emission
  reduction