Neoclassical growth theory

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Neoclassical growth theory

• Putting it out of its misery

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So long, so low

• Most students of economics begin their study of
  long-run growth with the neoclassical model of
  capital accumulation. When discussing what we
  know about growth, this model is the natural
  place to start (Mankiw 1995 275)
• Relevance of neoclassical growth theory boils
  down to question
• Can process of growth be summarised by the
  equation

• And simultaneously be
• Consistent with the rest of neoclassical theory?
• Consistent with reality?
• Consistent with the data? (yes, a separate
  question)
• Capable of providing guidance for Development?

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The adding up problem

• Constant returns
• For consistency with marginal productivity theory
  of income distribution

• Substituting

• Gather terms

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The adding up problem

• With the well known result that growth model
  only consistent with theory of income
  distribution under constant returns to scale.
• With increasing returns, theory cant explain
  income distribution some output generates no
  income
• Not an assumption
• If we assume that the production function has
  constant returns to scale, we can write the
  production function as (Mankiw 1995 276)
• But a necessary condition for theoretical
  consistency
• Consistent with reality?
• Only if its 2-dimensional!

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The adding up problem

• Simplest real world case of increasing returns
• Chemical process taking place in a container
• Material costs proportional to area
• Processing capacity proportional to volume

• 1 metre sides
• Area 6 m2
• Volume 1 m3

• OutputCost ratio 16

• 6 metre sides
• Area 216 m2
• Volume 216 m3

• OutputCost ratio 11

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The adding up problem

• Why does problem occur?
• Neoclassical model
• Inherently static
• Cant cope with changing output levels
• Inherently micro
• Micro concept of diminishing marginal
  productivity incoherent at macro level
• Bhaduri 1969 consider change in output and
  change in incomes given

• Change output

• Expand profit

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The adding up problem

• In general, dY/dK is

iff

• So

or

• Perhaps valid at level of single firm/industry
• But at level of economy, changing K changes
  distribution of income, thus

• Given diminishing marginal productivity

• So profit cant equal marginal product of
  capital!
• Neoclassical theory inherently static/micro
• So why use it to analyse growth?

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The adding up problem

• But why does the neoclassical aggregate
  production function appear to work so well?
• A considerable body of independent work tends to
  corroborate the original Cobb-Douglas formula,
  but, more important, the approximate coincidence
  of the estimated coefficients with the actual
  shares received also strengthens the competitive
  theory of distribution and disproves the
  Marxian. (Douglas, 1976 914, cited in Felipe
  McCombie 2001 6-7).
• Because the CDPF with CRS is an algebraic
  transformation of the accounting identity for
  income distribution with relatively constant
  shares.

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Bah! Humbug!

• Cobb-Douglas is

where

• Accounting identity for NNP is

• Numerous authors (Phelps-Brown 1957, Simon Levy
  1963, Shaikh 1974, 1980, 1987, 2002, McCombie
  Dixon 1991) have shown that one is simply an
  algebraic transformation of the other (given
  stylised facts of relatively constant income
  shares relatively constant growth of money
  wage)

• Define

• Then

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Bah! Humbug!

• Differentiate w.r.t. time

• Divide by w/w, k/k r/r to put RHS in terms of
  rates of growth

• Divide both sides by v

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Bah! Humbug!

• Define income shares for W P

• Substitute

• (dr/dt)/r trendless
• (dw/dt)/w grows at a roughly constant rate
• Substitute constant rate of growth (dB/dt)/B for
  1st term
• Replace s with b

• Integrate

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Bah! Humbug!

• Take exponentials

• Expand out what v(t) and k(t) are

• We have transformed the income allocation
  identity into a constant returns to scale
  Cobb-Douglas production function

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Bah! Humbug!

• Close fit of Cobb-Douglas production function
  thus artefact of algebraic relation of it to
  national income accounting identity
• Closer real data is to assumptions of constant
  income shares and constant wages growth, closer
  the fit will be
• Same literature also shows
• CDPF can fit numerous non-neoclassical output
  functions (including word Humbug drawn on
  graph, Goodwin predator/prey data) devoid of
  marginal product etc. characteristics
• Equivalence of estimated wage/profit rate to
  marginal products of labour/capital
  illusoryagain product of equivalence to
  accounting identity

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Bah! Humbug!

• Neoclassical growth/development literature
  ignores critique (see e.g. Mankiw 1995)
• Probably because erroneously believe Solow 1974
  rebutted Shaikh 1974
• See McCombie 2000-2001, Shaikh 2002
• Still trumpet regressions as proof of relevance
  of theory
• Moreover, these correlations are quite strong a
  regression of income per person on these two
  variables alone, using a sample of ninety eight
  countries, yields an adjusted R2 of 59 percent.
  It is possible that reverse causality is part of
  the story here (Mankiw 1995 277-8)

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Bah! Humbug!

• New Growth Theory simply a red-herring
• Introduction of additional terms (e.g. Human
  Capital) simply improves fit of slightly
  nonlinear CD form to data
• Capital with externalities simply allows
  coefficients to be jigged to fit data
• Neoclassical endogenous growth models take
  extreme production position of CD, add additional
  sectors but still founded on accounting
  identity transformation
• Neoclassical growth model little more than
  numerology, irrelevant to actual issues of growth
  and development.

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Much Ado About Nothing

• Additional failings of model result from
  deficiencies of neoclassical mindset
• A more challenging goal is to explain the
  variation in economic growth that we observe in
  different countries and in different times. For
  this purpose, the neoclassical models assumption
  of constant, exogenous technological change need
  not be a problem (Mankiw 1995 280 et. seq.)
• (New Growth Theory successes in improving
  empirical performance resulting from dropping
  some of these assumptions simply an artefact of
  data-fitting)

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A really new growth theory?

• For true model of growth development, we need
• Historically founded analysis that acknowledges
  origin of much underdevelopment in colonial
  period
• Evolutionary perspective on relationships between
  investment, growth technological change
• Genuine model of production (multi-sectoral,
  dynamic)
• Acknowledgement of relation between capital flows
  and investment

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A really new growth theory?

• Recommendations of such a theory likely to be
  very different to those from a neoclassical
  perspective
• The implications of recent work on economic
  growth for policymakers are far from clear some
  recent work on economic growth suggests that a
  more activist government could be beneficial
  but the problem is that economists have not
  yet produced a persuasive way of measuring the
  magnitude of these externalities Without a
  solution to this measurement problem, modern
  growth theory does not offer any clear policy
  prescriptions policymakers would do well to
  heed the first rule for physicians do no harm.
  This may seem like a modest conclusion from an
  ambitious literature. But sometimes modesty is
  all that economists have a right to offer.
  (Mankiw 1995 309)
• Laissez-faire by lazy thinking

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A final curly

• Economic growth often visually portrayed to
  students as outward movement in PPF (groovya two
  good model!)

Biscuits
PPF2
(groovya two good model!)
PPF1
Beer

• Nonlinear shape of PPF seen as
• Improvement on Ricardo
• Based on diminishing marginal productivity

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A final curly

• Each industry experiences DMP as output increases
• But
• Movement along any production function involves
  constant capital
• Shift of resources from one industry to another
  involves change in capital.

Biscuits
F(L,K)
F(L,K)
L

• Under what conditions will shift guarantee curved
  shape of PPF?

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A final curly

• Only guarantee of curved PPF is if adding capital
  simply extends production function with same
  amount of capital
• Graphically, any point on any PF can be reached
  by adding labour to fixed capital, or adding
  capital substracting labour

mlt1,ngt1
Biscuits
F(L,K)F(mL,nK)
F(mL,nK)F(L,K)
L
L

• Both function and derivative must be reproduced

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A final curly

• Two mathematical conditions for any given L,K

and

• Variation in Eulers formula
• Only function that guarantees this result is a
  straight line
• No diminishing returns in either industry
• In general, even with two industries displaying
  DMP, no way to guarantee concave shape of PPF
• Any shape, from concave to Ricardo to convex
  possible

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References

• Bhaduri, A., (1969). 'On the significance of
  recent controversies in capital theory a Marxian
  view', Economic Journal, 79 532-539.
• Felipe, J. McCombie, J.S.L., (2001). How Sound
  are the Foundations of the Aggregate Production
  Function?, Department of Economics School of
  Business, University of Otago No. 0116.
• Mankiw, G., (1995). The growth of nations,
  Brookings Papers on Economic Activity 1 275-326.
• Phelps-Brown, E.H. (1957). The Meaning of the
  Fitted Cobb-Douglas Function, Quarterly Journal
  of Economics, 7 546-60.
• Simon, H. A. and Levy, F. K. , (1963). A Note on
  the Cobb-Douglas Function, Review of Economic
  Studies, 30(2) 93-4.
• Shaikh, A. M., (1974). Laws of Algebra and Laws
  of Production The Humbug Production Function,
  Review of Economics and Statistics, 61 115-20.
• (1980). Laws of Algebra and Laws of Production
  Humbug II, in Edward J. Nell (ed.), Growth,
  Profits and Property Essays in the Revival of
  Political Economy, Cambridge University Press
  80-95.
• (1987). The Humbug Production Function, in
  Eatwell, J., Milgate,M., and Newman, P. (eds.),
  The New Palgrave A Dictionary of Economic Theory
  and Doctrine, Macmillan, London.
• (2001). Nonlinear Dynamics and Pseudo-Production
  Functions,
• McCombie, J.S.L. and Dixon, R., (1991).
  Estimating technical change in aggregate
  production functions a critique, International
  Review of Applied Economics, 24-46.
• (2000-2001). The Solow residual, technical
  change, and aggregate production functions,
  Journal of Post Keynesian Economics, 23 267-97.

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