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Neoclassical growth theory

- Putting it out of its misery

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?

The adding up problem

- Constant returns
- For consistency with marginal productivity theory

of income distribution

- Substituting

- Gather terms

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!

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

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

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?

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.

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

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

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

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

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

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)

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.

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)

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

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

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

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?

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

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

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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