Empirical evidence claiming to
support the neoclassical micro
foundations of macroeconomics:
A statistical artefact
Marc Lavoie
An artefact: definition
An artefact or artifact is a spurious finding
caused by faulty procedures.
 In the fantasy literature, an artifact is a
magical tool with great power.
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INTRODUCTION -- JUSTIFICATION
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Heterodox economists often claim that neoclassical production functions,
substitution effects, etc., make little sense in our world of fixed coefficients
and income effects. Claims to that effect also arose from the Cambridge
capital controversies.
Neoclassical economists, however, have come up with a large number of
empirical studies that seem to “verify” neoclassical theory, in particular when
fitting Cobb-Douglas production functions (Q = eμt LαKβ).
The purpose of this lecture is to explain this apparent paradox, and show
that the “good fits” of neoclassical number crunchers is no evidence at all.
Students can embrace heterodox microeconomics and its alternative
assumptions without remorse: the numerous studies of empirical “evidence”
supporting neoclassical production functions are worthless.
Outline
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Cambridge capital (1960s) controversies anew
The equations that could verify the validity of the neoclassical theory
of production and labour demand are no different from those of
national accounting.
Labour theory
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Lavoie 2000
 Anadyke-Danes & Godley 1989
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Production functions
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McCombie 2000, McCombie and Felipe
Shaikh 1974, 2005
Neoclassical production functions and labour demand functions are
not behavioural concepts that can be empirically refuted.
Neoclassical production functions are artefacts: they claim to
measure the output elasticities with respect to capital and labour,
whereas in reality they are estimating the profit share and the wage
share in income!
The Cambridge capital controversies
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They put in jeopardy the neoclassical concepts of
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Scarcity
Substitution
Marginalism
Capital as a primary factor of production
The measure of multifactor technical progress
On the basis of models with fixed technical coefficients but with several
techniques, or even an infinity of techniques.
 These are static models, with profit maximization
 These models provide cases of (See Cohen and Harcourt 2003):

Reswitching (a technique which was optimal at high interest rates, and
then abandoned, becomes optimal again at low interest rates).
 Capital reversal (or real Wicksell effects: a lower interest rate is
associated with a technique that is less mechanized (K/L is lower), even
without reswitching.
 An infinitely small change in the interest rate can generate an enormous
change in the K/L ratio (discontinuity, rejection of the discrete postulate).
LS
w/p
w/p
LD
LD
L/K
L/K
Neoclassical
Garegnani 1970
w/p
LD
L/K
Garegnani 1990
The replies of neoclassical authors to
the Cambridge-Sraffian arguments
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Neoclassical authors minimize the capital
paradoxes, making an analogy with Giffen goods
in microeconomics.
They look for the conditions that would be
required to keep production functions as ‘well
behaved’
They claim that general equilibrium theory is
impervious to the critique.
They claim that they have the Faith, or they
plead ignorance.
Empiricism (It works, therefore it exists).
Empiricism, from the very beginning
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Bronfenbrenner 1971: Cobb-Douglas production
functions work, not for magical reasons, but because its
many applications have demonstrated that it can explain
empirical facts.
Ferguson 1978: The validity of neoclassical theory is an
empirical question, not a theoretical one.
Sato (1974): « The neoclassical postulate is itself in
principle empirically testable in the form of a production
function estimation of the CES and other varieties. This
can make us go beyond purely theoretical speculations
on this matter ».
Present empiricism
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« The estimated elasticities that seem to confirm
the central prediction of the theory of labor
demand are not entirely an artefact produced by
aggregating data. … The Cobb-Douglas function
is not a very severe departure from reality in
describing production relations» (Hamermesh
1986).
« The neoclassical production function is the
cornerstone of the [neoclassical growth] theory
and is used in virtually all applied aggregate
analyses ».(Prescott 1998).
Two examples of how neoclassical theories
of labour demand seem to be supported by
empiricism (and really are not).
Layard/Nickell as revised by French
authors vs Lavoie
 Layard/Nickell vs Godley
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The WS-PS model of Layard, Nickell and Jackman (1991)
revised by Cotis, Méary and Sobczak (1998, CMS).
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These studies tend to show that unemploymen rates in
Europe are rising because real wages are too high
relative to productivity growth. The CMS French test
was:
WS :
w – p = a1U + a4wedge + γt
PS :
w – p = b1U + b2(q – n) + b5t
 Profit-maximizing first-order conditions of a neoclassical
production function, well-behaved, with diminishing
returns, etc., show that the following conditions must hold
in the PS equation: b1= b2 = 1
w, p, q, n, logarithmic values
q = output; n = active population ; U = unemployment rate
But the PS equation can be also precisely derived
from the national accounting identities
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PQ = WL + RPK
Take the logarithmic derivative
X’ = (dX/dt)\X growth rate
P’ + Q’ = α (W’ + L’) +(1-α)(R’ + P’ + K’)
W’ – P’ = (Q’ – L’) +{(1-α)/α}(Y’ – K’ – R’)
Layard makes use of two approximations, which are :
U = (N – L)/L = x
and x = log(1+x) , when x tends towards zero
1+x = 1+(N – L)/L = N/L
Hence U = log (N/L) = log N – log L
dU/dt = N’ – L’ or else L’ = N’ – dU/dt
PS :
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w – p = U + (q – n) + b5t
Hence, starting from the national accounts:
W’ – P’ = (Q’ – L’) +{(1 – α)/α}(Q’ – K’ – R’)
But since: L’ = N’ – dU/dt
W’ – P’ = dU/dt + (Q’ – N’) +{(1 – α)/α}(Q’ – K’ – R’)
Integrating, and omitting the constant, the national account
equations become:
w – p = U + (q – n) + {(1 – α)/α}h.t
With:
h = Q’ – K’ – R’
This is also the PS relation, but this time extracted from the
national accounts! Thus it comes as no surprise that the
authors conclude that their model is « not rejected by the
data ». And it not surprising that the regressions of Layard et
alii allow them to verify that indeed, b1= b2 = 1.
Consequences
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The empirical results drawn from the WS-PS model do
not (necessarily) depend on behavioural relations based
on profit maximizing with well-behaved production
functions, with neutral technical progress and
diminishing returns.
Quite the opposite: the correlations and signs that have
been obtained rest most likely on the national income
identities, and as such, they have no causal or
explanatory power.
The usual estimates of the neoclassical labour demand
functions are only artefacts. They are meaningless.
Further consequences
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In other words, economists that use PS-WS models are
only providing estimates of what the determinants of the
equlibrium rate of unemployment would be (a kind of
NAIRU) if the neoclassical theory of labour demand,
based on aggregate production functions and decreasing
returns, were valid.
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These estimates cannot provide any support for
neoclassical theories of equilibrium unemployment.
Thus, paraphrasing Nicholas Kaldor (1972: 1239), we
see that the estimates based on PS equations or similar
equations can only help to « illustrate » or « decorate »
neoclassical theory and its assumptions of profitmaximization, decreasing returns, and equilibrium
unemployment. In no way can these estimates confirm
or corroborate neoclassical theory.
A «reductio ad absurdum» proof:
Godley and Anadyke-Danes (1989)
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These two authors intend to demonstrate
that even when, by construction, the
described economy has no relationship
whatsoever between employment and real
wages, standard econometric analysis will
seem to verify a negative relationship
between employment and real wages.
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Godley starts out with a markup theory based on
historical costs.
PQ = (1+θ)WL
P = (1+θ)WL/Q
In logs, we have:
p = φ(w – q + l) + (1-φ)(w-1 – q-1 + l-1)
φ is the proportion of goods sold in the current period.
If φ = 1,
p = (w – q + l)
l = – (w – p) + q
Right away, we see that, for a given output level, we
automatically get a negative relationship between employment
and real wages when prices are set through a markup.
But this negative relationship only reflects the fact, that, with a
given markup, the real wage will be lower if labour
productivity is lowered [(w – p) = q – l ] !
With the Layard approximation, U = n – l, we would have:
(w – p) = U + (q – n)
The PS curve!
The Godley Experiment
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Godley assumes, by construction, that the
nominal wage, output and employment all grow
independently of each other, with prices set on
the basis of a lagged markup (φ =.75)
w = (1.07 + random) + w-1
q = (1.05 + random) + q-1
l = (1.01 + random) + l-1
Godley gets as a regression:
l = 1.3 – 0.94 (w – p) – 0.12l-1 + .73q + .01t
(7.4)
(1.0)
(1.0)
(4.2)
l = 1.3 – 0.94 (w – p) – 0.12l-1 + .73q + .01t
(7.4)
(1.0)
(1.0)
(4.2)
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Employment seems to entertain a statistically significant
negative relationship with real wages, as well as a
positive time trend, as Layard et alii would like it to be
(note that employment does not seem to depend on
output q, in contrast to what post-Keynesians would
argue, and that it does not depend on past employment).
But we know that, by construction, employment is
completely independent of real wages, and that current
employment only depends on past employment.
Empirical studies thus manage to give support to the
neoclassical theory of labour demand even in those
cases where we know that, by construction, neoclassical
theory is irrelevant (real wages and employment are
independent of each other, while prices are set on a
cost-plus basis and not on marginal principles).
But it is possible to generalize even
further ….…
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Neoclassical aggregate production functions are
completely meaningless.
When they are correctly specified, they are
necessarily confirmed, in other words they
cannot be falsified.
The coefficients of the production functions of
the Cobb-Douglas type, as obtained through
econometric analysis, don’t measure the
elasticities of factors of production: they only
measure the shares of labour and profits in
national income!
Several authors in the past have rejected the aggregate
Cobb-Douglas functions (or other similar CES or translog
functions), because they simply reproduce the identities of
the national accounts:
 Phelps-Brown 1957
 Simon and Levy 1963
 Shaikh 1974, 1980, 2005
 Herbert Simon 1979
 Samuelson 1979
 McCombie and Dixon 1991
 McCombie 1987, 1998, 2000, 2001
 Felipe and McCombie 2000, 2002, 2005, 2006
 (Lavoie 1987, 1992, 2000)
 Fisher 1971(in his work on aggregation)
Enlightning simulations …
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Fisher (1971) has shown that even if conditions of
aggregation did not hold, the aggregate Cobb-Douglas
function did seem to « work » properly, provided the
wage share was constant enough within the set of data.
Fisher concludes that one must reverse the usual
argument.
Rather than saying that the wage share in national
income is constant because technology is of the CobbDouglas type, « it ought to be said that the apparent
success of the Cobb-Douglas production function must
be attributed to the fact that the wage share is roughly
constant ».
But here are some even more compelling
« reductio ad absurdum » arguments
against the neoclassical production function
…
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McCombie (2001) takes two firms i each producing in
line with a Cobb-Douglas function
Qit = A0LαitK1- αit
With α = 0.25 (labour elasticity of output).
Inputs and outputs are identical: there is no aggregation
problem (the 1971 Fisher problem is avoided).
If L and K grow through time, with no technical progress, with
some random fluctuations, the econometric regression will
yield an α coefficient close to 0.25 as expected.
In this case, the estimate is based on physical data, and there is
no problem.
However ….
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Start again with the same two firms, without technical
progress, and try to estimate an aggregate production function
using deflated monetary values, as must be done in
macroeconomics and often in microeconomics. To do so,
assume, by construction, that firms impose a markup equal to
1.33 (θ = 0.33) with P = (1+θ)WL/Q, which implies that the wage
share is 75%. In this case the regression will yield an estimate
of the α coefficient that turns out to be 0.75.
Thus, we started with production functions and physical data
according to which the labour elasticity of production is 0.25.
Yet, the estimated aggregate production function (in deflated
monetary terms) tells us that this elasticity is 0.75.
In other words, estimates of aggregate production functions
(both at the industry of macro levels) measure wage shares
and profit shares, not the elasticities of factors of production.
These aggregate production functions are useless to provide
any information about the kind of technology in use or about
elasticities.
Why is this so?
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Because, production functions, when they are correctly
estimated, only reproduce the relationships of the
national accounts.
If the wage share is approximately constant, and if
technical progress is adequately estimated, one will
always discover that a Cobb-Douglas production function
provides a good fit.
If the wage share is not constant, then CES or translog
functions will yield better fits. But these production
functions are subject to the very same criticisms as the
Cobb-Douglas function (Dixon and McCombie 1991).
If technical progress is misrepresented (for instance
through a linear function in time, rather than by a nonlinear one, the elasticity estimates will not equal the profit
and wage shares, and the elasticities may even turn out
to be negative.
Cobb-Douglas vs national accounts
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The Cobb-Douglas function:
With constant returns to scale: α+β=1
With factors of production paid according to their marginal productivity (w/p =
dQ/dL)
With output per head and capital per head, y = Q/L et k = K/L, and calling β (beta)
the capital elasticity of output, the Cobb-Douglas function yields:
log y = μt + β log k
Or in growth terms, taking the log difference, Δlog:
y’ = μ + βk’
The national accounts:
Taking the log derivative of the national accounts per unit of labour yields
essentially the same result:
y’ = τ + πk’
with τ = α(w/p)’ + πr’
Or else in logs:
log y = τt + π log k
With π the profit share, α the wage share, and r the profit rate.
Thus, one is not surprised to find out that the best econometric estimates of
aggregate production functions, as claimed by Jorgenson (1974), confirm that
α+β=1.
TONTERIAS
HUMBUG
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Shaikh 1974 (with capital per head on the
horizontal axis, and output per head on the
vertical axis)
Even a technology that yields capital-output
ratios that look like the word HUMBUG can be
represented by a Cobb-Douglas function, using
the method put forth by Solow (1957).
Another « ad absurdo » proof
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Shaikh (2005) shows that:
Variables generated by a Goodwin-cycle model,
with a Leontief input-output technology (fixed technical
coefficients)
and constant markup pricing,
so that neither marginal productivity nor marginal cost
pricing exist,
will still yield econometric estimates that seem to
support the existence of a neoclassical production
function with factors of production being paid at
productivity, and with elasticities equal to the profit and
wage shares, as neoclassical theory of perfect
competition would have it,
provided technical progress is specified appropriately.
Cobb-Douglas cannot be falsified as long as
technical progress is adequately represented
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Sometimes the Cobb-Douglas function yields non-sensical results,
and hence is not « verified », as pointed out by Lucas, Romer, and
Shaikh, as shown in the following Table.
The trick is avoiding to impose a linear trend to technical progress.
Rather one must introduce a non-linear trend (some sine function, or
a Fournier series), because technical progress is highly variable.
Solow (1957) in his equation, y’ = μ + βk’, creates a technical
progress variable which is exactly equal to: μ = α(w/p)’ + πr’, which
he derived straightforwardly from the national accounts. In other
words, he tested the national accounts identity, while claiming he
had corroborated the neoclassical theory of income distribution, and
got the Nobel Prize for this!
Indeed, nowadays, neoclassical authors that still « test » the CobbDouglas production function adjust the data by making corrections to
the capital stock, deflating the capital index by taking into account
the rate of capacity utilization, which is tightly linked to the rate of
technical progress, thus obtaining a good « fit » with their
regressions.
Table 1: Cobb-Douglas production functions fitted to actual and simulated aggregate data (OLS)
With constant time trend: log y = cste + μt + βlog k
Dependent Variable
ln(yt) = y’
ln(yt)
Goodwin
Data
US
Data
Goodwin
Data
US Data
Constant
-3.442*
(-9.768)
-2.109*
(-4.561)
0.0205*
(6.871)
0.015*
(6.340)
Time
0.020*
(9.705)
0.009*
(4.488)
ln(kt)
0.022
(0.219)
0.395*
(2.929)
-.0029
(-0.280)
0.063
(0.636)
ln(kt)
Adj. R2
0.999
0.977
-0.018
-0.012
D.W.
2.036
0.185
2.974
1.930
Implied Wage Share
[Actual Wage Share]
0.978
[0.840]
0.605
[0.810]
1.0029
[0.840]
0.937
[0.810]
Implied Profit Share β
[Actual Profit Share π]
0.022
[0.160]
0.395
[0.190]
-.0029
[0.160]
0.063
[0.190]
Source: Anwar Shaikh, Eastern Economic Journal (2005)
Figure 7: Rates of Technical Change
0.06
Source:
Shaikh 2005
Rate
of technical
change
Rate
of Technical
Change
Goodwin
data
Set A
0.04
0.02
0.00
-0.02
Rate ofofTechnical
Change
Rate
technical
change
Set
USB data
-0.04
50
55
60
65
70
75
80
85
90
95
00
Table 2: Constant returns Cobb-Douglas functions with variable time trends for
technical change (OLS)
log y = cste + log At + β log k
Dependent Variable
ln(yt)
Growth terms
ln(yt)
Data A
Goodwin
Data B
USA
Data A
Goodwin
Data B
USA
-2.932*
(-245.72)
-2.825*
(-550.96)
-0.000158*
(-2.093)
.0000638*
(1.198)
ln(At)
1.027*
(392.366)
1.012*
(421.009)
ln(kt)
0.158*
(81.209)
0.193*
(114.295)
Constant
ln(At)
ln(kt)
1.021*
(244.31)
0.156*
(45.321)
1.007*
(544.43)
0.201*
(137.045)
Adj. R2
0.9999
0.9999
0.9997
0.9997
D.W.
0.311
0.286
1.834
1.515
Implied Wage Share
[Actual Wage Share]
0.844
[0.840]
0.799
[0.810]
0.842
[0.840]
0.807
[0.810]
Implied Profit Share β
[Actual Profit Share π]
0.156
[0.160]
0.201
[0.190]
0.158
[0.160]
0.193
[0.190]
Real wage
W/P
y
True relationship (Leontief)
yt= ρkt
y2
y1
Pseudo
neoclassical
production
function
y0
ρ
Rate of profit
Source: Shaikh, 1990
R
k
k0
k1
k2
Capital-labour ratio
A recap
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The studies of Shaikh and those of McCombie and Felipe show that
the econometric estimates of neoclassical production functions
based on deflated monetary values, as is the case at the macro and
industry levels when direct physical data is not used, yield pure
artefacts (purely imaginary results). This affects:
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Labour demand functions and NAIRU measures;
Measures of multifactor productivity (Solow residuals, technical
progress);
Estimates of endogenous growth, theories of economic
development;
Theories of income distribution;
Measures of output elasticities with respect to labour and capital;
Measures of potential output;
Theories of Real business cycles.
Instrumentalism at its worse
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Virtually, there is nothing left of applied neoclassical
macroeconomics that relies on production functions.
Instrumentalism is the philosophy of science that claims
that assumptions need not be realistic, as long as they
help making predictions. Instrumentalism is endorsed by
the Chicago school, Milton Friedman (1953), and many
neoclassical economists (often without realizing it). The
VAR methodology used in time-series econometrics is
another example of instrumentalism.
Neoclassical economists are pushing instrumentalism to
the hilt: what counts is their ability to make predictions
(based on estimates of elasticities), even if these
predictions are meaningless (the estimates do not
measure elasticities, but instead measure something
else – profit shares and wage shares)!
Conclusion
Heterodox economists need not fear the
mountain of empirical evidence that seems
to support neoclassical microeconomics.
 Most, perhaps all, of this evidence is an
artefact.
 Obviously, it follows that macroeconomics
ought to be based on alternative
(heterodox) foundations.

Main References
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Anyadike-Danes m., Godley w. [1989], «Real wages and employment: A sceptical
view of some recent econometric work», Manchester School, 57 (2), juin.
Cohen a. and Harcourt, g.c. {2003], «Whatever happened to the Cambridge capital
controversies», Journal of Economic Perspectives, Winter.
Felipe j., McCombie j.s.l. [2005], «How sound are the foundations of the aggregate
production function», Eastern Economic Journal, Summer 2005.
Felipe j., McCombie j.s.l. [2006], «The tyranny of the identity: growth accounting
revisited», International Review of Applied Economics, 20 (3).
Garegnani p. [1990], «Quantity of Capital», in Eatwell, Millgate and Newman (eds),
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Lavoie m. [2000], « «Le chômage d’équilibre: réalité ou artefact statistique», Revue
Économique, vol. 51, no. 6, Novembre, 2000, pp. 1477-1484.
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criticisms of the Cobb-Douglas production function», Review of Political Economy,
April 1998.
McCombie j.s.l., [2001], «What does the aggregate production show? Second
thoughts on Solow’s “Second thoughts on growth theory”», Journal of Post Keynesian
Economics, Summer.
McCombie J.S.L., Dixon R. [1991], «Estimating technical change in aggregate
production functions: a critique», International Review of Applied Economics, 5 (1).
Shaikh a. [1974], «Laws of production and laws of algebra: the humbug production
function», Review of Economics and Statistics, 56 (1), février.
Shaikh a. [1990], «Humbug production function», in Eatwell, Millgate and Newman
(eds), Capital Theory: The new Palgrave, Macmillan, 1990.
Shaikh a. [2005], «Non-linear dynamics and pseudo production functions», Eastern
Economic Journal, Summer 2005.
Simon h.a. [1979], «On parsimonious explanations of production relations»,
Scandinavian Journal of Economics, 81 (4).