[OPE-L:5569] Price-Value Correlations

Alan Freeman (a.freeman@greenwich.ac.uk)
Fri, 3 Oct 1997 01:12:18 -0700 (PDT)

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Hi everyone,

I guess I should break my over-long silence by coming in on
the price-value correlation argument, since I started it. I
wrote most of this Sunday so it is not up-to-date on the
recent flurry of interesting contributions.

First off, I do think the word 'Humbug' should go. It implies
that the writers are not worth listening to, and they are.
This is my fault; I made an indirect reference to Anwar's
'Humbug Production Function' in a footnote to my 1997 IWGVT
paper and it caught on. I think the analogy is appropriate but
the word is not.

Point (1): One of Ochoa's (1984) findings seems to have got
missed or understated, namely the intertemporal relation between
changes in price and changes in value. This was the core point
in Shaikh's (1984) article in our book. His famous assertion to
have verified Ricardo's "930rice theory" is based on the
inter-temporal, not the cross-sectional results.

I think this is not a statistical artefact, and instrumentalises
Marx's suggestion that values 'regulate' prices. I don't see why
this should manifest itself in correlations at any particular moment
in time; on the contrary since the instantaneous divergences are
what give rise to the intertemporal regulation much recent research
is, it seems to me, looking for the wrong thing.

Point (2): To study dynamic change Ochoa deflates successive
I/O matrices to make his unit of measurement comparable
between points in time, which I think throws a clearer light
on the correlation issue. In this he follows Leontief (1953:3)
who wanted to study structural change in time, and says:

separate 1919 and 1929 price indices were compiled for
each group of goods and services comprised in the output
of an individual sector of the economy, 1939 prices being
used as a base. Each row of the 1919 and 1929 input-
output table was then divided by the appropriate index.
The resulting tables 1,2, and 3 show the input-output
structure of the American economy for the years 1919,
1929 and 1939 in comparable physical units. For each of
the 13 different outputs these are defined as 'the amount
of that particular kind of goods or services purchasable
for one dollar at their 1939 price.

The words "at their 1939 price" are significant. The use of
constant prices means that quantity information is provided
by the price data. Hence in his 1919 and 1929 tables a unit of
output does not sell for a dollar and even though output is
measured in (1939) dollars, unit prices vary from sector to

The exception, of course, is 1939 itself in which the unit of
quantity measurement coincides with the unit of price measurement.
However, all modern input-output tables are constructed like
Leontieff's 1939 table, not like his 1919 or 1929 tables.

His 1939 table may be viewed as a degenerate case in which the
unit of measurement is the dollar of the same year in which the
table was produced. Every commodity is reduced to a single measure,
namely, the amount that can be purchased with a dollar.

The point is not that dollars are used as a unit of quantity.
Though confusing, this is not ruled out. The real problem is that
there is no variation in unit price because, since we are using
current dollars, the measure of the output of anything 'is' its
price. The price of a dollar of everything is always exactly one
dollar, whereas prices per ton vary enormously. Any variation
in unit prices is thus wholly due to variations in whatever is
used as weight, because of the degeneracy in the original data.

However, of course, value per dollar does vary, whatever
definition of value is adopted. The value of one dollar's
output from the oil industry is about five times bigger than
the value of a dollar's output from the steel industry, for
example. If we want to ask whether values are dispersed, the
simplest, most obvious and least biassed procedure is to
interrogate the value per dollar of each sector.

Point (3): As Tsoulfidis [5510] notes, Ochoa (1984:29) indeed
drew attention to this problem. As he delicately puts it:

Unfortunately, our 'physical' units are one dollar's
worth of sectoral output at prevailing market prices.
This makes m(i) [unit price of sector i - AF] = 1 for all
i. We are thus deprived of any variation in one of our
variables, and hence the concepts of covariance and
correlation have no meaning.

Just as unfortunately, some of his successors seem to have
made more of his results than his warnings. The point is that
because there is no variation in price per unit output,
correlations or regressions are statistically inappropriate.
Exactly as he says, they 'have no meaning'. If we place the
price of a unit of any output on the x-axis, and value of the
same unit on the y-axis, then all data points will have the
same x-coordinate. There is nothing to regress against or
correlate with. The measurement procedure destroys all
quantity information by measuring everything in the same unit.

Point (4): The use of aggregate data instead of 'value per
dollar' simply applies weights to the values and prices, the
same weight to each. This is identical to re-scaling. In
effect by referring to the aggregate output of the oil sector
as its 'price' we are taking this aggregate output as the unit
of production.

Point (5): Scaling does not recover lost information; it adds
extraneous information. It makes the dispersion appear less and
the correlation greater. As Ochoa points out (p30):

we can increase or decrease the extent of common
variation of P and M [aggregate price and aggregate value
 AF] by judicious manipulation of the physical units. In
fact, by appropriately re-scaling the physical units
used, we can make R-squared vary from 0 to

Correlating aggregate value against aggregate price is
mathematically identical to manipulating the physical unit; it
is as if we said that the unit of output is the whole of the
output. With even a small dispersion of output sizes we will
get impressively large R-squares.

I therefore conclude the exact opposite from Cockshott and
Cottrell (1997) who say their procedure is scientifically more
valid because it 'adds information'. This is all very well,
but the information added has nothing to do with the question
being asked. If I take a hundred billiard balls and 'add
information' by labelling them, then it is the labels which
differ, not the balls. Unless there is some independent
objective basis for putting a particular label on a particular
ball, the extra information tells us about the label, not the

This is the point of testing with random weightings; if we
have a genuinely objective measure of the dispersion in the
original distribution, it should not vary when the weighting
is changed.

Allin [5497] objects that the correlations are greater for
labour-content than for steel or electricity. The issue is not
the relative size of two different correlations, however, but
the absolute significance attached to one of them. Of course,
since the y-magnitudes are dispersed, correlations in weighted
or scaled variables can 'report on' this original, unweighted
dispersion, which itself is higher for steel- than for labour-
content. But they tell us nothing we could not learn from
direct inspection of the original distribution, and distort
its dispersion, making it appear smaller than it really is.
The bigger the dispersion in the scale factor, the worse the

The least distorted measure of dispersion is to add nothing
extraneous at all, that is, to compare unit values with unit
prices. Therefore I think any weighting will necessarily
introduce a spurious source of variation and should be
rejected on grounds of statistical merit. Correlation, as
Ochoa states, is simply a statistically incorrect technique.

Point (6): Tsoulfidis [5510] reports MADs (Mean Average
Deviations) of about 20%. I have no quarrel with what I think
is essentially an unweighted measure of dispersion. I find
similar results though they are strongly affected by outliers
as Valle reports.

But let's not lose sight of what we are studying, namely a
distribution. It is not really a vector at all but a list of
values per dollar. Statistics has much simpler measures for
measuring the dispersion of distributions. I'd be interested
in the standard deviation of the results reported in this
discussion. I found, after removing outliers, a standard
deviation of 0.11 for the 1984 101-sector UK tables.

Moreover there is a spread of values which should also be
reported, preferably using commonly-accepted statistical
measures that make no assumptions about distribution. The
ratio of my top to bottom decile averages, for example, was
40% after removing outliers.

Hmmm. A 40pread is a 'close' relation?

Point (7): Cockshott, Cottrell and Michaelson (1995) do not
speak of 40preads or even 20 0eviations. They refer to the

'ideal' result from the standpoint of value theory, of a
zero intercept and a unit slope [of value against price -

Value theory is confirmed for them if values are identically
equal to prices. The assertion is not that values are close to
prices, but in practice indistinguishable from them. The
hypothesis under test is not resemblance, closeness, relation
or even 'prediction'. It is identity. The underlying issue is
not the 'relation' between values and prices but a false claim
that the difference is so small that it is irrelevant.

Point (8): 'Irrelevant' for Paul and Allin has a specific
meaning. They offer their results as evidence, not just that
one theory is better than another, but that the theoretical
discussion should not take place at all. As Paul [3821]

Once you see the actual figures from I/O tables, the
finer points about whether you should transform the
inputs or not become very much secondary matters, not
really worth going into print about. They are of some
interest from the standpoint of the history of thought,
but of very little practical bearing on how capitalism
really operates.

This is not a throwaway remark; it articulates a definite
criterion of judgement: theoretical differences don't matter
if the result is empirically indistinguishable. Paul and
Allin's 1997 IWGVT paper elevates this into a methodological
principle. This applies their own statistical technique to

assess the relative merits of three variant formulae for
predicting observed prices, namely "standard" Marxian
values (or vertically integrated labour coefficients),
Sraffian prices of production and prices of production as
interpreted by the "Temporal Single System" (TSS)

This is not a proposition about value; it is a proposition
about theories. The scientific test of your theory is whether
it reproduces my facts.

The application of this principle takes extreme forms. In
[4296] Paul proposed a ban (his own words) on "all further
discussion on topics that are already covered in Capital".
Allin [4578] approvingly quotes the following:

If we take in our hand any volume ... let us ask, Does it
contain any abstract reasoning concerning quantity or
number? No. Does it contain any experimental reasoning
concerning matter of fact and existence? No. Commit it
then to the flames: for it can contain nothing but
sophistry and illusion."

I know irritation makes for excess, but I don't think
censorship and book-burning are random expressions of
frustration. They are the logical conclusion of a coherent
view on method. This articulates a widespread prejudice, the
governing philosophy of the mainstream journals, that
statistical finesse is a valid substitute for theoretical
clarity. The essence of this dogmatic and sectarian view is
that a theory has the right to suppress all other theories on
the basis of 'facts' which it manufactures from within itself.
I think the time has come to confront this prejudice, and the
most fruitful procedure is to examine the underlying
theoretical approach.

Point (9): Nearly every empirical worker on value agrees that
price data may be used as the basis for value calculations. So
how can value differ from price? It makes no sense unless we
study where price data enters the calculations.

For the vertically-integrated approach, a dollar represents a
different number of hours in each sector. A pound's worth of
steel transfers more or less value to outputs than a pound's
worth of electricity. This calls for a complicated procedure
to work out exactly how much value a dollar represents in each
sector.[2] Single System approaches  whether TSS or SSS 
start from the money price of constant capital. A dollar, at
this point in the circuit, directly represents a number of
hours which it transfers to the product; the MELT tells us how
many. Adding the hours worked by living labour gives total
value, and dividing by the use-value produced gives unit

In no sense does either procedure make value and price identical.
As far as I know only the value-form school holds anything like
this idea and I'm not even sure about that. The dualist view
separates value from price at all points on the circuit; the
SS view asserts that money represents labour-time only at a
definite point in the circuit - when it enters the labour-

Clear theoretical differences between these approaches
therefore arise, not because any of them seek to suppress the
distinction between value and price but because each makes
this distinction in different ways. I fully agree with Valle
[5541] and I would put the question this way: this is a difference
of meaning, not of calculation. It cannot be resolved without
enquiring into the different meanings which different theories
assign to different concepts; in other words, without the debate
which Paul and Allin keep asking us to ban, keep out of print,
confine to the history-books, commit to the flames or otherwise
generally stop from happening.

Point (10): In no sense does this imply empirical evidence is
unnecessary, though it certainly implies it is insufficient.
In the course of this dispute, empirical facts can and should
be considered. The point is: what counts as an empirical fact?

Empirically, as anyone can see and all I/O tables show, the
money value added in any business or sector is distributed
very differently from the time worked. This is a matter of
'fact and existence' precisely because everyone can verify it.
Its status as a fact is independent of any particular theory.

Paul and Allin introduce an entirely new dimension. The facts
they submit consist of assertions generated by their own theory.
Their evidence is not the original data that everyone accepts
but a re-working of that data with a statistical method that
is specific to their theory. What they treat as a fact does not
exist until their theory has worked over everyone else's facts.

These facts are then proposed not only as an adequate test of
their own theory, but as a test of everyone else's too.

This is already theoretically questionable. The emperor's
tailor cannot be the judge of the emperor's clothes; a measure
of value is a product of a theory of value, and we can assess
it empirically only against a further fact which can be verified
without recourse to that theory. If we start granting theories
the right to judge other theories with their own facts, we
might as well throw in the rationalist towel and let the
Creationists judge us with the bible.

But their argument also falls by the very criteria that they
declare unchallengeable, namely the facts themselves. If we
separate out that part of the facts which everyone accepts from
the part which they have processed, what we find is an average
deviation of 20-30% and a spread of 40 0n vertically-integrated
labour coefficients per dollar, with outliers even farther apart.

This neither confirms value as identical to price nor proves that
discussions about it are a waste of time and space. On the contrary
it provides very strong evidence that the two are very different,
underlining the need for the very theoretical enquiry into the origin
of the difference which they claim to have proven irrelevant.

Point (11): Here is where the correlation dispute enters.

When we study the claim that a 40pread is so small it
doesn't matter, we find the proof rests on a statistically
unacceptable procedure. It uses a calculation which the leading
authority describes as 'having no meaning' to transform a highly
significant 40pread into a piddling 1.5%, a figure whose
magnitude itself varies randomly with the variation in sector
sizes resulting from the arbitrary decisions of the statisticians,
on the basis of which all discussion is ruled out of order.

It is disingenuous to say that this is less piddling for steel
or electricity. An absolute, not a relative claim is at stake:
the claim being advanced is not that 1.5 0s smaller than 3%,
but that it is so small it doesn't matter.

This is not an empirical result; it is an act of technical
legerdemain. It is no more justified than fiddling with the
origin of axes to make a flat curve look like a steep one. With
a rubber ruler I can prove any length equal to any other length:
this does not give me the right to set myself up as the emperor
of the empirical.

Point (12): The reason I am so concerned about this, apart
from its authoritarian undertones, is the danger to everyone
else's work. If it becomes 'received tradition' that Marx's
theory stands or falls on the basis of a statistical method
which is in fact false, sooner or later the error will be
pointed out by someone much less charitable, with a fat grant
from a rich foundation to put down upstart 'Marxists'. A wide
body of scholarly work will be compromised and most serious of
all, orthodoxy will get a golden opportunity to heap further
abuse on Marx's own work.

Point (13): I want to be clear what I am asking, since I think
Paul and Allin's general line of enquiry is highly original
and will prove very fruitful, and I sympathise with it. I also
think their results have great objective merit. But I think
they have set the stakes too high by making more claims than
the numbers can sustain. I think the time has come to climb
down gracefully; I don't ask them to admit their theory is
wrong, just to stop trying to use its facts to prove everyone
else's theory is wrong. I don't think this is an unreasonable

Actually, however, my main complaint is not against Paul and
Allin at all; I chose to examine their argument because I
think it is the most coherent theoreticisation of a much more
general prejudice, rampant in economics, that questions of
concept and method can be settled by numbers and technique.

There is a precedent: Solow's evasion of the Capital
Controversy, against which Anwar quite rightly directed his
article on the 'Humbug Production Function'. That is why I
think the analogy is appropriate though the word is not.

The economics profession suppressed Anwar's response and this
was probably a turning point in the triumph of technique over
reason. It would be a supreme irony if, at the exact point
when doubting voices in the profession are questioning the
direction taken, we were to become its advocates.

Point (14): If, instead of trying to make the contentious
products of one particular theory the final arbiter of all other
theory, we sought out factual evidence that we all agree on,
and let the light of as much theory as possible shine upon it,
then I think the outcome would be a much more open and fruitful


[1] Despite Paul's [5488] protestation of disinterest in
Marx's own views, he is solicitous enough to attach the poor
man's name to his favourite theory. Sadly if Paul's findings
are refuted, so is Marx. Unless, of course, we can rescue Marx
by showing that the failed method is not in the least
'Marxian' but uniquely Pauline.

[2] A naove person might think Paul and Allin's 'Occam-
simplicity' criterion ruled this out. But then, it should also
rule out MAWDs, correlations and vector distances in favour of
the good old-fashioned deciles and standard deviations which
are taught in every undergraduate text for the very good
reason that they are simple enough for every undergraduate to


Cockshott, P., A. Cottrell and G. Michaelson (1995) "Testing
Marx", Capital and Class #55

Cockshott, P, and A. Cottrell, "The Scientific status of the
Labour Theory of Value", paper to the 1997 IWGVT conference.

Freeman, A (1997) "The Quantification of Value", paper to the
1997 IWGVT conference

Leontieff, W (ed) (1953) "Studies in the Structure of the US
Economy", New York: IASP

Ochoa, E. M.(1984) 'Labour values and prices of production: an
interindustry study of the US Economy, 1947-1972', PhD Thesis,
New School for Social Research.

Shaikh (1984) 'The Transformation from Marx to Sraffa' in
Mandel and Freeman (1984) (eds) "Ricardo, Marx, Sraffa: the
Langston Memorial Volume", Verso

Cited documents from the 1997 IWGVT are on