Allin has, I think, identified the problem as I see it though I haven't
had time to follow through his construction and see if it is exactly the same
as mine. I will be doing this for my paper for the next EEA mini-conference
and this is only a preliminary reply.
"Do I have the objection right?"
Yes, I think so. I will also reformulate the objection in another
way at the end of this reply, which might make it easier to follow.
"The objection looks quite plausible at first glance, but actually it is
spurious. The easiest way to see why is, I think, as follows. Suppose
for a moment that the objection were valid. Then, in principle at any
rate, there is an obvious correction one could apply. One could obtain
the z vector, i.e. the vector of scales of the various industries, and
divide the elements of the industry-level price and labour-content vectors
by the elements of z. Then we'd be back at what we "ought" to be
studying. "
"The trouble with this notion is that the z vector doesn't exist. I don't
mean it's not published by the BEA or the CSO -- it doesn't exist in
principle. What, for instance, is the scale of the electricity industry?
Is it the number of kilowatt-hours produced per year? The number of
watt-seconds? The number of terawatt-hours? What is the scale of the oil
industry? Is is measured in barrels, thimblefuls or metric tonnes? The
beer industry: bottles, fluid ounces, cases, gallons? If the elements of
the putative z vector all had the same dimension, then the choice of a
unit of measurement, while arbitrary, would not be problematic because it
would simply scale all the elements of z correspondingly. But the
putative "z" is composed of incommensurables. There's no such animal.
This is, however, a very accurate statement of the reason I am disinclined
to accept the whole methodology of using I/O matrices as if they were
the 'technical' matrices beloved of the Sraffians.
The A-matrix of linear production theory is intended to be a disaggregation
of the output of an economy in *physical* units, whatever that might be.
Let me define a 'valid' A-matrix to be a matrix to which Sraffian or
Pasinettian linear production theory might apply. In order to meet the
requirements imposed by this theory, it is indeed necessary that the output
of each sector be a distinct and well-defined use-value, *independently* of
its exchange-value. This is clearly necessary to the entire premise of
this theory, which holds that the prices of commodities are determined
independently of their values, on the basis of physical or 'technical'
magnitudes.
The question is, then 'is an input-output matrix a valid A-matrix'? Can
linear production theory validly accept an IO-matrix and treat it as
if it were a matrix of physical coefficients?
Allin has perfectly indentified the reasons that I cannot. There is in fact
no physical unit that corresponds to the output of a sector.
Because the putative 'z' is composed of incommensurables, it is necessary
*prior* to constructing the actual number which is recorded in the data
as the output of this sector, to reduce the magnitudes of which 'z' is
composed to a common, homogenous measure. This is actually done by recording
the *price* of the output of this sector.
Thus the magnitudes from which an i/o matrix is derived are actually *not*
physical quantities but price (and hence, I would say, value) quantities.
Yet the empirical practice which has arisen on the basis of this data,
acts as if they were physical quantities. I think this is circular.
Leontieff himself was quite clear about this. He said that in constructing
an IO matrix (I've lost the exact citation but it is easily located), we use
'price as a scale of measurement'. We measure steel output not in pounds
of iron but in pounds sterling, or dollars, etc.
Therefore, for example, any change in relative prices will change the
structure of the IO matrix *even* if there is no change in its physical
structure. The claim that this matrix can serve as a proxy for physical
magnitudes cannot be true, because to each physical matrix there corresponds
infinitely many IO matrices.
Now, this has been overlooked in the literature because when one constructs
the coefficient matrix, one divides a price by a price and the result is
dimensionless. Therefore, it is claimed, the resultant matrix is a
legitimate proxy for a matrix of physical quantities. But this is not so,
because as stated above, to any given matrix of physical quantities,
there corresponds an uncountably infinite number of coefficient matrices.
Thus if the price of steel doubles and the price of iron halves while
the price of coal remains constant, then the coefficients giving the
consumption of iron and coal in the production of steel will not remain
constant, even if there is no change in the structure of physical
production.
This contradiction becomes evident in the argument that Allin puts
forward. It is *because* the putative 'z' vector cannot legitimately
be construed as a physical magnitude that we have to interrogate a lot
more closely what it is we are actually doing, when we construct 'values'
from IO matrices.
I think what we are actually doing is not at all without merit and
I think the work of Allin and Paul has shown up some very interesting
results (as has the work of Anwar's collaborators). I am particularly
impressed by Anwar's argument that these results demonstrate deep
structural properties of the economy, and I think that your finding
that the correlations concerned arise only when labour is taken as
the 'source of value' are very important.
But I think it is illegitimate to take this work as confirmation of
the theory the vertically-integrated labour-embodied magnitudes are
accurate predictors of prices.
A reformulation
===============
Suppose an the economy was actually behaving as v=va+l. In this
case, all goods would be selling at or very close to their values.
In that case, va would *actually* represent not just the value
but the price of constant capital.
In that case, the value-added in each sector would be directly
proportional to the hours worked in that sector (l), assuming an
equal intensity of labour.
Already we can see there is a problem because if we compare
the value-added in almost any two sectors in money terms, and
divide this value-added either by the hours worked in that sector
or by the wages received, or by almost any proxy for labour-time
that we choose, we find that this ratio (pounds per hour) differs
wildly from sector to sector. Nor is this difference, in
my opinion, explainable in terms of rents or other disturbing
factors, though this is empirically discussable.
Assuming also an equal rate of exploitation, we ought also to find,
therefore, that profits in each sector are proportional to (l).
This too differs wildly from sector to sector and is equally
hard to explain on the basis of rents or other accidental
disturbances.
Now consider what would happen if we now constructed an input-output
matrix from an economy in this state, and 'reconstructed' values using
the Petrovic-Ochoa-Cottrell-Cockshott technique. In this case we ought
to find that these 'reconstructed' values were the same as actually
observed prices. Obviously, since the ground assumption is that goods
are actually selling at or very close to prices.
Let us call the two magnitudes concerned 'sectoral aggregate predicted
prices' (SAPP) and 'sectoral aggregate actual prices'(SAAP), to be
neutral. What comes out of the actual work done by yourselves is a
high correlation between these two. My criticism is that this correlation
is in fact a result of the dispersion in SAAP because the sectors
are of different sizes. (the 'z' vector)
Now though we might question what it could mean, it is perfectly *practical*
to divide the SAPP vector element-wise by the SAAP.
How could we interpret this result, given that, as we both agree,
the elements of the SAAP vector do not in fact represent a physical
magnitude?
Well, notice that if our theoretical economy conformed as
hypothesised to v=va+l, then all these magnitudes should be 1.
The aggregate SAAP of every sector should be identical to its
SAPP and if we divide one by the other, we should get unity.
In terms of the 'value' and 'price' interpretation of this, we
can 'read' the result as follows just to fix ideas: if we
intepret SAPPs as values and SAAPs as prices, then we are calculating
in each sector the value of goods that sell for one pound, or
'value per unit price'. We can also incidentally calculate the
inverse ratio or price per unit value. In this case goods that
sell *above* their value would have a price per unit value higher
than 1, or value per unit price lower than 1, and vice versa.
On the hypothesis that v=va+l is true, for every sector these
ratios would all be 1. Output whose value was $1 would sell for $1.
I calculated these magnitudes for the British economy from the 1984
IO data.
I found that in fact these 'value per price' ratios had a
dispersion from about 0.2 to 4. Even eliminating the flankers
we find that there is a price-per-unit-value dispersion easily
as low as 0.5 and as high as 2.
That is, goods whose price is $1 can have a value, calculated
using your technique, that is as high as $2 and as low as 50c.
This is what leads me to conclude that goods do not actually
sell for the value predicted by this technique, and I am
quite concerned that so many people are going around saying
publicly that this is the case. I think this leaves us, the
marxists, very exposed in the academic world and at some point
someone a lot less friendly than myself is going to catch on.
I think these empirical results are extremely interesting and
a lot of things flow from them, but one thing that does not
flow from them, and should not be claimed from them is that
goods actually sell for their V.I.L.E values.
"Paul C and I have argued (drawing on Farjoun and Machover) that the proper
object of study is simply the ratio of price to embodied labour across the
various industries, with each industry weighted according to the
proportion of total social labour it accounts for. We examine the
coefficient of variation of this variable, and assess whether its
dispersion is broad or narrow compared with other variables of interest in
Marxian economics. It turns out to follow a rather narrow distribution
(compared, e.g. to the rate of profit). And we also show that the
dispersion of price/labour-content is very much narrower than that of
price/steel-content, or price to electricity-content, or price to
oil-content -- which provides, if you wish, a more pragmatic refutation of
the idea that the "closeness" of price and labour-content is some sort of
statistical artifact. It's not; and I find it puzzling that some Marxists
seem so concerned to argue that it is.
As indicated above I think this is a very interesting result.
I am quite happy with the idea that in order to understand a 'real'
economy one might decide that the necessary 'object of study' is a
magnitude such as the one you describe. I think that we should be at
liberty to define as many objects of study as we have theories. One
of the properties of a legitimate theory is that it defines its own
objects of study.
What worries me is when wider claims are made for these objects
of study than can be maintained on the basis of the evidence.
The 'closeness' of SAPP and SAAP is a real thing. I would not at
all seek to deny its importance. What I deny is that we can
interpret SAPPs as Marx's labour values.
One further point is that since we can get the same result with
almost any IO matrix including one constructed from random numbers, I
am cautious as to what it tells us about the real world. I think
what this work may in fact demonstrate is a structural property
of IO matrices *in general*, which is related to sparseness. The
point about labour is that it is totally non-sparse. There is a
labour input of considerable magnitude in every sector.
What these results seem to show the correlation between SAAPs and
SAPPs will be much better for inputs which are non-sparse, that is
are of considerable magnitude (by some criterion to be investigated)
in every sector.
This is relevant to Marx's deduction of values from the fact that
labour is involved in the production of every commodity and provides
substantiation for it.
But I would be unhappy if this argument were reduced to a purely
quantitative argument. I think it is primarily a logical argument.
Alan