[OPE-L:2210] Re: Empirical method

Allin Cottrell (cottrell@wfu.edu)
Tue, 14 May 1996 10:02:53 -0700

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A further reply to Alan on Empirical Method.

I had responded to what I took to be Alan's objection to the
methodology employed by Shaikh and others (including Paul Cockshott
and myself) regarding the empirical correlation of market prices
and embodied labour-times. From Alan's reply it seems that I
had his objection right (or mostly right); but Alan has now come
back with some further arguments questioning that methodology.

One of my points was that since the physical outputs of the various
sectors of the economy are measured in heterogeneous natural units,
there is really no such thing as a vector of "scales" of the
different industries -- yet the existence of such a vector was, I
argued, presupposed by Alan's critique.

Alan begins by (apparently) accepting that there is no ('z') vector
of "scales", but then gives this point a further critical inflection:

This [i.e. what I said, AC] 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...

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...

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.

It is certainly true that the I-O matrices for the UK and the USA use
monetary magnitudes. The intersectoral flows are in pounds- or
dollars-worth of product. The per-unit i-o coefficients are derived from
these, and therefore represent, for instance, the number of dollars-worth
of coal required to produce a dollar's worth of steel.

[We should note, however, that it is in principle quite possible to
draw up I-O tables in kind -- and these would be required for the
purposes of socialist planning. The classic planning exercise is this:
given a vector of target final outputs along with the i-o structure of
the economy, derive the required vector of gross outputs. To be useful
for planning purposes, the gross output vector has to be specified in
disaggregated physical terms. This requires in turn that the i-o
coefficients be expressed in terms of physical input per unit physical
output. One faces a more or less arbitrary choice of physical units
for each product (e.g., kilowatt-hours or terwatt-hours for electricity),
but this is not a problem so long as the same units are used consistently
whenever the product of a given industry enters the calculations: i.e.,
in the target final output vector, in the denominator of that industry's
input coefficients, and in the numerator of the i-o coefficients for the
industries that use the given industry's product as input.

Thus I am saying that _given_ the planners' choices of units of measure-
ment for the various products, a vector of "scales" can be drawn up. But
since this vector depends on n choices of units, it has no "independent"
existence and cannot play the theoretical role it is assigned in (what
I take to be) Alan's objection to the "Shaikh methodology".]

Alan continues:

Therefore... 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

It is true that changes in relative prices will affect the i-o
coefficients as measured in the standard national I-O tables, even if
the physical i-o structure remains unchanged. But what follows?
In the empirical work Alan is talking about, what we need to "get"
from the I-O tables is a measure of total (direct-plus-indirect)
embodied labour-time (in order to compare this, in some way or other,
with market price). And from this point of view, Alan's observation
is not a problem. We start (iteration round 0) with an approximation
to embodied labour per pound of output that is simply the direct labour-
time per pound of output. At round 1 of the iteration we add in a
first approximation to the indirect labour, namely the sum, across
the non-labour inputs, of (pounds-worth of input i per pounds-worth
of the output in question) times (direct labour input per pounds-worth
of input i). And so on. Taking the physical i-o structure as given,
a change in the price of input i will have mutually cancelling effects
on the calculation. (Pounds-worth of input i per pounds worth of
the output in question) will (say) increase, but direct labour per
pounds-worth of input i will fall correspondingly.

Alan then proceeds to a "reformulation" of the problem at hand, which
deserves careful attention:

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.

To my way of thinking, v=va+l is a definition of value, and I would
wish to reformulate Alan's hypothetical condition above as "Suppose
the economy was behaving as (p proportional to v=va+l)". But let's

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.

What study is Alan referring to, I wonder? In the actual empirical
studies I have seen, this variable -- the "apparent rate of surplus
value", if you will -- is in fact rather narrowly distributed. Of
course, this distribution will be _degenerate_ only if the distribution
of price/embodied labour is also degenerate, and nobody is claiming that
is the case.

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

Paul and I have indeed found a statistical tendency for the rate of
profit to be inversely correlated with organic composition. I'm not
sure what "wildly" means here.

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.

True enough.

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)

But I thought you had accepted that there is no 'z' vector. This is
the very objection that falls foul of the criticism in my last posting.

Now though we might question what it could mean, it is perfectly
*practical* to divide the SAPP vector element-wise by the SAAP.

Yes. Or vice versa.

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

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.

Yes -- again with the qualification that I'd express this situation
as one where p = v = va+l.

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.

The latter measure -- price per unit labour-content -- is what
Farjoun and Machover call "specific price", and it is the variable
that Paul and I have concentrated on in our most recent work.

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.

"Someone a lot less friendly than myself is going to catch on". The
implication here is that the claims made by those employing
this sort of methodology are more or less fraudulent. This is
nonsense. Alan seems to be quite shaky on the understanding of
the statistical/stochastic nature of the claim he is disputing.
Once again, nobody is saying that the distribution of specific
price is degenerate. Alan quotes the _range_ of the variable (on
the basis of a study of his own which may well be a careful and
accurate one, but which has not, to my knowledge, been published
or subject to any sort of peer review), but this is a statistic
which contains little information. We have calculated coefficients
of variation for specific price and other "marxian magnitudes",
and the claim is that specific price is narrowly distributed
_relative to other relevant variables_. I am aware of no serious
statistical work of any kind which takes the _range_ of the
forecast errors as an adequate measure of the predictive power
of an estimator.

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.

I don't know what Alan means when he says "we can get the same
result... with random numbers." My suspicion is that he's talking
about the sort of exercise I alluded to in my last posting:
set up two random vectors x and y; multiply both, element-wise,
by a third random vector z; then look at the correlation between
the two vectors of products. If that's the case, he has not taken
on board the criticism I offered. If he means something quite
different, all I can say is "Let's see it."

But anyway, the fact that "there is a labour input of considerable
magnitude in every sector" seems to me eminently a feature of "the
real world". If that is what stands behind the narrow distribution of
specific price, that is surely no objection to the analysis.