Herewith responses to some of the specific points in Alan's
(AF) last posting on price-value correlations, empirical
methodology and all that. I owe Andrew a response too and
will try to get to that before long.
AF: "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." (emphasis added)
AC: I agree that the intertemporal findings are important,
but I think they complement, rather than substituting for,
the cross-sectional price-value findings.
AF: "[S]ince the instantaneous [price-value] divergences are
what give rise to the intertemporal regulation much recent
research is, it seems to me, looking for the wrong thing."
AC: The size of the instantaneous divergences thrown up in
the process of "regulation" is also of interest. Ricardo
(I'll leave Marx out of it for the moment!) clearly believed
that relative prices were largely governed by embodied
labour-times; he sometimes, however, dropped back to the
somewhat weaker claim that, at any rate, significant
_changes_ in price were to be explained by changes in
required labour-times. I think he would have been
interested, and perhaps pleased, to see the contemporary
evidence that he was right on both counts.
AF: "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."
AC: I was attempting to use the facts regarding the relative
sizes of the different correlations as a means of clarifying
the significance of one of them. If the price-value
correlation were merely a statistical artifact, then one
would expect to find the same artifactual correlation using
steel, electricity, etc. But one doesn't; the other
correlations are much lower (and the standard deviations of
price-to-x-content much higher).
AF: "[L]et's not lose sight of what we are studying, namely
a distribution [of ratios of price to value, or vice
versa].... Statistics has much simpler measures [than
correlation] for measuring the dispersion of distributions.
I'd be interested in the standard deviation of the results
reported in this discussion."
AC: OK, but it's not as if that hasn't been done. Paul and
I reported standard deviations of price-to-value ratios (and
also of price-to-price-of-production ratios, etc.) in our
Bergamo conference paper (shortly to appear in a volume
edited by Riccardo Bellofiore). We also report coefficients
of variation in our July 1997 Cambridge Journal article.
AF: "Cockshott, Cottrell and Michaelson (1995) ... refer to the
'ideal' result from the standpoint of value theory, of a
zero intercept and a unit slope [of value against price -
AF]
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."
AC: No; obviously prices and values are not empirically
indistinguishable (let alone conceptually
indistinguishable). If, in relation to the linear model
y_i = a + b*x_i + u_i,
the data are consistent with the joint hypothesis a=0 and
b=1, that does not mean that y_i = x_i. Not unless the
variance of u_i is zero, and of course it's not. We have
regularly reported measures of the dispersion of the
price-value residual in the context of regressions we ran.
The 1995 paper that Alan cites offers mean absolute errors
and maximum errors, clearly showing non-degeneracy of the
price-value relationship. It is probably true, however,
that if one is dealing with large aggregates of heterogenous
commodities (such as those entering the workers'
"consumption bundle"), one can take the price-value "errors"
as mutually cancelling, and so treat the observed monetary
magnitude as a reasonable approximation to the value
magnitude.
In addition to the above, Alan discusses the paper that Paul
and I presented at the 1997 IWGVT sessions. This paper ran
a statistical comparison of the "simple labour theory of
value", the theory of prices of production, and the TSS
(temporal single system) theory, considered as predictors of
market prices. Alan has two main objections.
(1) We run an unfair "test" of the ability of various value
theories to predict, reproduce or explain... a bunch of
"data" of our own manufacture!
AF: "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....
These facts are then proposed not only as an adequate test
of their own theory, but as a test of everyone else's too."
AC: I think this is a misunderstanding. The data that we
ask the various theories to account for are simply the
aggregate prices of the output of the various industrial
sectors of the US economy, as recorded in the input-output
table for 1987. The theories are allowed to use any data
they like, and to process their input data in any way. We
just come along "afterwards" and do some information
accounting: we measure the size of the data input on the one
hand, and the output, in the sense of the reduction in
uncertainty regarding those sectoral aggregate prices, on
the other. Essentially, we are measuring the degree of
dispersion of the actual prices in relation to the
predictors generated by the various theories; we use a
metric (the information-theoretic concept of entropy) that
allows us to quantify the data input and output in bits
(binary digits). The theories are awarded brownie points
for predicting a lot on the basis of a little, and in this
comparison the "simple labour theory of value", which
requires the smallest data input, comes out well. (We do
report some correlations -- the statistic than Alan rejects
-- but these are secondary to the main line of argument.)
(2) We are anti-theoretical, attempting to reduce everything
at issue to a matter of statistical finesse.
AF: "[T]heoretical differences don't matter if the result is
empirically indistinguishable. Paul and Allin's 1997 IWGVT
paper elevates this into a methodological principle." We
are close to subscribing to "a widespread prejudice, the
governing philosophy of the mainstream journals, that
statistical finesse is a valid substitute for theoretical
clarity."
AC: I do not consider myself agin' theory. "Observation of
the facts" is a useless if not impossible exercise without
some prior theoretical understanding. But I believe (a)
that the ultimate test of theory is its ability to predict
observable facts, and (b) that without an anchor to the
empirical, theory degenerates into navel-gazing,
intellectual narcissism.
Part of the motivation behind the work Paul and I have done
is a belief that Marxian economists have, for the last few
decades, devoted an inordinate amount of intellectual energy
to the "transformation problem". What is/was that problem?
In the standard formulation it arises from the fact that
Marx "began" by assuming that market prices fluctuate around
values (= embodied labour times), while, come vol. III, it
was admitted that prices actually fluctuate around prices of
production: the question then arises, How much of the
analysis predicated on the former assumption can be salvaged
(and how exactly can it be salvaged) when one shifts to the
latter? Now the point is that the assumption that prices
"actually" fluctuate around prices of production (or that
prices of production live at a "lower level of abstraction"
than values) is basically an empirical one. But it has
_not_ generally been treated as such; rather, it has simply
been regarded as a maintained hypothesis -- given on the
authority of Smith, Ricardo and Marx, and/or too "obviously
true" to be worthy of examination. Following Farjoun and
Machover, Paul and I have sought to question this
assumption, and we find it problematic. We find that the
propositions (a) that prices are randomly distributed about
values and (b) that prices are randomly distributed about
prices of production give roughly equal predictive leverage.
Yes, industries with higher (lower) than average organic
composition show some tendency to sell their product at a
price higher (resp. lower) than value; but -- contrary to
the theory of prices of production -- industries with higher
(lower) than average organic composition tend to sell their
output at prices lower (resp. higher) than price of
production.
This finding is not the end of the road; it stands in need
of theoretical explanation. Our intention is not to
eliminate theoretical debate, but to reorient such debate --
to try to ensure that it is empirically informed, and does
not slide off into a purely internal conundrum.
Allin Cottrell
Department of Economics
Wake Forest University