A reply to the PIAF:
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From: owner-ope-l@galaxy.csuchico.edu on behalf of Allin Cottrell
Sent: Monday, October 20, 1997 3:55 PM
To: ope-l@galaxy.csuchico.edu
Subject: [OPE-L:5631] andrew: random profits
I'm very glad Allin has taken up my suggestion and actually done the hard work
of testing how the "relative labor coefficients determine relative prices"
theory performs in relation to the naive hypothesis that prices equal costs
plus a random cut of surplus-value. The numbers he reports give us a much
better feel for the meaning of the aggregate sectoral correlations. I do hope
that others will follow him in this, and that future studies will report such
numbers and discuss their implications.
Evidently, Allin has tested two variants of the naive hypothesis: the variant
I proposed (NH1), in which price equals *actual costs* plus a random share of
total profit, and a second variant (NH2) in which "price is composed of the
*value* of the inputs plus a random share of total profit" (my emphasis),
where "value" is computed by a vector of vertically integrated labor
coefficients (VILCs).
Allin reports that the correlation between the sectoral aggregate prices
generated by NH1 and the actual sectoral aggregate prices is "over 0.99 most
of the time." This means that NH1 gives us predictions for prices that are
somewhat closer to actual prices than are sectoral aggregate VILCs, at least
for this data set, since the correlation between sectoral aggregate price and
sectoral aggregate VILC is, Allin reports, 0.9779. It seems safe to conclude
that knowledge of sectoral costs and economy-wide profit allows one to account
for intersectoral variations in price at least as well as does knowledge of
VILCs.
Allin's variant, NH2, yielded correlation coefficients "mostly in the range
0.92 to 0.95; in 10,000 trials there were _no_ correlations as large as
0.9779." Although these correlations are slightly lower, they too confirm in
a striking manner my intuition that the aggregate sectoral price-value
correlations are very misleading and must be interpreted with extreme care.
As I've noted, it is because we are accustomed to think of the correlation
coefficient as ranging from 0 to 1 (or -1 to 1) that a correlation of 0.9779
seems at first to be strong support for the notion that VILCs determine
prices. But, for this data set, a *reasonable* lower bound for the range of
the correlation coefficient turns out to be about 0.935 -- *if* one accepts
NH2 as a reasonable null hypothesis. One can account for almost all of the
variation in sectoral prices, 93.5%, even if one has no knowledge of how
surplus-value is distributed (and even if one uses input VILCs rather than
actual costs to measure the non-profit component of price).
Perhaps we have here a 93% know-nothing theory of value?
0.9779 is 660f the way between the lower and upper bounds for the
correlation coefficient (0.935 and 1). Since the sole difference between NH2
and the VILCs is that the prices in the former case "contain" random profit,
while the VILCs "contain" actual surplus-value, it is clear that, in
actuality, the redistribution of surplus-value is sizably less than would
occur were it distributed randomly. Hence, knowledge of surplus-value clearly
improves one's ability to account for intersectoral variations in profit. How
much it improves one's ability, I hesitate to say, because I find it difficult
to interpret the distance of the value/price correlation from the lower and
upper bounds. Use of the shift-share index would permit more rigorous and
meaningful inferences to be drawn concerning the distribution of
surplus-value.
On the other hand, I think the results permit the following conclusion.
Knowledge of surplus-value produced allows one to account for some
intersectoral variation in prices, but knowledge of actual costs allows one to
account for even more. If you don't know costs but know surplus-value, that
gets you closer to actual price than if you have no knowledge of either (NH2).
On the other hand, if you know costs but not surplus-value (NH1), that gets
you closer to actual price than if you know surplus-value but not costs (the
VILC measure). Here again, however, techniques other than correlation would
better measure the relative effects I think.
Allin argues that my variant of the naive hypothesis, NH1, is not a fair null
hypothesis against which to test his theory, but that his variant, HN2, is:
"running that "theory" [NH1] ("explaining" the prices of outputs by reference
to the sum of the prices of inputs) against the labour theory of value would
not be a fair contest."
I think the opposite is the case. HN2 is essentially a hybrid, since it
employs the no-knowledge-of-surplus-value-distribution feature of NH1, but
also the "costs = value of inputs" feature of Allin's theory. Were anyone to
hold to NH2, they'd have to contend along with Allin that costs are determined
by the labor needed to replace inputs. So NH2 in effect tests a weaker
version of his own hypothesis against his own hypothesis, instead of against
an alternative hypothesis.
Putting the same thing differently, NH1 has a clear meaning as a naive,
minimalist notion of price determination -- firms recoup actual costs and get
some random share of profit -- but NH2 does not.
Putting the same thing differently again, a test of Allin's theory against NH2
is actually a test of whether knowledge of where *surplus-value* is produced
helps one to account for the distribution of *profit*. As I have noted, the
answer is yes, although the degree to which this helps is as yet unclear. In
any case, the test of Allin's theory against HN2 is NOT a test of whether
relative *VILCs* account for relative *prices*, because that test eliminates
one source (and, as I've noted, the apparently more important source) of
deviation between VILCs and prices -- the deviation of the "value" of inputs
from actual costs. Clearly, his results show that his theory can account for
some of the actual distribution of profit, and that is a mark in favor of it.
But equally clearly, they show that his theory's relative inability to account
for costs is a mark against it.
Furthermore, what is "unfair" about NH1? Evidently, that actual costs are a
"price" variable, so that NH1 unfairly uses prices to predict prices.
(Correct me if I'm wrong.) Yet let's not be confused by the word "price."
The VILCs used to compute the "value" of inputs are just as much prices as are
the actual input prices. Moreover, just as the VILCs differ from *output*
prices, so do *input* prices (sorry about this Ajit, but it is true). Allin's
theory holds that output prices are determined by costs based on VILCs; NH1
holds that output prices are determined by costs based on input prices. So,
in principle, there's no problem here of using the dependent variable to
explain itself.
It may be the case -- and it seems to be the case -- that input prices are
closer to output prices than are VILCs, but this does not follow from
deduction. It is not tautological. It is an *empirical* hypothesis, and
should be tested as such. By claiming that VILCs explain output prices,
Allin's theory in effect implicitly presents itself as an alternative to the
hypothesis that actual input costs are better determinants of prices than are
VILC-costs.
Although I said that *in principle*, there's no problem here of using the
dependent variable to explain itself, multiple turnovers in one year may imply
that some output prices during the year also become input prices during the
same year. But this just requires more sophisticated measurement to remove
this effect, and does not count as a *conceptual* objection to the hypothesis
that output prices depend on the costs of inputs.
More refined testing along a number of lines is needed. Allin's computations
are a very welcome first step, IMO.
Andrew Kliman