A response to Alejandro Valle's ope-l 5504.
Alejandro: "1. Petrovich disussed briefely that MAD is better than
correlation coeficients because spurios correlation is present in this
problem. Ochoa adopted MAD in his excelent analysis of value-price deviations
for the US economy. By the way, MAD claculated for Ochoa are lower than 20%."
I'm very glad to read this. Alejandro, who has done work in this area, and I
agree that spurious correlation is present when aggregate prices and values
are correlated. This was the crucial criticism that Alan raised and I
reiterated. It follows, doesn't it, that the aggregate correlations are very
misleading and fail to test what they purport to test?
Ochoa has also noted that spurious correlation is present.
Alejandro: "2. A MAD of 27 0oes not mean that value and prices 'differ quite
significantly' as Andrew assert[s]. The problem of 'reasonable
correspondence' between empirical data and a theoretical law is a very
hard one. It is convinient for this 'The problem of measuring in modern
physics' of T.S. Kuhn. He showed that there is no rule for deviations in
physics: a very large deviation could be aceptable in astronomy and not in
another sort of problems."
Well, if a MAD of 27 0oes not mean that values and prices differ quite
significantly, it also doesn't mean that they fail to differ quite
significantly, either. This is a matter of judgment. But it is certainly
true, isn't it, that a MAD of 200r 27% means that we should reject the
conclusion that variations in values account for ("explain") almost all of the
variations in prices?
I agree that what constitutes reasonable correspondence between empirical data
and a theoretical law depends on the problem at hand. The problem in this
case, however, is that if there's any "theoretical law" involved, I don't know
about it. I don't mean that I reject the supposed law; rather, I don't know
that anyone has given a *theoretical reason* for why price-value deviations
should be small.
But it is also possible to understand "reasonable correspondence" as a matter
of how well the data support the claims made for them, i.e., the conclusions
drawn from them, irrespective of theory. For instance, Shaikh wants to put
the "transformation problem" in the proper "perspective," i.e. to suggest that
since prices are actually "very close" to values, it doesn't matter if he
can't resolve the theoretical problem because it lacks empirical significance.
Similarly, Cockshott and Cottrell have asked whether Marx "needed to
transform."
The data lead to an unambiguous answer: yes, he did. MAD's of 20-27 0mply
that the amount of value that is redistributed across sectors and across
countries is not negligible. In other words, it is illegitimate to conclude
that the factors which cause redistribution of value are unimportant in
accounting for ("explaining") observed price magnitudes.
The more important point, by far, is that the presence of significant value
redistribution means that one needs to be able to explain how, and in what
sense, the law of value holds, even though prices *do* differ from values --
and the numbers must add up. So when I said that they prices and values
"differ quite significantly," I meant that they differ enough that the data do
not permit one to dismiss the theoretical problem that led the Ricardian
school to disintegrate and has more recently led also to a disintegration of
"Marxian economics." The problem is a real one and it must be addressed
honestly, in theoretical terms, and not dismissed by reference to misleading
and meaningless aggregate correlations.
In addition to the *size* of price-value differences that we've been
discussing, there's the issue of their *predictability*. Appealing to his
reading of Farjoun and Machover, Paul Cockshott in particular suggests that
the deviations are essentially random, with perhaps phenomena like rent
playing a minor role.
I do not know what tests of this claim he has conducted, but I have performed
a simple test myself. According to nearly everybody, *one* determinant of
prices is the capital/labor ratio or value composition of capital or whatever.
I say "one" because this proposition does not imply that profit rates
actually equalize (I don't think they do), only that a *tendency* exists for
prices to be positively related to value compositions. The Cockshott
hypothesis, in contrast, is that prices are *not* affected by value
compositions.
Using Alan Freeman's data for 9 major sectors of the UK economy in 1992, I
have run the following regression:
ln(P/L) = a + b*(ln[C/L])
where P is the sector's aggregate price, L is the number of worker-years
worked in the sector, and C is the consumed constant capital ("intermediate
purchases"). a and b are constants, of course, and the purpose of the
regression was to test the Cockshott (null) hypothesis that b = 0. The
alternative hypothesis of almost everyone else is that b > 0.
(Notes: I used P/L, not P, as the dependent variable, in order to try to
remove the effects of differences in industry size. Consumed constant capital
was used as a proxy for total constant capital because I don't know the
latter.)
The results are:
ln(P/L) = 0.6884 + 0.7964*(ln[C/L])
(9.907) (8.860)
The numbers in parentheses are Student's t's. The b coefficient of 0.7964 has
the positive sign that almost everyone expects. Moreover, even with a paltry
7 degrees of freedom, it is possible to reject the null hypotheses that b = 0
at the .001 level (1-tailed test). In other words, it is almost impossible
that the "true" b is less than or equal to 0.
I think it is important that the value of b is so large, moreover. The
equation suggests that if we have two industries, one of which has a C/L
double that of the other, it will also have a P/L 80% above the other.
The r-squared = 0.918, so the "value composition" accounts for 920f the
movement in price per labor-year. F = 78.5.
The regression results can also be used to test the prevalent claim that
values are good predictors of prices. The question is: good compared to
what? Using the estimated equation to give predicted aggregate P's (not
P/L's), I found that in 7 of the 9 cases, the equation gave a predicted
aggregate P that was closer to the actual one than the aggregate value was.
I also computed the sum of the absolute values of the differences between
sectoral values and prices (DVP), and compared them with the sum of the
absolute values of the differences between predicted and actual sectoral
prices (DPAP) (everything measured in thousands of labor-years):
DVP: 6411.2
DPAP: 2785.9
The latter figure is less than half (43%) of the former.
The 9-sector sum of prices is 17,284, so DVP amounts to 370f total price,
but DPAP amounts to only 16%.
So, are values good predictors of prices? Not compared to "value
compositions."
Undoubtedly a multivariate regression could perform even better, though
Cockshott and Cottrell will have their "information loss" arguments against
this, I guess.
I also tested whether the sectoral price-value ratios are random, by means of
a similar equation:
ln(P/V) = m + n*(ln[C/L])
Again, the Cockshott ("null") hypothesis is n = 0, and almost everyone else
predicts n > 0.
The results were:
ln(P/V) = 0.5464 + 0.3762*(ln[C/L])
(3.457) (2.685)
r-squared = 0.507. F = 7.2.
n has the positive sign almost everyone expects, and it is significant at the
.025 level (1-tailed test). The null hypothesis is rejected. The value
composition accounts for more than one-half of the variation in the
price-value ratios.
I'd be interested in other results using this methodology, with large and
different data sets.
One of the problems with some work in this area, I think it should be clear,
is that inappropriate and weak tests of the hypothesis that values "explain"
prices are employed, tests that make it all too easy to give an affirmative
answer. The simple tests I've employed herein, I think, have the advantage of
*comparing* alternative hypotheses (value compositions matter, value
compositions don't matter) instead of allowing one hypothesis to "win" because
only confirming evidence, not disconfirming evidence, is used to assess it.
Andrew Kliman