[OPE-L:5552] Re: Humbug Aggregate Price-Value Correlations

andrew kliman (Andrew_Kliman@classic.msn.com)
Tue, 30 Sep 1997 12:46:30 -0700 (PDT)

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The discussion now seems to be going in many directions at once, so rather
than take up everything in one post, I'll respond to each author (which may
take some time). This is my response to Tsoulfidis Lefteris's ope-l 5547.

Tsoulfidis: "Clearly, no index by itself gives an undisputed idea of the
true magnitude of these deviations. Efforts to devise new indexes such as
Klimans suggestion of shift share analysis are welcome, however it seems that
do not improve the situation in any substantial way. To my view there must be
a *subjective* element in determining whether the deviations are large or
small ...."

I agree that the shift-share numbers by themselves do not allow us to
determine whether price-value deviations are large or small. That was not the
reason I suggested the shift-share index. The reason I suggested it was to
provide an index with a clear economic meaning, along the lines Duncan had
recommended, i.e., an index that measures the degree to which surplus-value is
redistributed. (Unlike other metrics in use, it focuses specifically on the
redistribution of surplus-value, not also the lack of deviation of "price" C+V
and "value" C+V.) I'm glad to read that he thinks it fits the bill: "But a
number of the metrics of correlation are purely statistical, and it seems to
me that metrics that introduce meaningful economic quantities, like
shift-share, are inherently more interesting that purely statistical or
mathematical concepts of distance or correlation" (ope-l 5549).

I thought it was clear from my post that the shift-share index was not being
proposed as a way of telling whether price-value deviations were large or
small, because, after suggesting it, I immediately turned to the need to test
hypotheses. My point was that whether a shift-share number (or a MAD,
correlation, etc.) indicates that prices are "close" enough to values to
permit the conclusion that values "explain" prices depends on the ability to
reject the "naive hypothesis" that the surplus-value has been randomly
distributed. I asked for discussion of this criterion, objections in
particular, but the responses thus far haven't addressed it directly.

*If* one obtains a number that permits rejection of the naive hypothesis,
*then*, I agree, the "closeness" of prices and values becomes a subjective
matter. (If, on the other hand, one finds the requisite "closeness," but a
random distribution of surplus-value would yield the same or better degree of
"closeness" in, say, 10 cases out of 100, then it seems to me that "closeness"
alone doesn't support the conclusion that relative values determine relative
prices.) However:

(1) I have strong doubts about the legitimacy of throwing out outliers
("peculiar industries, such as the oil industry"). This is acceptable if the
data are suspect, and Tsoulfidis does try to make this claim, but it is
contradicted by the fact that the large oil industry price-value difference is
"a result so common with studies for other countries, see for example the
results of Alejandro Valle, Paul Cockshott et al. ..., and Ochoa." Another
justification for throwing out outliers is that their inclusion or exclusion
is not important to the hypothesis being tested. The problem here -- as I've
said before -- is that it is not at all clear what hypothesis is actually
being tested. Tsoulfidis gives *explanations* for why the oil industry has a
large price-value deviation, but it isn't clear that these explanations make
it theoretically justifiable to throw out the result. *If* the hypothesis is
that prices = values + some small and random deviation, then throwing out the
outlier is not justified. *If* the hypothesis is that compositions of capital
do not affect the deviations, then the appropriate procedure is to leave in
the observation and to *test*, directly, the explanatory impact of value
compositions on the whole data set.

In the absence of a clear justification, the studies seem suspect. It seems
as if the purpose of the exercise is to get deviations that look small "by any
means necessary."

(2) There are other issues at stake beside the "closeness" of prices and
values, and deciding them is not all that "subjective." For instance, are the
deviations random? Are they independent of value compositions? Even more
important is the issue of "reverse causation": are the prices determining the
"values" instead of vice-versa? (After all, price data are used to compute
the "physical data" in the first place.)

What is called for to decide these issues, after one gets the numbers, is
rigorous hypothesis testing and rigorous analysis. "Casual empiricism" is not
good enough. Rather than advancing reasons for the deviations that conform to
one's theory, one needs to test whether alternative explanations can be
rejected. This has not always been done.

Tsoulfidis: "Returning now to Klimans suggestion for the shift share
analysis, I am not sure it differs qualitatively from the other indexes. It
seems to me, intuitively (I must admit though that I haven't done any
particular research) that appart from the extreme values of 0 and 1 suffers
from the same limitations of the other indexes, and also (at first sight) does
not have any clear economic meaning."

Well, as I said, one advantage as against the MAD is that the values of the
shift-share index don't seem to be sensitive to the dispersion of industry
sizes or the ratio of surplus-value to value.

The economic meaning of the index is pretty clear to me: a value of .33 (the
expected value given that surplus-value is randomly distributed) means that
330f the surplus-value is redistributed, i.e. obtained elsewhere than in the
sector in which it is produced. Here's an example:

Ind. S Pr Diff. Abs. Diff.
---- --- --- ----- ----------
I 45 78 +33 33
II 35 17 -18 18
III 20 5 -15 15
----- --- --- --- ---
total 100 100 0 66

Taking 1/2 the total of the absolute differences and dividing by total S, we
get (1/2)*66/100 = 0.33. This means precisely that 330f all surplus-value
is shifted out of the industry in which it originates: 180f the total is
shifted out of II and 15 0s shifted out of III.

Tsoulfidis: "I especially liked the idea of running regressions of the ...
ratio of prices of production to values as the dependent variable and an
expression of composition of capital as the independent variable in an effort
to determine the direction of price value deviation."

I'm glad we agree about this. I had a specific purpose in mind, namely to
test the claim that deviations of prices (note: market prices, not production
prices) from values are not affected by value compositions.

T: "- there is some theoretical work on that published in CJE (1989?) by
Beilefield and also by Van Parys in AER (1983?).
Seton also claims that in a 3x3 sector economy one can verify Marxs claims
about the direction of price-value deviations but not in n sectors and also
does Pasinetti (1977)."

Thanks for the citations: I'll try to look these studies up. Pasinetti and I
suspect the others presuppose a difference between the "price" and "value"
compositions of capital. Both variants of the single-system interpretation
(simultaneous and temporal) reject this, and support the rejection on the
basis both of theoretical claims Marx's made and of the ability to replicate
his theoretical conclusions partly by means of the single-system notion.

T: "The big trouble with Klimans regressions is (of course) that he uses
only 9 observations (sectors) as he says, and ... his regressions does not
really test the value composition of capital ...."

I accept the latter point. Still, the regression was sufficient to show that
we can reject the hypothesis that price-value ratios are random, which was the
underlying point.

Note that the 9 sectors are just a less disaggregated version of the data that
others have used.

It seems to me that the paucity of degrees of freedom makes the results
*stronger* -- if you can reject the null hypothesis that value compositions
don't affect the price-value ratios when you have only 7 d.f., that is clearly
a stronger result than if you had 10,000 d.f., since in the latter case even a
coefficient that differed from 0 by the tiniest bit would permit rejection of
the null hypothesis.

T: "My joint (with Th. Maniatis) paper that I mentioned above, uses the
vertically integrated value composition of capital
and gave the following results

a=0.824 (17,4) b=1,212 (9.94) and R2 =76,1%
# of observations 33."

I *would* like to see this paper. I have some difficulty understanding the
numbers without the equation.

T: "One final point has to do with (Kliman's) numerical examples, which in my
view must be representative or typical of the situation under investigation,
one should not use extreme cases (no matter their number) and then say well
this conclusion does not hold, because of my counterexamples."

What seems to be under discussion is my demonstration that it is possible that
the *maximum* MAD is only 20%. I'm not sure how extreme a case this is. In
any case, I did not say or imply that MADs of 200r mean that the reported
MADs are large enough to *reject* the conclusion that relative values
determine relative prices. Instead, I said that, in the absence of additional
information, they do not allow us to *accept* the conclusion that relative
values determine relative prices. There's a difference.

To reiterate my reasoning: without additional knowledge of the properties of
the particular data set, we cannot determine whether 20 0s "close" or not
(e.g., low enough to reject the naive hypothesis); moreover, because the size
of the MAD is very sensitive to the properties of the particular data set, we
can't necessarily conclude from the replication of MADs of 200f so in a
variety of studies that the result is somehow robust. So yes, "examples ...
must be representative or typical of the situation under investigation," but
because the size of the MADs is very sensitive to the properties of the
particular data set, how do we know what is typical or representative? To be
able to compare MADs across different studies, we would need to know, at the
very minimum, that the coefficients of variation of industry values were
similar and that the ratios of total surplus-value to total value were
similar. Otherwise, cross-study comparisons are meaningless -- the same MAD
of 20 0mplies very different things in these different studies. To be able
to say whether MADs of this size are large or small, moreover, we would need
to know how confident we could be that they didn't arise from a random
distribution of surplus-value.

Thus, as I concluded, "Until we get some hard data along the lines I've
outlined, I suggest that no [one] be misled into thinking that the reported
MADs support the 'relative values determine relative prices' hypothesis."

Andrew Kliman