In OPE-L 439, Allin claimed that the division of aggregate sectoral
values (V) and prices (P) by aggregate sectoral costs (C) is sure to
destroy the correlation between the prices and values, because the
correlation between values and costs is so high.
In OPE-L 441, I demonstrated that this is not true. In OPE-L 443,
Allin now acknowledges that I was right and he was wrong: "if you
construct a data set where P/C and V/C are highly correlated, then
multiply through by C, you will preserve the correlation, provided
that V/C is not actually degenerate."
He goes on to argue that this case "is so artificial that it has
little bearing on any actual empirical work." I'm happy to hear
this. I read it as an acknowledgement that his data, like mine,
disclose no substantial or statistically significant influence of
surplus-value/cost on profit/cost. This means that the data
disconfirm the labor theory of relative prices.
He alters just one number of my example, which affects the
correlation coefficient substantially, and tries to argue that my
regression equation is therefore "terribly sensitive" to this kind
of thing. Now really, Allin, do you expect anyone to take this
seriously?! My little example contained only FIVE observations, so
an alteration of one number is an alteration of 20% of the
observations!
Let me remind you that my pooled regression equation contained EIGHT
HUNDRED AND EIGHTY-TWO observations -- 882, not 5. Yet I was still
unable to obtain a statistically significant correlation between V/C
and P/C, or a statistically significant elasticity (of price with
respect to value) -- even at the 30% confidence level, which is an
*extremely* lax test of significance. And the estimated value of
the elasticity was less than 0.06, nothing like the value of 1 that
the labor theory of relative prices predicts.
Allin writes: "To my knowledge, no supporter of the labour theory
of value has
ever expressed an expectation of finding a tight correlation between
the profit markup and the "markup" of value over cost."
By "labour theory of value," he means his own labour theory of
relative prices, not the theories of either Ricardo or Marx. As
Anwar Shaikh has noted, “It is worth recalling that neither Marx nor
Ricardo argue that cross-sectional variations are negligible.
Indeed, they both emphasize that at any moment in time prices of
production may significantly differ from values.”
In any case, note Allin's oh-so-careful wording: no supporter of
his theory has EXPRESSED an expectation that the markups are highly
correlated between the markups. Probably true, but completely
irrelevant. (Also irrelevant is the wordplay with the word
"markup." Call profit/cost and surplus-value/cost whatever you
wish.)
What *is* relevant is the theory in question and the hypotheses it
generates. I have demonstrated in my paper, and again on this list
(OPE-L 441), that the theory predicts a high correlation between the
markups and an elasticity of unity. In running regressions on the
markups, I was thus testing their theory, not something I myself
devised.
Since this is all-important, I repeat the demonstration that THEIR
THEORY DOES INDEED MAKE THE EXACT SAME PREDICTIONS FOR THE
COST-WEIGHTED VARIABLES THAT IT MAKES FOR THE SECTORAL AGGREGATES:
The equation being estimated is
Pj = A*Vj^b*exp(ej).
The proponents of the labor theory of relative prices claim that A =
1 and b = 1, i.e., that
Pj = Vj*exp(ej).
If this were true, then it would also be true that
(Pj/Cj) = (Vj/Cj)*exp(ej),
so that A = 1 and b = 1 in the equation
(Pj/Cj) = A*(Vj/Cj)^b*exp(ej).
So, deflation of the aggregates would not affect the results were
the labor theory of relative prices true.
Allin, you have read this demonstration in my paper. You have read
it in OPE-L 441. And now you have read it again. But you have not
said whether it is true or not. It is time to do so, no?
Allin writes: "The rest of Andrew's argument boils down to saying,
"if you know the money cost of production of a commodity already,
then knowing its value is not likely to help in predicting its
price".
This is completely untrue. My argument has nothing to do with
knowing money costs. Rather, my argument -- and I quote from my
post -- is that "ANY variable having the same probability
distribution (same variance, etc.) as the values would result in
average deviations that were just as small," so that values are no
better predictors of prices than any similarly low-variance variable
is. This claim is substantiated empirically in my paper. Over the
21-year period, the average NVD is 0.125, and the average NVD
between prices and a random variable that has the same probability
distribution as the values is also 0.125.
Indeed, what predicts even better than the values is any single real
number, appropriately normalized! That's because it has a zero
variance. For my data, it outperforms the values by an average of
7.5%. So, you want to predict prices? Spare yourself the trouble
of inverting your matrices and all that. Instead, pick a number,
any number ...!
Finally, Allin writes: "the notion behind the labour theory of
value [sic] is that you can predict prices quite well on the basis
of _just_ labour values ... . you can't do anything like as well on
the basis of knowing just oil contents, steel contents or whatever."
Again, complete ignorance beats out values as a predictor of prices.
If you think that 7.5% worse than complete ignorance still means
that values can predict prices "quite well," that's your business,
but you should at least let readers know what your standards are.
I have already explained in OPE-L 441 that the stuff about values
vs. oil contents, etc. is a meaningless factoid. Yet Allin has not
responded to my argument. He has not told us the variances of these
variables. He has not tested the predictive power of the values
against other variables that have the same variance (or zero
variance). Instead, he just repeats the factoid. But the mere
repetition of a meaningless factoid does not make it any more
meaningful.
Here, for the record, is the argument to which he has not responded:
"As I discuss in my paper, I too, like almost everyone else, found
that price-value deviations (including coefficients of variation)
were "small." But the smallness was merely an indication of the
lack of dispersion among the values (average variance = 0.003), not
any predictive power of values over prices. Thus, ANY variable
having the same probability distribution (same variance, etc.) as
the values would result in
average deviations that were just as small.
"I therefore submit that the comparison of values, oil values, etc.,
is only a fair one if these variables have similar variances.
(Indeed, I'm be *very* interested in learning what these variances
are.) If this isn't the case, I would suggest to Allin and Paul
that they perform their test for variables that have the same
variance as the values, as I did."
Andrew Kliman