> 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?!
I altered one price (out of only 5, agreed) by a little less
than 4 percent, and this made the difference between a highly
significant scaled price, scaled value correlation and no
significant correlation. Andrew's example was highly sensitive
in this sense: in order to preserve a price-value correlation
under his sort of scaling (using a variable that it itself very
highly correlated with value), you have to posit a fantastically
tight unscaled price-value correlation (in Andrew's example,
> 0.999), something which no defender of the labor theory of
value has ever expected to see.
> I have demonstrated in my paper, and again on this list
> (OPE-L 441), that the theory predicts a high correlation
> between the markups...
The theory makes no such claim. To get from the actual claim
that people have made (that prices and values are highly
correlated, or that price/value ratios are narrowly dispersed)
to Andrew's variant, namely that the correlation in question
ought to survive scaling by a variable that is as closely
correlated as you like with values, requires auxiliary
assumptions that defenders of the theory do not make.
The basic point is that we expect industry-level profits to
diverge from surplus value to a significant degree, for both
systematic and unsystematic reasons. If, therefore, profit
represented a very large portion of the price of commodities in
general, we would expect the labour theory of value, as an
empirical proposition, to be correspondingly weakened.
Andrew points out that
> Pj = Vj*exp(ej).
and
> (Pj/Cj) = (Vj/Cj)*exp(ej)
are equivalent. That's clearly true, but it says nothing about
the relationship between the sample correlation coefficients for
(Pj,Vj) and (Pj/Cj,Vj/Cj).
> So, deflation of the aggregates would not affect the results were
> the labor theory of relative prices true.
Were the theory _exactly_ true and were there no sampling error,
the point estimates would be the same for the coefficients in
the corresponding logarithmic regressions. But the standard
errors are not invariant. The standard error of a slope
coefficient has the variation in the independent variable in its
denominator, and Andrew's scaling reduces that variation almost
to the vanishing point. (Also NB, the estimate of the intercept
in a logarithmic regression is biased for well known reasons, as
pointed out in work that Paul and I have published).
> 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.
I'm not sure I understand what's Andrew's saying. If he means
that any variable having the same mean and variance as the
observed Vjs would be equally good for predicting the Pjs, then
that's plainly false. One such variable (call it Xj) is the set
of actual Vjs sorted from smallest to largest. In our UK
dataset, the correlation between (logs of) actual prices and
values is 0.977, while that between prices and these Xjs is 0.3.
Allin Cottrell.