# [OPE-L:6947] [OPE-L:439] Re: Re: New Evidence on Sectoral Prices and Values

Allin Cottrell (cottrell@ricardo.ecn.wfu.edu)
Thu, 18 Feb 1999 10:45:15 -0500 (EST)

Since Andrew likes parables, here is one. The price of a
personal computer is, say, 100 times that of a pizza. Why might
that be? Suppose an advocate of the labour theory of value does
some research with input-output tables and finds that the total
direct plus indirect labour time required to produce the
computer is 100 times that for the pizza (and finds many other
relationships of the same sort) and argues that prices can be
explained by reference to values.

Andrew's response: This is clearly spurious. That the price
and the value of the computer are both 100 times greater than
those of the pizza is merely a consequence of the fact that the
computer is 100 times "bigger" than the pizza, where "size" is
measured by the sum of the labour and non-labour (money) costs
of producing the respective items. Does this make sense to
anyone?

A little more technically, consider a regression of sectoral
prices (P_i) on sectoral labour values (V_i). In one form or
other, this is an indicator that has been taken seriously by the
authors Andrew targets (among other indicators). Andrew says
this sort of regression is subject to ``spurious correlation''
due to sectoral scale effects. He proposes to avoid this
problem by, as he says, ``deflating'' both the dependent and the
independent variables: each must be divided by a suitable
measure of sectoral scale.

Andrew's chosen scale measure is the sum of labour and
non-labour cost for the sectors. Unsurprisingly, this is very
highly correlated with his sectoral ``value'' measure. (One
would expect a high correlation in any case but the association
is magnified -- relative to the standard derivation of labour
values via the inversion of the input-output matrix -- by
Andrew's use of TSS values which directly build in the monetary
cost of non-labour inputs.) Andrew cites a correlation of 0.998
between his cost measure of scale and his ``values''.

Given this correlation, he might just as well have taken
sectoral values as his scale measure. That would have fully
exposed the effect of his procedure. Consider the result: We
divide both sectoral price and value by the scale measure. If
that measure is value itself, then our dependent variable is
P_i/V_i and our independent ``variable'' is V_i/V_i = 1 = a
constant. Now of course the correlation between any variable
and a constant is undefined, with zero in both the numerator and
the denominator (though many statistical packages will quote it
as zero).

Andrew has chosen a surefire way of destroying any correlation
between sectoral prices and values. Take the extreme case where
prices and values are perfectly correlated (and both are
perfectly correlated with ``costs''). Andrew's procedure is
bound to produce a ``zero'' correlation between his ``deflated''
prices and values (since both are constants).

Another way of looking at this is to consider an imaginary
economy in which all the industries are the same "size" (and
hence the scale issue is absent by assumption). Suppose that in
such an economy the ratio of price to value is perfectly uniform
across industries. Then the price-to-value correlation
coefficient is undefined (and so is the slope coefficient in a
linear regression of price on value). A close approximation to
this situation is likely to produce correlation coefficients and
slope coefficients not significantly different from zero, with
huge standard errors.

Thus, on the basis of his chosen methodology, Andrew would able
to prove that ``variations in value account for next to none
[none, actually] of the variation in prices'' *even in the case
where the ratio of price to value is perfectly uniform across
sectors*.

Paul Cockshott and I, for example, have focused on the
dispersion of the ratio of price to value across sectors. We
find this dispersion to be "small" -- but small relative to
what? For instance, relative to the dispersion of ratios of
price to the total embodied content of oil, electricity and
steel (as opposed to labour). We also find that the dispersion
of price to value ratios is of essentially the same magnitude as
the dispersion of ratios of actual prices to prices of
production -- a result that one would not expect on the standard
theory of prices of production.

Allin Cottrell.