# Re: [OPE] Kliman's 'uncontested proof'

From: Michael Webber <michaeljwebber@gmail.com>
Date: Wed Jun 16 2010 - 20:14:34 EDT

dave:
i'm sorry, but i don't understand the 'it should be clear' bit in your
last paragraph.

1 ln P_i - ln C_i = ln V_i - ln C_i + e_i
suppose that
2 ln C_i = ln V_i + f_i
then
3 ln P_i - [ ln V_i + f_i] = ln V_i - [ ln V_i + f_i] + e_i
or
4 ln P_i = ln V_i + f_i + e_i

If C is constant, then
5 ln P_i = ln V_i + e_i
otherwise, introducing this third variable reduces (but does not
eliminate) the correlation between P and V. the extent of the
reduction depends on the magnitude of f.

michael

On 17 June 2010 05:29, Dave Zachariah <davez@kth.se> wrote:
> I was recently prompted by Andrew Kliman about subjecting the labour
> theory of value to statistical tests. Kliman objects to measuring the
> correlation between industry sector outputs in terms of price P and
> labour-value V. Instead he suggest one must 'deflate' the outputs in
> some way.
>
> He seems to miss the fundamental point that given the constraints on the
> available data the specific test is precisely trying to quantify *how
> well* size in terms of price correlates with size in terms of
> labour-value. If they correlate weakly the labour theory of value would
> be a relatively weak theory of market exchange. Hence, deflating the
> output price and output labour-value with a third output size variable
> would make little sense for this test.
>
>
> Nevertheless Kliman insists that one must deflate price P and
> labour-value V with output costs C. In his paper in Cambridge Journal of
> Economics from 2005, he reports that when doing this the strong
> correlations between P and V reported in the literature is destroyed,
> indicating that they are all spurious. He shows this by means of a
> computer simulation but motivates this by a 'deductive proof'.
>
>    "For some reason, C[ockshott] &C[ottrell] simply ignore this proof.
>    I am at a loss to explain why they fail to discuss (or even mention)
>    it and why they seem not to recognize its validity. The proof is
>    straightforward and mathematically trivial." (p.318)
>
> His reasoning is as follows: If
>
>    ln P_i = ln V_i + e_i
>
> holds then it also holds that
>
>    ln P_i  -  ln C_i  = ln V_i  -  ln C_i  + e_i
>
> and hence correlations would be preserved. But since he finds that the
> latter does not hold he concludes must be that the first relationship
> does not hold in reality and "[a]s long as it remains unrefuted---and I
> do not see how it could possibly be refuted---my regression results stand."
>
> Well, it seems like the reviewers failed to notify him that P, V and C
> are *statistical* quantities. Effectively he is saying that if rho(P,V)
> is high then rho(P/C,V/C) is necessarily high or else the correlation
> between P and V is spurious. But is should be clear that if C is
> correlated with P and V this does not hold. And this is precisely the
> case if one lets C be output costs.
>
> This is the basis of what the author has labeled "the uncontested proof".
>
> //Dave Z
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```--
Michael Webber
Professorial Fellow
Department of Resource Management and Geography
The University of Melbourne
Mail address: 221 Bouverie Street, Carlton, VIC 3010
Phone: 0402 421 283
Email: mjwebber@unimelb.edu.au
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Received on Wed Jun 16 20:16:09 2010

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