File spoon-archives/marxism.archive/marxism_1994/94-07-31.000, message 108


Subject: Re: Labor and  value 
Date: Mon, 25 Jul 94 10:55:45 +0100
From: wpc-AT-cs.strath.ac.uk


Chriss Sciabarra  accepts the critique of Bohm Baverk of the
labour theory of value. The great weakness of this, and all
of the transformation problem arguments is their entirely
speculative character.

They rest upon a hypothesis - the existence of a uniform
rate of profit, which is empirically false, and if Farjoun
(Laws of Chaos - Verso) is right, is also mathematically 
unsound when dealing with stochastic phenomena.

When one turns to empirical evidence, the critics of the 
labour theory of value have none, whereas the advocates of
it have an increasing body of well founded statistics on
their side. Shaik (in Marx, Ricardo Sraffa, Verso) gives
figures for the US economy showing a high correlation between
prices and labour values, Ochoa (Cambridge Journal of Economics 13/3)
provides reinforcing evidence. I and others have used UK
input-output data to obtain very high correlations between
prices and values:


Although theorists may sometimes be inclined to forget, the 
equalized rate of profit is NOT a fact.  It is, however, an assumption 
that is absolutely crucial to all theories of Sraffian derivation.  
Farjoun  is able to show, for instance, that many 
Steedman-type examples, of the sort used to demonstrate the frailty 
of the LTV, fall apart and become economically meaningless given 
the slightest deviation from this assumption.

What IS a fact, is that the distribution of the rate of profit in 
capitalist economies is quite wide, and broadly stable over time.  
Yes, there are forces working in the direction of equalization, but 
there are complementary forces working in the direction of dis-
equalization; and the joint outcome of these forces seems to be an 
"equilibrium" degree of dispersion of profit rates (with different 
capitals occupying different places in the distribution at different 
times)  
It is therefore not at all obvious that a theory based centrally on 
the assumption of an equalized rate of profit has any claim to 
correctness, to the status of a benchmark against which the 
deficiencies of the LTV may be assessed.  

The greater the equilibrium dispersion of profit rates, the worse 
are Sraffian prices as approximations to actual prices -- or even to 
their "centers of gravity," discounting the effects of short-run supply-
demand disequilibria.  On the other hand, on the maintained 
hypothesis of an equalized rate of profit, the greater the dispersion of 
the value composition of capital, the worse are labor-values as 
approximations to actual prices.  Since both of these distributions are 
non-degenerate, the question of whether Sraffian prices or labor-
values offer the better systematic approximation to actual prices is an 
empirical one.  The evidence to date shows, with remarkable 
consistency across data-sets drawn from different capitalist 
economies and different time periods, that the two approximations 
are *roughly equally good*.  It is not the case that labor-values are a 
crude first approximation, and Sraffian prices a clearly superior 
second approximation.



Shaik has argued  that the question of
 whether prices are closely correlated with
 values is essentially an empirical one. One
 can in principle measure the degree of correlation
 between the two provide that one has independent
 measures of each. Shaik's method uses input-output
 table data to estimate labour contents and then
 measures the correlation between these and prices.
 He presents results derived from Italian and US
 input-output tables. These show, as one would expect
 from value theory, that relative prices are almost
 entirely determined by labour content. He obtains
 correlation coefficients of well over 90%.

 Since we are concerned
 with producing estimates of s/v
 for the UK economy,  we have 
repeated his experiments using the UK input-output
 tables  for 1984. The results are summarized  below
  Regression of prices against values
  -----------------------------------
	Equation		R^2	max error  SDEV err    avabs err
1	p = -.055 + 1.024 l	0.955	157		23	13.5	
2	p = -.039 + 1.014 l	0.961	65.4		16.5	11.8	
3	p = -.046 + 1.024 l	0.976	67		20	15	
4	p = -.049 + 1.024 p.p	0.980	57		15	10
\end{tabular}	
\end{table}
The commodity use matrix in Table 4 of the I/O tables was used 
to provide estimates of total labour content of the outputs of
 each commodity group. Both direct and indirect labour inputs were
 calculated using a recursive approximation:
 Recursion was terminated at a depth of 8 giving answers
 to 3 significant digits. In the tables, labour input is given in
 \pounds s. This amounts to measuring the price of the labour power used
 rather than being a direct measure of the labour used. We tried two
 alternative methods of going from these figures to estimates of abstract
 labour. 

Equation 1 Value/price correlation for all industries assuming uniform 
wage rates.

 A dummy wage rate of 1 per hour was assumed to be
 uniform across all industries. On this assumption the labour
 content of the outputs of all industries was calculated.
 The assumed wage rate was unrealistically low, but this 
is of no significance in computing the correlations since
 it is equivalent to a uniform scaling factor in our time
 unit. In this and all other cases, the variables enter the
 regressions in logarithmic form.

Equation 2. As above but excluding the oil industry

  Within the figures
 for all industries there was one with a very anomalously high
 price/value ratio - the oil industry. This is exactly what one
 would expect from the Ricardian/Marxian theory of differential
 rent. Non-marginal oil fields could be expected to sell their
 output at above its value. Excluding the oil industry from the
 correlation gave estimate 2.

Equation 3 Values assuming non-uniform wage rates. 

 In practice wages differ between industries.
 The actual hourly wage rates for the different 
industries in 1984 were obtained from the New Earnings
 Survey and  used to convert the  monetary figures for
 direct labour into hours. Again the oil industry was
 excluded from the final regression.

Equation 4 No oil industry, price of production is independent variable.

  Price of production was computed using the recursive application
 of formula $ Pprod_n= p'(cpprod_{(n-1)}+ vm)$ to all industries, 
where $ cpprod_{(n-1)}$ is the $(n-1)$th estimate
 of the price of production of the constant capital inputs,
 and $Pprod_n$ is the $n$th estimate of the price of production. 

Two questions arise in looking at the regression results: 
(1) is labour value an unbiased predictor of money price? and 
(2) how efficient is labour value as a predictor of money price? 
The short story is that, there appears to be a slight bias,
 but nonetheless the efficiency is very high.
In the regression of the log of aggregate price on the log of
 aggregate labour value, sector by sector, the 'ideal' result
 for the labour theory of value would be if the constant and
 slope were zero and one respectively. That would say that 
labour value is an unbiased predictor of money price. In
 each case the results were pretty close to this ideal, 
but the constant seems to want to be slightly negative,
 while the slope differs slightly from unity. 

If that result is robust, it says there is a slight bias: 
labour values give an underestimate of price in the case of
 larger industries (larger, that is, in terms of total labour content),
 and an overestimate in the case of smaller industries. 
On the efficiency of labour value as a predictor of price, 
there are various indicators. The R2 gives the percentage of 
the total variation in the log of price (i.e. sum of squared
 deviations of the log of price about its mean) that is 
'accounted for' by reference to labour values. This is
 pleasingly high, at about 96 to 98 per cent. One can get more
 information on this by looking at the residuals (actual money
 price minus predicted money price, industry by industry).


The fourth estimate shows that price of production is a slight
ly more efficient predictor of actual price than value is. This 
is in conformity with the modification to value theory
 presented by Marx in Capital III .
 We would expect price of production to
 predict market price more efficiently than
 value does, but, and this is the significant
 point, prices of production only introduce a
 minor correction to the underlying determination
 of market price by labour content.  

The correction term due to prices of production is so
 small that it can for practical purposes be ignored.
 This is especially the case when constructing estimates
 of ratios like s/v where each individual term is an aggregate
 of many different types of commodities. The term v for instance
 denotes a sum of value that is realized as all of the commodities
 upon which the wage is spent. Since these will be drawn from many
 industries, the, already small, random correction terms due to
 prices of production in each industry, will tend to cancel out.
 We thus conclude that it is valid to use monetary data from the
 National Income Statistics to produce estimates of value ratios like s/v.


\bibitem[7]{CSO} Input-output tables for the United Kingdom 1984, Central Statistical Office, HMSO, 1988.
\bibitem[8]{Roemer} Should Marxists be interested in Exploitation, Roemer, in Analytical
Marxism, CUP , 1986.

\end{thebibliography}
\end{document}


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