I will first deal with a technical point in the example he has
prepared before going on to deal with a couple of theoretical
issues that have been raised.
On dividing correlated random variables
=======================================
At 02:39 19/02/99 -0500, ope-l@galaxy.csuchico.edu wrote:
>
>
>My study deflates aggregate sectoral prices and values by dividing
>them by aggregate sectoral costs. This removes the effect of
>variations in industry size, and therefore removes the spurious
>correlation between prices and values that these variations produce.
>Once spurious correlation is eliminated, there is no reliable
>evidence of *any* relationship between values and prices.
>
>Yet Allin has now objected to my procedure. By deflating the
>variables by costs, "Andrew has chosen a surefire way of destroying
>any correlation between sectoral prices and values." The problem,
>supposedly, is that costs are too highly correlated with values.
>
>This is simply not true. An example will show that it isn't, and
>why.
>
>Let V, P, and C indicate sectoral aggregate values, prices and
>costs, and assume the following data:
>
> V P C
>---- ---- ----
> 226 225 200
> 460 464 400
> 702 699 600
> 952 956 800
>1210 1206 1000
>---- ---- ----
>3550 3550 3000
>
>The correlation between aggregate values and aggregate costs is
>0.9998, higher even than the 0.998 average correlation in the real
>data. According to Allin, if we now divide values and prices by
>costs, this is sure to destroy the correlation between them, because
>the correlation between values and costs is so high.
>
>The transformed variables are
>
>
> V/C P/C
>----- -----
>1.13 1.125
>1.15 1.160
>1.17 1.165
>1.19 1.195
>1.21 1.206
>
>
>A glance at these numbers is enough to confirm that the
>cost-weighted variables are highly correlated. In fact, r = 0.976,
>and r^2 = 0.953.
Paul Cockshott
--------------
In Kilman's example above a correlation between v/c and
p/c exists only because of the extraordinarily strong
correlation that he set up between prices and values
in his initial data.
For the initial data we have:
0.999814976 cost value correlation
0.999955042 price value correlation
The correlation between costs and values is less than
the correlation between prices and values. It is only
because of this that when one divides through by costs
one preserves a correlation between deflated prices
and deflated values.
If on the other hand, costs are more highly correlated
to values than values are to prices then deflating
both price and value by costs destroys the correlation
between the deflated variables. I have illustrated
this by the simple expedient of relabling Andrews
columns c and p, so that values are now more closely
correlated with costs than they are with values.
v c p v/c p/c
226 225 200 1.004444444 0.888888889
460 464 400 0.99137931 0.862068966
702 699 600 1.004291845 0.858369099
952 956 800 0.9958159 0.836820084
1210 1206 1000 1.00331675 0.829187396
0.999814976 price value correl
0.999955042 cost value correl
0.169741923 deflated price to value correlation
As one can see, this destroys the correlation between
the deflated variables.
Andrews failure to find a correlation between his deflated
variables in his empirical figures merely indicates that
his measure of values is more closely correlated to costs
than it is to market prices. This is altogether unsurprising,
and I fail to see why it has any bearing on the findings
by other authors that there is a strong correlation between
market prices and vertically integrated labour coefficients.
As far as I am aware no author has suggested that values
should be more closely correlated to market prices than they
are to values.
On Causal Relations
===================
As Reg points out the critical factor in determining whether
a correlation is spurious or not, is whether one has a causal
theory which is able to explain the correlation of two datasets
by a third, which itself acts as a cause of the other two.
>From a causal point of view I would dispute that total industry
costs measured in money terms explain or cause values. I would
say, with Reg, it is values, the labour time necessary
to produce things that are the cause both of costs and of prices.
The value of a commodity is, according to Marx, dependent upon
the amount of social labour required to produce it:
'The greateness of its value, of its relative value, depends
upon the greater or less amount of that social substance contained
in it; that is to say, on the relative mass of labour
necessary for its production.'
(Marx:Wages Prices, Profits chap VI)
This amount of labour is arrived at by adding together the
amount of labour directly expended to produce a commodity
with the amount of labour embodied in raw materials and
tools used.
'In calculating the exchangeable value of a commodity we
must add to the quantity of labour last employed the quantity
of labour previously worked up in the raw materials of the
commodity, and the labour bestowed on the implements, tools,
machinery, and buildings with which such labour is assisted.'
(Marx:Wages Prices, Profits chap VI)
So value is composed of newly added labour plus embodied
labour.
Kliman's costs are made up of wages plus the money price
of raw materials etc.
These costs are clearly determined by values.
Firstly, given the historically determined wage rates at any given
time, the wage bill of an industry will depend upon the
amount of labour time it must use to produce its annual product.
Secondly, since market prices are determined by labour values
the money price of raw materials etc will be determined by the
amount of labour required to produce these raw materials.
Costs are thus determined by values, subject only to
a) variations in wage rates between industries
b) variations in the market price of an industries raw
materials relative to their true values.
However, it should be observed, that Kliman ignores this
second source of variation by assuming that the values of
raw materials etc are identical with their market prices. He
also, if I am not mistaken, effectively assumes the same
hourly wage rates in all industries when deriving his
estimate of values. Thus Klimans estimate of cost and
his estimate of values will be more highly correlated
than true values are with costs.
According to Marx, if supply and demand are equal, the market
prices of commodities will correspond with their values
as determined by the respective quantities of labour required
for their production. But supply and demand never completely
balance so that market price oscillates sinking now under,
rising now above its relative value.
( Again see Marx:Wages Prices, Profits chap VI)
So market prices are determined by values subject to the oscillations
of supply and demand. But Klimans estimates of costs are insulated
from these oscillations, so it is only to be expected that he
finds costs are more highly correlated with values than prices are.
Alexandro asks:
What would be the theoretical explanation of the "labor theory of
relative prices"?
I would answer that market competition forces prices into alignment
with values.
Suppose than in an industry the market price falls below its value
by say 15%. Given that in any industry there is a range of producers
whose efficiency deviates significantly from the industry norm. This
decline in price below value will force the less efficient firms
into bankruptcy or into reducing the amount of labour they use.
It can readily be seen that if one limits the dispersion of market
price below values, one simultaneously limits the dispersion of
the relative market prices of other commodities above their relative values.
This in concise form is why labour values act as a pole of
attraction for market prices.
Paul Cockshott (clyder@gn.apc.org)