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. The linear regression equation (the log-linear is
almost identical) is:
P/C = 0.0178 + 0.9850(V/C)
(.147) (.126)
where the numbers in parentheses are standard errors.
There is an excellent fit between the cost-weighted prices and
values, almost exactly what the labor theory of relative prices
predicts (zero intercept, slope = 1, and a high r^2). It is also
almost exactly the same as the relationship between the sectoral
*aggregates* that people like Shaikh, Ochoa, and Cockshott and
Cottrell (and I!) have obtained.
If I had gotten results on the cost-weighted variables like this, I
would now be a convert to the labor theory of relative prices. But
I didn't, so I'm not. My results were nothing like this at all.
But such results ARE POSSIBLE, as the example demonstrates. So the
deflation of the aggregates by costs does not destroy any *valid*
correlation between prices and values. It only destroys *spurious*
correlation.
To understand *why* Allin's claim is wrong, keep in mind that the
cost-weighted variables are measures of the "percentage" markups
over costs: P/C = 1 + (profit/costs), and V/C = 1 +
(surplus-value/costs). Thus, in claiming that division of the
sectoral aggregates by costs must destroy the price-value
correlation, ALLIN IS IN EFFECT ASSERTING THAT THE MARKUPS CANNOT BE
HIGHLY CORRELATED! But this is obviously wrong. They can of course
be highly correlated, and in this example -- but not in the real
world -- they are.
I must admit to being surprised at Allin's challenge to my results,
because in my paper I went over all this. I demonstrated that, if
the labor theory of relative price were right about the functional
relationship between values and prices, then deflation of the
sectoral aggregates would not and could not alter this relationship.
Let me prove it again.
The equation being estimated is
Pj = A*Vj^b*exp(ej).
The proponents of this theory claim that A = 1 and b = 1, i.e., that
Pj = Vj*exp(ej).
If this were true, then it would also be true that
(Pj/Cj) = (Vj/Cj)*exp(ej),
so that A = 1 and b = 1 in the equation
(Pj/Cj) = A*(Vj/Cj)^b*exp(ej).
So, deflation of the aggregates would not affect the results were
the labor theory of relative prices true. HENCE, THE VERY FACT THAT
DEFLATION PRODUCES RADICALLY DIFFERENT RESULTS INDICATES THAT THE
THEORY IS FALSE.
Allin also writes: "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)."
Sure, but these results are meaningless. More precisely, they don't
mean what you would want us to believe they mean. I explain this in
some detail in my paper, but let me just provide a simple example
here. First, note that the ratio of price to value is NOT affected
by cost-weighting: P/V = (P/C)/(V/C). So we can work with the
cost-weighted variables. Consider the following data, by industry:
P/C V/C OIL-V/C
----- ----- -------
1.21 1.197 0.300
1.20 1.198 0.600
1.19 1.199 0.900
1.21 1.200 1.200
1.20 1.201 1.500
1.19 1.202 1.800
1.21333... 1.203 2.100
The correlation between the prices and the values is zero. The
correlation between the prices and the oil-"values" is also zero.
Neither "explanatory" variable explains any of the variation in
prices. But if we now take the ratios P/V and P/OIL-V, and compute
their coefficients of variation (CV), we find that the dispersion of
the price-value ratios is 0.0082, while the dispersion of the
price-oil value ratios is 0.8234, more than 100 times as great!
What accounts for the difference is that the values are clustered
tightly together, while the oil-values are more widely dispersed.
But, since they are both equally miserable "predictors" of prices,
so what?
This is not a fanciful example. As I discuss in my paper, I too,
like almost everyone else, found that price-value deviations
(including coefficients of variation) were "small." But the
smallness was merely an indication of the lack of dispersion among
the values (average variance = 0.003), not any predictive power of
values over prices. Thus, ANY variable having the same probability
distribution (same variance, etc.) as the values would result in
average deviations that were just as small.
I therefore submit that the comparison of values, oil values, etc.,
is only a fair one if these variables have similar variances.
(Indeed, I'm be *very* interested in learning what these variances
are.) If this isn't the case, I would suggest to Allin and Paul
that they perform their test for variables that have the same
variance as the values, as I did.
Ciao
Andrew