I have just completed a paper, "The Law of Value and Laws of
Statistics: Sectoral Values and Prices in the U.S. Economy,
1977-1997." What follows is a summary of the methods and findings.
I have already sent the paper to the individuals on this list who I
thought would be most interested in it. If anyone else is
interested in reading the whole thing, I will be happy to send you a
copy over e-mail as an attached Word 97 file. (Perhaps other
formats might work, but there are four tables, so I'm not sure.)
Ciao
Andrew
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The Law of Value and Laws of Statistics
Sectoral Values and Prices in the U.S. Economy, 1977-1997
1. Neither Ricardo nor Marx claimed that, at a moment in time,
relative values determine relative prices. During the last two
decades, however, a new school of thought has arisen does advance a
labor theory of relative prices. The paper conducts some new tests
of this theory’s claims regarding the cross-sectional relationship
between values and market prices, analyzing annual data for the U.S.
between 1977 and 1997.
2. With respect to *sectoral aggregate* prices and values, I found
that the average price-value correlation, and thus the r^2, were
slightly greater than the greatest of those reported in prior
studies. Various summary measures of price-value deviations (MAD,
RMS%E, etc.) were comparable to the lower end of those reported in
other studies, and unequivocally smaller than those reported for the
U.S. economy.
3. Yet as Alan Freeman has demonstrated, correlations between the
sectoral aggregates are upwardly biased, due to a failure to control
for variations in industry size. Since the aggregate values and
aggregate prices of large industries are both large, and those of
small industries are both small, the aggregates will move up and
down together even if unit prices and values do not. I therefore
eliminated the effect of variations in industry size by “deflating”
each sector’s aggregate price and aggregate value by its aggregate
cost. The cost-weighted variables can be understood as measures of
the “percentage” markup over costs, in price and value terms,
respectively.
4. Running 21 log-linear cross-sectional regressions of the
cost-weighted prices on the cost-weighted values (one for each
year), I found no support for the labor theory of relative prices.
Variations in values accounted for an average of just 0.3% of the
variation in prices, never more than 1%, and in no year was the
correlation coefficient significantly different from zero. Thus, I
found no reliable evidence that the size of an industry’s
surplus-value markup has *any* influence on the size of its profit
markup. The theory predicts that the elasticity of price with
respect to value equals 1, but my estimated elasticities were
negative in one-third of the years, never significantly different
from zero, and their average value was only 0.05.
5. Linear specifications, and a pooled version of the model, gave
very similar results. Even under the “best” specification of the
model, it was still impossible to reject the hypothesis of a zero
elasticity (and zero correlation) at the 30% confidence level. The
data thus suggest strongly that variations in industry size have
been responsible for almost all (if not indeed all) of the putative
explanatory power of sectoral values over sectoral prices.
6. Yet if relative values are not a determinant of relative prices,
why are the two so close? It turns out that they were *not* close
IN THE SENSE REQUIRED BY THE LABOR THEORY OF RELATIVE PRICES.
Because it is a theory of relative price determination, the
appropriate concept of closeness is likewise a relative one. If
relative values “regulate” relative prices, then an “average”
industry’s price must be RELATIVELY close to its value -- closer to
its own value than to the values of other industries.
7. To ascertain whether this was the case, I computed the average
price-value deviation (measured by the normalized vector distance
(NVD)), as well as the average of the entire set of possible
deviations that could be formed by pairing each price with each
value. The latter figure measures how close all prices are to all
values, so it must be larger than the actual average for prices to
be relatively close to their own values. Yet in 10 of the 21 years,
it turns out, it was the actual average deviation that was the
larger of the two. In all 21 years, the two figures were close to
one another. And their mean values throughout the period were
*almost identical*, 0.125 in both cases! Thus, on average, a
sector’s price was no closer to its own value than it was to other
sectors' values, contrary to what the labor theory of relative
prices predicts.
8. The usual measures of price-value deviation are thus small simply
because the data are closely clustered together. Almost all
sectors’ prices are close to almost all sectors’ values, that is
all. This is a mere statistical artifact, one that does not in the
least imply that values are good predictors of prices. Indeed,
they are miserably poor predictors. As the paper discusses, the
experiment detailed in point 7 offers very strong evidence that
*any* variable having the same probability distribution as the
values can predict prices just as well as they can. Those who wish
to predict prices, and who are satisfied with the observed fit
between prices and values, can thus save themselves considerable
effort and expense. Rather than computing values, they can choose
as their predictor *any* variable with a small variance.
9. It would be premature, however, to suggest that the “labor
theory of value” has no future. The intractable theoretical
difficulties that gave rise to the labor theory of relative prices
have since been resolved. When Marx’s theory is understood in light
of its temporal single-system interpretation, his aggregate
price-value equalities do hold, his claim that technical innovation
itself can lower the profit rate becomes internally coherent, and
several related difficulties also. Nor are the aggregate equalities
merely empty tautologies here, as they are in some other recent
interpretations. When conceived in temporal terms, they suggest
that the production of value and surplus-value influence economic
growth and profitability. Perhaps future empirical work on the law
of value can be directed to testing the hypotheses generated by this
claim.