# [OPE-L:5494] Re: Humbug Aggregate Price-Value Correlations

andrew kliman (Andrew_Kliman@classic.msn.com)
Fri, 19 Sep 1997 17:15:07 -0700 (PDT)

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Paul Cockshott has written: "Whether prices correspond to values is of course
a different question, and the answer is that on average they do, in the sense
that they are highly correlated."

In ope-l 5491, I reiterated Alan Freeman's point that aggregate price-value
correlations are meaningless, and illustrated this by means of an example in
which the correlation between *unit* prices and *unit* values is 0, but the
correlation between sectoral aggregates is 1.

In ope-l 5492, Jerry objected that "This doesn't address the issue that Paul
is posing. Paul asserts
above *as an empirical matter* that prices and values *are* highly
correlated."

Actually, it does address the issue quite directly, but I'm glad Jerry raised
the point, because I now see that I should have provided some more background
in order to make the issue clearer. Let me try to rectify the situation now.

The "prices" and "values" that Paul asserts to be highly correlated are in
fact merely the meaningless *sectoral aggregates*. It would be another matter
entirely were *unit* prices and values highly correlated.

The input/output data which are used to obtain the high correlations simply do
not permit computation of unit prices and values. The tables provide money
price aggregates only. It is impossible to obtain unit prices and values from
them because, first, each sector includes many, physically quite distinct
use-values, and second, the size of unit prices and values will depend on the
physical units chosen to measure use-value (grams, kilograms, pounds, tons,
etc.)

The appropriate methodology to deal with the latter problem is to focus on the
sectoral price-value *ratios*. The aggregate price of sector j can always be
written as Pj*Xj, where P is unit price and X is some index of physical
output. Similarly, the aggregate value is Vj*Xj. Now, *whatever* the
physical units one chooses to measure physical output, i.e., for *any and
every* Xj, the *ratio*

Pj*Xj Pj
----- = -- .
Vj*Xj Vj

Hence, this ratio will always give the ratio of *unit* price to *unit* value,
even though the unit prices and values themselves cannot be computed.

The appropriate procedure is then to study how these ratios differ across
sectors. When values and prices are measured in the same units (labor-time,
or money, etc.), then the closer the ratios are to unity, the smaller the
price-value deviations. (If all were unity, then prices would all equal
values.) Using data for the British economy, Alan found that the ratios are
generally rather far from unity. He also notes that the *same* pattern exists
in the more disaggregated data set used by Cockshott, et al.

It is also possible to encapsulate the price-value dispersions in a single
summary statistic, the mean absolute deviation (MAD) of the price-value
ratios. Using Alan's data, I computed a MAD of 27%. This is interpreted
thus: on average, a sector's ("unit") price-value ratio deviates from the
average ratio by plus or minus 27%. This, IMHO, suggests that prices and
values differ quite significantly. The 27 0.000000igure is a far cry from what the
aggregate correlations of .98 or .99 may -- very misleadingly -- seem to
imply.

Yet the underlying data are the same. How, then, can the two sets of
statistics be explained?

That was the burden of my earlier post (which of course relied on Alan's
insights). The sectoral aggregate correlations introduce spurious
correlation. Because they deal with aggregate prices and values instead of
unit prices and values, they pick up differences in industry size. As I
noted, large industries will have large aggregate prices and large aggregate
values, while small industries will have small aggregate prices and small
aggregate values. Thus, moving from one industry to another, if the aggregate
price is greater, so will the aggregate value be greater. If the aggregate
price is smaller, so will the aggregate value be smaller. The sectoral
aggregate prices and values will almost certainly have to move up and down
together. Even if the actual (unit) price-value deviations are large, the
large dispersion in industry sizes will swamp that effect.

Here's a simple example. Imagine 2 sectors, A and B. The unit price is A is
4, the unit value is 2. In B, the unit price is 1, the unit value is 3.
Thus, were we to compute the correlation of unit prices and values, it would
be negative -- going from A to B, the price falls but the value rises. Now,
however, imagine that physical output of A is 20, and physical output of B is
1. Then we have a sectoral price of A of 80, sectoral value of 40. In B, 1
and 3. So, going from A to B, the aggregate price falls massively, but now so
does the aggregate value. So the correlation coefficient will be strongly
positive. What's really going on, however, is simply that moving from A to B,
one moves from a much larger sector to a much smaller one. Because A is much
larger in "price" terms, but also in "value" terms, we get a large positive
correlation.

This is basically what I was showing with my 3-sector example. There we had a
zero correlation between unit prices and values, but the sectoral aggregate
prices and values were *perfectly* correlated, again due to sizable
differences in industry size.

So yes, Paul asserts as an empirical matter that the sectoral aggregate prices
are very highly correlated with the sectoral aggregate values. And he's right
about that. He's got the empirical evidence. But it is meaningless or, more
precisely, it doesn't imply what he wishes it to imply. All it implies is
that large sectors are large sectors, and small sectors are small sectors,
whether you measure size in price terms or in value terms. In short, it is a
99% labor theory of industry size.

I hope I've explained matters clearly now, Jerry. If not, let me know.

Andrew Kliman