# [OPE-L:5491] Humbug Aggregate Price-Value Correlations

andrew kliman (Andrew_Kliman@classic.msn.com)
Fri, 19 Sep 1997 09:26:41 -0700 (PDT)

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In ope-l 5488, Paul Cockshott wrote:

"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."

Imagine the following hypothetical 3-sector economy, with the following *unit*
prices (P) and *unit* values (V).

Sector P V
1 30 15
2 45 60
3 75 24

The correlation between *unit* prices and *unit* values is 0.

Assume that the physical output levels (X) in this economy are:

sector X
1 2,875,058
2 6,275,058
3 1,000,000

We then have the following series of *aggregate* sectoral prices and
*aggregate* sectoral values:

Sector PX VX
1 86,251,740 43,125,870
2 282,377,610 376,503,480
3 75,000,000 24,000,000
-------- ----------- -----------
sum 443,629,350 443,629,350

The correlation between the *aggregate* prices and *aggregate*
values is 1. To be precise, the correlation is closer to 1 than
0.999999999999999, if Excel can be believed.

The differences in the size of the sectors introduces massive spurious
correlation, as Alan Freeman demonstrated in one of his papers for this year's
IWGVT miniconference at the EEA Convention. It should come as no surprise
whatever that large sectors have large aggregate prices as well as large
aggregate values, and small sectors have small aggregate prices as well as
small aggregate values. It is more surprising, to me at least, that anyone
who understands the computations would consider the aggregate "price-value"
correlations to be meaningful.

Andrew Kliman