[OPE-L:5622] andrew: random profits

Allin Cottrell (cottrell@wfu.edu)
Mon, 20 Oct 1997 15:55:16 -0400 (EDT)

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This is in response to a suggestion from Andrew, regarding a
suitable null hypothesis against which to test the labour
theory of value. He suggested that we consider a "naive"
theory of price determination, according to which price is
composed of the value of the inputs plus a random share of
total profit (i.e. each industry's profit is a random number
from a uniform distribution, scaled such that the shares add
up to 1.0). The idea was (if I've got it right) that we
could see what degree of correlation emerged between "naive
prices" formed in this way, and market prices. And, by
repeated simulation of this mechanism, we could see whether
the observed correlation between prices and values does or
does not "beat" the values turned out by the naive theory.

I've had a rough, preliminary go at implementing this, using
data from the 1987 US input-output table. First, I obtained
an (unweighted) correlation between sectoral prices and
values of 0.9779. Next, I simulated Andrew's mechanism.
The resulting correlations were mostly in the range 0.92 to
0.95; in 10,000 trials there were _no_ correlations as
large as 0.9779.

I should explain that in implementing Andrew's suggestion I
used the "vertically integrated labour coefficient"
interpretation when calculating the values of the inputs.
If you take the _price_ of the inputs and add a random share
of profits you get a very high correlation (over 0.99 most
of the time) with observed sectoral prices. But running
that "theory" ("explaining" the prices of outputs by
reference to the sum of the prices of inputs) against the
labour theory of value would not be a fair contest.

I should stress the the above-mentioned results are
preliminary, and subject to checking.

Allin Cottrell
Department of Economics
Wake Forest University