# [OPE-L:5556] "shift-share index" (was Humbug)

Allin Cottrell (cottrell@wfu.edu)
Wed, 1 Oct 1997 06:24:09 -0700 (PDT)

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I'm trying to get clear on Andrew's proposal.

> As far as measurement is concerned, the degree of
> dispersion can be measured easily by means of a
> shift-share analysis. You simply take the absolute values
> of the sectoral differences between surplus-value and
> profit. Then you add them up. Then you halve that
> number, to eliminate the double counting of each
> difference (otherwise a shift of 40 units of value from
> sector A to sector B gets counted as a loss from A and as
> a gain to B, i.e., an absolute value of 80 units). Then
> you take that number and divide by total surplus-value in
> the economy.

This seems clear.

> The resulting number will basically range from 0 to 1. It
> will equal 0 when no surplus-value is redistributed, and
> it will be close to 1 when some sector that produces a
> negligible amount of surplus-value gets all the profit.
> (I say "basically," because the possibility of negative
> profits means that the upper bound is theoretically
> greater than 1.)

This too.

> HYPOTHESIS TEST:
> Is the measure of relationship (shift-share, MAD,
> correlation, etc.) small enough that one can reject (at
> the level of confidence of .01, .05, .10, etc.) the "naive
> hypothesis" that surplus-value is randomly distributed
> across sectors?
>
> In other words, the naive hypothesis is that
>
> Pj = (Cuj + Vj) + kj*(sum of S)
>
> where P is sectoral price, Cu used used-up constant
> capital, S is summed throughout the economy. kj is an
> evenly distributed continuous random variable between 0
> and 1, with the sum of kj's = 1. So the naive hypothesis
> is that sectors recoup their paid costs and get a random
> cut of the surplus-value on top of that.

>From the discussion that follows, I'm not 100lear on
this. If surplus value is "randomly" distributed as
described above, then in a case where all sectors are the
same "size" (in terms of C + V), isn't the mathematical
expectation of the shift-share index zero? I.e. the
expectation is that each of n sectors will get 1/n of the
surplus value -- but if they're all the same size then this
is just what is predicted by a simple, deterministic labour
theory of value, and the two alternatives that Andrew
considers are observationally equivalent?

Is this in the spirit of what Andrew is talking about:
suppose one ran a cross-sectional regression of sectoral
prices on sectoral (C + V)'s and sectoral S's (meaning the
surplus value actually produced in each sector):

Pi = a*(Ci + Vi) + b*(Si) + ui

Then what Andrew calls the "naive" theory would predict a=1
and b=0 (with all variation in realized surplus value across
sectors being assigned to the random term ui), while a
simple deterministic labour theory of value would predict
a=1 and b=1?

As a general comment, I'm not at all sure of the merit of
taking a _deterministic_ labour theory of value as one of
the alternatives. The work Paul C and I have done is
informed by Farjoun and Machover's stochastic account of the
LTV.

As a footnote, it seems to me that if Andrew wants to go on
referring to sectoral price-value correlations as
"meaningless" (on the alleged grounds of spurious
correlation) -- rather than arguing merely that they are not
the _best_ measure of association -- then he owes us a
response to the counter-argument that I've posted to ope a
couple of times now.

Allin Cottrell