Alejandro asked: "Is not possible to use another variable to
"deflate" the aggregates other than costs?"
Yes, but costs are the RIGHT choice. Think of it this way. Let P
be aggregate price, V aggregate value, C aggregate costs, and X
aggregate output. Note that
Pj Cj
Pj = ---*---*Xj
Cj Xj
and
Vj Cj
Vj = ---*---*Xj
Cj Xj
The first terms on the RHS were my regression variables. The middle
terms are per-unit costs.
You would need to get rid of the last term, Xj (if you knew it),
because it causes spurious correlation. Large sectors, large
prices, large values; small sectors, small prices, small values.
You need to eliminate the middle term because its inclusion makes
the regression meaningless. By regressing Pj on Vj, you're
regressing unit costs on unit costs.
(Or a slightly fuzzed-up version of unit costs, if you refuse to get
Marx right. The I-O coefficients are derived from cost data. The
computation of coefficients essentially removes the unit prices, but
then the LTRP studies put slightly different prices (value prices)
back in, and so they get a slightly inferior series of costs. It's
like dehydrating milk to get powdered milk, and then adding water to
the powdered milk. It was milk, and it is again milk. It's just
not as good the second time.)
In any case, guess what? You regress costs on costs and you get a
perfect correlation every time. This is not an *empirical* result;
it's a matter of definition. You're not explaining one thing on the
basis of another --distinct -- thing.
The regression of costs on costs biases the results upward, quite
markedly, because unit costs are a large share of total costs. You
would HAVE to get a very high price-value correlation, given any
reasonable unit cost data (even if you had a way to remove Xj), no
matter how much profit deviates from surplus-value. All such a
regression would tell you is what you already know: costs are a
large component of both prices and values.
Big surprise. Big deal. We need a *theory* to tell us that? We
need a bunch of people to do "empirical" research to verify it?
So you need to get rid of both Xj and unit costs. (And you can do
so without knowing Xj, because division by Cj gets rid of both Xj
and unit costs.) What you're left with is the cost-deflated prices
and values.
One more thing. Some people have been claiming on this list that
the values determine the costs. This is backwards. All the studies
use costs (I-O and wage data) to determine the values.
Ciao
Drewk