A few other posts in the thread (David's #458, Alan's #459, and
Allin's #464) do not seem to me to require a response on my part.
As for the posts to which I do need to respond, there are a number
of interesting points raised, and I would address each one
individually if I had time. But I don't, so I'll go straight to the
central issue. All of the criticisms pertain to it in one way or
another.
The issue is whether I "destroyed" a valid correlation by dividing
aggregate sectoral prices (P) and values (V) by aggregate sectoral
costs (C). I will argue, on the basis of a Monte Carlo experiment,
that this is not the case.
The experiment seems to me to be almost identical to the one Allin
reported in #457. Let me say that I think his approach is the
absolutely correct one, and that the results it yields are
sufficient to answer the question at hand conclusively.
The basic idea is this: Postulate that the labor theory of relative
prices is right (including the functional form of the value-price
relationship). Generate simulated data on the basis of this
postulated relationship. Simulate a value-cost relationship that
replicates the observed one, which will then give you a series for
costs. Divide the aggregate prices and values by aggregate costs,
and regress. The point of the regression is to see if the
price-value relationship -- which *IS* indeed present in the
simulated data, by construction -- remains intact after you divide
by costs. If not, you have introduced "spurious non-correlation,"
illegitimately destroyed a valid correlation.
Makes sense to Allin. Makes sense to me.
The only problem is that I wasn't able to replicate his results. As
far as I can tell, the only difference between what he did and what
I did was that he took actual sectoral values, while I used the
numbers 1-882 instead. But I can't see how that makes a difference
in the results. Yet maybe there's another difference, so let me
report what I did.
1. I specified a function in which sectoral price equals sectoral
value times a random exponential error term.
2. The random error term has two basic properties:
(a) a mean value of zero, so that V and P have the same expected
value
(b) it yields an average correlation between P and C that is very
close to the one in my data set (0.991)
2. I specified a sectoral cost-value relationship that resulted in:
(a) an average V/C that is very close to the one in my data set
(1.166)
(b) an average correlation between V and C that is very close to the
one in my data set (0.998).
In short: given the observed relationships between price and cost,
and between value and cost, what would the relationship between the
cost-weighted variables V/C and P/C look like if the labor theory of
relative prices were correct?
The theory predicts that, in a log-log regression on the sectoral
aggregates, (i) intercept term equals zero, (ii) the slope term (the
elasticity of price with respect to value) equals 1, and thus (iii)
price and value are positively correlated.
My recent study, summarized in OPE-L 433, found that none of these
predictions held true for the cost-weighted variables. I got
nothing like that at all, no matter how hard I tried.
But wouldn't I have gotten results that were just as lousy if the
labor theory of relative prices were true, because I divided
everything by costs? Aren't I Kliman the Destroyer (of Valid
Correlations)?
Nah.
Here are my results for 20 runs of 882 observations each. I'm
reporting the mean values of various measures as well as their
coefficients of variation (CV), which is the standard deviation
divided by the mean. The smallness of the CVs for most of the
measures indicates that there's really nothing to be gained by more
trials.
MEASURE AVERAGE CV
====================== ======= ======
correl V:C 0.998 0.0001
correl P:C 0.991 0.0005
average V/C 1.166 0.0014
average P/C 1.165 0.0026
intercept -0.004 -1.667
intercept's t-value 0.705 0.9166
(absolute value)
slope 1.012 0.0434
slope's t-value 17.910 0.0517
correl ln(V/C):ln(P/C) 0.516 0.0374
All the simulated results are just what the labor theory of relative
prices predicts. This is because, as I have noted in my paper and
on this list, were that theory correct, the values of the slope and
the intercept would be preserved under transformation. The
correlation between the cost-weighted variables is lower than
between the sectoral aggregates, but it is still fairly large and,
more importantly, positive and statistically significant. (It is
impossible for the correlation between the cost-weighted variables
to be as high as the correlation between the aggregates, since costs
are no longer being correlated with costs.)
Again, my results were nothing like this. These are very good
results. Mine were absolutely putrid. On the basis of this
experiment, I stand by my results.
Ciao
Andrew