I thank Allin for explaining his procedures. With the IWGVT
miniconference at the EEA quickly approaching, I don't have the time
to attempt to replicate his experiment, but I also don't think it is
necessary.
I accept the numbers. The methods, however, are inappropriate.
A quick glance at the figures Allin provides is enough to make clear
what the problem is. The whole point of the experiment is to
determine whether the ACTUAL, OBSERVED correlation between costs and
values is "too high," so that I destroyed a valid price-value
relationship when I deflated the sectoral aggregates by costs. Yet
Allin's methods ALTER the correlations between costs and values (and
costs and prices), so his results aren't relevant. If you want to
determine whether I destroyed a valid price-value relationship when
I deflated by costs, because the correlation between values and
costs in the ACTUAL data is "too high," you obviously have to
replicate the ACTUAL value-cost correlation.
What his experiment shows is merely what theory already tells us:
as the correlation between costs Cj and values Vj becomes extremely
high, the variation in the independent variable Vj/Cj all but
vanishes, and so the regression estimates go haywire. But the
variation in the independent variable in my ACTUAL data set -- which
depends on the ACTUAL correlation between costs and values -- was
sufficient to yield reliable estimates, especially in the pooled
models.
In my own simulations, I replicated the OBSERVED cost-value and
cost-price correlations, and found that deflation by costs did not
alter the price-value relationship. That's also what Allin's
results show.
In the first case he reports, the typical estimate based on the
transformed relationship, assuming the labor theory of relative
prices (LTRP) is true, is
slope coefficient: 1.01295 std. error: 0.116752.
He does not report the correlation between costs and values, but it
can be inferred, on the basis of what he does report, that the
correlation is *higher* than the correlation in the actual data.
So, given even a somewhat higher correlation than in the actual
data, deflation by cost would preserve a valid value-price
relationship. (His typical t-value (= slope/std. error) is about
8.68. This is about half of the typical t-value that I obtained in
my simulations. When he raises the correlation between values and
costs by reducing the error term e_i, the t-values decline markedly.
Hence, the lower the t-value, the higher the correlation between
values and costs. And since his t-value is about half of mine, it
is reasonable to conclude that his value-cost correlations are
higher than the actual ones.)
It is also important to note that Allin's results do NOT indicate
that deflation by costs destroys a valid relationship between values
and prices -- EVEN WHEN the correlation between values and costs
gets incredibly high. Rather, as I noted above, they suggest only
that the variation in the independent variable becomes too small to
produce efficient estimates. The figures he reports DO NOT permit
us to reject the hypothesis that the true value of the slope
coefficient is 1, even when the correlation between values and costs
approaches zero. (The standard errors become very large, reducing
the t-values.) So, if the correlation between values and costs is
too high, then one simply cannot draw any conclusion. That is quite
different from the claim that it makes one draw a wrong conclusion.
In my actual regressions, and in my simulations, the value-cost
correlations were not too high. The standard errors in the actual
regressions were low enough to reject the LTRP's claim of a unit
slope at an astronomical degree of confidence in the pooled models,
and at a very high level of confidence (always 97.5% or more, for
one-tailed tests) even in the much smaller cross-sectional data
sets. In my simulations, which produced correlations between values
and costs very similar to the actual ones, the average slope
coefficient was close to unity and the spread was narrow, confirming
that division by costs would preserve a valid relationship between
values and prices, if only one were to exist.
On the basis of the foregoing, I stand by my results.
Andrew Kliman