# [OPE-L:6946] [OPE-L:438] Re: New Evidence on Sectoral Prices and Values

Andrew Kliman (Andrew_Kliman@email.msn.com)
Thu, 18 Feb 1999 02:39:34 -0500

From: Alejandro Ramos <aramos@btl.net>
To: ope-l@galaxy.csuchico.edu <ope-l@galaxy.csuchico.edu>
Cc: multiple recipients of list <ope-l@galaxy.csuchico.edu>
Date: Thursday, February 18, 1999 12:17 AM
Subject: [OPE-L:437] New Evidence on Sectoral Prices and Values

Ale: "I mean, imagine we have n sectors and every price is equal to
every value,
so that Pj/Wj = 1 for every j. I can add all those ratios ( = n) and
divide
them by the amount of observations, i.e. n/n = 1, which means that
all of
them are equal. But if they are not equal that ratio is not equal to
1.
Then you may test that ratio statistically, I guess supposing that
it has
some probabilistic distribution."

Oh, now I see what you meant. Yes, it is common practice to measure
the deviations of Pj/Wj from 1, or something similar. That is
essentially what all of the measures of deviation such as MAD, MAWD,
RMS%E, etc. do. They are all statistics that give you the average
of this kind of deviation. I computed them, and found, like almost
everyone else has, that prices and values are "close" -- i.e., the
average deviation (i.e., the average of the absolutes values of
(Pj/Wj - 1), or something similar) is about 8% to 13%, depending on
the measure.

But again, all this is really meaningless, and you put your finger
on the reason. The measures of deviation are not being *tested*,
not being compared to a probability distribution. But my paper, I
believe for the first time, does do *something like* what you
suggest. It asks whether we could get average deviations as small
as the observed ones if in fact values had no ability to predict
prices. Specifically, it asks whether a random variable having the
same probability distribution as the values could give us
price-random variable deviations that are as small as the
price-value deviations. The answer is yes. So values have no more
ability to predict prices than does *any* variable having the same
(very small) variance.

So the key to the "closeness" of prices and values is the fact that
the values are all very close to one another. Any other variable
with this property would perform as well. Hence, what will perform
*even better* is a single number (because its numerical values
differ from one another not at all.) are all the same is a
zero-variance variable, a variable that takes on numerical values
that are so close to one another as to indistinguishable. In other
words, *any* single number.

So, you want to predict prices? Pick a number, any number. I.e.,
predict, for each and every p(j), that p(j) = k, where k is your
number. Now, normalize k so that its mean value after normalization
is equal to the mean of the prices. For my data set, this
normalized k gives you an average deviation from prices (measured by
the NVD) that is 7.5% less than the average deviation of values from
prices. Thus, if you know absolutely nothing about what determines
prices, you can predict a sector's price, on average, better than
you can by trying to predict it by means of values.

Ale: "The idea of the log-linear specification is that you have a
linear model
but you get the logs of your variables, isn't it? Does this mean
that the
ratio of your linear model is actually a measure of "elasticity"?
(Am I
right?) However, this should be an elasticity corresponding to the
whole
"industry", not to particular commodities. Does this make sense?
More
generally, how is solved (by the current literature) of the
causality
order? I mean, you can put "values" as independent variable and
"prices" as
dependent but you can also put them in reverse order. What does
happen with
the correlation in that case? Would this mean that prices
"determine" (or
predict?) values?"

Generally what is does is that one estimates a linear model. If the
model is not originally linear, then one "linearizes" it. For
instance, the original form of the model I estimated is

p = A*v^b*exp(e)

so that, taking natural logs:

ln p = ln A + b(ln v) + e.

b is the elasticity of price with respect to value: d(ln p)/d(ln v)
= b. I don't really understand the rest of what you say about
elasticity. Essentially b doesn't pertain to any particular
commodity or industry, but is the average relationship for all
industries.

As for causality, you assume it rather than prove it, especially in
a model like this with only 2 variables and no lags. The value of b
will depend on which variable you choose as the independent one, but
the correlation coefficient in this case will be the same whichever
you choose. So yes, IF you had a positive relationship between the
two variables, you still wouldn't know whether values determine
prices or prices determine values -- or whether some third variable
or set of variables is determining both.

But you don't have to worry about that in this case, because there
is no reliable evidence of any positive relationship, not even a
weak one. So the causality, or lack thereof, clearly goes both
ways -- values do not determine prices and prices do not determine
values.

Ciao

Andrew