In response to the PIAF:
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From: owner-ope-l@galaxy.csuchico.edu on behalf of Allin Cottrell
Sent: Tuesday, October 21, 1997 3:21 PM
To: ope-l@galaxy.csuchico.edu
Subject: [OPE-L:5626] Re: ope-l: RE: In defence of correlation
Allin wrote: "That there remains systematic variation in the residuals of a
regression of Y on X does not make X a biased predictor of
Y, as statisticians use the term."
I'm not exactly sure what Allin means by this, but my point was that a
sector's aggregate value differs from its aggregate price, even on average.
Thus, I think the value is what statisticians call a biased estimator of the
price. Here's the way Wonnacott and Wonnacott (_Introductory Statistics_, pp.
148-49) put it:
"An unbiased estimator is one that is, *on the average*, right on target ...
Formally, we state the definition,
theta-hat is an unbiased estimator of theta if E(theta-hat) = theta.
... Of course, an estimator theta-hat is called biased if E(theta-hat) is
different from theta; in fact, bias is defined as this difference,
Bias = E(theta-hat) minus theta."
They have an accompanying graph of a biased estimator, theta-hat. Theta-hat
is normally distributed, with a mean that is higher than the "true theta." In
parallel manner, if you were to take a series of observations of a particular
sector's aggregate prices and values, and re-norm them so that the aggregate
price always equaled (say) 1, you'd get a distribution of values with a mean
different from 1, often very different.
Whatever terminology one uses, I think that makes values undesirable as
predictors of prices.
BTW, Paul's claim that the economy-wide price-value ratio = 1 reminds me of
the joke about the econometricians who go deer-hunting. I'll adapt it
slightly. One econometrician consistently shoots 15 degrees left of target;
the second consistently shoots 15 degrees right of target. The third and
fourth exclaim "Got him!"
Andrew Kliman