On Tue, 21 Oct 1997, andrew kliman wrote:
> In response to the PIAF:
What's this "PIAF"?
> 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.
What you are saying is that the prediction of a sector's
aggregate price conditional on its value alone is not, in
general, the same as the prediction conditional on both
value and organic composition. But no, that is not what's
called bias. To take a more familiar econometric example,
suppose consumption is a increasing function of disposable
income and a decreasing function of the rate of interest.
Then the prediction of consumption based on income alone
will in general not be the same as that conditional on both
income and the interest rate; and further, the prediction
based on income alone will systematically overstate
(understate) consumption for periods of high (resp. low)
interest rates. That does not make income a "biased"
predictor of consumption: it produces the right prediction
at the average interest rate.
Allin Cottrell