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Re: st: Regression Techniques


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Regression Techniques
Date   Thu, 21 Feb 2008 22:32:05 -0500

Tam Phan <tamdphan@gmail.com>:
I won't claim to have worked through your examples (the exposition is
not entirely clear to me).  But I will say that it sounds fishy.

The usual way to estimate demand is to find a set Z of variables z*
that shift supply and not demand, then to estimate
  ivreg q (p=z*)
which regresses q on the projection of p on Z, throwing away the bit
of p that is orthogonal to Z (the endogenous bit).  The idea is that a
regression model
  q = a + b (phat) + e
or a regression model
  q = a + b (p) + v (p-phat) + e
can give a consistent estimate of the true coef if Z satisfies some
strong conditions.  Your approach seems to be to find X that shifts q
and regress the piece of q that is orthogonal to X on price.  If qnorm
= q - qhat + qbar then the regression model is:
  q - qhat + qbar = c + d (p) + u
so if
   v (p-phat) = qhat - qbar
you are OK. Perhaps there are other conditions under which
plim(b)=plim(d).  Do you have references for your proposed methods?
What is X supposed to be?  What conditions is it supposed to satisfy?

I recommend you read the Stata Journal 7(4) pp. 465–541 if you haven't already.



On Thu, Feb 21, 2008 at 9:04 PM, Tam Phan <tamdphan@gmail.com> wrote:
> Hello Stata Community:
>
> I have recently encountered two methodology of linear regression
> techniques.  The main objective of the two techniques is to establish
> the effects of price on the demand of certain products/items.  Below
> are two techniques outlined:
>
> (1) Y=a+X'b+e  where X= explanatory variables, excluding price, Y is
> the observed quantity purchased for a particular product
> (2) Ynorm=e+average(Y)
> (3) Ynorm= a + b(price)+Ei
>
> After performing regression in (1), Ynorm is calculated by the sum of
> the residuals and the average of the original Y.  This Ynorm is then
> regress with price as the single explanatory variable.  The claim is
> that the fitted values in (3) will produce the "demand" of a product
> with only the effects of price and Ei.  What are your thoughts on
> this?
>
> Technique two:
>
> (1) Y= a + X'b1 + b2(price) +e
> (2) Ynorm = a +b1*(average(X)) + b(2price) +e
>
> Technique two only has one stage of regression (1), then the demand is
> "normalize" by multiplying the coefficients by the average of their
> respected explanatory variables, then whats left over is the quantity
> sold, in terms of price. Again, what are your thoughts?
>
> Which technique is "better?"  Advantages/disadvantages?
>
> TP

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