Austin,
The example you pointed out is exactly the technique describe in (1).
What about the second methodology, where only one regression is
perform.
Y=a+bX+v(price)+e
Ynorm=a+b(average(X))+v(price)+e (Essentially, to calculate the fitted
Ynorm, after the regression, one would multiply the other explanatory
variables (excluding price) by the coefficient and the average of the
respective explanatory variables, for price, the coefficient is
multiply by the observed price instead of the average price. Any
thoughts on this?
On Fri, Feb 22, 2008 at 5:06 AM, Tam Phan <[email protected]> wrote:
>
> ---------- Forwarded message ----------
> From: Austin Nichols <[email protected]>
> Date: Feb 21, 2008 10:32 PM
> Subject: Re: st: Regression Techniques
> To: [email protected]
>
>
> Tam Phan <[email protected]>:
> 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 <[email protected]> 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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