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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 * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Regression Techniques***From:*"Tam Phan" <tamdphan@gmail.com>

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