I am trying to estimate a demand function: Y=K * X1^b1 * X2^b2 * X3 ^(-1-b1) in log form: ln Y = ln K + b1 ln X1 + b2 ln X2 + (-1-b1) ln X3 As the regression coefficients are related for 2 of the regressors, I am not sure of the appropriate methodology or function in R to handle this. Any hints? thx, Tarun [[alternative HTML version deleted]]
open up the brackets (-1-b1) and you would get an equation in which you would have to estimate only b1 and b2... then you can proceed by the normal method.. On Tue, Apr 20, 2010 at 4:44 PM, rajiv guha <dabruha@gmail.com> wrote:> I am trying to estimate a demand function: > Y=K * X1^b1 * X2^b2 * X3 ^(-1-b1) > > in log form: > ln Y = ln K + b1 ln X1 + b2 ln X2 + (-1-b1) ln X3 > > As the regression coefficients are related for 2 of the regressors, I am > not > sure of the appropriate methodology or function in R to handle this. Any > hints? > > thx, > Tarun > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. >[[alternative HTML version deleted]]
I think you'll need the offset option.
ln( Y ) = ln( K ) + b1 ln( X1 ) + b2 ln( X2 / X3 ) + 1 ln( 1 / X3 )
as in:
glm( log(Y) ~ log( X1 ) + I(log( X2 / X3 )),
offset=I(log( 1 / X3 )))
-tgs
On Tue, Apr 20, 2010 at 7:14 AM, rajiv guha <dabruha@gmail.com> wrote:
> I am trying to estimate a demand function:
> Y=K * X1^b1 * X2^b2 * X3 ^(-1-b1)
>
> in log form:
> ln Y = ln K + b1 ln X1 + b2 ln X2 + (-1-b1) ln X3
>
> As the regression coefficients are related for 2 of the regressors, I am
> not
> sure of the appropriate methodology or function in R to handle this. Any
> hints?
>
> thx,
> Tarun
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
[[alternative HTML version deleted]]