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Re: st: Question on estimation procedure


From   Elena Quercioli <elena.liquorice@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Question on estimation procedure
Date   Mon, 12 Nov 2012 17:37:55 -0500

Oops, my bad. I omitted to state that d1=0.

Would you have any suggestions on how to estimate the non-linear model
I illustrated?

Your help would be greatly appreciated.

Elena

On Sat, Nov 10, 2012 at 6:14 PM, Christopher Baum <kit.baum@bc.edu> wrote:
>
> <>
> How do I find the best MLE fit for Y on a^d1 X1 and a^d2 X2 where I
> wish to estimate the coefficient on each (as well as a constant, say).
>
> To be precise, I want to input the data {X1,X2,Y} and parameters
> d1,d2>0, and have STATA tell me the best fit c_0, c_1, c_2, and
> geometric base a>0 so that:
>
> Y = c_0 + c_1 a^d1 X1 + c_2 a^d2 X2
>
> I should mention also that my theory requires 0<a<1.
>
> I do not think this model is identified (even with the restriction that
> 0<a<1). You have three data vectors: iota, X1, X2, and four parameters:
> c0, c1, c2, a. Although you have introduced some mild nonlinearities with
> the given power transformations, I don't think you can identify
> four parameters from these three data vectors.
>
> Kit
>
>
> Kit Baum   |   Boston College Economics & DIW Berlin   |
> http://ideas.repec.org/e/pba1.html
>                              An Introduction to Stata Programming  |
> http://www.stata-press.com/books/isp.html
>   An Introduction to Modern Econometrics Using Stata  |
> http://www.stata-press.com/books/imeus.html
>
>
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