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re: st: Question on estimation procedure


From   Christopher Baum <kit.baum@bc.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   re: st: Question on estimation procedure
Date   Sat, 10 Nov 2012 23:14:52 +0000

<>
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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