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re: Re: Re: st: Question on estimation procedure


From   Christopher Baum <kit.baum@bc.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   re: Re: Re: st: Question on estimation procedure
Date   Wed, 14 Nov 2012 00:18:09 +0000

<>
Elena said

My question was meant to get at STATA (estimation) capabilities and
not identifiability; here, in essence, is what I want to know. I want
to simultaneously estimate the common base and other coefficients of
this geometric function:

 Y = c_0 + c_1[X_1+a^d2 X_2 + a^d3 X_3]

any ideas?


As Nick said, it makes no sense to talk about what Stata (not STATA) can or cannot do if mathematically there 
is no solution to the problem. In that case, what software you use is irrelevant, as no software
can solve such a problem.

This form of the function is also not identified. Picking arbitrary values for d2 and d3,

sysuse auto, clear

//  Y = c_0 + c_1[X_1+a^d2 X_2 + a^d3 X_3]
forv alpha = 0.75(0.05)1.2 {
	nl (price = {c0} + {c1} * mpg + {c1} *`alpha'^2 * weight + {c1} * `alpha'^3 * turn)
	nlcom [c1]_cons * `alpha'^2
}

As you can see, there is a locus of c1 * alpha^2 combinations which yield the same coefficient on weight. 
Therefore, there is no solution to this optimization problem if alpha is treated as a parameter to be estimated, as you can
readily verify by changing alpha to an additional parameter and asking -nl- to solve that problem. It can't (but neither
can -ml-, or -gmm-, or any other method).

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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