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

[Elena Quercioli <elena.liquorice@gmail.com>]

I am unsure if I properly communicated that the exponents d1 and 2 are
known, and need not be estimated. To wit, the model *is* identified,
as we can see quickly by recursive reasoning:
1. By varying X_1, we pin down c_1,
2. then by varying X_2 or by varying X_3, since we know c_1, we can pin down a.

In fact, it is overidentified (too few parameters for the data), and I
want Stata to pick the best fit.

I wanted to know how to do this in Stata. Thank you for your help.

Cheers Elena

On Tue, Nov 13, 2012 at 7:18 PM, Christopher Baum <kit.baum@bc.edu> wrote:
>
> <>
> 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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