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From |
Elena Quercioli <elena.liquorice@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: Re: Re: st: Question on estimation procedure |

Date |
Wed, 14 Nov 2012 15:36:13 -0500 |

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 > > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**re: Re: Re: st: Question on estimation procedure***From:*Christopher Baum <kit.baum@bc.edu>

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