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

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