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Re: st: RE: RE: RE: RE: nested parameters


From   "Brian P. Poi -- StataCorp" <bpoi@stata.com>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: RE: RE: RE: RE: nested parameters
Date   Thu, 24 Jul 2003 11:19:32 -0500 (CDT)

Dear Paul

As Nick suggested, we can write your model as

   Y1t = a + h(Y2t - bXt)+cZt+et

       = a + hY2t + gXt + cZt + et

We can recover b as -g/h and then use the delta method to get the
standard error of b.  In Stata that is easy to do using the -nlcom-
command:

   regress Y1t Y2t Xt Zt
   nlcom -1*_b[Xt] / _b[Y2t]

-- Brian
   bpoi@stata.com



On Thu, 24 Jul 2003, Metcalfe, Paul wrote:

> It would be less problematic if the software calculated the standard errors
> itself rather than having to work out how to do it manually.  But I guess
> that if Nick knows of no straightforward solution in Stata then, much to my
> chagrin, I will be forced to use E-views, where it is easy to estimate this
> sort of model including the standard errors. 
> 
> 
> -----Original Message-----
> From: Nick Cox [mailto:n.j.cox@durham.ac.uk]
> Sent: Thursday, July 24, 2003 4:11 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: RE: RE: nested parameters
> 
> 
> That's a nicety I would happily ignore myself,
> but I defer to sharper minds on these matters.
> 
> Turn and turn about, I am not clear that getting
> standard errors from your first formulation is any
> less or any more unproblematic.
> 
> Nick
> n.j.cox@durham.ac.uk
> 
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of
> > Metcalfe, Paul
> > Sent: 24 July 2003 15:48
> > To: 'statalist@hsphsun2.harvard.edu'
> > Subject: st: RE: RE: nested parameters
> >
> >
> > Thanks for the reply Nick.
> > I may be missing something myself, namely a braincell or two, but my
> > understanding is that there is a problem in calculating the
> > standard error
> > of the parameter b, which in Nick's suggested
> > parameterisation is -g/h. I
> > don't think the standard errors for g and h cannot be used
> > directly to
> > derive the standard error for b. But I may be wrong and if so I'd be
> > grateful to know.
> >
> >
> >
> > -----Original Message-----
> > From: Nick Cox [mailto:n.j.cox@durham.ac.uk]
> > Sent: Thursday, July 24, 2003 1:36 PM
> > To: statalist@hsphsun2.harvard.edu
> > Subject: st: RE: nested parameters
> >
> >
> > I may be missing somethig, but the nesting here seems benign.
> > You could reparameterise to
> >
> > Y1t = a + h Y2t + gXt + cZt + et
> >
> > after which it looks like a standard regression model.
> >
> > Nick
> > n.j.cox@durham.ac.uk
> >
> > > -----Original Message-----
> > > From: owner-statalist@hsphsun2.harvard.edu
> > > [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of
> > > Metcalfe, Paul
> > > Sent: 24 July 2003 13:11
> > > To: 'statalist@hsphsun2.harvard.edu'
> > > Subject: st: nested parameters
> > >
> > >
> > > I would like to estimate a model of the form: Y1t = a +
> > > h(Y2t - bXt)+cZt+et
> > > where a, h, b and c are the parameters to estimate and et
> > > is the error term.
> > > Is there a way to estimate this in stata?
> > >
> > >
> > >

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