# Re: st: random coefficient models

 From "easycalcs" <[email protected]> To [email protected] Subject Re: st: random coefficient models Date Mon, 20 Oct 2003 22:24:04 -0000

```There's no need at the estimation stage to know the variance of e(i)
or n(i):

Substititute for b(i) in the y equation

y = b0+Bx(i)+v(i)

where v(i)=e(i)+x(i)n(i)

The new equation has a heteroskedastic error
Var[v(i)]= Var[e(i)]+x(i)^2Var[(n(i)] = Var[e(i)]{1+kx(i)^2}
where k= Var[e(i)]/Var[n(i)]

If e(i) and n(i) are iid ~ normally, a loglikelihood formulation can
be set up. If the weights are computed as w(i)=(1+kx(i))^1/2 the
weighted least squares is y(i)/w(i) on 1/w(i) and x(i)/w(i). A
concentrated loglikelihood may be established (with unknown paramter
k) where the residual sum of (weighted) least is formulated in terms
of the unknown parameter k. This is then maximised wrt k!

Does anyone have the formulation/Stata specification proc for such a
concentrated loglikelihood function? I'm not a Stata coder! Thanks.

--- In [email protected], "Stephen P. Jenkins"
<stephenj@e...> wrote:
> On Mon, 20 Oct 2003 12:54:33 -0400 Steven Devaney
> <DevaneySP@n...> wrote:
>
> > Hello again
> >
> > Off-list I was asked to clarify what I meant.
> >
> > What I am interested in is whether anyone knows about or has
written an MLE procedure for estimating B in the set-up?
> >
> > y(i) = b0 + b1(i) + e(i)
> >
> > where
> >
> > b1(i) = B + n(i)
> >
> > I was hoping to use Hildreth and Houck, but cannot constrain
xtrchh so that t = 1.
>
> If t = 1 (single cross-section), can you identify the variance of
the
> b1(i), or equivalently the variance of the n(i) ?
>
>
> Stephen
> ----------------------
> Professor Stephen P. Jenkins <stephenj@e...>
> Institute for Social and Economic Research (ISER)
> University of Essex, Colchester, CO4 3SQ, UK
> Tel: +44 (0)1206 873374. Fax: +44 (0)1206 873151.
> http://www.iser.essex.ac.uk
>
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```