Actually in this simple model X can equal W.
This is because the Inverse Mills' Ratio is a nonlinear function of W
so this can avoid perfect collinearity if W has a long enough support.
In practice though, it is better to have at least one variable
excluded from X in order to achieve better identification.
robert
On 10/16/06, Nishant Dass <[email protected]> wrote:
Philip,
Thank you for your succinct answer as well as the refernce;
I will check the book.
Regards,
Nishant
--- Philip Fridborn <[email protected]>
wrote:
> Hi,
> According to Wooldridge (2002) Econometric analysis of
> x-section and panel data
> you must have at least one variable in the selection
> model that is not included
> in the y-equation. This variable(-s) is supposed to
> affect z but not y.
> So, X and W do not have to be completely distinct.
>
> Philip Fridborn
>
> Citerar Nishant Dass <[email protected]>:
>
> > Dear list-members,
> >
> > If I have the following Heckman selection model:
> >
> > y = a + b.X + e (2nd stage)
> > z = c + d.W + u (selection equation)
> >
> > Would you know whether X and W have to be completely
> > distinct?
> >
> > I thought they ought to be distinct but I have seen
> some
> > papers that use variables that are common to both X and
> W.
> >
> >
> > Does anyone have a good answer or know of a definitive
> > source on this?
> >
> > Thanks for your suggestions.
> >
> > Nishant
> >
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