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RE: st: IV with oprobit / mprobit?


From   Bart Vanneste <bartvanneste@yahoo.com>
To   statalist@hsphsun2.harvard.edu
Subject   RE: st: IV with oprobit / mprobit?
Date   Thu, 16 Mar 2006 14:40:59 -0800 (PST)

Thanks very much for the useful reactions!

I should have been more precise. I have a continuous
dependent variable and a discrete endogenous regressor
(with 3 categories): 
y_cont = x_discrete + e

Could I also extend Rivers and Vuong (1988) when the x
is categorical (i.e. not ordered), comparable to a
multinomial probit?

Many thanks,
Bart

--- "Brian P. Poi" <bpoi@stata.com> wrote:

> On Wed, 15 Mar 2006, Tobias Hofmann wrote:
> 
> > Dear Bart, dear all,
> >
> > Please read this e-mail even if you are not
> interested in my response to
> > Bart's question as you might be in the position to
> answer my follow-up
> > question. ;-]
> >
> > There seems to be no ado-file like IVoprobit or
> IVmprobit. However, you
> > should be able to do something like that "by
> hand". I'm certainly not expert
> > on this field, but here is an example of how such
> a "self made" code could
> > look like:
> 
>    (message trimmed)
> 
> > * First-stage ordered probit:
> > oprobit y2 z x
> > predict p1 p2 p3, p
> > * Second-stage OLS:
> > regress y1 p2 p3 x
> 
>    (message trimmed)
> 
> >
> > Now, here is/are my follow-up question(s):
> >
> > a) What would the above code have to look like if
> I wanted Stata to return
> > ROBUST corrected standard errors, i.e. if I wanted
> to use the
> > Huber/White/sandwich estimator of variance?
> >
> > b) What would it have to look like to use
> clustering, let's say, using the
> > variable "foreign" to specify to which group each
> observation belongs?
> >
> 
> Tobias,
> 
> First, note that the two-step variant of the
> official Stata command 
> -ivprobit- runs linear regression in the first
> stage, and probit in the 
> second stage.  That is, there is one or more
> continuous endogenous 
> regressors in a model where the dependent variable
> is dichotomous.
> 
> In your program, the first stage is fit via
> -oprobit- and the second stage 
> via -regress-, which implies to me that you are
> envisioning a model in 
> which the endogenous regressor is an ordered
> categorical variable and the 
> dependent variable is continuous.
> 
> If you are interested in a model like -ivprobit-
> with an ordered dependent 
> variable, then the two-step estimator of Rivers and
> Vuong for probit 
> (1988, Journal of Econometrics) could probably be
> extended in a 
> straightforward way.  Newey's efficient estimator
> (1987, Journal of 
> Econometrics) might also be a viable option, though
> it would a bit more 
> work to code, since it makes use of a two-step
> estimator like Rivers and 
> Voung's.  The maximum likelihood estimator as used
> by -ivprobit- could 
> also be generalized.  (These ideas should be taken
> as conjecture -- in 
> principle they should work, though I haven't done
> the algebra to guarantee 
> that they will work or are practical to implement.)
> 
> If, on the other hand, you mean a model where the
> endogenous regressor is 
> an ordered categorical variable, then I don't have
> anything to add, other 
> than a guess that the treatment effects literature
> may have something to 
> say.
> 
> HTH
> 
>     -- Brian Poi
>     -- bpoi@stata.com
> *
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