RE: st: IV with oprobit / mprobit?

["Brian P. Poi" <bpoi@stata.com>]

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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