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RE: st: IV with oprobit / mprobit?


From   "Brian P. Poi" <bpoi@stata.com>
To   statalist@hsphsun2.harvard.edu
Subject   RE: st: IV with oprobit / mprobit?
Date   Wed, 15 Mar 2006 09:37:33 -0600 (CST)

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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