Wednesday, March 15, 2006

RE: st: IV with oprobit / mprobit?

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:

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> * First-stage ordered probit: > oprobit y2 z x > predict p1 p2 p3, p > * Second-stage OLS: > regress y1 p2 p3 x

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> > 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? >


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.


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