### Wednesday, March 15, 2006

## Re: st: IV with oprobit / mprobit?

I have also not done the algebra, but I sincerely doubt that the example Tobias coded, where one excluded instrument is used to identify the effects of two endogenous dummy variables, can possibly be right.

A model in which the endogenous regressor is an ordered categorical variable and the dependent variable is continuous can be fitted using -ivreg-, since its consistency does not depend on the endog var having a particular distribution, and trading a tiny efficiency gain for a well-understood estimator, with no known errors in the code, is well worth it, IMHO.

See -help _robust- and [P] _robust for help on robust var and clusters.

On 3/15/06, Brian P. Poi <bpoi@stata.com> wrote: > (message trimmed) 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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