Re: st: model with censored dependent variable and binary endogenous variable

[Malgosia Madajewicz <mm1174@columbia.edu>]

Thank you for the reply.

I actually have a two-equation model. The equation for the endogenous 
variable should be estimated as a probit. The second-stage equation for the 
censored dependent variable of interest should be estimated as a Tobit. I'd 
rather not use Heckman, because I don't need to rely on functional form for 
identification. I have an IV. So I essentially want to do the equivalent of 
2SLS, but 2SLS itself would give inconsistent estimators.

Yes, I see that I could write a ml procedure, but I have never done this 
before and I wonder if anyone has already written a procedure to do 
something similar which I could use as an example?

Thanks in advance,

Malgosia

At 08:56 AM 7/20/2004, you wrote:

> > could anyone offer any advice about estimating a model in which the
> > dependent variable is censored and which has a binary endogenous
> > variable?  The dependent variable takes both positive and negative
> > values, but has a mass at 0. I also need to use pweights and estimate
> > clustered standard errors (I'm using survey data).
>
> This is what I would do.
>
> . set imho on :)
>
> It looks like you have three equations here.
>
> The first one takes care of the binary endogeneous variable. Let's say
> this is probit.
>
> The second one takes care of the point mass at zero, so it is a probit
> again, where the dependent variable is an indicator of whether your
> variable of interest hits zero or not. This is a standard way -- see for
> instance -zip- in Stata.
>
> The third one is the equation for the regression if the dependent variable
> is not zero.
>
> You can try to get hold of this stage by stage. You would need to extract
> the inverse Mills' ratio from the first equation in the spirit of Heckman
> / treatreg model (so all concerns regarding identification in such models
> apply). Then you plug it into the second and the third equations. You can
> get cluster-corrected standard errors with probit and regress without much
> problem, but it is going to be tough to ensure that you have the same
> coefficients across the second and the third equations, if that's a
> concern to you.
>
> Your ultimate choice would be to write a maximum likelihood estimator with
> the suite of -ml- commands. As far as this is a relatively straightforward
> (although rather involved) observation-by-observation likelihood, Stata
> can handle the -[pw=] , cluster(psu)- automatically with its -lf- form of
> the -ml- routine. I think it suffices to specify something like -svy-
> somewhere in the header of your maximum likelihood program, but I am not
> 100% sure about that.
>
>  ---                                    Stas Kolenikov
>  --       Ph.D. student in Statistics at UNC-Chapel Hill
>  - http://www.komkon.org/~tacik/  -- Stas.Kolenikov@unc.edu
>
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