[Limdep Nlogit List] Bivariate Probit Selection for a Tobit model

[Steven Yen]

Professor FLETSCHNER:

I have a paper forthcoming soon in Applied Economics, which is similar to what 
you are doing:

Lin, B., and S.T. Yen. 2007. "Grain Consumption in the US." Applied Economics 
38:in press.

In that paper, I have a "bivariate Tobit model" (whole grains and fine grains 
consumption) with two binary endogenous variables (nutrition knowledge and 
food label use). I have one more equation than you need, and mine was lower 
censored at zero, but adjustment to upper censoring should be straightforward. 
The paper is probably coming out any time now. Let me know if it sounds like 
what you need.

Steven Yen
Department of Agricultural Economics
The University of Tennessee
http://web.utk.edu/~syen/
Check out two postdoc openings at:
http://web.utk.edu/~syen/postdoc.html

>===== Original Message From William Greene <wgreene at stern.nyu.edu> =====
>Diana.  I don't think instrumental variables is the right answer
>either.  I'm not sure what the instruments would be, and, moreover,
>since you are not using least squares, the IV method really doesn't
>fit.  Two things strike me, but so far as I know, they are not worked
>out in the literature. (1) If you use the predicted probabilities
>from two individual probits - they need not be fit jointly as a BVP
>model - in place of the actual H and W, you get a model that now has
>u+B2(H-PH)+B3(W-PW) as the disturbance.  MLE ***might*** be consistent.
>If so, then a correction in the spirit of Murphy and Topel might be
>the answer for the standard errors.  I'm not ready to plant my feet
>in concrete on this one, but it's a thought. (2) There might be a GMM
>estimator available based on the conditional mean function in the
>tobit model given the two dummy variables.  If so, it would once again
>involve the predicted probabilities in the probit model.
>   I emphasize, once again, these are speculations.  I have not actually
>worked out a solution to this problem.  Maybe one of the other people
>reading this list server has also worked on this problem, or has seen
>something in the literature.  (Maybe there's a "Bayesian" MCMC answer
>out there also.)
>  Regards,
>  Bill
>
>
>----- Original Message -----
>From: "Diana Fletschner" <fletschn at u.washington.edu>
>To: "Limdep and Nlogit Mailing List" <limdep at limdep.itls.usyd.edu.au>
>Sent: Thursday, August 30, 2007 7:05:17 PM (GMT-0500) America/Bogota
>Subject: Re: [Limdep Nlogit List] Bivariate Probit Selection for a Tobit 
model
>
>
>Thank you, Bill. No wonder I couldn't find this anywhere. Do you have a
>suggestion on an alternative model to fit for a problem in which I would
>like to estimate:
>
>y = b0 + b1 X  + b2H + b3W + u  where y has an upper limit of 1 (about 30%
>of the sample is there) and
>
>H = 1 if husband participated in the program and 0 otherwise
>W=1 if wife participated in the program and 0 otherwise.
>
>As you can guess, I am interested in b2 and b3.
>
>A possibility is to use instrumental variables but I haven't found how to
>adjust the covariance matrix given that I am instrumenting two variables.
>
>Diana
>
>
>----- Original Message -----
>From: "William Greene" <wgreene at stern.nyu.edu>
>To: "Limdep and Nlogit Mailing List" <limdep at limdep.itls.usyd.edu.au>
>Sent: Thursday, August 30, 2007 4:41 PM
>Subject: Re: [Limdep Nlogit List] Bivariate Probit Selection for a Tobit
>model
>
>
>> Diana.  The bivariate probit selectiion model is only supported
>> for the linear model, not the tobit model.  Note, the linear
>> model is estimated using two step least squares.  The tobit model
>> would have to be fit using ML, for a trivariate normal based log
>> likelihood.  I have never seen it derived.
>> /Bill Greene
>>
>> ----- Original Message -----
>> From: "Diana Fletschner" <fletschn at u.washington.edu>
>> To: "Limdep and Nlogit Mailing List" <limdep at limdep.itls.usyd.edu.au>
>> Sent: Thursday, August 30, 2007 4:57:34 PM (GMT-0500) America/Bogota
>> Subject: [Limdep Nlogit List] Bivariate Probit Selection for a Tobit model
>>
>>
>> Hello--
>>
>> I am trying to estimate a Tobit model with a Bivariate Probit selection
>> but cannot get the results I am interested in. This is what I have:
>>
>> Bivariate Probit;
>>    Lhs = p1, p2;
>>    rhs = x1;
>>    rh2 = x2;
>>    wts = ...;
>>    hold for SELECT$
>>
>> Select;
>>    Lhs = y;
>>    Rhs = x3, p1, p2;
>>    wts = ...;
>>    all;
>>    tobit$
>>
>> The output I get is only for the Bivariate Probit and the 2sls of the
>> second regression. I do not obtain the Tobit (corrected) results. Is there
>> a way to obtain these results? I would like to use the entire sample for
>> the Tobit to be able to say something about the parameters associated with
>> p1 and p2.
>>
>> Any help would be much appreciated!
>> Diana
>> _______________________________________________
>> Limdep site list
>> Limdep at limdep.itls.usyd.edu.au
>> http://limdep.itls.usyd.edu.au
>>
>>
>> --
>> Professor William Greene
>> Department of Economics
>> Stern School of Business
>> New York University
>> 44 West 4th St., Rm. 7-78
>> New York, NY   10012
>> http://www.stern.nyu.edu/~wgreene
>> 212.998.0876
>>
>> _______________________________________________
>> Limdep site list
>> Limdep at limdep.itls.usyd.edu.au
>> http://limdep.itls.usyd.edu.au
>>
>
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>
>--
>Professor William Greene
>Department of Economics
>Stern School of Business
>New York University
>44 West 4th St., Rm. 7-78
>New York, NY   10012
>http://www.stern.nyu.edu/~wgreene
>212.998.0876
>
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>Limdep site list
>Limdep at limdep.itls.usyd.edu.au
>http://limdep.itls.usyd.edu.au

Steven Yen
http://web.utk.edu/~syen/
Check out our postdoc opening at:
http://web.utk.edu/~syen/postdoc.html