Re: st: RE: Econometrically sound to use Mills ratio after mprobit?

["R.E. De Hoyos" <redeho@hotmail.com>]

Stephen,

You are assuming that the selection problem in a multinomial context can be 
accounted for by the same technique as in the binary problem (Heckman 1979). 
Using the multinomial logit as the first-step estimation, Bourguignon et al. 
(2004) have shown that this is not the right way to approach the problem.

Generally speaking, the selection problem in a multinomial context can be 
define as:

   y1 = xb + u1
   y^*_m = zl + u_m,    m = 1...M (outcomes)

Where y^* is a latent function and E(u1 | x,z)=0. Define p1...pM as the 
conditional probabilities of observing each of the M outcomes. Then, the 
selectivity-adjusted y1 can be estimated as:

    y1 = xb + mu(p1...pM) + e1

You would need to take into account the conditional probabilities of 
observing NOT ONLY outcome (1) but all other outcomes as well. The problem 
is how to parameterize function mu(.)?

Rafa
PS. I have a working paper version of the reference, if you are interested I 
can send it to you off-list.

Reference:

F. Bourguignon, M. Fournier & M. Gurgand, �Selection bias corrections based 
on the multinomial logit model : Monte-Carlo comparisons�, Journal of 
Economic Surveys, forthcoming



----- Original Message ----- 
From: "Stephen Johnston" <sjohns21@umbc.edu>
To: <statalist@hsphsun2.harvard.edu>
Sent: Monday, April 10, 2006 5:01 PM
Subject: Re: st: RE: Econometrically sound to use Mills ratio after mprobit?



> Hello Miet,
>
> Thanks for your advice.  Here is how I understand the procedure to  work, 
> I read this on an archived statalist post and I have tested it.
>
> mprobit y x1 x2 x3
>
> predict phat if e(sample), xb outcome (1)
>
> capture drop phat
> capture drop mills
>
> gen mills = normden(phat)/norm(phat)
>
> reg y2 x1 x2 mills
>
> For the "outcome" command in the predict line, you have to specify  which 
> of the choice outcomes (in your dependent variable) you are  predicting a 
> probability for.  In this case the probability predicted  for the choice 
> that is set equal to 1.  You can then generate an IMR  for each choice in 
> y.
>
> You can check that this works by generating the inverse mills ratio  from 
> a probit and then including it in an OLS equation - then use the  twostep 
> command for the heckman procedure to make sure the results  match.  For 
> this you will not need to specify an outcome since it  will be generated 
> from a probit.  I hope this helps.  Let me know if  you have any trouble.
>
> Thanks,
> Stephen
>
>
> On Apr 10, 2006, at 4:35 AM, Maertens, Miet wrote:
>
>
> > Dear Stephen,
> >
> > Maybe the following two articles by Wooldridge and by Lechner can help
> > you further:
> > http://www.msu.edu/~ec/faculty/wooldridge/current%20research/ ape1r5.pdf
> > http://ideas.repec.org/p/iza/izadps/dp91.html
> >
> > I'm also trying to perform a similar estimation with stata but I'm
> > struggling with calculating the Inverse Mills ratio's.  Could you  let me
> > know how exactly you are implementing the procedure?
> >
> > Thanks,
> > Miet
> >
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Stephen
> > Johnston
> > Sent: 07 April 2006 18:35
> > To: statalist@hsphsun2.harvard.edu
> > Subject: st: Econometrically sound to use Mills ratio after mprobit?
> >
> > Hello,
> >
> > I am estimating a multinomial probit for a selection equation with 3
> > choices and I am interested in using the inverse mills ratio
> > generated from the MNP in a second step equation.  I know how to
> > implement this procedure, however, I have not been able to find any
> > literature that proves that the Heckman two-step estimation procedure
> > can appropriately and directly extend from a probit selection
> > equation to a multinomial probit selection equation.  Does anyone
> > know of any papers that address this issue?
> >
> > Thanks,
> > Stephen
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