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Re: st: logit with sample selection


From   "R.E. De Hoyos" <redeho@hotmail.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   Re: st: logit with sample selection
Date   Mon, 25 Sep 2006 18:18:38 -0400

Nishant,

Lee (1984) shows that Heckman's model can be generalized to other selectivity problems. The trick is to take the linear prediction of the logit (or the multinomial logit, or any other model with a non-normal distribution), and make a transformation to normal. Doing this, you are back into Heckman's bivariate normal distribution, hence you are able to compute and use the Mill's ratio in your objective function.

Your SE still have to account for the two-step procedure involved.

I hope this helps,
Rafa
_______________________
Rafael E. De Hoyos
DEC Prospects Group
The World Bank
Washington, DC 20433

----- Original Message ----- From: "Nishant Dass" <nishant_dass@yahoo.com>
To: <statalist@hsphsun2.harvard.edu>
Sent: Monday, September 25, 2006 11:44 AM
Subject: Re: st: logit with sample selection



Hi Ian, Jean, Anders, and Maarten,

Thank you everyone for responding to my query.

I am quite sure that the formula suggested by Ian wouldn't
work because, as indicated by Maarten, it would have to be
something that reflects the bivariate logistic
distribution.  I am aware of the bivariate normal formula
mentioned below but it wouldn't apply for a logit model.

I was only wondering whether there is something similar for
a logit model because I had found this link in the
archives, which shows the IMR calculation for -mlogit- (but
not for -logit- explicitly.)  Check this:
http://www.stata.com/statalist/archive/2003-04/msg00465.html

As for Jean's suggestion about -heckprob-: I didn't want to
use that because 1) I have already tried it and it's taking
forever to converge, and 2) -logit- fits my data better
than -probit- and so, I wanted to use something like
"heckman + logit".

Finally, Anders' suggestion: it is not immediately clear to
me how -gllamm- is applicable in my case but I will check
again.

In any case, thanks a lot for the discussion.

If anyone can check the above link and add something for
-logit-, that'd be great.

Thanks,

Nishant



--- Ian Watson <iangwatson@gmail.com> wrote:

Nishant

The approach you outline will work. The steps in Stata
are straightforward.

For example, if participation has two outcomes (working
or not working),
and you want an inverse mills ratio for the working
outcome:

logit work  age edu children region
capture drop phat
capture drop imr
predict phat if e(sample), xb
gen imr = normden(phat)/norm(phat)


(Note that the capture drop lines are only needed if you
insert this
code into a do file which runs multiple times).


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