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Re: endogenous switching [was st: To: <statalist@hsphsun2.harvard.edu>]


From   "Renzo Comolli" <renzo.comolli@yale.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   Re: endogenous switching [was st: To: <statalist@hsphsun2.harvard.edu>]
Date   Sun, 21 Nov 2004 12:45:30 -0500

Dear Irfan,

I am not sure why you are using logit for the migration step. If there are
good reasons to use logit instead of probit what I say in the following
might need to be modified or might not apply altogether

Your case appears to be a case of Lee 1978 model, explained both on Maddala
"limited dependent variable" book, and in Greene's textbook under the
heading "treatment effect".

If you want to estimate your model by full information maximum likelihood,
you can use -movestay-
. findit movestay
There are a couple of warnings on statalist about it, read them!

If you want to estimate the model using the twostep procedure, you can
either follow the procedure I detail or read the post listed below. I
realize it might be to difficult too understand without having read one of
the three references above:
1. Estimate the reduced form probit on the same x variables you put in the
wage equations and the extra variables that belong to the selection equation
(forget about the wage difference at this stage)
2. gen mills = normden(gammahat)/norm(gammahat) if place==1 //urban
3. replace mills = -normden(gammahat)/(1-norm(gammahat)) if place==0 //rural
4. gen copy_of_mills_for_safekeeping=mills
5. regress log_income x-variables mills if place==1
6. replace mills=0
7. predict ln_w_hat_urban, xb
8. replace mills=copy_of_mills_for_safekeeping //i don't think this passage
is strictly speakig necessary but...
9. regress log_income x-variables mills if place==0
10. replace mills=0
11. predict ln_w_hat_rural, xb
12. drop mills copy_of_mills_for_safekeeping
13. gen difference_hat=ln_w_hat_urban-ln_w_hat_rural
14. estimate structural probit using difference_hat and the other selection
variables.

There is also a very clever trick explained by Mike Johnson that saves you a
lot of work, but be carful because I believe the sign of one of the
coefficients of the inverse mills ratios get switched around (I did not have
time to look into this more), so when you go and interpret the results watch
out!
http://www.stata.com/statalist/archive/2004-09/msg00562.html

Best,
Renzo

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*From   sirfan@zab.net.pk 
To   undisclosed-recipients: ; 
Subject   st: To: <statalist@hsphsun2.harvard.edu> 
Date   Sun, 21 Nov 2004 12:45:25 +0500 (PKT) 
----------------------------------------------------------------------------
----

Dear All

I am trying to estimte a rural to urban migration model where one of the
regressors is a hypothetical rural-urban wage difference. The wage
difference is estimted by seperately estimating wages for rural
non-migrants and urban migrants and then subtracting.

The issue is that the wage difference is endogenous to the
logit(migration) model and should be estimated in a two-step procedure.
The literature suggests using Heckman. But I cannot figure how to enter an
endogenous wage difference (of two variables) in the Heckman syntax.

Any assitance will be appreciated.

irfan


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