# Re: st: Heckman & simultaneous Equations procedures (?)

 From "Renzo Comolli" <[email protected]> To <[email protected]> Subject Re: st: Heckman & simultaneous Equations procedures (?) Date Mon, 27 Dec 2004 19:17:17 -0500

```Dear Rashid:

The reason why we are going through this procedure rather than using -reg3-
is that migration/not-migration is a zero-one decision. It is probably
possible to use -reg3- (but you should check for other issues) if you were
prepared to use a linear probability model for the migration/non-migration
step. That is to say, if you use -reg3- it is possible that the predicted
probability of migration is either higher than one or smaller than zero.
That's why usually people don't use -reg3- for this type of problems. The
procedure that I referred to is "close in spirit" to -reg3-. Rather than
describing here the whole thing myself (that would take several pages) I
refer you to one or more of the following references.

Greene "Econometrics Analysis". The section is called "treatment effect". If
you have the 5th edition it is at page 787, but I suggest you read the
chapter on limited dependent variables from the beginning. I you read the
whole chapter the logic will be pretty clear and you should be pretty clear
on how comes that the endogeneity of the wage differential is taken care of.
Greene stops short of the final step though.

Maddala "Limited-dependent and qualitative variables in econometrics"
explains the procedure under the heading "Lee's binary choice model". Note
though that, for historical reasons, equation 11.20 is set up with a
negative sign in front of the error; this might confuse you because it
switches the signs of the inverse mills ratios. Also the fact that there is
a typo in formula 11.23 does not help (the typo is that the minus in front
of sigma2epsilon* should be a plus)

The original references are
Lee, Lung-Fei (1978) "Unionism and Wage Rates: A Simultaneous Equations
Model with Qualitative and Limited Dependent Variables", International
Economic Review, Vol. 19(2), pp. 415-433
Lee, Lung-Fei (1979) "Identification and Estimation in Binary Choice Models
with Limited (Censored) Dependent Variables", Econometrica, Vol. 47,
pp.415-433.

I want to point out that the first step as you describe it here is NOT
correct. The correct first step involves estimating a probit of migration on
the migration regressors AND THE WAGE EQUATIONS REGRESSORS (but not the
wages per se). You see now how this procedure is closer in spirit to -reg3-
Also be sure that in step two you compute the right inverse mills ration
(each equation has its own)

I gave a sketch of the code here
http://www.stata.com/statalist/archive/2004-11/msg00622.html
http://www.stata.com/statalist/archive/2004-11/msg00626.html
but this sketch presupposes you have a knowledge of the material and you
just want to see the code.

You could also use the command -movestay- that does full-information maximum
likelihood, but as I point out here
http://www.stata.com/statalist/archive/2004-11/msg00453.html
there is a bug in the code for -mspredict-. If the bug were fixed, you could
use -movestay- to estimate the reduced form migration equation and the two
wage equation, then use -mspredict- to predict the wage in two regimes and
could then estimate the structural form probit.
But I received no confirmation that the way that I have proposed to correct
the bug is right, so I don't suggest you rely on this procedure.
To learn about -movestay- M. Lokshin and Z. Sajaia "Maximum likelihood
estimation of endogenous switching regression models" Stata Journal
4(3):282--289

Best,
Renzo Comolli

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*From   Rashid Memon <[email protected]>
To   [email protected]
Subject   st: Heckman & simultaneous Equations procedures (?)
Date   Mon, 27 Dec 2004 13:39:55 +0000 (GMT)

----------------------------------------------------------------------------
----

Dear All

I am looking at the effect of the rural-urban wage
differential on
rural-urban migration. I am following the methodology
Renzo Conelli posted
some time ago:

I first estimate the probit (migration on its
dependent variables except the
wage differential).

Calculate the inverse mills ratio and then plug it in
the wage equations.

Estimate the wage equations and get predicted values
to calculate the wage
differential

Plug in the wage differential in the migration Probit
again.

My concern is this: Since the wage differential is
endogenous, should'nt a
simultaneous equation procedure be used. I am a bit
confused on how to
combine a ML methodology (probit) with a simultaneous
equation procedure
(say, reg3)

Any assistance will be appreciated.

Thanks

Rashid

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