Dear Renzo
Many thanks for this.
I agree with you on not using reg3. I do not indeed
want to use a linear
probability method.
The confusion emanated from the fact that I had not
appreciated the
closeness of your method with reg3. I see your logic
now.
Also, you are right in that the first step includes
estimating the Probit on
regressors from both the migration and the wage
equations. I
had done exactly that, but missed it when writing the
mail.
Where I did go wrong was that I did not estimate the
mills ratio separately
for the two equations. But now that I do, the sign of
the wage
difference in the migration equation is counter
intuitive. :(
I guess I will have to go back to my references.....
Rashid
p.s. My apologies for misspelling your name in my
earlier mail.
----- Original Message -----
From: "Renzo Comolli" <[email protected]>
To: <[email protected]>
Sent: Monday, December 27, 2004 4:17 PM
Subject: Re: st: Heckman & simultaneous Equations
procedures (?)
> 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
>
>
>
--------------------------------------------------------------------------
--
> ----
> *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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