# st: Simultaneous Equations Models

 From "dyap82" To statalist@hsphsun2.harvard.edu Subject st: Simultaneous Equations Models Date Tue, 23 Sep 2003 05:44:07 -0000

```Dear Renzo

Thanks for your reply but I think I confused you a bit with my
questions so I'll rephrase exactly what I am asking.

Is it possible to test endogeneity in the following model:

Y1 = a0 + a1Y1 + a3X3 + e1
Y2 = a0 + a2Y2 + a4X4 +e1

When

1. Y1 and Y2 are binary (I am using Maddala (1983) to manipulate the
covariances to get correct standard errors)
2. Y1 is binary and Y2 is continuous (I am using CDSIMEQ)

I'll post my inverse mills question again in another mail to avoid
confusion as its a different issue.

Thanks again

Danny

--- In statalist@yahoogroups.com, "Renzo Comolli"
<renzo.comolli@y...> wrote:
> Hi Danny,
>
> Your email is full of questions
> I try to answer some of them, to the best of my knowledge, but be
> that I am NOT an expert
> My best advice is to type
> . help heckman
> . help hausman
> and start from there (it is convenction of this list to put a dot
before
> commands you can type as is in stata, but you have to type them
without the
> dot)
> In the stata manual there is much more (the volueme called
reference G-M),
> you should really try to read the manual with a professor or a
teaching
>
> >>I was wondering if is a way to test endogeneity in the following
model
> >>Y1= a0 + a1Y1 + a3X2 + e1
> >>Y2 = a0 + a2Y2 + a4X2 +e1
>
> Either there are a lot of typos, or the system is not identified
and don't
> think there is anything you can do.
>
> If you mean a Heckman type model, then it should look more like
this
> Y1= a0        + a3X2 + e1
> Y2= b0 + b1X3 + a4X2 + e2
>
> >>Y1 is continuous, Y2 is binary
> Y1 is observed only if Y2 is positive and suitable assumption on
errors,
> Than this is the standard Heckman Two-steps set up
>
> . heckman Y1 X2, twostep select(X2 X3)
> Stata by default considers the constant, so you are all set with
that.
>
> The test for endogeneity is computed automatically by stata in the
Heckman
> procedure. It is that Prob>chi2 at the very bottom, if that is
0.000 it
> means it is quite definitely endogenous (better, it is endogenous
with a
> significance level that is so small that the machine cannot
compute it, i.e.
> a confidence level so close to 1 that the machine cannot compute
it). If
> Prob>chi2 0.049999 or smaller, then it is significant at 5%,
confidence 95%.
> If Prob>chi2 0.099999, significant 10%, confidence 90%
>
> >>I want to estimate a Cragg model, but I want to do it manually
rather
> >>than through the heckman procedure because I need the inverse
mills ratio
> >>for another equation.
> >>Is there any way to compute and save the "inverse mills ratio"
from a
> probit
> >>equation in Stata?
> I have a good news.
> You can both use the preprogrammed command for heckman and ask
stata to
> remember the inverse mills ratio
> You just write exactly what I wrote above with the following added
option
> . heckman Y1 X2, twostep select(X2 X3)
> mills(these_are_inverse_mills_ratio_for_Dany)
>
> This line, on top of doing all the rest also saves the inverse
mills ratio
> in a variable called these_are_inverse_mills_ratio_for_Dany
>
> >>Y1 and Y2 are binary (probit)
> I would do the following (BUT!! the validity of this procedure
needs to be
> verified either with books or prof or TA)
> Obtain the inverse mills ratio exactly as before
> . heckman Y1 X2, twostep select(X2 X3)
> mills(these_are_inverse_mills_ratio_for_Dany)
> Then run a probit on X2 and the inverse mills ratio as follows
> . probit Y1 X2 these_are_inverse_mills_ratio_for_Dany
>
> >>I know there is the Hausman test but this only applies to OLS I
believe.
> Is there anything else out there?
> No, the Hausman test is WAY more general than that.
> .help hausman
> explains a little bit more.
> On the other hand, if your plan were to use the Hausman test to
chose
> >>a. Y1 and Y2 are binary (probit)
> >>b. Y1 is continuous, Y2 is binary
> I don't think it is going to work.
>
>
>
> The funny thing is that you might not have many any of this at
all -
> unfortunately, it comes to my mind only now :(
> You might have meant
>
> Y1= a0 + a1Y2 + a2X2        + e1
> Y2= b0 + b1Y1        + b3X3 + e2
> I.e. what you could have meant is that the X are different
> If that is what you meant, then the route to follow is quite
different. Let
> us know.
>
> Ciao
> Renzo
>
>
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