# st: Re: RE: Re: diagnostics for the treatreg procedure

 From "Rodrigo A. Alfaro" To Subject st: Re: RE: Re: diagnostics for the treatreg procedure Date Mon, 28 Aug 2006 15:20:42 -0400

```Mark,

I checked that -treatreg, two- is not a IV estimator, it is
Heckman-type model. I thought that -treatreg, two-
computed Procedure 18.1 of Wooldridge (2002, p623):
(1) Estimate the binary response by ML, obtain fitted prob
(2) Run the outcome equation using the fitted probabilities
as instruments. This is a IV model, for which a Sargan test
makes more sense.

I agree that a kind of "overidentification" test it would be
easy to do it by ML (basically some LR at the end). But
my concern was that properties of MLE relies on the
assumption of the distribution (normality) for what I
prefer a two-step IV procedure (as Wooldridge).

I tried the exercise below and I saw that IV results are
very similar to Heckman -treatreg, two-, using logit,
probit or cloglog for the second equation. But MLE are
very different.

Maybe, Yang can do this procedureby hand and use your
-ivreg2- instead of my -reg- to compute the Sargan-test.

Rodrigo.

qui {
sysuse auto, clear
replace price=price/1000
probit foreign weight length mpg
est store IV11
predict forp
logit foreign weight length mpg
est store IV21
predict forl
cloglog foreign weight length mpg
est store IV31
predict forc
reg price mpg foreign (mpg forp)
est store IV12
reg price mpg foreign (mpg forl)
est store IV22
reg price mpg foreign (mpg forc)
est store IV32
treatreg price mpg, treat(foreign = weight length mpg) two
est store HECK
treatreg price mpg, treat(foreign = weight length mpg)
est store MLE
}

est table *, se eq(1) b(%6.4f)

----- Original Message -----
From: "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To: <statalist@hsphsun2.harvard.edu>
Sent: Monday, August 28, 2006 11:39 AM
Subject: st: RE: Re: diagnostics for the treatreg procedure

Rodrigo,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> Rodrigo A. Alfaro
> Sent: 28 August 2006 16:07
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Re: diagnostics for the treatreg procedure
>
> Hi Mark,
>
> Interesting conversation. I have a question about the procedure.
> It seems to me that Yang wants to do ML instead of two-step IV.
> Why he wants that? The two-step IV does not require that
> probit should be corretly specified in compare with ML. In
> other words, he could solve the problem via-ML with a logit!!
>
> Rodrigo.

In fact, Yang wanted to do 2-step treatreg because he was following the
method used by an earlier paper.  But the ML overid test is easier to
do.

When you say "two-step IV", do you mean the same thing as two-step
treatreg?  Two-step treatreg uses the assumption of normality in the
probit eqn (just like heckman).

I couldn't see an easy way to do the overid test for two-step treatreg
that doesn't change the nature of the treatreg model.  Simple (two-step)
IV would generate an overid statistic, but that drops the normality
assumption in the treatment equation, which is an identifying
restriction.

Cheers,
Mark

>
> ----- Original Message -----
> From: "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
> To: <statalist@hsphsun2.harvard.edu>
> Sent: Sunday, August 27, 2006 8:40 PM
> Subject: st: diagnostics for the treatreg procedure
>
>
> Dear Statalisters:
>
> I had the following off-list conversation about how to generate an
> overid stat for a treatreg estimation.  It occurred to me
> that it might
> be of general interest, so I'm posting it here.
>
> Both I and my correspondent would be very interested in any comments
> other Statalisters might have.
>
> Cheers,
> Mark
>
> >>>>-----Original Message-----
> >>>>From: Yang Lu [mailto:ylu1@stern.nyu.edu]
> >>>>Sent: 26 August 2006 02:52
> >>>>To: Schaffer, Mark E
> >>>>Subject: diagnostics for the treatreg procedure
> >>>>
> >>>>Hi, Mark,
> >>>>
> overidentification test for
> >>>>treatreg regression. You mentioned you had programmed one. I am
> >>>>wondering whether you could kindly share it with me, when
> you fell
> >>>>comfortable. Thanks a lot.
> >>>>
> >>>>cheers,
> >>>>yang
>
> >>Schaffer, Mark E wrote:
> >>
> >>>Yang,
> >>>
> >>>If I'm not mistaken, the overid test for treatreg is
> actually pretty
> >>>easy to do by hand for the ML version.  The trick is to do
> an LR test
> >>>of the overidentifed treatreg system of interest vs. a
> just-identified
> >>>version.
> >>>
> >>>Using the example from the manual, say you estimate
> >>>
> >>>treatreg ww wa cit, treat(wc=wmed wfed)
> >>>
> >>>There's one endogenous variable in the outcome equation, and 4
> exclusion
> >>>restrictions: wa and cit don't appear in the treatment
> eqn, and wmed
> >>>and wfed don't appear in the outcome equation.  There's
> also one more
> >>>identifying restriction, namely normality in the treatment (probit)
> eqn.
> >>>To get a test of your 4 overidentifying/exclusion
> restrictions, just
> do
> >>>an LR test of the above vs. a just-identified system with no
> exclusion
> >>>restrictions.  The single identifying restriction is
> normality.  Thus
> >>>
> >>>use http://www.stata-press.com/data/r9/labor.dta, replace
> >>>gen wc=(we>12)
> >>>
> >>>treatreg ww wa cit, treat(wc=wmed wfed) est store troverid
> >>>
> >>>treatreg ww wa cit wmed wfed, treat(wc=wmed wfed wa cit) est store
> >>>trjustid
> >>>
> >>>lrtest troverid trjustid, df(4)
> >>>
> >>>will give you an overid test for this example.
> >>>
> >>>Cheers,
> >>>Mark
>
> >>Hi, Mark,
> >>
> >>Thanks a lot for your reply. I really appreciate it. My question is
> >>slightly different from the one you just mentioned. In the
> treatment
> >>model, I have one endogenous variable and 3 instrument
> variables. I am
>
> >>trying to do the Sargan type overidentification test to show the
> >>validity of the instruments. My model is as follows:
> >>
> >>treatreg y x1 x2 x3, treat(dummy=iv1 iv2 iv3 x1 x2 x3)
> >>
> >>Notice that I have already included x1 x2 x3 in my
> selection model. So
>
> >>in this case, I do test as follows:
> >>
> >>treatreg y x1 x2 x3, treat(dummy=iv1 iv2 iv3 x1 x2 x3) est store
> >>troverid
> >>
> >>treatreg y iv1 iv2 iv3 x1 x2 x3, treat(dummy=iv1 iv2 iv3 x1
> x2 x3) est
>
> >>store trjustid
> >>
> >>lrtest troverid trjustid, df(2)
> >>
> >>Is this the correct test to show the validity of
> instruments, like the
>
> >>Sargan test? Thanks a lot.
> >>
> >>cheers,
> >>yang
>
> Schaffer, Mark E wrote:
>
> >Hi Yang.  You are doing ML estimation of a system, so the
> term "Sargan
> >test" is probably inappropriate - Sargan developed his
> statistic in the
>
> >context of IV/2SLS estimation.  The corresponding ML test for single
> >eqn estimation is the Anderson-Rubin statistic for LIML.  I
> don't think
>
> >the ML statistic for a system has a name per se.  But all
> these tests
> >are basically the same thing.
> >
> >In the example I sent you, there were 5 identifying
> restrictions - two
> >exclusions from each eqn, plus the normality assumption.  The test I
> >sent was a test of the 4 overidentifying restrictions in the system,
> >the normality assumption being maintained.  The test has 4 dofs since
> 5-1=4.
> >
> >Your example is a special case, since you have exclusions
> from only the
>
> >outcome equation.  You have 4 identifying restrictions: the 3
> >exclusions plus the 1 normality assumption.  The test in
> >is done correctly, except that there should be 4-1=3 dofs.
> >
> >Can I share this with Statalist?  I should have replied to the list
> >with your first email.  It's the kind of thing that is of general
> >interest, plus if I've made a mistake, someone may spot it.
> >
> >Cheers,
> >Mark
> >
> >Prof. Mark Schaffer
> >Director, CERT
> >Department of Economics
> >School of Management & Languages
> >Heriot-Watt University, Edinburgh EH14 4AS tel
> +44-131-451-3494 / fax
> >+44-131-451-3296

*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```