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:[email protected]]
>>>>Sent: 26 August 2006 02:52
>>>>To: Schaffer, Mark E
>>>>Subject: diagnostics for the treatreg procedure
>>>>
>>>>Hi, Mark,
>>>>
>>>>I saw your post on STATA list about the 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 your example
>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
>email: [email protected]
>web: http://www.sml.hw.ac.uk/ecomes
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