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# Re: st: RE: Testing for instrument relevance and overidentification when the endogeneous variable is used in interaction terms

 From Jason Wichert To statalist@hsphsun2.harvard.edu Subject Re: st: RE: Testing for instrument relevance and overidentification when the endogeneous variable is used in interaction terms Date Tue, 4 Jun 2013 13:47:16 +0200

```Mark,

Thank you very much for your feedback (and all the other excellent
comments on 2SLS you made on statalist). It's not the usual regression
101, so it actually took me a couple of days to work through all the
respective IV statistics, hence my late reply.

subsequently extended to incorporate the endogenous interaction terms.

In the base case of just that one endogenous variable, i.e.

ivreg2 y ex1 ex2 (en = z1 z2)

I intend to present the first stage F-statistics (to reject weak
identification of my endogenous variable), results from the
Sargan/Hansen overidentification test (to test whether the instruments
are jointly exogenous), as well as a partial R² (to assess instrument
relevance), and a Hausman test for endogeneity.

In the extended case of (*gasp*)

ivreg2 y ex1 ex2 (ex1)^2 (ex2)^2 (en ex1_en ex2_en (ex1)^2_en
(ex2)^2_en = z1 z2 ex1_z1 ex1_z2 (ex1)^2_z1 (ex1)^2_z2 ex2_z1 ex2_z2
(ex2)^2_z1 (ex2)^2_z2)

I intend to present results from the Sargan/Hansen overidentification
test, results from the Anderson/Rubin (1949) [or potentially
Stock/Wright (2000)] test to indicate that all the endogenous
regressors are jointly significant in the second stage, the
Kleibergen/Paap (2006) statistic of underidentification of the model
(i.e. the joint endogenous regressors) , the Cragg/Donald (1993)
statistic of weak identification of the model, the Angrist/Pischke
(2009) statistics for identification of each of the endogenous
regressors, as well as a Hausman test for endogeneity.

Is there something blatant obvious I’m missing or anything I could
well leave out, particularly in the extended case? In particular I’m

a) the necessity of the A/R-test, considering most all of my
endogenous variables are highly significant in the second stage, as
indicated by their respective t- and p-values,

b) the necessity of presenting both K/P as well as C/D statistics,

c) the necessity of the Hausman test in the extended case.

On Fri, May 31, 2013 at 8:30 PM, Schaffer, Mark E <M.E.Schaffer@hw.ac.uk> wrote:
> Jason,
>
> I think the key point is that in your estimation
>
> ivreg2 y ex (en en_ex = z ex_z)
>
> just looking at the two standard first-stage F stats isn't enough.  You can easily get 2 large first-stage F stats, and yet the model is underidentified because there isn't enough information in your instruments to simultaneously identify the coeffs on both your endogenous regressors.
>
> To see if both coeffs are identified, you should use either the weak- or the under-identification statistic reported by ivreg2.  You can also use the Angrist-Pischke (A-P) first-stage F stats to see whether one or the other coeffs is identified.  More details about these in the ivreg2 help file and the references therein.
>
> HTH,
> Mark
>
>> -----Original Message-----
>> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
>> statalist@hsphsun2.harvard.edu] On Behalf Of Jason Wichert
>> Sent: 29 May 2013 21:18
>> To: statalist@hsphsun2.harvard.edu
>> Subject: st: Testing for instrument relevance and overidentification when the
>> endogeneous variable is used in interaction terms
>>
>> Dear Statalisters,
>>
>> I have encountered some difficulties concerning 2SLS estimation when the
>> endogeneous variable is also used to construct interaction terms.
>>
>> After digging through the archives, I found a lot of helpful comments
>> concerning the procedure:
>>
>> http://www.stata.com/statalist/archive/2012-05/msg00970.html
>> http://www.stata.com/statalist/archive/2011-08/msg01485.html
>> http://www.stata.com/statalist/archive/2011-12/msg00705.html
>> http://www.stata.com/statalist/archive/2010-04/msg00759.html
>> http://www.stata.com/statalist/archive/2005-05/msg00150.html
>> http://www.stata.com/statalist/archive/2008-10/msg01009.html
>> http://www.stata.com/statalist/archive/2004-08/msg00779.html
>>
>> Following this advice, I am running an equation of the basic form
>>
>> ivreg2 y ex (en en_ex = z ex_z)
>>
>> In my case, there are two exogeneous variables interacted with the
>> endogeneous variable. Furthermore, I need interactions of those squared
>> exogeneous variables and the endogeneous variables. Leaving additional
>> control variables and further instruments aside, this already leads to the
>> following simplified regression:
>>
>> ivreg2 y ex1 ex2 (en ex1_en ex2_en (ex1)^2_en (ex2)^2_en = z ex1_z ex2_z
>> (ex1)^2_z (ex2)^2_z)
>>
>> So far, so good. However, I’m not sure as to how exactly examine instrument
>> relevance and exogeneity, and which statistics/tests to report.
>>
>> As regards instrument relevance, as to be assessed by the first stage F
>> statistic, the F-statistics on “en” clearly differ depending on whether I
>> instrument solely for “en”, or whether I also instrument for the linear and
>> non-linear interaction terms built around “en”. Which F statistic is the correct
>> one to refer to?
>>
>> Considering I have multiple instruments Z, I am also not sure which
>> overidentification tests and results I should rely on and report.  As holds for
>> the F statistics, the tests of overidentifying restrictions (Sargan N*R-sq test as
>> well as Basmann test) provided by both ivreg2 and overid differ between
>> instrumenting solely “en” or also for the interaction terms build around “en”.
>>
>> Any help is greatly appreciated!
>> Jason
>>
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>
>
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