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

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

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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