RE: st: RE: ivreg2 questions (shea r2 and AP Statistic)

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

Vidhya,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of Vidhya Soundararajan
> Sent: 16 July 2013 19:25
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: ivreg2 questions (shea r2 and AP Statistic)
> 
> Dear Mark,
> 
> Thank your for this. I reinstalled ivreg2 and this is the December 27,
> 2012 version. I think I had this version earlier as well.
> 
> The Shea R2 of my latest specification (changed after my last email) are 0.38,
> 0.29, and 0.62 for the three first-stage regressions of my
> (three) endogenous regressors. I do realize that the interaction of my
> regressors are making things complicated here. Thank you for pointing that
> out. The AP F-stat for these first stage regressions are 0.18,0.13, and 29.71
> respectively, which is slightly better than the previous model where I had 0.02
> as the highest F-stat among the three.
> I am not sure if all the three first stage statistics need to be "high" or I can just
> consider the highest F-stat here. I am guessing it is the former. Please throw
> some light on this.

You might want to have a look at the discussion in the Angrist-Pischke book.  The AP F test is really meant for the case where you have one endogenous regressor of interest, some others that are not of interest, and you want an F stat for just the first regressor.

If all 3 regressors are of interest, then you (also) want to be looking at a test of whether all 3 are jointly identified.  This would be the usual underidentification (or weak identification) test stats.

HTH,
Mark

> Thanks again!
> Vidhya
> 
> 
> 
> On Tue, Jul 16, 2013 at 1:23 PM, Schaffer, Mark E <M.E.Schaffer@hw.ac.uk>
> wrote:
> > Vidhya,
> >
> > First, you need to make sure that you have the latest version of ivreg2,
> including the latest version of the Mata library it uses, livreg2.mlib.  There's no
> easy facility for working out which version the latter is (as far as I know -
> anyone else on the list have ideas on this?) so the easiest thing to do is just try
> reinstalling.
> >
> > When you say the Shea partial r-sq is 0.5, do you mean for all 3 endogenous
> regressors?
> >
> > I don't think you should put too much weight on the Shea statistic, to be
> honest.  The construction of it ignores at one point the endogeneity of the other
> regressors, and because you are using interactions, your endogenous
> regressors may be highly correlated with each other.  Ignoring the endogeneity
> in the construction of the statistic could make a big difference.
> >
> > The Statalist posting you identified below,
> >
> > http://www.stata.com/statalist/archive/2010-02/msg01336.html
> >
> > shows how to construct the Shea and AP stats by hand.  It could be
> illuminating to repeat the procedure and compare the results at each stage as
> you construct the statistics.
> >
> > HTH,
> > Mark
> >
> >> -----Original Message-----
> >> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> >> statalist@hsphsun2.harvard.edu] On Behalf Of Vidhya Soundararajan
> >> Sent: 11 July 2013 00:23
> >> To: statalist@hsphsun2.harvard.edu
> >> Subject: st: ivreg2 questions (shea r2 and AP Statistic)
> >>
> >> Dear statalist users,
> >>
> >> I have a model with three endogenous variables. Three because I have
> >> one endogenous variable (E), another that is an interaction of E with
> >> an included instrument (A), which makes it endogenous (E * A), and
> >> third one which is another interaction term (E*A*A).
> >>
> >> My model is:
> >>
> >> L = β0 + β1 * A+ β2 * A*A+ β3 * E + β4 * E*A+ β5 * E*A*A+ β6 * X + ε
> >>
> >> I have three instruments for these ->  F, F*A, and F*A*A.
> >>
> >> There are three first stage regressions and so the test for weak
> >> instruments is not a simple test based on the F-statistic of each of
> >> the first stage regressions. I realize that in the case of multiple
> >> endogenous regressors, I can either look at the Angrist and Pischke
> >> (2009) F-statistics on excluded instruments or the partial Shea R2.
> >>
> >> In terms of results of ivreg2, I find that:
> >>
> >> 1. I find that the F-statistic from individual first stage
> >> regressions for each of the three endogenous regressors are high, which is
> good!
> >> 2. The shea R2 is about 0.5 which is good as well.
> >> 3. But the AP F-statistic are very smal (in the order of 0.02) 4.
> >> Kleibergen-Paap Wald rk F statistic is 18.81
> >>
> >> There is one statalist page which cleanly explains both shea and AP
> >> statistics and what the difference is
> >> (http://www.stata.com/statalist/archive/2010-02/msg01336.html). But
> >> it is also mentioned here that the two are closely related and that
> >> AP is preferred because of well defined distribution for testing purposes.
> >> Even though, they are similar in spirit, I am not sure why my shea R2
> >> is giving me different (better) results than the AP F-stat. Should I
> >> now conclude now that my system is weakly identified? But I am
> >> thinking may be that AP F-statistic is low because my three
> >> endogenous regressors are probably correlated (that two endogenous
> >> regressors are just interaction terms of E)? Does this interaction play a role?
> >>
> >> Someone please help me with the interpretation.
> >>
> >> Best,
> >> Vidhya
> >>
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----- 
Sunday Times Scottish University of the Year 2011-2013
Top in the UK for student experience
Fourth university in the UK and top in Scotland (National Student Survey 2012)

We invite research leaders and ambitious early career researchers to 
join us in leading and driving research in key inter-disciplinary themes. 
Please see www.hw.ac.uk/researchleaders for further information and how
to apply.

Heriot-Watt University is a Scottish charity
registered under charity number SC000278.


*
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