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

[Vidhya Soundararajan <vidhyahere@gmail.com>]

Dear Mark,

I am interested in identifying all three endogenous regressors. I do
want to test if all three are jointly identified. By the usual under
identification and weak identification tests, do you mean the
Kleibergen-Paap rk Wald F statistic (for clustered standard errors)?

Best,
Vidhya

On Tue, Jul 16, 2013 at 5:16 PM, Schaffer, Mark E <M.E.Schaffer@hw.ac.uk> wrote:
> 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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