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

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

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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