st: RE: Useful first stage statistics in IV with multiple endogenous regressors

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

Nick,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Nick Sanders
> Sent: Thursday, November 25, 2010 9:00 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Useful first stage statistics in IV with 
> multiple endogenous regressors
> 
> Happy Thanksgiving fellow stataphiles,
> 
> I'm running an IV with two endogenous regressors (x1 and x2) 
> and two instruments (z1 and z2) using xtivreg2. I'd like to 
> report some relevant statistics showing the validity of the 
> instruments from the first stage regression, but I find 
> myself in a bit overwhelmed by the sheer number of tests and 
> results available. I'd appreciate people's thoughts on what 
> they would consider to be the most convincing "strength of 
> instrument" tests to report (let's assume for now that my 
> instruments are justifiably excludable).
> 
> In a single endogenous variable situation, my instinct would 
> be to report the first-stage F stat and start with the 
> "larger than 10" rule, but my reading of Angrist and Pischke 
> is that the Cragg-Donald F-test isn't as informative in a 
> two-endogenous variable world. This makes me consider the 
> reported "F test of excluded instruments" and the 
> "Angrist-Pischke multivariate F test of excluded 
> instruments", provided after each of the x1 and x2 first 
> stage regressions, as alternatives. But which is most 
> relevant in demonstrating instrument strength? Does the 
> "greater than 10" rule apply here as well? Or is there a 
> better statistic to report for demonstrating instrument 
> strength in a world of multiple endogenous regressors? What 
> about for showing the strength of one of the two instruments 
> (say, z1) in particular, beyond reporting the t-stat and the 
> partial r-squared from the first stage regression?

This is tricky, and the answer depends on your application.

Are you interested in *both* your endogenous regressors?  Or is one of
them really the one you're interested in, and the other is just there as
a kind of control but isn't actually of any interest?

If so, then the Angrist-Pischke first-stage F stat for the endogenous
regressor of interest is what you should focus on.

The problem with the Cragg-Donald statistic in the >1 endog regressor
case is that it will indicate whether you have a weak IV problem, but
that could be because of one endog regressor or the other, or even both.
But if you are interested in *both* endogenous regressors, this is
useful for you.

BTW, don't report the "partial R2".  The A-P statistic effectively
replaces it.

Hope this helps.

--Mark

> Thanks very much,
> Nick
>  
> --
> Nicholas J. Sanders, Ph.D.
> Postdoctoral Fellow
> Stanford Institute for Economic Policy Research
> 366 Galvez St, Room 228
> Stanford, CA 94305
> 
> 
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