st: RE: Interpreting Kleibergen Paap weak instrument statistic

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

James,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Fitzgerald, James
> Sent: 21 June 2012 14:02
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Interpreting Kleibergen Paap weak instrument statistic
> 
> Hi Statalist users
> 
> I am using xtivreg2 to estimate a GMM-IV model (I specify the 
> following options; fe robust bw(2) gmm2s). I am not assuming 
> i.i.d errors, and thus when testing for weak instruments I am 
> using the Kleibergen Paap rk wald F statistic rather than the 
> Cragg Donald wald F statistic.
> 
> xtivreg2 produces Stock-Yogo critical values for the Cragg 
> Donald statistic assuming i.i.d errors, so I'm not sure how 
> to interpret the KP rk wald F stat. 
> 
> The help file for ivreg2 (Baum, Schaffer and Stillman, 2010) 
> does however mention the following: 
> 
> When the i.i.d. assumption is dropped and ivreg2 is invoked 
> with the robust, bw or cluster options, the 
> Cragg-Donald-based weak instruments test is no longer valid.  
> ivreg2 instead reports a correspondingly-robust 
> Kleibergen-Paap Wald rk F statistic.  The degrees of freedom 
> adjustment for the rk statistic is (N-L)/L1, as with the 
> Cragg-Donald F statistic, except in the cluster-robust case, 
> when the adjustment is N/(N-1) * (N_clust-1)/N_clust, 
> following the standard Stata small-sample adjustment for 
> cluster-robust. In the case of two-way clustering, N_clust is 
> the minimum of N_clust1 and N_clust2.  The critical values 
> reported by ivreg2 for the Kleibergen-Paap statistic are the 
> Stock-Yogo critical values for the Cragg-Donald i.i.d. case.  
> The critical values reported with 2-step GMM are the 
> Stock-Yogo IV critical values, and the critical values 
> reported with CUE are the LIML critical values.
> 
> 
> My understanding of the end of the paragraph is that the KP 
> stat can still be compared to the Stock-Yogo values produced 
> by STATA in determining whether or not instruments are weak.
> 
> If someone could confirm or reject this I would be eternally 
> grateful!!

I wrote that paragraph, so the ambiguity is partly my fault.  But the
problem is that there are no concrete results in the literature for
testing for weak IVs when the i.i.d. assumption fails.  The only thing
one can do (that I'm aware of, anyway) is to point to stats that have an
asymptotic justification in a test of underidentification, which is what
the output of -ivreg2- does.  That is, the K-P stat can be used to test
for underidentification without the i.i.d. assumption, and under i.i.d.
it has the same distribution under the null as the Cragg-Donald stat.
This justification is different from that underlying the Stock-Yogo
critical values, so this is pretty hand-wavey.

The alternative is weak-instrument-robust estimation, a la
Anderson-Rubin, Moreira, Kleibergen, etc.  The Finlay-Magnusson
-rivtest- command, available via ssc ideas in the usual way, supports
this.  Also see their accompanying SJ paper (vol. 9 no. 3).  The command
doesn't directly support panel data estimation, which is what you have,
but you could just demean your variables by hand.

HTH,
Mark


> Best wishes
> 
> James Fitzgerald
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