RE: st: Validity of ivreg2-tests for underidentification and weak instruments if errors are not i.i.d. etc.

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

Anne,

> -----Original Message-----
> From: Anne Tausch [mailto:anne.tausch@googlemail.com] 
> Sent: 10 February 2012 17:49
> To: statalist@hsphsun2.harvard.edu
> Cc: Schaffer, Mark E; baum@bc.edu; Steven Stillman
> Subject: Validity of ivreg2-tests for underidentification and 
> weak instruments if errors are not i.i.d. etc.
> 
> Dear Mark Schaffer, hello everybody,
> 
> I really appreciate your willingness to answer my questions 
> regarding the tests for underidentification/weak instruments 
> that are implemented in ivreg2. My questions are about the 
> validity of certain tests in particular circumstances and are 
> stated below.
> 
> Unfortunately, I wasn't able to find the answers in the 
> articles of you, Christopher Baum and Steven Stillman (or elsewhere).
> 
> Many thanks and best wishes
> 
> Anne
> 
> My questions are:
> 
> 1. Is the chi-square test of Angrist and Pischke valid in the 
> presence of heteroskedasticity and autocorrelation?

Yes.  I'm assuming you're asking -ivreg2- to report HAC or cluster-robust stats.  The A-P test stat will also be HAC or cluster-robust.

> And what 
> about Shea's partial r-square? Is that valid in the case of 
> non i.i.d errors?

Actually, Shea's partial r-square isn't really valid even in the iid case and doesn't have a distribution that allows you to use it for formal testing.  If you really want an R-sq, you're better off using the A-P version.  You can get the A-P R-sq after an -ivreg2- estimation from the saved matrix e(first).

> 
> 2. In the case of multiple endogenous regressors, the Angrist 
> and Pischke F statistic can be used to asses whether a 
> particular endogenous regressor is weakly identified by 
> comparing the empirical value to the critical values of Stock 
> and Yogo. Is this test still valid in the presence of
> heteroskedasticity and autocorrelation?

Sort of.  It's as valid for assessing weak identification as the HAC-robust F statistic in the 1-endogenous-regressor case, which is to say, "sort of valid".  The weak identification test critical values that Stock and Yogo worked out are for the iid case only, and so using a HAC-robust, or heteteroskedasticity-robust, or cluster-robust test stat with these critical values has only an informal justification.  (As in: "It's the best we can do for now".)

> 3. If one has just one endogenous regressor and just one 
> excluded instrument variable: Can one still use the rule of 
> thumb that F should be greater than 10? Oder does that rule 
> only make sense when one has more than one excluded instrument?

The Staiger-Stock (1997, Econometrica) rule of thumb of "F>=10" applies in this case too.

HTH,
Mark


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