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st: RE: cragg-donal test for weak instruments with heteroskedasticity

From   "Schaffer, Mark E" <>
To   <>
Subject   st: RE: cragg-donal test for weak instruments with heteroskedasticity
Date   Fri, 25 Jul 2008 14:28:50 +0100


> -----Original Message-----
> From: 
> [] On Behalf Of 
> sara borelli
> Sent: Friday, July 25, 2008 1:57 PM
> To:
> Subject: st: cragg-donal test for weak instruments with 
> heteroskedasticity
> Dear All,
> I a estimating the following model:
> Y= aX + bY1 + cY2 + u
> I am using standard errors robust and clustered at the 
> neighborhood level;
> X = vector of eogenous regressors
> Y1, Y2  are endogenous
> Z1 Z2 excluded instruments
> I want to test weather my IVs are non-weak. I know that in 
> the case of a single endogenous variable I should use the 
> "rule of thumb" that the first stage F-statistic >10 (Steiger 
> and Stock 1997).
> But Stock and Yogo (2002) say to use the Cragg -Donald 
> Statistics in presence of multiple endogenous regressors. I 
> know this statistics is not valid under heteroskedasticity. I 
> would like to know if there is a way to compute a robust 
> analog of the Cragg-Donal statistics in Stata

The Cragg-Donald statistic is a test statistic for the rank of a matrix.
Anderson (1951) derived an earlier and similar test based on canonical

-ivreg2-, downloadable from ssc-ideas in the usual way, reports a
generalization of these to the case of heteroskedastic and/or
autocorrelated errors, due to Kleibergen and Paap.  The K-P stat reduces
to C-D and Anderson tests in the iid case.

The K-P stat is implemented in Stata by -ranktest-, so you'll need to
install this as well.

> and in case if 
> it would still be valid to compare it to the tabulated values 
> of Stock and Yogo(2002). Alternatively, would be wrong to 
> simply refer to the old "rule of tumb" that the F-statistics 
> should be at least 10, even in presence of multiple 
> endogenous variables? 

As far as I know, critical values have not been tabulated for non-iid
case (and it would be hard to, since the form of
heteroskedasticity/autocorrelation will make a difference to how they

Either of your suggestions seems sensible to me.

Mark (coauthor of -ivreg2- and -ranktest-)

Prof. Mark E. Schaffer
Department of Economics
School of Management & Languages
Heriot-Watt University
Edinburgh EH14 4AS  UK
44-131-451-3494 direct
44-131-451-3296 fax

> Thank you for any help
> Sara Borelli
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