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RE: st: RE: why F statistics are different forAnderson-Rubin test of joint significance of endogenous regressors?


From   "Jian Zhang" <jzh@ucdavis.edu>
To   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>, statalist@hsphsun2.harvard.edu
Subject   RE: st: RE: why F statistics are different forAnderson-Rubin test of joint significance of endogenous regressors?
Date   Mon, 21 Aug 2006 16:49:46 -0700 (PDT)

Thanks, Mark!  Is F -statistic supposed to equal chi_sqre divided by the number of constraints 
tested asymptotically?  For example, for the robust case (i.e runing regression:ivreg2 lw s expr 
tenure rns smsa _I* (iq=med kww age mrt), ffirst robust),
F_statistic(4, 742)=25.77 Chi_sqre(4)==105.31.  

Are we supposed to have F*4=Chi_Sqre since Chi_sqre(I.e., Wald test) is equal to F*the number of 
constraints tested asymptotically?  However in this case 25.77*4=103.08, which is not equal to 
105.31 although it is close.   Am I missing something here? Many thanks!

Best regards,
Jian Zhang


> Jian Zhang,
> 
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu 
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Jian Zhang
> > Sent: Monday, August 21, 2006 8:12 AM
> > To: statalist@hsphsun2.harvard.edu
> > Subject: st: why F statistics are different forAnderson-Rubin 
> > test of joint significance of endogenous regressors?
> > 
> > Dear Statalisters,
> > 
> > I have been playing the examples provided at the end of the 
> > documentation for ivreg2 using the Griliches data ( can be 
> > obtained at the end of the help file of command ivreg2).  I 
> > found there is a discrepancy of the two F statistics under 
> > the Anderson-Rubin test of joint signficance of endogenous 
> > regressors for the non-robust case and the robust case.  For 
> > example, when I run
> > ivreg2 lw s expr tenure rns smsa _I* (iq=med kww age mrt), 
> > ffirst , the outputs show that Anderson-Rubin test of joint 
> > significance of endogenous regressors B1 in main equation, Ho:B1=0
> > F-statistic=24.33 and Chi_square=98.99.
> > 
> > For the robust case (i.e runing regression:ivreg2 lw s expr 
> > tenure rns smsa _I* (iq=med kww age mrt), ffirst robust),
> > F_statistic=25.77 Chi_squre==105.31.  
> > 
> > Under the two cases, F statistics are different.  It seems to 
> > me that they are supposed be same.
> 
> This question is easy to answer.  They are different because one is
> heteroskedasticity-robust, and one is not.
> 
> Cheers,
> Mark
> 
> Prof. Mark E. Schaffer
> Director
> Centre for Economic Reform and Transformation
> Department of Economics
> School of Management & Languages
> Heriot-Watt University
> Edinburgh EH14 4AS  UK
> 44-131-451-3494 direct
> 44-131-451-3296 fax
> http://www.sml.hw.ac.uk/cert
>  
>    
> > F-statistic is a function of sum of squared 
> > residuals(Unrestricted) and sum of squred residuals 
> > (resitricted).  since the estimates of the coefficients under 
> > both robust and non-robust cases are same, the sum of squared 
> > residuals for both unrestricted and restricted have to be same too.  
> > Thus the F_statistics for both robust and non-robust cases 
> > are supposed to be same.  But Why does STATA report different 
> > F_statistics for Anderson-Rubin test of Joint significance?  Is there 
> > anyone understanding what is going on?    Thank you very much!
> > 
> > 
> > Best regards,
> > Jian Zhang
> > 
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