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


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: why F statistics are different forAnderson-Rubin test of joint significance of endogenous regressors?
Date   Mon, 21 Aug 2006 09:17:36 +0100

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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