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RE: st: RE: why F statistics are different forAnderson-Rubin test of joint significance of endogenous regressors?
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!
> Jian Zhang,
> > -----Original Message-----
> > From: email@example.com
> > [mailto:firstname.lastname@example.org] On Behalf Of Jian Zhang
> > Sent: Monday, August 21, 2006 8:12 AM
> > To: email@example.com
> > 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.
> Prof. Mark E. Schaffer
> 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
> > 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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