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

 From "Jian Zhang" To statalist@hsphsun2.harvard.edu Subject st: why F statistics are different forAnderson-Rubin test of joint significance of endogenous regressors? Date Mon, 21 Aug 2006 00:11:31 -0700 (PDT)

```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.
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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