st: RE: C statistics with IVREG2

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Rosaria,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of Rosaria Vega Pansini
> Sent: 16 December 2013 17:12
> To: statalist@hsphsun2.harvard.edu
> Subject: st: C statistics with IVREG2
> 
> Hi all,
> I'm trying to compare two IV models with different instruments, one of
> them suspected endogenous.
> We compared Sargan stats calcultated over the two models: the first
> with the full set of instruments and the second excluding the
> suspected endogenous instrument.
> The results appears to be different to those obtained  including the
> orthog  option in IVREG2 command.
> 
> As an example, here are the two models we are comparing;
> 
> Model 1:
> ivreg2 hours educ  age kidslt6 kidsge6 nwifeinc (lwage=exper expersq
> motheduc)
> Sargan statistic (overidentification test of all instruments): 3.716
> 
> Model 2:
> ivreg2 hours educ  age kidslt6 kidsge6 nwifeinc,gmm (lwage=exper expersq)
> Sargan statistic (overidentification test of all instruments): 0.858
> J1-J2= 2.858
> 
> Model 3:
> ivreg2 hours educ  age kidslt6 kidsge6 nwifeinc  (lwage=exper
> expersq motheduc), orthog(motheduc)
> 
> C statistic (exogeneity/orthogonality of suspect instruments): 2.625
> 
> Can anyone help in explaining this difference, i.e. the difference
> between the C-statistics (model 3) and the (simple) difference between
> the two Sargan statistics (Model 1 - Model 2)?

The explanation is buried deep in the -ivreg2- help file:

"To guarantee that the C statistic is non-negative in finite samples, the estimated covariance matrix of the full set orthogonality conditions is used to calculate both Sargan-Hansen statistics (in the case of simple IV/2SLS, this amounts to using the MSE from the unrestricted equation to calculate both Sargan statistics). ... For further discussion, see Hayashi (2000), pp. 218-22 and pp. 232-34."

If you do it by hand using the difference between the two Sargan stats, as you did, you aren't guaranteed to get a non-neg stat in finite samples.

For another illustration of this trick, have a look at the sigmamore and sigmaless options of the -hausman- command.

HTH,
Mark



> 
> Thank you very much for your help
> Rosaria
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