st: RE: Re: About weakiv

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

Tak Wai,

That's interesting.  Maybe try the F-stat version of AR?  You can either calculate it from the reported chi-sq stat, or do the AR test by hand.  If I understand your DGP correctly, the AR test will have an F distribution, so the F-stat version of the test should be properly sized.

--Mark

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of Chau Tak Wai
> Sent: 19 December 2013 14:14
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Re: About weakiv
> 
> Mark,
> 
> I have used the -small- option all the way.
> 
> Thanks,
> Tak Wai
> 
> ========================
> 
> Tak Wai,
> 
> Your simulation is set up with 100 obs.  The AR test has many degrees of
> freedom (you have 15 instruments), and I think you're using the large-
> sample (chi-sq) version of the test stat.
> 
> Maybe AR won't be so oversized if you use a small-sample correction?  You
> could try using the -small- option of -weakiv-, and maybe compare that to
> doing the AR test by hand using an F test.
> 
> HTH,
> Mark
> 
> 
> > Dear Mark and other Statalist users,
> >
> > Thanks a lot for Mark's reply.
> >
> > Indeed my aim is to see how good it performs under heteroscedasticity,
> > and it should be robust even when the DGP is homoscedastic.
> >
> > When I remove the robust option of ivregress before weakiv, the
> > following results are obtained: (I have used rho=0.9 here)
> >
> > clrtest 1000 .082 .274502 0 1
> > artest 1000 .166 .3722668 0 1
> > wtest 1000 .867 .3397446 0 1
> >
> > Wald test is large, but it agrees with 2SLS. It is the case because
> > it's highly overidentified (15 instruments and 1 endo regressor) with
> > average first-stage F of 2.
> >
> > CLR test now looks OK (though a little over rejects) while AR test
> > seriously over-rejects. It looks problematic as these tests are
> > supposed to be robust to weak IV.
> >
> > I haven't checked about condivreg yet.
> >
> > Hope the information helps.
> >
> > Tak Wai
> >
> > P.S. Sorry, since I only subscribe the digest version, I cannot reply
> > the email of the reply directly.
> > ========
> >
> > Tak Wai,
> >
> > Does the issue come up when you don't use the -robust- version?  You
> could double-check in that case against -condivreg-, which will report the CLR
> stat but only for the iid case.
> >
> > If it's specific to -robust-, maybe have a look at the Finlay-Magnusson 2009
> SJ paper cited in the weakiv help file.  They say at one point that:
> >
> > " For linear IV models under homoskedasticity, Andrews, Moreira, and
> > Stock (2007) provide a formula for computing the p-value function of the
> CLR test (which is embedded in the condivreg command). Although this is not
> the correct p-value function when homoskedasticity is violated, our
> simulations indicate that it provides a good approximation."
> >
> > --Mark
> >
> >> Dear Statalisters,
> >>
> >> I have a question about weakiv. I have tried to run some simulations
> >> to understand the performance of CLR test. But in the following code
> >> with
> >> 15 instruments and 1 endogenous regressor, the result seems to be far
> >> from what it should be. I cannot spot the error of my code. So I
> >> would like to ask if it's the problem of my code or a bug in the procedure.
> >>
> >> I may have coded things badly, so advice is welcome!
> >>
> >> Thank you very much in advance!
> >>
> >> The code is as follows:
> >>
> >> capture program drop sim_iv_clr_15
> >> program define sim_iv_clr_15, rclass
> >> version 11
> >> syntax [, obs(integer 100) mu2k(real 3) b(real 1) rho(real 0.5) ]
> >> drop _all set obs `obs'
> >> tempvar y x z1 z2 z3 z4 z5 z6 z7 z8 z9 z10 z11 z12 z13 z14 z15 u gen
> >> `z1' = rnormal(0,1) gen `z2' = rnormal(0,1) gen `z3' = rnormal(0,1)
> >> gen `z4' = rnormal(0,1) gen `z5' = rnormal(0,1) gen `z6' =
> >> rnormal(0,1) gen `z7' = rnormal(0,1) gen `z8' = rnormal(0,1) gen `z9'
> >> = rnormal(0,1) gen `z10' = rnormal(0,1) gen `z11' = rnormal(0,1) gen
> >> `z12' = rnormal(0,1) gen `z13' = rnormal(0,1) gen `z14' =
> >> rnormal(0,1) gen `z15' = rnormal(0,1)
> >>
> >> gen `u' = rnormal(0,1)
> >>
> >> gen `x' =
> >>
> sqrt(`mu2k'/`obs')*(`z1'+`z2'+`z3'+`z4'+`z5'+`z6'+`z7'+`z8'+`z9'+`z10'+`z11'+`z12
> '+`z13'+`z14'+`z15')+`u'
> >> gen `y' = `b'*`x'+(`rho')*`u'+sqrt(1-`rho'^2)*rnormal(0,1)
> >>
> >> local z `z1' `z2' `z3' `z4' `z5' `z6' `z7' `z8' `z9' `z10' `z11' `z12'
> >> `z13' `z14' `z15'
> >> *check first stage
> >> regress `x' `z'
> >> return scalar fsf=e(F)
> >>
> >> ivregress 2sls `y' (`x' = `z'), robust return scalar beta2sls=_b[`x']
> >> return scalar se2sls=_se[`x']
> >>
> >> ivregress liml `y' (`x' = `z'), robust return scalar betaliml=_b[`x']
> >> return scalar seliml=_se[`x']
> >>
> >> ivreg2 `y' (`x'=`z' ), fuller(1) robust return scalar betaf1=_b[`x']
> >> return scalar sef1=_se[`x']
> >>
> >> ** check the related tests at null of true value ivregress 2sls `y'
> >> (`x' = `z'), robust weakiv, null(1.0) small return scalar
> >> clrp=e(clr_p) return scalar arp=e(ar_p) return scalar wp=e(wald_p)
> >>
> >> **test at true value - 0.25
> >> ivregress 2sls `y' (`x' = `z'), robust weakiv, null(0.75) small
> >> return scalar clrpa=e(clr_p) return scalar arpa=e(ar_p) return scalar
> >> wpa=e(wald_p)
> >>
> >> **test at true value +0.25
> >> ivregress 2sls `y' (`x' = `z'), robust weakiv, null(1.25) small
> >> return scalar clrpb=e(clr_p) return scalar arpb=e(ar_p) return scalar
> >> wpb=e(wald_p)
> >>
> >> end
> >>
> >> local betatrue 1.0
> >> local nobs 100
> >> simulate fsf=r(fsf) beta2sls=r(beta2sls) se2sls=r(se2sls) /* */
> >> betaliml=r(betaliml) seliml=r(seliml) betaf1=r(betaf1) sef1=r(sef1)/*
> >> */ clrp=r(clrp) arp=r(arp) wp=r(wp) clrpa=r(clrpa) arpa=r(arpa)
> >> wpa=r(wpa) clrpb=r(clrpb) arpb=r(arpb) wpb=r(wpb), /* */ reps(1000):
> >> sim_iv_clr_15, obs(`nobs') b(`betatrue') mu2k(1.0) rho(0.5)
> >>
> >> **I generate a dummy variable for rejection gen clrtest=(clrp<0.05)
> >> gen artest=(arp<0.05) gen wtest=(wp<0.05)
> >>
> >> The results are then given by
> >> For tests at true value
> >> clrtest | 1000 .253 .4349485 0 1
> >> artest | 1000 .437 .4962633 0 1
> >> -------------+-------------------------------------------------------
> >> -------------+-
> >> wtest | 1000 .355 .4787528 0 1
> >>
> >> For tests at true - 0.25
> >> clrtesta | 1000 .324 .4682342 0 1
> >> -------------+-------------------------------------------------------
> >> -------------+-
> >> artesta | 1000 .49 .5001501 0 1
> >> wtesta | 1000 .797 .4024338 0 1
> >>
> >> For tests at true +0.25
> >> clrtestb | 1000 .351 .4775218 0 1
> >> artestb | 1000 .509 .5001691 0 1
> >> wtestb | 1000 .052 .2221381 0 1
> >>
> >> So at least at the true value it is quite far from the nominal size of 0.05.
> >>
> >> Sincerely,
> >> Tak Wai Chau
> >>
> 
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