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st: Re: About weakiv


From   Chau Tak Wai <chau.takwai@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: About weakiv
Date   Thu, 19 Dec 2013 20:50:08 +0800

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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