st: About weakiv

[Chau Tak Wai <chau.takwai@gmail.com>]

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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