st: Re: About weakiv

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

Hi, all,

I have updated the program to evaluate the test in a few ways. 1. weakiv
with robust; 2. weakiv without robust; 3. condivreg (no robust); 4. F
stat in AR form with robust. The codes and results are shown below. I
have increased the sample size to 300, and the AR statistic provided by
weakiv with robust seem to over-reject the null relative to other
methods. This may also lead to over-rejection for the CLR test. If there
seems to be a bug in the robust version, hope the following results may
help debugging it.

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 yt
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)

**cross check: without using robust
ivregress 2sls `y' (`x' = `z')
weakiv, null(1.0) small
return scalar clrp2=e(clr_p)
return scalar arp2=e(ar_p)
return scalar wp2=e(wald_p)

** use another ado routine, not robust
condivreg `y' (`x'=`z' ), ar test(1.0)
return scalar clrp3=e(p_LR)
return scalar arp3=e(p_AR)

** test AR using traditional method, robust var
gen `yt'=`y'-`b'*`x'
regress `yt' `z', robust
return scalar arF4=e(F)

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)

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 300
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) clrp2=r(clrp2) arp2=r(arp2)
wp2=r(wp2) clrp3=r(clrp3) arp3=r(arp3) arF4=r(arF4)/*
*/ 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(0.1)

**construct test statistics and results
gen t2sls=(beta2sls-`betatrue')/se2sls
gen tliml=(betaliml-`betatrue')/seliml
gen tf1=(betaf1-`betatrue')/sef1

gen t2slsa=(beta2sls-`betatrue'+0.25)/se2sls
gen tlimla=(betaliml-`betatrue'+0.25)/seliml
gen tf1a=(betaf1-`betatrue'+0.25)/sef1
gen t2slsb=(beta2sls-`betatrue'-0.25)/se2sls
gen tlimlb=(betaliml-`betatrue'-0.25)/seliml
gen tf1b=(betaf1-`betatrue'-0.25)/sef1

gen ttest2sls=(abs(t2sls)>1.96)
gen ttestliml=(abs(tliml)>1.96)
gen ttestf1=(abs(tf1)>1.96)
gen clrtest=(clrp<0.05)
gen artest=(arp<0.05)
gen wtest=(wp<0.05)
gen clrtest2=(clrp2<0.05)
gen artest2=(arp2<0.05)
gen wtest2=(wp2<0.05)
gen clrtest3=(clrp3<0.05)
gen artest3=(arp3<0.05)
gen artest4=(arF4>invFtail(15,`nobs'-16,0.05))

gen ttest2slsa=(abs(t2slsa)>1.96)
gen ttestlimla=(abs(tlimla)>1.96)
gen ttestf1a=(abs(tf1a)>1.96)
gen clrtesta=(clrpa<0.05)
gen artesta=(arpa<0.05)
gen wtesta=(wpa<0.05)

gen ttest2slsb=(abs(t2slsb)>1.96)
gen ttestlimlb=(abs(tlimlb)>1.96)
gen ttestf1b=(abs(tf1b)>1.96)
gen clrtestb=(clrpb<0.05)
gen artestb=(arpb<0.05)
gen wtestb=(wpb<0.05)

su

Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
fsf | 1000 1.989075 .6686453 .5584267 4.559362
beta2sls | 1000 1.046762 .1902355 .400066 1.668987
se2sls | 1000 .1928713 .0385838 .1219964 .4041867
betaliml | 1000 .9003882 2.734562 -78.64992 12.28343
seliml | 1000 211.6659 6518.227 .1293966 206121.8
-------------+--------------------------------------------------------
betaf1 | 1000 1.002532 .4538258 -.7728926 3.102209
sef1 | 1000 .5586889 .7411543 .1270225 5.205231
clrp | 1000 .4279222 .2941029 .0000795 .9686568
arp | 1000 .3841276 .2947135 2.71e-06 .9976762
wp | 1000 .4900556 .2838048 .0016207 .9998908
-------------+--------------------------------------------------------
clrp2 | 1000 .4726739 .2929098 .0007298 .9756876
arp2 | 1000 .4613457 .293643 .0001723 .9985789
wp2 | 1000 .4919608 .2827918 .0009518 .9998832
clrp3 | 1000 .4931547 .2886754 .0013392 .9787179
arp3 | 1000 .5050222 .2926132 .0004048 .9989961
-------------+--------------------------------------------------------
arF4 | 1000 1.126271 .4503785 .2536111 3.402767
clrpa | 1000 .3805249 .3046617 1.62e-06 .9678711
arpa | 1000 .3481354 .290572 8.98e-07 .9931965
wpa | 1000 .2324543 .2744134 1.10e-06 .9984452
clrpb | 1000 .371495 .3055804 2.81e-06 .959181
-------------+--------------------------------------------------------
arpb | 1000 .3407169 .2877087 1.78e-06 .9990297
wpb | 1000 .348814 .3055344 .0000736 .9968536
t2sls | 1000 .2679759 .9578728 -2.616042 3.152151
tliml | 1000 .0361009 .8693161 -2.454555 2.892277
tf1 | 1000 .0512138 .8852093 -2.484029 2.921904
-------------+--------------------------------------------------------
t2slsa | 1000 1.611938 1.021119 -1.267857 4.872668
tlimla | 1000 .7455774 .9830085 -1.574504 4.198492
tf1a | 1000 .8109588 .9943123 -1.550451 4.269866
t2slsb | 1000 -1.075986 .9566182 -3.964227 1.77621
tlimlb | 1000 -.6733755 .9044783 -3.64242 1.739805
-------------+--------------------------------------------------------
tf1b | 1000 -.7085311 .9179014 -3.680793 1.75169
ttest2sls | 1000 .043 .2029586 0 1
ttestliml | 1000 .016 .1255379 0 1
ttestf1 | 1000 .018 .1330176 0 1
clrtest | 1000 .11 .3130463 0 1
-------------+--------------------------------------------------------
artest | 1000 .144 .3512654 0 1
wtest | 1000 .043 .2029586 0 1
clrtest2 | 1000 .063 .2430845 0 1
artest2 | 1000 .077 .2667248 0 1
wtest2 | 1000 .042 .2006895 0 1
-------------+--------------------------------------------------------
clrtest3 | 1000 .051 .2201078 0 1
artest3 | 1000 .062 .2412762 0 1
artest4 | 1000 .11 .3130463 0 1
ttest2slsa | 1000 .385 .4868388 0 1
ttestlimla | 1000 .13 .3364717 0 1
-------------+--------------------------------------------------------
ttestf1a | 1000 .143 .350248 0 1
clrtesta | 1000 .186 .3893014 0 1
artesta | 1000 .183 .38686 0 1
wtesta | 1000 .385 .4868388 0 1
ttest2slsb | 1000 .18 .3843797 0 1
-------------+--------------------------------------------------------
ttestlimlb | 1000 .074 .2619019 0 1
ttestf1b | 1000 .086 .2805043 0 1
clrtestb | 1000 .175 .3801572 0 1
artestb | 1000 .192 .3940702 0 1
wtestb | 1000 .18 .3843797 0 1

******* rho=0.5
clear
local betatrue 1.0
local nobs 300
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) clrp2=r(clrp2) arp2=r(arp2)
wp2=r(wp2) clrp3=r(clrp3) arp3=r(arp3) arF4=r(arF4)/*
*/ 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)

. su

Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
fsf | 1000 2.024847 .6701931 .5740368 4.831673
beta2sls | 1000 1.24525 .1796135 .5240726 1.854688
se2sls | 1000 .173738 .0368764 .0928082 .3488971
betaliml | 1000 .0126125 28.26287 -889.5311 26.34858
seliml | 1000 327270.1 1.03e+07 .1150639 3.26e+08
-------------+--------------------------------------------------------
betaf1 | 1000 1.027248 .4093937 -.7209634 3.021829
sef1 | 1000 .5349395 .7022094 .112703 5.234337
clrp | 1000 .4391295 .3053888 .0000104 .9532101
arp | 1000 .3849927 .2981145 1.01e-06 .9954741
wp | 1000 .2573638 .2911204 2.16e-07 .9941927
-------------+--------------------------------------------------------
clrp2 | 1000 .4766389 .2989577 .0000587 .9668206
arp2 | 1000 .4532889 .2976167 .0002123 .9987825
wp2 | 1000 .2582972 .2911485 7.71e-07 .9941952
clrp3 | 1000 .4940738 .2948846 .0001081 .9697951
arp3 | 1000 .4964008 .2963669 .0004908 .9991418
-------------+--------------------------------------------------------
arF4 | 1000 1.131203 .4643455 .2852084 3.564459
clrpa | 1000 .3813428 .3045638 7.62e-07 .9599406
arpa | 1000 .3544708 .2948629 1.44e-07 .9985713
wpa | 1000 .0615626 .1487517 2.36e-13 .989473
clrpb | 1000 .3573862 .3093374 5.02e-06 .9679686
-------------+--------------------------------------------------------
arpb | 1000 .3306423 .2857347 .0000268 .9998677
wpb | 1000 .4925148 .2864962 .0006367 .9990597
t2sls | 1000 1.543295 1.139573 -1.653001 5.184616
tliml | 1000 .2409014 .9227463 -1.751008 4.002587
tf1 | 1000 .3212997 .944274 -1.7258 4.053029
-------------+--------------------------------------------------------
t2slsa | 1000 3.042114 1.331998 -.7846958 7.326546
tlimla | 1000 .9852943 1.196789 -1.067041 5.599939
tf1a | 1000 1.123272 1.21262 -.9787121 5.766745
t2slsb | 1000 .0444763 .9989699 -2.660775 3.415459
tlimlb | 1000 -.5034916 .774259 -2.587835 2.566712
-------------+--------------------------------------------------------
tf1b | 1000 -.480673 .795856 -2.611754 2.672471
ttest2sls | 1000 .355 .4787528 0 1
ttestliml | 1000 .051 .2201078 0 1
ttestf1 | 1000 .06 .2376057 0 1
clrtest | 1000 .117 .3215811 0 1
-------------+--------------------------------------------------------
artest | 1000 .156 .3630369 0 1
wtest | 1000 .355 .4787528 0 1
clrtest2 | 1000 .069 .253581 0 1
artest2 | 1000 .09 .286325 0 1
wtest2 | 1000 .349 .4768925 0 1
-------------+--------------------------------------------------------
clrtest3 | 1000 .061 .2394501 0 1
artest3 | 1000 .07 .2552747 0 1
artest4 | 1000 .111 .3142893 0 1
ttest2slsa | 1000 .776 .4171307 0 1
ttestlimla | 1000 .21 .407512 0 1
-------------+--------------------------------------------------------
ttestf1a | 1000 .238 .4260722 0 1
clrtesta | 1000 .169 .3749394 0 1
artesta | 1000 .186 .3893014 0 1
wtesta | 1000 .776 .4171307 0 1
ttest2slsb | 1000 .039 .1936918 0 1
-------------+--------------------------------------------------------
ttestlimlb | 1000 .025 .1562031 0 1
ttestf1b | 1000 .024 .1531256 0 1
clrtestb | 1000 .211 .4082225 0 1
artestb | 1000 .202 .4016931 0 1
wtestb | 1000 .039 .1936918 0 1

****rho=0.9
clear
local betatrue 1.0
local nobs 300
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) clrp2=r(clrp2) arp2=r(arp2)
wp2=r(wp2) clrp3=r(clrp3) arp3=r(arp3) arF4=r(arF4)/*
*/ 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(0.9)

. su

Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
fsf | 1000 2.035955 .6604241 .5463604 4.59914
beta2sls | 1000 1.44179 .1285521 .8505121 1.867863
se2sls | 1000 .1227545 .0347788 .0621307 .3481258
betaliml | 1000 .8520995 1.848659 -55.81694 1.520073
seliml | 1000 25.93037 796.7733 .0845153 25196.78
-------------+--------------------------------------------------------
betaf1 | 1000 1.015304 .2662472 -.1234837 1.540497
sef1 | 1000 .4551579 .4818527 .0820186 5.84322
clrp | 1000 .4620662 .3026814 .0000137 .9511231
arp | 1000 .36521 .295989 .000068 .9998782
wp | 1000 .0355579 .1137253 6.65e-23 .9456689
-------------+--------------------------------------------------------
clrp2 | 1000 .4868896 .292084 .0000111 .9511231
arp2 | 1000 .434738 .2942256 .0005332 .9998143
wp2 | 1000 .0357715 .1145948 2.53e-23 .9488348
clrp3 | 1000 .4978822 .2895032 .0000214 .9511233
arp3 | 1000 .4782224 .2936219 .0011465 .999872
-------------+--------------------------------------------------------
arF4 | 1000 1.150363 .4478659 .1567113 2.860618
clrpa | 1000 .3932872 .3109746 9.55e-06 .9511231
arpa | 1000 .3379416 .2926447 .0000178 .9940948
wpa | 1000 .0049185 .0369914 0 .7727929
clrpb | 1000 .2994276 .2921822 7.49e-08 .9511231
-------------+--------------------------------------------------------
arpb | 1000 .3025138 .2795973 3.27e-06 .9998758
wpb | 1000 .2321103 .2962862 7.16e-11 .9958413
t2sls | 1000 4.047884 1.867733 -.4294076 9.853053
tliml | 1000 .2971751 .9116821 -.9958801 5.948726
tf1 | 1000 .4617053 .9595486 -1.005183 6.221221
-------------+--------------------------------------------------------
t2slsa | 1000 6.224931 2.370604 .2887236 13.48693
tlimla | 1000 1.064115 1.350182 -.7798916 8.906771
tf1a | 1000 1.313411 1.403974 -.7144105 9.269311
t2slsb | 1000 1.870836 1.388323 -1.147539 6.517281
tlimlb | 1000 -.4697649 .5260411 -1.484372 2.990681
-------------+--------------------------------------------------------
tf1b | 1000 -.3900002 .56222 -1.423636 3.173131
ttest2sls | 1000 .859 .3481957 0 1
ttestliml | 1000 .068 .2518719 0 1
ttestf1 | 1000 .091 .287753 0 1
clrtest | 1000 .098 .2974634 0 1
-------------+--------------------------------------------------------
artest | 1000 .162 .3686352 0 1
wtest | 1000 .859 .3481957 0 1
clrtest2 | 1000 .059 .2357426 0 1
artest2 | 1000 .091 .287753 0 1
wtest2 | 1000 .864 .3429601 0 1
-------------+--------------------------------------------------------
clrtest3 | 1000 .048 .2138732 0 1
artest3 | 1000 .066 .2484063 0 1
artest4 | 1000 .121 .3262905 0 1
ttest2slsa | 1000 .977 .1499783 0 1
ttestlimla | 1000 .198 .3986916 0 1
-------------+--------------------------------------------------------
ttestf1a | 1000 .256 .4366402 0 1
clrtesta | 1000 .157 .3639828 0 1
artesta | 1000 .189 .3917045 0 1
wtesta | 1000 .977 .1499783 0 1
ttest2slsb | 1000 .448 .4975375 0 1
-------------+--------------------------------------------------------
ttestlimlb | 1000 .002 .044699 0 1
ttestf1b | 1000 .003 .0547174 0 1
clrtestb | 1000 .256 .4366402 0 1
artestb | 1000 .23 .4210431 0 1
wtestb | 1000 .448 .4975375 0 1

Best,
Tak Wai Chau
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