-------------------------------------------------------------------------------------------
log: /Users/baum/doc/Stata/USUG_2007/baumUKSUG2007smcltalk/ivsmcltalk.smcl
log type: smcl
opened on: 4 Feb 2008, 08:58:09
. *** OLS vs IV estimates
. use griliches76.dta
(Wages of Very Young Men, Zvi Griliches, J.Pol.Ec. 1976)
. xi i.year
i.year _Iyear_66-73 (naturally coded; _Iyear_66 omitted)
. eststo clear
. eststo:regress lw iq s expr tenure
Source | SS df MS Number of obs = 758
-------------+------------------------------ F( 4, 753) = 92.70
Model | 45.9575602 4 11.48939 Prob > F = 0.0000
Residual | 93.3285897 753 .12394235 R-squared = 0.3300
-------------+------------------------------ Adj R-squared = 0.3264
Total | 139.28615 757 .183997556 Root MSE = .35205
------------------------------------------------------------------------------
lw | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | .0038838 .0010984 3.54 0.000 .0017275 .0060402
s | .0947161 .0067992 13.93 0.000 .0813685 .1080638
expr | .0390324 .0064421 6.06 0.000 .0263857 .0516791
tenure | .0362904 .0078746 4.61 0.000 .0208317 .0517491
_cons | 3.879516 .1087541 35.67 0.000 3.666019 4.093013
------------------------------------------------------------------------------
(est1 stored)
. eststo:ivreg2 lw s expr tenure (iq=med)
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics consistent for homoskedasticity only
Number of obs = 758
F( 4, 753) = 65.77
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = 0.0752
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9948
Residual SS = 128.8078366 Root MSE = .4122
------------------------------------------------------------------------------
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | .0224682 .0119996 1.87 0.061 -.0010505 .0459869
s | .0377993 .0373956 1.01 0.312 -.0354948 .1110934
expr | .0460304 .0087797 5.24 0.000 .0288226 .0632383
tenure | .0275642 .0107888 2.55 0.011 .0064185 .0487099
_cons | 2.716219 .7575702 3.59 0.000 1.231409 4.201029
------------------------------------------------------------------------------
Underidentification test (Anderson canon. corr. LM statistic): 8.708
Chi-sq(1) P-val = 0.0032
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 8.751
Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38
15% maximal IV size 8.96
20% maximal IV size 6.66
25% maximal IV size 5.53
Source: Stock-Yogo (2005). Reproduced by permission.
------------------------------------------------------------------------------
Sargan statistic (overidentification test of all instruments): 0.000
(equation exactly identified)
------------------------------------------------------------------------------
Instrumented: iq
Included instruments: s expr tenure
Excluded instruments: med
------------------------------------------------------------------------------
(est2 stored)
. esttab, label stat(rmse) mtitles(OLS IV) nonum
----------------------------------------------------
OLS IV
----------------------------------------------------
iq score 0.00388*** 0.0225
(3.54) (1.87)
completed years of~g 0.0947*** 0.0378
(13.93) (1.01)
experience, years 0.0390*** 0.0460***
(6.06) (5.24)
tenure, years 0.0363*** 0.0276*
(4.61) (2.55)
Constant 3.880*** 2.716***
(35.67) (3.59)
----------------------------------------------------
rmse 0.352 0.412
----------------------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. *** IV, IV (robust) vs IV-GMM estimates
. eststo clear
. eststo:ivreg2 lw s expr tenure (iq=med kww age)
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics consistent for homoskedasticity only
Number of obs = 758
F( 4, 753) = 82.57
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = 0.2706
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9959
Residual SS = 101.5955325 Root MSE = .3661
------------------------------------------------------------------------------
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | -.005087 .0047901 -1.06 0.288 -.0144754 .0043014
s | .1221904 .0159051 7.68 0.000 .091017 .1533638
expr | .0356544 .0069244 5.15 0.000 .0220827 .049226
tenure | .0405027 .0084751 4.78 0.000 .0238918 .0571136
_cons | 4.44105 .3123805 14.22 0.000 3.828796 5.053304
------------------------------------------------------------------------------
Underidentification test (Anderson canon. corr. LM statistic): 43.103
Chi-sq(3) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 15.093
Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 13.91
10% maximal IV relative bias 9.08
20% maximal IV relative bias 6.46
30% maximal IV relative bias 5.39
10% maximal IV size 22.30
15% maximal IV size 12.83
20% maximal IV size 9.54
25% maximal IV size 7.80
Source: Stock-Yogo (2005). Reproduced by permission.
------------------------------------------------------------------------------
Sargan statistic (overidentification test of all instruments): 62.791
Chi-sq(2) P-val = 0.0000
------------------------------------------------------------------------------
Instrumented: iq
Included instruments: s expr tenure
Excluded instruments: med kww age
------------------------------------------------------------------------------
(est1 stored)
. eststo:ivreg2 lw s expr tenure (iq=med kww age), robust
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity
Number of obs = 758
F( 4, 753) = 79.80
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = 0.2706
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9959
Residual SS = 101.5955325 Root MSE = .3661
------------------------------------------------------------------------------
| Robust
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | -.005087 .0050608 -1.01 0.315 -.0150061 .004832
s | .1221904 .0162798 7.51 0.000 .0902826 .1540982
expr | .0356544 .0069916 5.10 0.000 .0219512 .0493576
tenure | .0405027 .0089728 4.51 0.000 .0229164 .058089
_cons | 4.44105 .3362515 13.21 0.000 3.782009 5.100091
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 36.930
Chi-sq(3) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Kleibergen-Paap rk Wald F statistic): 14.369
Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 13.91
10% maximal IV relative bias 9.08
20% maximal IV relative bias 6.46
30% maximal IV relative bias 5.39
10% maximal IV size 22.30
15% maximal IV size 12.83
20% maximal IV size 9.54
25% maximal IV size 7.80
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 49.842
Chi-sq(2) P-val = 0.0000
------------------------------------------------------------------------------
Instrumented: iq
Included instruments: s expr tenure
Excluded instruments: med kww age
------------------------------------------------------------------------------
(est2 stored)
. eststo:ivreg2 lw s expr tenure (iq=med kww age), gmm2s robust
2-Step GMM estimation
---------------------
Estimates efficient for arbitrary heteroskedasticity
Statistics robust to heteroskedasticity
Number of obs = 758
F( 4, 753) = 83.09
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = 0.2458
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9957
Residual SS = 105.0480035 Root MSE = .3723
------------------------------------------------------------------------------
| Robust
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | -.0067642 .005053 -1.34 0.181 -.016668 .0031395
s | .1279205 .0162386 7.88 0.000 .0960935 .1597475
expr | .0367674 .0069872 5.26 0.000 .0230729 .050462
tenure | .0442816 .0089293 4.96 0.000 .0267805 .0617828
_cons | 4.522535 .3360249 13.46 0.000 3.863939 5.181132
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 36.930
Chi-sq(3) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Kleibergen-Paap rk Wald F statistic): 14.369
Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 13.91
10% maximal IV relative bias 9.08
20% maximal IV relative bias 6.46
30% maximal IV relative bias 5.39
10% maximal IV size 22.30
15% maximal IV size 12.83
20% maximal IV size 9.54
25% maximal IV size 7.80
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 49.842
Chi-sq(2) P-val = 0.0000
------------------------------------------------------------------------------
Instrumented: iq
Included instruments: s expr tenure
Excluded instruments: med kww age
------------------------------------------------------------------------------
(est3 stored)
. esttab, label stat(rmse) mtitles(IV IVrob IVGMMrob) nonum
--------------------------------------------------------------------
IV IVrob IVGMMrob
--------------------------------------------------------------------
iq score -0.00509 -0.00509 -0.00676
(-1.06) (-1.01) (-1.34)
completed years of~g 0.122*** 0.122*** 0.128***
(7.68) (7.51) (7.88)
experience, years 0.0357*** 0.0357*** 0.0368***
(5.15) (5.10) (5.26)
tenure, years 0.0405*** 0.0405*** 0.0443***
(4.78) (4.51) (4.96)
Constant 4.441*** 4.441*** 4.523***
(14.22) (13.21) (13.46)
--------------------------------------------------------------------
rmse 0.366 0.366 0.372
--------------------------------------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. *** Tests of overidentifying restrictions
. eststo clear
. eststo:ivreg2 lw s expr tenure (iq=med kww age), gmm2s robust
2-Step GMM estimation
---------------------
Estimates efficient for arbitrary heteroskedasticity
Statistics robust to heteroskedasticity
Number of obs = 758
F( 4, 753) = 83.09
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = 0.2458
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9957
Residual SS = 105.0480035 Root MSE = .3723
------------------------------------------------------------------------------
| Robust
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | -.0067642 .005053 -1.34 0.181 -.016668 .0031395
s | .1279205 .0162386 7.88 0.000 .0960935 .1597475
expr | .0367674 .0069872 5.26 0.000 .0230729 .050462
tenure | .0442816 .0089293 4.96 0.000 .0267805 .0617828
_cons | 4.522535 .3360249 13.46 0.000 3.863939 5.181132
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 36.930
Chi-sq(3) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Kleibergen-Paap rk Wald F statistic): 14.369
Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 13.91
10% maximal IV relative bias 9.08
20% maximal IV relative bias 6.46
30% maximal IV relative bias 5.39
10% maximal IV size 22.30
15% maximal IV size 12.83
20% maximal IV size 9.54
25% maximal IV size 7.80
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 49.842
Chi-sq(2) P-val = 0.0000
------------------------------------------------------------------------------
Instrumented: iq
Included instruments: s expr tenure
Excluded instruments: med kww age
------------------------------------------------------------------------------
(est1 stored)
. eststo:ivreg2 lw s expr tenure (iq=med kww), gmm2s robust
2-Step GMM estimation
---------------------
Estimates efficient for arbitrary heteroskedasticity
Statistics robust to heteroskedasticity
Number of obs = 758
F( 4, 753) = 73.34
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = 0.1813
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9954
Residual SS = 114.029907 Root MSE = .3879
------------------------------------------------------------------------------
| Robust
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | .0180792 .0060816 2.97 0.003 .0061595 .0299988
s | .0513881 .0195616 2.63 0.009 .013048 .0897281
expr | .0439692 .0078796 5.58 0.000 .0285254 .059413
tenure | .0302889 .0087102 3.48 0.001 .0132173 .0473606
_cons | 2.988533 .3944466 7.58 0.000 2.215432 3.761634
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 26.252
Chi-sq(2) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Kleibergen-Paap rk Wald F statistic): 14.892
Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93
15% maximal IV size 11.59
20% maximal IV size 8.75
25% maximal IV size 7.25
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 0.282
Chi-sq(1) P-val = 0.5955
------------------------------------------------------------------------------
Instrumented: iq
Included instruments: s expr tenure
Excluded instruments: med kww
------------------------------------------------------------------------------
(est2 stored)
. esttab, label stat(j jdf jp) mtitles(age no_age) nonum
----------------------------------------------------
age no_age
----------------------------------------------------
iq score -0.00676 0.0181**
(-1.34) (2.97)
completed years of~g 0.128*** 0.0514**
(7.88) (2.63)
experience, years 0.0368*** 0.0440***
(5.26) (5.58)
tenure, years 0.0443*** 0.0303***
(4.96) (3.48)
Constant 4.523*** 2.989***
(13.46) (7.58)
----------------------------------------------------
j 49.84 0.282
jdf 2 1
jp 1.50e-11 0.595
----------------------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. *** C (GMM distance) test of a subset of overidentifying restrictions
. ivreg2 lw s expr tenure (iq=med kww age), gmm2s robust orthog(age)
2-Step GMM estimation
---------------------
Estimates efficient for arbitrary heteroskedasticity
Statistics robust to heteroskedasticity
Number of obs = 758
F( 4, 753) = 83.09
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = 0.2458
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9957
Residual SS = 105.0480035 Root MSE = .3723
------------------------------------------------------------------------------
| Robust
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | -.0067642 .005053 -1.34 0.181 -.016668 .0031395
s | .1279205 .0162386 7.88 0.000 .0960935 .1597475
expr | .0367674 .0069872 5.26 0.000 .0230729 .050462
tenure | .0442816 .0089293 4.96 0.000 .0267805 .0617828
_cons | 4.522535 .3360249 13.46 0.000 3.863939 5.181132
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 36.930
Chi-sq(3) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Kleibergen-Paap rk Wald F statistic): 14.369
Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 13.91
10% maximal IV relative bias 9.08
20% maximal IV relative bias 6.46
30% maximal IV relative bias 5.39
10% maximal IV size 22.30
15% maximal IV size 12.83
20% maximal IV size 9.54
25% maximal IV size 7.80
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 49.842
Chi-sq(2) P-val = 0.0000
-orthog- option:
Hansen J statistic (eqn. excluding suspect orthog. conditions): 0.275
Chi-sq(1) P-val = 0.6003
C statistic (exogeneity/orthogonality of suspect instruments): 49.567
Chi-sq(1) P-val = 0.0000
Instruments tested: age
------------------------------------------------------------------------------
Instrumented: iq
Included instruments: s expr tenure
Excluded instruments: med kww age
------------------------------------------------------------------------------
. *** C (GMM distance) test of endogeneity of a regressor
. ivreg2 lw s expr tenure (iq=med kww), gmm2s robust endog(iq)
2-Step GMM estimation
---------------------
Estimates efficient for arbitrary heteroskedasticity
Statistics robust to heteroskedasticity
Number of obs = 758
F( 4, 753) = 73.34
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = 0.1813
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9954
Residual SS = 114.029907 Root MSE = .3879
------------------------------------------------------------------------------
| Robust
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | .0180792 .0060816 2.97 0.003 .0061595 .0299988
s | .0513881 .0195616 2.63 0.009 .013048 .0897281
expr | .0439692 .0078796 5.58 0.000 .0285254 .059413
tenure | .0302889 .0087102 3.48 0.001 .0132173 .0473606
_cons | 2.988533 .3944466 7.58 0.000 2.215432 3.761634
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 26.252
Chi-sq(2) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Kleibergen-Paap rk Wald F statistic): 14.892
Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93
15% maximal IV size 11.59
20% maximal IV size 8.75
25% maximal IV size 7.25
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 0.282
Chi-sq(1) P-val = 0.5955
-endog- option:
Endogeneity test of endogenous regressors: 6.490
Chi-sq(1) P-val = 0.0108
Regressors tested: iq
------------------------------------------------------------------------------
Instrumented: iq
Included instruments: s expr tenure
Excluded instruments: med kww
------------------------------------------------------------------------------
. *** Test of exclusion of an instrument
. ivreg2 lw s expr tenure age (iq=med kww), gmm2s robust
2-Step GMM estimation
---------------------
Estimates efficient for arbitrary heteroskedasticity
Statistics robust to heteroskedasticity
Number of obs = 758
F( 5, 752) = 85.91
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = 0.3818
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9965
Residual SS = 86.10164994 Root MSE = .337
------------------------------------------------------------------------------
| Robust
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | .0080733 .0047316 1.71 0.088 -.0012004 .017347
s | .0420584 .0172895 2.43 0.015 .0081716 .0759452
expr | .0053162 .0073158 0.73 0.467 -.0090225 .0196548
tenure | .0118452 .0080135 1.48 0.139 -.0038609 .0275513
age | .052537 .006308 8.33 0.000 .0401735 .0649005
_cons | 3.105592 .334664 9.28 0.000 2.449663 3.761522
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 32.815
Chi-sq(2) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Kleibergen-Paap rk Wald F statistic): 18.873
Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93
15% maximal IV size 11.59
20% maximal IV size 8.75
25% maximal IV size 7.25
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 3.866
Chi-sq(1) P-val = 0.0493
------------------------------------------------------------------------------
Instrumented: iq
Included instruments: s expr tenure age
Excluded instruments: med kww
------------------------------------------------------------------------------
. *** Analysis of first stage regressions
. ivreg2 lw s expr tenure (iq=med kww), first
First-stage regressions
-----------------------
First-stage regression of iq:
OLS estimation
--------------
Estimates efficient for homoskedasticity only
Statistics consistent for homoskedasticity only
Number of obs = 758
F( 5, 752) = 64.09
Prob > F = 0.0000
Total (centered) SS = 140399.3259 Centered R2 = 0.2988
Total (uncentered) SS = 8316271 Uncentered R2 = 0.9882
Residual SS = 98448.15814 Root MSE = 11.44
------------------------------------------------------------------------------
iq | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
s | 2.480376 .2177002 11.39 0.000 2.053004 2.907749
expr | -.4446049 .2109757 -2.11 0.035 -.8587763 -.0304335
tenure | .2372269 .2602616 0.91 0.362 -.2736987 .7481525
med | .4114398 .1626099 2.53 0.012 .0922165 .7306632
kww | .3100834 .0637504 4.86 0.000 .1849335 .4352334
_cons | 55.11403 3.050712 18.07 0.000 49.12511 61.10296
------------------------------------------------------------------------------
Included instruments: s expr tenure med kww
------------------------------------------------------------------------------
Partial R-squared of excluded instruments: 0.0416
Test of excluded instruments:
F( 2, 752) = 16.34
Prob > F = 0.0000
Summary results for first-stage regressions
-------------------------------------------
Variable | Shea Partial R2 | Partial R2 | F( 2, 752) P-value
iq | 0.0416 | 0.0416 | 16.34 0.0000
Underidentification tests
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
Anderson canon. corr. N*CCEV LM statistic Chi-sq(2)=31.56 P-val=0.0000
Cragg-Donald N*CDEV Wald statistic Chi-sq(2)=32.93 P-val=0.0000
Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F-statistic 16.34
See main output for Cragg-Donald weak id test critical values
Weak-instrument-robust inference
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and overidentifying restrictions are valid
Anderson-Rubin Wald test F(2,752)= 5.60 P-val=0.0038
Anderson-Rubin Wald test Chi-sq(2)=11.29 P-val=0.0035
Stock-Wright LM S statistic Chi-sq(2)=11.13 P-val=0.0038
Number of observations N = 758
Number of regressors K = 5
Number of instruments L = 6
Number of excluded instruments L1 = 2
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics consistent for homoskedasticity only
Number of obs = 758
F( 4, 753) = 76.06
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = 0.1868
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9954
Residual SS = 113.2686615 Root MSE = .3866
------------------------------------------------------------------------------
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | .0178162 .0059106 3.01 0.003 .0062317 .0294006
s | .0520467 .0192293 2.71 0.007 .014358 .0897355
expr | .0442787 .0074016 5.98 0.000 .0297719 .0587855
tenure | .0297485 .0090632 3.28 0.001 .0119849 .0475121
_cons | 3.007415 .3813668 7.89 0.000 2.25995 3.75488
------------------------------------------------------------------------------
Underidentification test (Anderson canon. corr. LM statistic): 31.563
Chi-sq(2) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 16.337
Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93
15% maximal IV size 11.59
20% maximal IV size 8.75
25% maximal IV size 7.25
Source: Stock-Yogo (2005). Reproduced by permission.
------------------------------------------------------------------------------
Sargan statistic (overidentification test of all instruments): 0.236
Chi-sq(1) P-val = 0.6271
------------------------------------------------------------------------------
Instrumented: iq
Included instruments: s expr tenure
Excluded instruments: med kww
------------------------------------------------------------------------------
. *** Test of redundant instruments
. ivreg2 lw s expr tenure (iq=med kww mrt), gmm2s robust redundant(mrt)
2-Step GMM estimation
---------------------
Estimates efficient for arbitrary heteroskedasticity
Statistics robust to heteroskedasticity
Number of obs = 758
F( 4, 753) = 92.93
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = 0.3195
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9962
Residual SS = 94.77728956 Root MSE = .3536
------------------------------------------------------------------------------
| Robust
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | .0074936 .0053383 1.40 0.160 -.0029693 .0179566
s | .0873873 .0168376 5.19 0.000 .0543862 .1203885
expr | .0419055 .0070187 5.97 0.000 .0281491 .0556618
tenure | .0360493 .0082091 4.39 0.000 .0199598 .0521388
_cons | 3.589868 .3534248 10.16 0.000 2.897168 4.282568
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 27.814
Chi-sq(3) P-val = 0.0000
-redundant- option:
IV redundancy test (LM test of redundancy of specified instruments): 3.859
Chi-sq(1) P-val = 0.0495
Instruments tested: mrt
------------------------------------------------------------------------------
Weak identification test (Kleibergen-Paap rk Wald F statistic): 10.450
Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 13.91
10% maximal IV relative bias 9.08
20% maximal IV relative bias 6.46
30% maximal IV relative bias 5.39
10% maximal IV size 22.30
15% maximal IV size 12.83
20% maximal IV size 9.54
25% maximal IV size 7.80
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 29.272
Chi-sq(2) P-val = 0.0000
------------------------------------------------------------------------------
Instrumented: iq
Included instruments: s expr tenure
Excluded instruments: med kww mrt
------------------------------------------------------------------------------
. *** IV-GMM, LIML and GMM-CUE estimation
. eststo clear
. eststo:ivreg2 lw s expr tenure (iq=med kww), gmm2s robust
2-Step GMM estimation
---------------------
Estimates efficient for arbitrary heteroskedasticity
Statistics robust to heteroskedasticity
Number of obs = 758
F( 4, 753) = 73.34
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = 0.1813
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9954
Residual SS = 114.029907 Root MSE = .3879
------------------------------------------------------------------------------
| Robust
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | .0180792 .0060816 2.97 0.003 .0061595 .0299988
s | .0513881 .0195616 2.63 0.009 .013048 .0897281
expr | .0439692 .0078796 5.58 0.000 .0285254 .059413
tenure | .0302889 .0087102 3.48 0.001 .0132173 .0473606
_cons | 2.988533 .3944466 7.58 0.000 2.215432 3.761634
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 26.252
Chi-sq(2) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Kleibergen-Paap rk Wald F statistic): 14.892
Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93
15% maximal IV size 11.59
20% maximal IV size 8.75
25% maximal IV size 7.25
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 0.282
Chi-sq(1) P-val = 0.5955
------------------------------------------------------------------------------
Instrumented: iq
Included instruments: s expr tenure
Excluded instruments: med kww
------------------------------------------------------------------------------
(est1 stored)
. eststo:ivreg2 lw s expr tenure (iq=med kww), liml robust
LIML estimation
---------------
k =1.00031
lambda =1.00031
Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity
Number of obs = 758
F( 4, 753) = 72.21
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = 0.1846
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9954
Residual SS = 113.5698821 Root MSE = .3871
------------------------------------------------------------------------------
| Robust
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | .017921 .0061533 2.91 0.004 .0058608 .0299813
s | .0517257 .0197542 2.62 0.009 .0130082 .0904431
expr | .0443182 .0079168 5.60 0.000 .0288015 .0598348
tenure | .0296993 .0087853 3.38 0.001 .0124804 .0469182
_cons | 3.000853 .3991823 7.52 0.000 2.21847 3.783236
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 26.252
Chi-sq(2) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Kleibergen-Paap rk Wald F statistic): 14.892
Stock-Yogo weak ID test critical values: 10% maximal LIML size 8.68
15% maximal LIML size 5.33
20% maximal LIML size 4.42
25% maximal LIML size 3.92
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 0.281
Chi-sq(1) P-val = 0.5960
------------------------------------------------------------------------------
Instrumented: iq
Included instruments: s expr tenure
Excluded instruments: med kww
------------------------------------------------------------------------------
(est2 stored)
. eststo:ivreg2 lw s expr tenure (iq=med kww), cue robust
initial: neg GMM obj function -J = -.2800569
rescale: neg GMM obj function -J = -.2800569
Iteration 0: neg GMM obj function -J = -.2800569
Iteration 1: neg GMM obj function -J = -.27958082
Iteration 2: neg GMM obj function -J = -.2795808
CUE estimation
--------------
Estimates efficient for arbitrary heteroskedasticity
Statistics robust to heteroskedasticity
Number of obs = 758
F( 4, 753) = 72.64
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = 0.1785
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9954
Residual SS = 114.4206733 Root MSE = .3885
------------------------------------------------------------------------------
| Robust
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | .0182125 .0061123 2.98 0.003 .0062327 .0301924
s | .0509811 .0196652 2.59 0.010 .0124381 .0895241
expr | .0439934 .0079334 5.55 0.000 .0284442 .0595426
tenure | .0302229 .0087319 3.46 0.001 .0131087 .0473372
_cons | 2.980213 .3963628 7.52 0.000 2.203356 3.75707
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 26.252
Chi-sq(2) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Kleibergen-Paap rk Wald F statistic): 14.892
Stock-Yogo weak ID test critical values: 10% maximal LIML size 8.68
15% maximal LIML size 5.33
20% maximal LIML size 4.42
25% maximal LIML size 3.92
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 0.280
Chi-sq(1) P-val = 0.5970
------------------------------------------------------------------------------
Instrumented: iq
Included instruments: s expr tenure
Excluded instruments: med kww
------------------------------------------------------------------------------
(est3 stored)
. esttab, label stat(rmse) mtitles(IVGMM LIML GMM-CUE) nonum
--------------------------------------------------------------------
IVGMM LIML GMM-CUE
--------------------------------------------------------------------
iq score 0.0181** 0.0179** 0.0182**
(2.97) (2.91) (2.98)
completed years of~g 0.0514** 0.0517** 0.0510**
(2.63) (2.62) (2.59)
experience, years 0.0440*** 0.0443*** 0.0440***
(5.58) (5.60) (5.55)
tenure, years 0.0303*** 0.0297*** 0.0302***
(3.48) (3.38) (3.46)
Constant 2.989*** 3.001*** 2.980***
(7.58) (7.52) (7.52)
--------------------------------------------------------------------
rmse 0.388 0.387 0.389
--------------------------------------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. *** Stock-Yogo critical values for Cragg-Donald F statistic and robust equivalent
. ivreg2 lw s expr tenure (iq=med kww)
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics consistent for homoskedasticity only
Number of obs = 758
F( 4, 753) = 76.06
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = 0.1868
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9954
Residual SS = 113.2686615 Root MSE = .3866
------------------------------------------------------------------------------
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | .0178162 .0059106 3.01 0.003 .0062317 .0294006
s | .0520467 .0192293 2.71 0.007 .014358 .0897355
expr | .0442787 .0074016 5.98 0.000 .0297719 .0587855
tenure | .0297485 .0090632 3.28 0.001 .0119849 .0475121
_cons | 3.007415 .3813668 7.89 0.000 2.25995 3.75488
------------------------------------------------------------------------------
Underidentification test (Anderson canon. corr. LM statistic): 31.563
Chi-sq(2) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 16.337
Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93
15% maximal IV size 11.59
20% maximal IV size 8.75
25% maximal IV size 7.25
Source: Stock-Yogo (2005). Reproduced by permission.
------------------------------------------------------------------------------
Sargan statistic (overidentification test of all instruments): 0.236
Chi-sq(1) P-val = 0.6271
------------------------------------------------------------------------------
Instrumented: iq
Included instruments: s expr tenure
Excluded instruments: med kww
------------------------------------------------------------------------------
. ivreg2 lw s expr tenure (iq=med kww), gmm2s robust
2-Step GMM estimation
---------------------
Estimates efficient for arbitrary heteroskedasticity
Statistics robust to heteroskedasticity
Number of obs = 758
F( 4, 753) = 73.34
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = 0.1813
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9954
Residual SS = 114.029907 Root MSE = .3879
------------------------------------------------------------------------------
| Robust
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | .0180792 .0060816 2.97 0.003 .0061595 .0299988
s | .0513881 .0195616 2.63 0.009 .013048 .0897281
expr | .0439692 .0078796 5.58 0.000 .0285254 .059413
tenure | .0302889 .0087102 3.48 0.001 .0132173 .0473606
_cons | 2.988533 .3944466 7.58 0.000 2.215432 3.761634
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 26.252
Chi-sq(2) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Kleibergen-Paap rk Wald F statistic): 14.892
Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93
15% maximal IV size 11.59
20% maximal IV size 8.75
25% maximal IV size 7.25
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 0.282
Chi-sq(1) P-val = 0.5955
------------------------------------------------------------------------------
Instrumented: iq
Included instruments: s expr tenure
Excluded instruments: med kww
------------------------------------------------------------------------------
. *** Regression on an endogenous dummy variable: IV and Basmann methods
. sysuse auto,clear
(1978 Automobile Data)
. eststo clear
. eststo:regress price foreign,robust
Linear regression Number of obs = 74
F( 1, 72) = 0.20
Prob > F = 0.6577
R-squared = 0.0024
Root MSE = 2966.4
------------------------------------------------------------------------------
| Robust
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
foreign | 312.2587 701.7814 0.44 0.658 -1086.717 1711.234
_cons | 6072.423 431.2084 14.08 0.000 5212.825 6932.021
------------------------------------------------------------------------------
(est1 stored)
. eststo:ivreg2 price (foreign=mpg displacement), endog(foreign) gmm2s robust
2-Step GMM estimation
---------------------
Estimates efficient for arbitrary heteroskedasticity
Statistics robust to heteroskedasticity
Number of obs = 74
F( 1, 72) = 12.16
Prob > F = 0.0008
Total (centered) SS = 635065396.1 Centered R2 = -0.8552
Total (uncentered) SS = 3447834321 Uncentered R2 = 0.6583
Residual SS = 1178158035 Root MSE = 3990
------------------------------------------------------------------------------
| Robust
price | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
foreign | -5612.9 1587.631 -3.54 0.000 -8724.599 -2501.201
_cons | 7675.546 679.7433 11.29 0.000 6343.274 9007.818
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 29.152
Chi-sq(2) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Kleibergen-Paap rk Wald F statistic): 23.153
Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93
15% maximal IV size 11.59
20% maximal IV size 8.75
25% maximal IV size 7.25
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 1.465
Chi-sq(1) P-val = 0.2262
-endog- option:
Endogeneity test of endogenous regressors: 15.520
Chi-sq(1) P-val = 0.0001
Regressors tested: foreign
------------------------------------------------------------------------------
Instrumented: foreign
Excluded instruments: mpg displacement
------------------------------------------------------------------------------
(est2 stored)
. qui logit foreign mpg displacement price
. predict double forhat
(option pr assumed; Pr(foreign))
. eststo:ivreg2 price (foreign=forhat), gmm2s robust
2-Step GMM estimation
---------------------
Estimates efficient for arbitrary heteroskedasticity
Statistics robust to heteroskedasticity
Number of obs = 74
F( 1, 72) = 0.23
Prob > F = 0.6329
Total (centered) SS = 635065396.1 Centered R2 = 0.0021
Total (uncentered) SS = 3447834321 Uncentered R2 = 0.8162
Residual SS = 633759971 Root MSE = 2926
------------------------------------------------------------------------------
| Robust
price | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
foreign | 426.5552 877.1113 0.49 0.627 -1292.551 2145.662
_cons | 6038.443 467.1296 12.93 0.000 5122.886 6954
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 34.426
Chi-sq(1) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Kleibergen-Paap rk Wald F statistic): 196.260
Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38
15% maximal IV size 8.96
20% maximal IV size 6.66
25% maximal IV size 5.53
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 0.000
(equation exactly identified)
------------------------------------------------------------------------------
Instrumented: foreign
Excluded instruments: forhat
------------------------------------------------------------------------------
(est3 stored)
. esttab, label stat(rmse) se mtitles(OLS IV-GMM Basmann) nonum
--------------------------------------------------------------------
OLS IV-GMM Basmann
--------------------------------------------------------------------
Car type 312.3 -5612.9*** 426.6
(701.8) (1587.6) (877.1)
Constant 6072.4*** 7675.5*** 6038.4***
(431.2) (679.7) (467.1)
--------------------------------------------------------------------
rmse 2966.4 3990.1 2926.5
--------------------------------------------------------------------
Standard errors in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. *** The forbidden regression
. use griliches76.dta, clear
(Wages of Very Young Men, Zvi Griliches, J.Pol.Ec. 1976)
. qui regress iq s expr tenure
. predict double iqhat, xb
. label var iqhat iqhat
. generate double iq2hat = (iqhat^2)/1000
. generate double s2 = s^2
. generate double expr2 = expr^2
. generate double tenure2 = tenure^2
. generate double sexpr = s*expr
. generate double sten = s*tenure
. generate double xten = expr*tenure
. eststo clear
. eststo: regress lw iqhat iq2hat tenure
Source | SS df MS Number of obs = 758
-------------+------------------------------ F( 3, 754) = 94.71
Model | 38.1228132 3 12.7076044 Prob > F = 0.0000
Residual | 101.163337 754 .134168882 R-squared = 0.2737
-------------+------------------------------ Adj R-squared = 0.2708
Total | 139.28615 757 .183997556 Root MSE = .36629
------------------------------------------------------------------------------
lw | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iqhat | -.1131037 .0541035 -2.09 0.037 -.2193151 -.0068924
iq2hat | .6787579 .256789 2.64 0.008 .1746515 1.182864
tenure | .0369274 .0079612 4.64 0.000 .0212986 .0525562
_cons | 10.01075 2.840088 3.52 0.000 4.43533 15.58617
------------------------------------------------------------------------------
(est1 stored)
. generate double iq2 = (iq^2)/1000
. eststo: ivreg2 lw tenure (iq iq2 = s s2 expr expr2 tenure2 sexpr sten xten)
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics consistent for homoskedasticity only
Number of obs = 758
F( 3, 754) = 42.36
Prob > F = 0.0000
Total (centered) SS = 139.2861498 Centered R2 = -0.7673
Total (uncentered) SS = 24652.24662 Uncentered R2 = 0.9900
Residual SS = 246.164499 Root MSE = .5699
------------------------------------------------------------------------------
lw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
iq | -.2576697 .0678624 -3.80 0.000 -.3906775 -.1246618
iq2 | 1.396272 .3309028 4.22 0.000 .7477143 2.044829
tenure | .0361486 .012388 2.92 0.004 .0118685 .0604287
_cons | 17.06217 3.424798 4.98 0.000 10.34969 23.77466
------------------------------------------------------------------------------
Underidentification test (Anderson canon. corr. LM statistic): 42.894
Chi-sq(7) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 5.608
Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 17.70
10% maximal IV relative bias 10.22
20% maximal IV relative bias 6.20
30% maximal IV relative bias 4.73
10% maximal IV size 25.64
15% maximal IV size 14.31
20% maximal IV size 10.41
25% maximal IV size 8.39
Source: Stock-Yogo (2005). Reproduced by permission.
------------------------------------------------------------------------------
Sargan statistic (overidentification test of all instruments): 17.872
Chi-sq(6) P-val = 0.0066
------------------------------------------------------------------------------
Instrumented: iq iq2
Included instruments: tenure
Excluded instruments: s s2 expr expr2 tenure2 sexpr sten xten
------------------------------------------------------------------------------
(est2 stored)
. esttab, label mtitles(Forbidden NL-IV) nonum se
----------------------------------------------------
Forbidden NL-IV
----------------------------------------------------
iqhat -0.113*
(0.0541)
iq2hat 0.679**
(0.257)
tenure, years 0.0369*** 0.0361**
(0.00796) (0.0124)
iq score -0.258***
(0.0679)
iq2 1.396***
(0.331)
Constant 10.01*** 17.06***
(2.840) (3.425)
----------------------------------------------------
Observations 758 758
----------------------------------------------------
Standard errors in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. log close
log: /Users/baum/doc/Stata/USUG_2007/baumUKSUG2007smcltalk/ivsmcltalk.smcl
log type: smcl
closed on: 4 Feb 2008, 09:03:43
-------------------------------------------------------------------------------------------