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st: RE: Anderson-Rubin Wald Test in ivreg2
From
"Schaffer, Mark E" <[email protected]>
To
<[email protected]>
Subject
st: RE: Anderson-Rubin Wald Test in ivreg2
Date
Fri, 11 Jun 2010 13:27:28 +0100
Bahareh,
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of
> bahareh sehatzadeh
> Sent: Thursday, June 10, 2010 7:07 PM
> To: [email protected]
> Subject: st: Anderson-Rubin Wald Test in ivreg2
>
> Greetings,
> I will be grateful if someone can help me with the test results in
> ivreg2. I specifically want to know what will Anderson-Rubin Wald test
> and Stock-Wright LM S statistics show when we only have one endogenous
> regressor since they are supposed to test the joint significance of
> all endogenous regressors.
The very short answer is that in your case, all = 1.
A slightly longer answer is that in your case, the AR and SW confidence
intervals would include zero at any standard level of confidence, even
though the standard Wald 10% confidence intervals using the estimated
parameter and SE doesn't include zero. This can easily happen. The
traditional method of using IV to estimate a parameter and SE will
usually generate more precise estimates, but this precision comes with a
price that you might, or might not, want to pay.
A somewhat longer answer, with references to the relevant literature, is
in the paper that discusses these tests as implemented in -ivreg2-.
It's listed in the -ivreg2- help file but I am copying it here:
Baum, C. F., Schaffer, M.E., and Stillman, S. 2007. Enhanced routines
for instrumental variables/GMM estimation and testing. The Stata
Journal, Vol. 7, No. 4, pp. 465-506.
http://ideas.repec.org/a/tsj/stataj/v7y2007i4p465-506.html.
Working paper version: Boston College Department of Economics Working
Paper No. 667. http://ideas.repec.org/p/boc/bocoec/667.html.
HTH.
Cheers,
Mark
> I am copying the results I got from running
> my model as I think everything looks good except these tests. I
> appreciate your time and consideration.
> Sincerely,
> Bahareh Sehatzadeh.
>
>
> . ivreg2 q9_walk_freq dum_dog empl_schl res_1_3 JerseyCity (cars=
> lu_entropy6 hom_own den_pop00_bg res_mlt_fam), first
>
> First-stage regressions
> -----------------------
>
> First-stage regression of cars:
>
> OLS estimation
> --------------
>
> Estimates efficient for homoskedasticity only
> Statistics consistent for homoskedasticity only
>
> Number
> of obs = 889
> F( 8,
> 880) = 66.04
> Prob >
> F = 0.0000
> Total (centered) SS = 1147.75928
> Centered R2 = 0.3752
> Total (uncentered) SS = 3503
> Uncentered R2 = 0.7953
> Residual SS = 717.1662165 Root
> MSE = .9028
>
> --------------------------------------------------------------
> ----------------
> cars | Coef. Std. Err. t P>|t|
> [95% Conf. Interval]
> -------------+------------------------------------------------
> ----------------
> dum_dog | .3460319 .0711321 4.86 0.000
> .2064235 .4856403
> empl_schl | .3338154 .0645232 5.17 0.000
> .207178 .4604528
> res_1_3 | .4416355 .0983916 4.49 0.000
> .2485258 .6347451
> JerseyCity | -.3897836 .0893173 -4.36 0.000
> -.5650834 -.2144837
> lu_entropy6 | -.3648791 .179012 -2.04 0.042
> -.7162193 -.0135388
> hom_own | .6853242 .0788627 8.69 0.000
> .5305433 .8401051
> den_pop00_bg | -7.38e-06 2.27e-06 -3.26 0.001
> -.0000118 -2.93e-06
> res_mlt_fam | .4163419 .0999191 4.17 0.000
> .2202342 .6124495
> _cons | .9164409 .1345124 6.81 0.000
> .6524383 1.180443
> --------------------------------------------------------------
> ----------------
> Included instruments: dum_dog empl_schl res_1_3 JerseyCity
> lu_entropy6 hom_own
> den_pop00_bg res_mlt_fam
> --------------------------------------------------------------
> ----------------
> F test of excluded instruments:
> F( 4, 880) = 28.00
> Prob > F = 0.0000
> Angrist-Pischke multivariate F test of excluded instruments:
> F( 4, 880) = 28.00
> Prob > F = 0.0000
>
>
>
> Summary results for first-stage regressions
> -------------------------------------------
>
> (Underid)
> (Weak id)
> Variable | F( 4, 880) P-val | AP Chi-sq( 4) P-val |
> AP F( 4, 880)
> cars | 28.00 0.0000 | 113.13 0.0000 |
> 28.00
>
> Stock-Yogo weak ID test critical values for single endogenous
> regressor:
> 5% maximal IV relative
> bias 16.85
> 10% maximal IV relative
> bias 10.27
> 20% maximal IV relative
> bias 6.71
> 30% maximal IV relative
> bias 5.34
> 10% maximal IV size
> 24.58
> 15% maximal IV size
> 13.96
> 20% maximal IV size
> 10.26
> 25% maximal IV size
> 8.31
> Source: Stock-Yogo (2005). Reproduced by permission.
>
> Underidentification test
> Ho: matrix of reduced form coefficients has rank=K1-1
> (underidentified)
> Ha: matrix has rank=K1 (identified)
> Anderson canon. corr. LM statistic Chi-sq(4)=100.36
> P-val=0.0000
>
> Weak identification test
> Ho: equation is weakly identified
> Cragg-Donald Wald F statistic
> 28.00
>
> Stock-Yogo weak ID test critical values for K1=1 and L1=4:
> 5% maximal IV relative
> bias 16.85
> 10% maximal IV relative
> bias 10.27
> 20% maximal IV relative
> bias 6.71
> 30% maximal IV relative
> bias 5.34
> 10% maximal IV size
> 24.58
> 15% maximal IV size
> 13.96
> 20% maximal IV size
> 10.26
> 25% maximal IV size
> 8.31
> Source: Stock-Yogo (2005). Reproduced by permission.
>
> Weak-instrument-robust inference
> Tests of joint significance of endogenous regressors B1 in
> main equation
> Ho: B1=0 and orthogonality conditions are valid
> Anderson-Rubin Wald test F(4,880)= 0.88
> P-val=0.4762
> Anderson-Rubin Wald test Chi-sq(4)= 3.55
> P-val=0.4703
> Stock-Wright LM S statistic Chi-sq(4)= 3.54
> P-val=0.4724
>
> Number of observations N = 889
> Number of regressors K = 6
> Number of endogenous regressors K1 = 1
> Number of instruments L = 9
> Number of excluded instruments L1 = 4
>
> IV (2SLS) estimation
> --------------------
>
> Estimates efficient for homoskedasticity only
> Statistics consistent for homoskedasticity only
>
> Number
> of obs = 889
> F( 5,
> 883) = 18.32
> Prob >
> F = 0.0000
> Total (centered) SS = 1148.704162
> Centered R2 = 0.0809
> Total (uncentered) SS = 14398
> Uncentered R2 = 0.9267
> Residual SS = 1055.785386 Root
> MSE = 1.09
>
> --------------------------------------------------------------
> ----------------
> q9_walk_freq | Coef. Std. Err. z P>|z|
> [95% Conf. Interval]
> -------------+------------------------------------------------
> ----------------
> cars | -.2052962 .1140756 -1.80 0.072
> -.4288803 .0182879
> dum_dog | .5441911 .0976409 5.57 0.000
> .3528184 .7355637
> empl_schl | .1556036 .0875423 1.78 0.075
> -.015976 .3271833
> res_1_3 | -.2545317 .1158542 -2.20 0.028
> -.4816018 -.0274617
> JerseyCity | .2553529 .1147131 2.23 0.026
> .0305194 .4801864
> _cons | 4.013131 .159152 25.22 0.000
> 3.701199 4.325063
> --------------------------------------------------------------
> ----------------
> Underidentification test (Anderson canon. corr. LM
> statistic): 100.357
> Chi-sq(4)
> P-val = 0.0000
> --------------------------------------------------------------
> ----------------
> Weak identification test (Cragg-Donald Wald F statistic):
> 27.996
> Stock-Yogo weak ID test critical values: 5% maximal IV
> relative bias 16.85
> 10% maximal IV
> relative bias 10.27
> 20% maximal IV
> relative bias 6.71
> 30% maximal IV
> relative bias 5.34
> 10% maximal IV size
> 24.58
> 15% maximal IV size
> 13.96
> 20% maximal IV size
> 10.26
> 25% maximal IV size
> 8.31
> Source: Stock-Yogo (2005). Reproduced by permission.
> --------------------------------------------------------------
> ----------------
> Sargan statistic (overidentification test of all
> instruments): 0.255
> Chi-sq(3)
> P-val = 0.9683
> --------------------------------------------------------------
> ----------------
> Instrumented: cars
> Included instruments: dum_dog empl_schl res_1_3 JerseyCity
> Excluded instruments: lu_entropy6 hom_own den_pop00_bg res_mlt_fam
> --------------------------------------------------------------
> ----------------
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