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# st: Anderson-Rubin Wald Test in ivreg2

 From bahareh sehatzadeh To statalist@hsphsun2.harvard.edu Subject st: Anderson-Rubin Wald Test in ivreg2 Date Thu, 10 Jun 2010 14:06:56 -0400

```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. I am copying the results I got from running
my model as I think everything looks good except these tests. I
Sincerely,

. 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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```