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st: RE: Anderson-Rubin Wald Test in ivreg2


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Anderson-Rubin Wald Test in ivreg2
Date   Fri, 11 Jun 2010 13:27:28 +0100

Bahareh,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> bahareh sehatzadeh
> Sent: Thursday, June 10, 2010 7:07 PM
> To: statalist@hsphsun2.harvard.edu
> 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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