Quantcast

Anderson-Rubin Wald Test in ivreg2

classic Classic list List threaded Threaded
2 messages Options
Reply | Threaded
Open this post in threaded view
|  
Report Content as Inappropriate

Anderson-Rubin Wald Test in ivreg2

bahareh sehatzadeh
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
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
------------------------------------------------------------------------------
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
Reply | Threaded
Open this post in threaded view
|  
Report Content as Inappropriate

RE: Anderson-Rubin Wald Test in ivreg2

Schaffer, Mark E
Bahareh,

> -----Original Message-----
> From: [hidden email]
> [mailto:[hidden email]] On Behalf Of
> bahareh sehatzadeh
> Sent: Thursday, June 10, 2010 7:07 PM
> To: [hidden email]
> 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
> --------------------------------------------------------------
> ----------------
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>


--
Heriot-Watt University is a Scottish charity
registered under charity number SC000278.


*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
Loading...