# Anderson-Rubin Wald Test in ivreg2

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## 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. 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/
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## RE: Anderson-Rubin Wald Test in ivreg2

 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/