# 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/