Stata: Data Analysis and Statistical Software

Will AR Wald/F and StockWright LM statistics always give consistent results? In what possible way, can one test perform better than the other to test robust weak instrument? Or in what situation can these two be inconsistent?
Appreciated,
Jingjing YE



 xi: ivreg2 employed (i.exogamy interaction emp_ratio = iv1 iv2 iv3_edu1 iv3_e
> du2 iv3_edu3 iv3_edu4 iv4_edu1 iv4_edu2 iv4_edu3 iv4_edu4 edu1_msa edu2_msa e
> du3_msa edu4_msa) exogamy_msa `missing' `control' `spouse' [pw=perwt], cluste
> r(metaread) ffirst
i.exogamy         _Iexogamy_0-1       (naturally coded; _Iexogamy_0 omitted)
i.age             _Iage_19-62         (naturally coded; _Iage_19 omitted)
i.edu             _Iedu_0-4           (naturally coded; _Iedu_0 omitted)
i.racesing        _Iracesing_0-4      (naturally coded; _Iracesing_0 omitted)
i.central         _Icentral_0-2       (naturally coded; _Icentral_0 omitted)
i.region          _Iregion_11-42      (naturally coded; _Iregion_11 omitted)
i.bpl_r           _Ibpl_r_150-700     (naturally coded; _Ibpl_r_150 omitted)
i.fe_age          _Ife_age_19-54      (naturally coded; _Ife_age_19 omitted)
i.fe_edu          _Ife_edu_0-4        (naturally coded; _Ife_edu_0 omitted)
i.fe_bpl_r        _Ife_bpl_r_0-2      (naturally coded; _Ife_bpl_r_0 omitted)
(sum of wgt is     1.7417e+06)
Warning - collinearities detected
Vars dropped:       missing_iv2 missing_edu1_msa missing_edu2_msa
                    missing_edu3_msa missing_edu4_msa missing_eng_msa
                    missing_lny_msa missing_exogamymsa


Summary results for first-stage regressions
-------------------------------------------

Variable    | Shea Partial R2 |   Partial R2    |  F( 14,   278)    P-value
_Iexogamy_1 |     0.0091      |     0.0072      |       11.53       0.0000
interaction |     0.0104      |     0.0086      |       15.71       0.0000
emp_ratio   |     0.0222      |     0.0339      |       19.47       0.0000

NB: first-stage F-stat cluster-robust

Underidentification tests
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
Kleibergen-Paap rk LM statistic             Chi-sq(12)=42.51   P-val=0.0000
Kleibergen-Paap rk Wald statistic           Chi-sq(12)=186.91  P-val=0.0000

Weak identification test
Ho: equation is weakly identified
Kleibergen-Paap Wald rk F statistic                13.28
See main output for Cragg-Donald weak id test critical values

Weak-instrument-robust inference
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and overidentifying restrictions are valid
Anderson-Rubin Wald test     F(14,278)=3.29      P-val=0.0001
Anderson-Rubin Wald test     Chi-sq(14)=46.28    P-val=0.0000
Stock-Wright LM S statistic  Chi-sq(14)=18.34    P-val=0.1917

NB: Underidentification, weak identification and weak-identification-robust
    test statistics cluster-robust

Number of clusters             N_clust  =        279
Number of observations               N  =      79686
Number of regressors                 K  =        140
Number of instruments                L  =        151
Number of excluded instruments       L1 =         14

IV (2SLS) estimation
--------------------

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and clustering on metaread

Number of clusters (metaread) = 279                   Number of obs =    79686
                                                      F(139,   278) =   639.20
                                                      Prob > F      =   0.0000
Total (centered) SS     =  13667.47635                Centered R2   =   0.0638
Total (uncentered) SS   =  62166.93622                Uncentered R2 =   0.7942
Residual SS             =  12795.24587                Root MSE      =    .4007

------------------------------------------------------------------------------
             |               Robust
    employed |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 _Iexogamy_1 |   .6541899   .1993359     3.28   0.001     .2634987    1.044881
 interaction |  -.8226884   .3065279    -2.68   0.007    -1.423472   -.2219047
   emp_ratio |   .5106566   .1719288     2.97   0.003     .1736823    .8476308
 exogamy_msa |   .0004792   .0002147     2.23   0.026     .0000584    .0009001
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic):             42.509
                                                   Chi-sq(12) P-val =   0.0000
------------------------------------------------------------------------------
Weak identification test (Kleibergen-Paap rk Wald F statistic):         13.278
Stock-Yogo weak ID test critical values:  5% maximal IV relative bias    18.47
                                                              10% maximal IV relative bias    10.25
                                                                20% maximal IV relative bias     5.93
                                                               30% maximal IV relative bias     4.39
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments):        12.670
                                                                         Chi-sq(11) P-val =   0.3155
------------------------------------------------------------------------------


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