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# st: ivreg2: Anderson-Rubin Wald significant, and Stock-Wright S not significant - explanation?

 From Jonathan Richards To "statalist@hsphsun2.harvard.edu" Subject st: ivreg2: Anderson-Rubin Wald significant, and Stock-Wright S not significant - explanation? Date Fri, 7 Sep 2012 02:41:40 +0000

```Hey everyone-

After using ivreg2, the weak-instrument-robust test statistics, the Anderson-Rubin Wald test is significant and the Stock-Wright LM S statistic is not. Thus, based on the Anderson-Rubin Wald statistic, I should reject the null that B=0, and based on the Stock-Wright LM S, I should fail to reject. I don't know what to make of this.

Can anyone shed some light on this? I would appreciate any insight.

Thanks-

Brent

PS Here's my output:

xtivreg2 nzwages ///
> ravensR1 readinglevelR1 writinglevelR1 mathR1 ///
> daded mumed agechildr3 (NCG8 = cropstolenR1), liml first fe cluster(clustid)

FIXED EFFECTS ESTIMATION
------------------------
Number of groups =        21                    Obs per group: min =        26
avg =      43.2
max =        51

First-stage regressions
-----------------------

First-stage regression of NCG8:

FIXED EFFECTS ESTIMATION
------------------------
Number of groups =        21                    Obs per group: min =        26
avg =      43.2
max =        51

OLS estimation
--------------

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

Number of clusters (clustid) = 21                     Number of obs =      907
F(  8,    20) =    11.21
Prob > F      =   0.0000
Total (centered) SS     =  24112.07691                Centered R2   =   0.0729
Total (uncentered) SS   =  24112.07691                Uncentered R2 =   0.0729
Residual SS             =  22354.95047                Root MSE      =    5.046

--------------------------------------------------------------------------------
|               Robust
NCG8 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
ravensR1 |  -.0361332   .0294914    -1.23   0.235    -.0976512    .0253847
readinglevelR1 |  -.4871586   .1570078    -3.10   0.006    -.8146711   -.1596461
writinglevelR1 |  -.6210914    .256217    -2.42   0.025    -1.155551   -.0866321
mathR1 |  -.7838349   .4316283    -1.82   0.084    -1.684196    .1165259
daded |  -.0544231   .0580238    -0.94   0.359    -.1754586    .0666125
mumed |   -.011695    .050537    -0.23   0.819    -.1171132    .0937233
agechildr3 |  -.0573995   .0446936    -1.28   0.214    -.1506288    .0358297
cropstolenR1 |  -5.699977   1.316356    -4.33   0.000    -8.445848   -2.954107
--------------------------------------------------------------------------------
agechildr3 cropstolenR1
------------------------------------------------------------------------------
Partial R-squared of excluded instruments:   0.0288
Test of excluded instruments:
F(  1,    20) =    18.75
Prob > F      =   0.0003

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

Variable    | Shea Partial R2 |   Partial R2    |  F(  1,    20)    P-value
NCG8        |     0.0288      |     0.0288      |       18.75       0.0003

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(1)=2.81     P-val=0.0937
Kleibergen-Paap rk Wald statistic           Chi-sq(1)=19.84    P-val=0.0000

Weak identification test
Ho: equation is weakly identified
Kleibergen-Paap Wald rk F statistic                18.75
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(1,20)=  5.77      P-val=0.0262
Anderson-Rubin Wald test     Chi-sq(1)=6.10      P-val=0.0135
Stock-Wright LM S statistic  Chi-sq(1)=2.66      P-val=0.1028

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

Number of clusters             N_clust  =         21
Number of observations               N  =        907
Number of regressors                 K  =          8
Number of instruments                L  =          8
Number of excluded instruments       L1 =          1

LIML estimation
---------------
k               =1.00000
lambda          =1.00000

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

Number of clusters (clustid) = 21                     Number of obs =      907
F(  8,    20) =    11.67
Prob > F      =   0.0000
Total (centered) SS     =  160.1779314                Centered R2   =  -0.1584
Total (uncentered) SS   =  160.1779314                Uncentered R2 =  -0.1584
Residual SS             =  185.5557754                Root MSE      =    .4576

--------------------------------------------------------------------------------
|               Robust
nzwages |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
NCG8 |  -.0483625   .0287696    -1.68   0.093    -.1047499    .0080249
ravensR1 |  -.0045641   .0029854    -1.53   0.126    -.0104153    .0012872
readinglevelR1 |  -.0186649   .0230798    -0.81   0.419    -.0639005    .0265708
writinglevelR1 |   -.103645   .0286921    -3.61   0.000    -.1598804   -.0474095
mathR1 |  -.0308976   .0515261    -0.60   0.549    -.1318868    .0700917
daded |   -.022506   .0047281    -4.76   0.000    -.0317729   -.0132392
mumed |  -.0091565   .0058051    -1.58   0.115    -.0205343    .0022213
agechildr3 |   .0055488    .005227     1.06   0.288     -.004696    .0157935
--------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic):              2.809
Chi-sq(1) P-val =    0.0937
------------------------------------------------------------------------------
Weak identification test (Kleibergen-Paap rk Wald F statistic):         18.750
Stock-Yogo weak ID test critical values: 10% maximal LIML size           16.38
15% maximal LIML size            8.96
20% maximal LIML size            6.66
25% maximal LIML size            5.53
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):         0.000
(equation exactly identified)
------------------------------------------------------------------------------
Instrumented:         NCG8
agechildr3
Excluded instruments: cropstolenR1
------------------------------------------------------------------------------

.
end of do-file

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