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


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: ivreg2: Anderson-Rubin Wald significant, and Stock-Wright S not significant - explanation?
Date   Fri, 7 Sep 2012 08:11:53 +0100

Jonathan,

The p-values aren't wildly different (p=0.10 vs. p=0.01), and of course
Wald and LM stats differ in finite samples.  Plus you are using
cluster-robust stats, and you have only 21 clusters - not really enough
to make the use of the cluster-robust reliable, imho - so stats using
this VCE will also be somewhat unreliable. 

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of Jonathan Richards
> Sent: 07 September 2012 03:42
> To: statalist@hsphsun2.harvard.edu
> Subject: st: ivreg2: Anderson-Rubin Wald significant, and Stock-Wright
S not
> significant - explanation?
> 
> 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
>
------------------------------------------------------------------------
--------
> Included instruments: ravensR1 readinglevelR1 writinglevelR1 mathR1
daded
> mumed
>                       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
> Included instruments: ravensR1 readinglevelR1 writinglevelR1 mathR1
daded
> mumed
>                       agechildr3
> Excluded instruments: cropstolenR1
>
------------------------------------------------------------------------
------
> 
> 
> .
> end of do-file
> 
> 
> 
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