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st: Xtivreg: Cragg-Donald and Angrist-Pischke multivariate F test


From   vikramfinavker <vikramfinavker@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Xtivreg: Cragg-Donald and Angrist-Pischke multivariate F test
Date   Mon, 18 Apr 2011 12:53:44 -0700 (PDT)

Hi,

I apologies for asking so many questions. I read the help files but i am
still confused. 

could someone please advise me on following questions? 

1. My cragg-donal f test is low == so does it mean my instruments are
weak???

2. in first stage regressions the Angrist-Pischke stat is higher than 10 for
both of my endogenous variables ==what does this mean? (The Angrist-Pischke
(AP) first-stage chi-squared and F statistics are tests of
underidentification and weak identification, respectively, of individual
endogenous regressors.  They are constructed by
"partialling-out" linear projections of the remaining endogenous regressors. 
The AP chi-squared Wald statistic is distributed as chi2(L1-K1+1)) under the
null that the particular endogenous regressor
in question is unidentified.  In the special case of a single endogenous
regressor, the AP statistic reported is identical to underidentification
statistics reported in the ffirst output, namely the
Cragg-Donald Wald statistic (if i.i.d.) or the Kleibergen-Paap rk Wald
statistic (if robust, cluster-robust, AC or HAC statistics have been
requested); see above.  Note the difference in the null
hypotheses if there are two or more endogenous regressors:  the AP test will
fail to reject if a particular endogenous regressor is unidentified, whereas
the Anderson/Cragg-Donald/Kleibergen-Paap tests
of underidentification will fail to reject if any of the endogenous
regressors is unidentified.
)
3. My Underidentification test (Anderson canon. corr. LM statistic) has p
value <0.0000 so my model is identified, right?

following is the regression output;

xtivreg2 vw1edf1dec  vw1excessftseallsh vw1pretaxmargin vw1eqvol
vw1lntotassets vw1cashholdmve ( vw1totadertotototass vw1mvgroslev = vw1rd
> s fxsales2 irheg09 vw1lntotsal vw1ndts4mv) d2-d11 yr_99 - yr_09, fe
> endog(vw1totadertotototass vw1mvgroslev) first
Warning - singleton groups detected.  40 observation(s) not used.

FIXED EFFECTS ESTIMATION
------------------------
Number of groups =       168                    Obs per group: min =        
2
                                                               avg =      
4.8
                                                               max =       
10

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

First-stage regression of vw1totadertotototass:

FIXED EFFECTS ESTIMATION
------------------------
Number of groups =       168                    Obs per group: min =        
2
                                                               avg =      
4.8
                                                               max =       
10

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

Estimates efficient for homoskedasticity only
Statistics consistent for homoskedasticity only

                                                      Number of obs =     
804
                                                      F( 31,   605) =    
2.51
                                                      Prob > F      =  
0.0000
Total (centered) SS     =    62.546986                Centered R2   =  
0.1140
Total (uncentered) SS   =    62.546986                Uncentered R2 =  
0.1140
Residual SS             =  55.41514715                Root MSE      =   
.3026

------------------------------------------------------------------------------
vw1totader~s |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]
-------------+----------------------------------------------------------------
vw1excessf~h |   .0384102    .036696     1.05   0.296    -.0336569   
.1104772
vw1pretaxm~n |   .0004605    .000724     0.64   0.525    -.0009613   
.0018823
    vw1eqvol |   .1327014   .1017105     1.30   0.192    -.0670472     
.33245
vw1lntotas~s |   .0347029   .0547706     0.63   0.527    -.0728606   
.1422665
vw1cashh~mve |   .0505698   .1063086     0.48   0.634    -.1582089   
.2593485
          d2 |   .1919997   .2871285     0.67   0.504    -.3718899   
.7558892
          d3 |    .050883   .1669135     0.30   0.761    -.2769172   
.3786833
          d4 |   .0059934   .1663872     0.04   0.971    -.3207732   
.3327601
          d5 |   .1648939   .1575696     1.05   0.296    -.1445559   
.4743438
          d6 |   .0232018   .1802202     0.13   0.898    -.3307313   
.3771349
          d7 |   .0507423   .1511599     0.34   0.737    -.2461194   
.3476041
          d8 |   .1010815   .1640024     0.62   0.538    -.2210017   
.4231647
          d9 |  -.0412872   .2107097    -0.20   0.845    -.4550984    
.372524
         d10 |  -.1081474    .339063    -0.32   0.750    -.7740308   
.5577361
         d11 |   .0721896   .1639032     0.44   0.660    -.2496988    
.394078
       yr_99 |  -.0951907   .1235803    -0.77   0.441    -.3378892   
.1475078
       yr_00 |   .0104751   .1351841     0.08   0.938    -.2550119   
.2759621
       yr_01 |   .3617244   .1591978     2.27   0.023      .049077   
.6743719
       yr_02 |  -.0543225   .1411907    -0.38   0.701    -.3316059   
.2229609
       yr_03 |    .052008   .1420102     0.37   0.714    -.2268849   
.3309009
       yr_04 |   .1177188   .1547854     0.76   0.447    -.1862631   
.4217007
       yr_05 |   .1370147   .1467961     0.93   0.351    -.1512772   
.4253065
       yr_06 |   -.133557   .1501707    -0.89   0.374    -.4284761   
.1613621
       yr_07 |  -.2991139   .1295071    -2.31   0.021     -.553452  
-.0447758
       yr_08 |  -.0114607     .16627    -0.07   0.945    -.3379972   
.3150758
       yr_09 |   .0471283   .1542313     0.31   0.760    -.2557654    
.350022
      vw1rds |   .0568986   .4764428     0.12   0.905     -.878784   
.9925813
    fxsales2 |   -.001177   .0013182    -0.89   0.372    -.0037658   
.0014117
     irheg09 |   .2763797   .0433383     6.38   0.000     .1912679   
.3614915
 vw1lntotsal |  -.0313166   .0432096    -0.72   0.469    -.1161756   
.0535424
  vw1ndts4mv |  -.1224033   .3349813    -0.37   0.715    -.7802706    
.535464
------------------------------------------------------------------------------
Included instruments: vw1excessftseallsh vw1pretaxmargin vw1eqvol
vw1lntotassets
                      vw1cashholdmve d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 yr_99
yr_00
                      yr_01 yr_02 yr_03 yr_04 yr_05 yr_06 yr_07 yr_08 yr_09
                      vw1rds fxsales2 irheg09 vw1lntotsal vw1ndts4mv
------------------------------------------------------------------------------
F test of excluded instruments:
  F(  5,   605) =     8.79
  Prob > F      =   0.0000
Angrist-Pischke multivariate F test of excluded instruments:
  F(  4,   605) =    10.47
  Prob > F      =   0.0000

First-stage regression of vw1mvgroslev:

FIXED EFFECTS ESTIMATION
------------------------
Number of groups =       168                    Obs per group: min =        
2
                                                               avg =      
4.8
                                                               max =       
10

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

Estimates efficient for homoskedasticity only
Statistics consistent for homoskedasticity only

                                                      Number of obs =     
804
                                                      F( 31,   605) =   
37.20
                                                      Prob > F      =  
0.0000
Total (centered) SS     =  8.489144095                Centered R2   =  
0.6559
Total (uncentered) SS   =  8.489144095                Uncentered R2 =  
0.6559
Residual SS             =  2.921290552                Root MSE      =  
.06949

------------------------------------------------------------------------------
vw1mvgroslev |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]
-------------+----------------------------------------------------------------
vw1excessf~h |  -.0326741   .0084254    -3.88   0.000    -.0492207  
-.0161274
vw1pretaxm~n |  -.0004029   .0001662    -2.42   0.016    -.0007294  
-.0000765
    vw1eqvol |   .1847591   .0233528     7.91   0.000     .1388967   
.2306215
vw1lntotas~s |   .0731947   .0125754     5.82   0.000      .048498   
.0978913
vw1cashh~mve |   .1376241   .0244085     5.64   0.000     .0896884   
.1855598
          d2 |  -.0001399   .0659249    -0.00   0.998    -.1296094   
.1293295
          d3 |   .0014031   .0383235     0.04   0.971      -.07386   
.0766663
          d4 |  -.0123032   .0382026    -0.32   0.748     -.087329   
.0627226
          d5 |   .0090432   .0361781     0.25   0.803    -.0620067    
.080093
          d6 |  -.0375485   .0413787    -0.91   0.365    -.1188118   
.0437148
          d7 |  -.0561937   .0347064    -1.62   0.106    -.1243534   
.0119659
          d8 |  -.0721108   .0376551    -1.92   0.056    -.1460613   
.0018397
          d9 |  -.0911533   .0483791    -1.88   0.060    -.1861646   
.0038581
         d10 |   .0374496   .0778491     0.48   0.631    -.1154377   
.1903369
         d11 |   .0159557   .0376323     0.42   0.672    -.0579501   
.0898615
       yr_99 |  -.0140984   .0283741    -0.50   0.619    -.0698221   
.0416254
       yr_00 |  -.0317021   .0310383    -1.02   0.307    -.0926581   
.0292539
       yr_01 |  -.0239389   .0365519    -0.65   0.513     -.095723   
.0478452
       yr_02 |   .0764995   .0324175     2.36   0.019      .012835   
.1401639
       yr_03 |   .0017854   .0326056     0.05   0.956    -.0622486   
.0658194
       yr_04 |    .035376   .0355388     1.00   0.320    -.0344184   
.1051704
       yr_05 |  -.0065693   .0337045    -0.19   0.846    -.0727613   
.0596227
       yr_06 |  -.0300386   .0344793    -0.87   0.384    -.0977522   
.0376751
       yr_07 |   .0162423   .0297349     0.55   0.585    -.0421539   
.0746385
       yr_08 |   .0052692   .0381757     0.14   0.890    -.0697038   
.0802422
       yr_09 |  -.0345044   .0354116    -0.97   0.330     -.104049   
.0350402
      vw1rds |  -.1743845   .1093916    -1.59   0.111    -.3892179   
.0404488
    fxsales2 |  -.0001981   .0003027    -0.65   0.513    -.0007924   
.0003963
     irheg09 |   .0334521   .0099505     3.36   0.001     .0139104   
.0529939
 vw1lntotsal |  -.0137215    .009921    -1.38   0.167    -.0332052   
.0057622
  vw1ndts4mv |   .8395952   .0769119    10.92   0.000     .6885485    
.990642
------------------------------------------------------------------------------
Included instruments: vw1excessftseallsh vw1pretaxmargin vw1eqvol
vw1lntotassets
                      vw1cashholdmve d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 yr_99
yr_00
                      yr_01 yr_02 yr_03 yr_04 yr_05 yr_06 yr_07 yr_08 yr_09
                      vw1rds fxsales2 irheg09 vw1lntotsal vw1ndts4mv
------------------------------------------------------------------------------
F test of excluded instruments:
  F(  5,   605) =    26.39
  Prob > F      =   0.0000
Angrist-Pischke multivariate F test of excluded instruments:
  F(  4,   605) =    31.41
  Prob > F      =   0.0000



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

                                           (Underid)            (Weak id)
Variable     | F(  5,   605)  P-val | AP Chi-sq(  4) P-val | AP F(  4,  
605)
vw1totaderto |       8.79    0.0000 |       44.01   0.0000 |       10.47
vw1mvgroslev |      26.39    0.0000 |      132.08   0.0000 |       31.41

Stock-Yogo weak ID test critical values for single endogenous regressor:
                                    5% maximal IV relative bias    18.37
                                   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)=39.89    P-val=0.0000

Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic                                       8.10

Stock-Yogo weak ID test critical values for K1=2 and L1=5:
                                    5% maximal IV relative bias    13.97
                                   10% maximal IV relative bias     8.78
                                   20% maximal IV relative bias     5.91
                                   30% maximal IV relative bias     4.79
                                   10% maximal IV size             19.45
                                   15% maximal IV size             11.22
                                   20% maximal IV size              8.38
                                   25% maximal IV size              6.89
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(5,605)=      12.01     P-val=0.0000
Anderson-Rubin Wald test           Chi-sq(5)=     63.12     P-val=0.0000
Stock-Wright LM S statistic        Chi-sq(5)=     57.42     P-val=0.0000

Number of observations               N  =        804
Number of regressors                 K  =         28
Number of endogenous regressors      K1 =          2
Number of instruments                L  =         31
Number of excluded instruments       L1 =          5

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

Estimates efficient for homoskedasticity only
Statistics consistent for homoskedasticity only

                                                      Number of obs =     
804
                                                      F( 28,   608) =   
14.74
                                                      Prob > F      =  
0.0000
Total (centered) SS     =   3219.94508                Centered R2   =  
0.2599
Total (uncentered) SS   =   3219.94508                Uncentered R2 =  
0.2599
Residual SS             =  2383.133334                Root MSE      =   
1.936

------------------------------------------------------------------------------
  vw1edf1dec |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------------
vw1totader~s |  -3.034654   .9885563    -3.07   0.002    -4.972189  
-1.097119
vw1mvgroslev |   14.48846   2.485216     5.83   0.000     9.617527   
19.35939
vw1excessf~h |  -.7801844   .2733838    -2.85   0.004    -1.316007   
-.244362
vw1pretaxm~n |   .0102553   .0038112     2.69   0.007     .0027855    
.017725
    vw1eqvol |  -.8942745   .9533853    -0.94   0.348    -2.762875   
.9743263
vw1lntotas~s |  -1.541133   .2996431    -5.14   0.000    -2.128422  
-.9538429
vw1cashh~mve |    3.05282   .8282883     3.69   0.000     1.429405   
4.676235
          d2 |   3.484726   1.833916     1.90   0.057     -.109683   
7.079136
          d3 |   .8835653   1.064034     0.83   0.406    -1.201902   
2.969033
          d4 |   .7729139   1.064498     0.73   0.468    -1.313463   
2.859291
          d5 |   .6254325   1.026037     0.61   0.542    -1.385562   
2.636427
          d6 |   .3913967   1.147668     0.34   0.733    -1.857992   
2.640786
          d7 |   1.306506   .9816525     1.33   0.183    -.6174975    
3.23051
          d8 |   1.135615   1.078756     1.05   0.292    -.9787081   
3.249938
          d9 |   1.881111   1.365601     1.38   0.168     -.795417   
4.557639
         d10 |  -.5767593   2.088488    -0.28   0.782    -4.670121   
3.516602
         d11 |   .7251487   1.048418     0.69   0.489    -1.329713    
2.78001
       yr_99 |  -.1658262   .7943723    -0.21   0.835    -1.722767   
1.391115
       yr_00 |   .3909581   .8647931     0.45   0.651    -1.304005   
2.085922
       yr_01 |   2.065182   1.086524     1.90   0.057    -.0643666    
4.19473
       yr_02 |  -.9824023   .9153829    -1.07   0.283     -2.77652   
.8117152
       yr_03 |  -.1611752   .9105961    -0.18   0.860    -1.945911    
1.62356
       yr_04 |   1.086254   .9950872     1.09   0.275    -.8640816   
3.036589
       yr_05 |   .6030185   .9416998     0.64   0.522    -1.242679   
2.448716
       yr_06 |  -1.317055   .9650863    -1.36   0.172     -3.20859   
.5744793
       yr_07 |  -.7846946   .8991489    -0.87   0.383    -2.546994   
.9776049
       yr_08 |  -1.013266    1.01814    -1.00   0.320    -3.008783   
.9822514
       yr_09 |   .9545142   .9933404     0.96   0.337    -.9923972   
2.901426
------------------------------------------------------------------------------
Underidentification test (Anderson canon. corr. LM statistic):         
39.891
                                                   Chi-sq(4) P-val =   
0.0000
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic):               
8.097
Stock-Yogo weak ID test critical values:  5% maximal IV relative bias   
13.97
                                         10% maximal IV relative bias    
8.78
                                         20% maximal IV relative bias    
5.91
                                         30% maximal IV relative bias    
4.79
                                         10% maximal IV size            
19.45
                                         15% maximal IV size            
11.22
                                         20% maximal IV size             
8.38
                                         25% maximal IV size             
6.89
Source: Stock-Yogo (2005).  Reproduced by permission.
------------------------------------------------------------------------------
Sargan statistic (overidentification test of all instruments):          
4.604
                                                   Chi-sq(3) P-val =   
0.2032
-endog- option:
Endogeneity test of endogenous regressors:                             
29.006
                                                   Chi-sq(2) P-val =   
0.0000
Regressors tested:    vw1totadertotototass vw1mvgroslev
------------------------------------------------------------------------------
Instrumented:         vw1totadertotototass vw1mvgroslev
Included instruments: vw1excessftseallsh vw1pretaxmargin vw1eqvol
vw1lntotassets
                      vw1cashholdmve d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 yr_99
yr_00
                      yr_01 yr_02 yr_03 yr_04 yr_05 yr_06 yr_07 yr_08 yr_09
Excluded instruments: vw1rds fxsales2 irheg09 vw1lntotsal vw1ndts4mv

I really appreciate your help.

Thanks a lot.

--
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