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  • 2SLS using ivreg2

    im using the command ivreg2 for 2 SLS and im facing problem when i add i.year i.SIC_WRDS_2 , actually the endogeneity test result does not appear and warning sign appear for me this is my code for 2sls

    ivreg2 hard_final_Exact_new Firm_Size_w ROA_four_w DCAPEX_w TAX_rate_w KZ_one_w DDIVi_w Leverage_w Book_Market_s_w UNION dividends_w FREE_CASH_FLOW_w CASH_FLOW_VOLATILITY_w Governance_Score_w Fund_Status_w FUNDING_RATIO_w Platn_Size_w Pension_contrib_four_w ACTUAL_RETURN_w CSR_Committee SustainabilityScore_w i.year i.SIC_WRDS_2 (csopresence1 = CSO_Percentage ) , first endog(csopresence1) robust cluster (id)



    Warning: estimated covariance matrix of moment conditions not of full rank.
    overidentification statistic not reported, and standard errors and
    model tests should be interpreted with caution.
    Possible causes:
    number of clusters insufficient to calculate robust covariance matrix
    singleton dummy variable (dummy with one 1 and N-1 0s or vice versa)
    partial option may address problem.




    HTML Code:
          ivreg2  hard_final_Exact_new   Firm_Size_w   ROA_four_w     DCAPEX_w TAX_rate_w  KZ_one_w    DDIVi_w   Leverage_w    Book_Market_s_w UNION  dividends_w  FREE_CASH_FLOW_w  CASH_FLOW_VOLATILITY_w  Governance_Score_w    Fund_Statu
    > s_w  FUNDING_RATIO_w  Platn_Size_w  Pension_contrib_four_w  ACTUAL_RETURN_w  CSR_Committee    SustainabilityScore_w    i.year    i.SIC_WRDS_2    (csopresence1 = CSO_Percentage )   , first endog(csopresence1) robust    cluster (id)
    
    First-stage regressions
    
    
    
    First-stage regression of csopresence1:
    
    Statistics robust to heteroskedasticity and clustering on id
    Number of obs =                   3336
    Number of clusters (id) =          263
    
    Robust
    csopresence1  Coefficient  std. err.      t    P>t     [95% conf. interval]
    
    CSO_Percentage    1.097992   .0907797    12.10   0.000     .9200013    1.275983
    Firm_Size_w    .0121108     .02667     0.45   0.650    -.0401809    .0644024
    ROA_four_w   -.1025899   .7043419    -0.15   0.884    -1.483588    1.278408
    DCAPEX_w    .8024182   .5033664     1.59   0.111    -.1845285    1.789365
    TAX_rate_w    .0011333   .0314563     0.04   0.971    -.0605428    .0628094
    KZ_one_w    .0479463   .0252224     1.90   0.057    -.0015071    .0973997
    DDIVi_w   -4128.335   7197.016    -0.57   0.566    -18239.47    9982.802
    Leverage_w   -.2111824   .1469058    -1.44   0.151    -.4992196    .0768547
    Book_Market_s_w   -.0231991   .0605911    -0.38   0.702    -.1419996    .0956014
    UNION   -.0992665   .1675468    -0.59   0.554    -.4277743    .2292413
    dividends_w    1.089643   1.323025     0.82   0.410    -1.504403    3.683689
    FREE_CASH_FLOW_w    .4497031   .6689588     0.67   0.501    -.8619195    1.761326
    CASH_FLOW_VOLATILITY_w    1.150295   .8068628     1.43   0.154    -.4317149    2.732305
    Governance_Score_w   -.0000811   .0006863    -0.12   0.906    -.0014268    .0012646
    Fund_Status_w    .6693949   .6632205     1.01   0.313    -.6309766    1.969766
    FUNDING_RATIO_w   -.0515603   .1082133    -0.48   0.634    -.2637333    .1606128
    Platn_Size_w    .0495668   .0200231     2.48   0.013     .0103076     .088826
    Pension_contrib_four_w    .1194941   1.410955     0.08   0.933    -2.646956    2.885944
    ACTUAL_RETURN_w   -.0670515   .0799868    -0.84   0.402    -.2238811    .0897782
    CSR_Committee    .0889497   .0272679     3.26   0.001     .0354858    .1424136
    SustainabilityScore_w     .001427   .0009573     1.49   0.136      -.00045     .003304
    
    year 
    2005    -.0088024   .0123333    -0.71   0.475    -.0329843    .0153794
    2006    -.0349848   .0188321    -1.86   0.063    -.0719088    .0019393
    2007    -.0523651   .0293687    -1.78   0.075    -.1099481    .0052179
    2008    -.0641598    .042688    -1.50   0.133    -.1478579    .0195383
    2009    -.0747544   .0365587    -2.04   0.041    -.1464348    -.003074
    2010    -.0929572   .0369199    -2.52   0.012    -.1653457   -.0205687
    2011     -.092446   .0393399    -2.35   0.019    -.1695796   -.0153125
    2012    -.0818239   .0395148    -2.07   0.038    -.1593003   -.0043476
    2013    -.0700623    .041613    -1.68   0.092    -.1516525    .0115279
    2014    -.0886871    .041059    -2.16   0.031    -.1691912   -.0081831
    2015    -.0765017   .0447721    -1.71   0.088     -.164286    .0112826
    2016    -.0633824     .04783    -1.33   0.185    -.1571623    .0303975
    2017    -.0987523   .0484569    -2.04   0.042    -.1937614   -.0037432
    2018    -.1196817    .054697    -2.19   0.029    -.2269258   -.0124376
    2019    -.1588183   .0594671    -2.67   0.008    -.2754151   -.0422215
    2020    -.1710352   .0651368    -2.63   0.009    -.2987484    -.043322
    2021    -.2086016   .0659653    -3.16   0.002    -.3379393    -.079264
    2022    -.1012898   .0864433    -1.17   0.241    -.2707785    .0681989
    
    SIC_WRDS_2 
    13     .0736134   .2369962     0.31   0.756    -.3910632    .5382901
    14     .2287164   .2434955     0.94   0.348    -.2487035    .7061363
    20     .2149059   .2912886     0.74   0.461    -.3562216    .7860333
    21     .1147433   .3006407     0.38   0.703    -.4747207    .7042073
    23     .4745806   .2932425     1.62   0.106    -.1003777    1.049539
    26     .1602168   .3010061     0.53   0.595    -.4299637    .7503972
    27     .2742583   .2487849     1.10   0.270    -.2135324     .762049
    28     .2451585    .296396     0.83   0.408    -.3359829    .8262999
    29    -.0209918   .2428064    -0.09   0.931    -.4970604    .4550769
    34     .1962369   .2430616     0.81   0.420    -.2803322     .672806
    35     .2500212   .3052323     0.82   0.413    -.3484455    .8484879
    36     .1649337   .2523935     0.65   0.513    -.3299324    .6597998
    37     .1717966   .2793391     0.62   0.539    -.3759015    .7194947
    38     .1874449   .2357533     0.80   0.427     -.274795    .6496847
    39       .20663   .2513227     0.82   0.411    -.2861365    .6993965
    40     .0957867    .317558     0.30   0.763    -.5268469    .7184204
    42     .3643892   .2367241     1.54   0.124    -.0997539    .8285323
    45     .3854578   .2629495     1.47   0.143    -.1301053    .9010208
    48     .3334553   .3174844     1.05   0.294     -.289034    .9559447
    49     .2274079   .2879681     0.79   0.430    -.3372091    .7920248
    50     .1988547    .243241     0.82   0.414     -.278066    .6757755
    51      .145865   .2349346     0.62   0.535    -.3147695    .6064996
    53     .1850267   .2249239     0.82   0.411      -.25598    .6260334
    54     .0291998   .2170815     0.13   0.893    -.3964302    .4548298
    55     .3693436    .230422     1.60   0.109     -.082443    .8211302
    56     .1660768   .2369974     0.70   0.484    -.2986022    .6307558
    58      .100971   .2324042     0.43   0.664    -.3547022    .5566443
    59     .5067339   .2283996     2.22   0.027     .0589126    .9545553
    60     .1046779   .2468537     0.42   0.672    -.3793264    .5886821
    61     -.107855   .2740907    -0.39   0.694    -.6452626    .4295526
    62      .067392   .2405542     0.28   0.779    -.4042608    .5390449
    63     .1309878   .2387393     0.55   0.583    -.3371066    .5990823
    64     .0149947   .2770663     0.05   0.957     -.528247    .5582365
    70     .0373064   .2236936     0.17   0.868     -.401288    .4759007
    72     .3207766   .2422015     1.32   0.185     -.154106    .7956593
    73     .2236427   .2353691     0.95   0.342    -.2378438    .6851292
    80     .1387708   .2637979     0.53   0.599    -.3784558    .6559975
    87     .0552034   .2434282     0.23   0.821    -.4220844    .5324913
    99    -.0079205   .2893155    -0.03   0.978    -.5751793    .5593383
    
    _cons   -.6292929   .3297123    -1.91   0.056    -1.275757    .0171715
    
    F test of excluded instruments:
    F(  1,   262) =   146.29
    Prob > F      =   0.0000
    Sanderson-Windmeijer multivariate F test of excluded instruments:
    F(  1,   262) =   146.29
    Prob > F      =   0.0000
    
    
    
    Summary results for first-stage regressions
    
    
    (Underid)            (Weak id)
    Variable      F(  1,   262)  P-val  SW Chi-sq(  1) P-val  SW F(  1,   262)
    csopresence1      146.29    0.0000       150.37   0.0000       146.29
    
    NB: first-stage test statistics cluster-robust
    
    Stock-Yogo weak ID F test critical values for single endogenous regressor:
    10% maximal IV size             16.38
    15% maximal IV size              8.96
    20% maximal IV size              6.66
    25% maximal IV size              5.53
    Source: Stock-Yogo (2005).  Reproduced by permission.
    NB: Critical values are for i.i.d. errors only.
    
    Underidentification test
    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)=43.88    P-val=0.0000
    
    Weak identification test
    Ho: equation is weakly identified
    Cragg-Donald Wald F statistic                                     296.81
    Kleibergen-Paap Wald rk F statistic                               146.29
    
    Stock-Yogo weak ID test critical values for K1=1 and L1=1:
    10% maximal IV size             16.38
    15% maximal IV size              8.96
    20% maximal IV size              6.66
    25% maximal IV size              5.53
    Source: Stock-Yogo (2005).  Reproduced by permission.
    NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
    
    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(1,262)=       9.20     P-val=0.0027
    Anderson-Rubin Wald test           Chi-sq(1)=      9.45     P-val=0.0021
    Stock-Wright LM S statistic        Chi-sq(1)=         .     P-val=     .
    
    NB: Underidentification, weak identification and weak-identification-robust
    test statistics cluster-robust
    
    Number of clusters             N_clust  =        263
    Number of observations               N  =       3336
    Number of regressors                 K  =         79
    Number of endogenous regressors      K1 =          1
    Number of instruments                L  =         79
    Number of excluded instruments       L1 =          1
    
    IV (2SLS) estimation
    
    
    Estimates efficient for homoskedasticity only
    Statistics robust to heteroskedasticity and clustering on id
    
    Number of clusters (id) =          263                Number of obs =     3336
    F( 78,   262) =   142.11
    Prob > F      =   0.0000
    Total (centered) SS     =  72.35851319                Centered R2   =   0.0077
    Total (uncentered) SS   =           74                Uncentered R2 =   0.0297
    Residual SS             =  71.79926397                Root MSE      =    .1467
    
    
    Robust
    hard_final_Exact_new  Coefficient  std. err.      z    P>z     [95% conf. interval]
    
    csopresence1    .0801542   .0264878     3.03   0.002      .028239    .1320694
    Firm_Size_w   -.0078716   .0055547    -1.42   0.156    -.0187586    .0030154
    ROA_four_w   -.3641893   .1255164    -2.90   0.004     -.610197   -.1181817
    DCAPEX_w    .0200928   .1687929     0.12   0.905    -.3107352    .3509209
    TAX_rate_w   -.0069881   .0133136    -0.52   0.600    -.0330823    .0191061
    KZ_one_w   -.0116238    .009556    -1.22   0.224    -.0303532    .0071057
    DDIVi_w    4011.996   4007.044     1.00   0.317    -3841.667    11865.66
    Leverage_w    .0193079   .0389954     0.50   0.621    -.0571216    .0957374
    Book_Market_s_w   -.0119774   .0154124    -0.78   0.437    -.0421851    .0182303
    UNION    .0093873   .0289523     0.32   0.746    -.0473582    .0661328
    dividends_w   -.2672219   .4100998    -0.65   0.515    -1.071003    .5365589
    FREE_CASH_FLOW_w    .2570271   .1226137     2.10   0.036     .0167086    .4973455
    CASH_FLOW_VOLATILITY_w   -.0511036   .1569072    -0.33   0.745    -.3586361    .2564289
    Governance_Score_w    .0002583   .0001433     1.80   0.071    -.0000225    .0005392
    Fund_Status_w   -.3053186   .1467278    -2.08   0.037    -.5928998   -.0177373
    FUNDING_RATIO_w   -.0054256   .0238981    -0.23   0.820     -.052265    .0414138
    Platn_Size_w    .0000947   .0041335     0.02   0.982    -.0080069    .0081963
    Pension_contrib_four_w   -1.295574    .416823    -3.11   0.002    -2.112532   -.4786159
    ACTUAL_RETURN_w    .0085612   .0451347     0.19   0.850    -.0799012    .0970235
    CSR_Committee   -.0061234   .0067271    -0.91   0.363    -.0193082    .0070614
    SustainabilityScore_w    .0000651   .0001901     0.34   0.732    -.0003074    .0004376
    
    year 
    2005    -.0098083   .0073261    -1.34   0.181    -.0241673    .0045507
    2006     -.005745   .0074425    -0.77   0.440    -.0203321    .0088421
    2007     .0048789   .0108217     0.45   0.652    -.0163312    .0260891
    2008     .0163541   .0207674     0.79   0.431    -.0243492    .0570574
    2009     .0324826   .0175828     1.85   0.065     -.001979    .0669442
    2010     .0131961   .0146464     0.90   0.368    -.0155103    .0419025
    2011        .0002   .0129329     0.02   0.988    -.0251479     .025548
    2012     .0102419   .0159234     0.64   0.520    -.0209673    .0414511
    2013     .0026298   .0139868     0.19   0.851    -.0247838    .0300435
    2014     .0047771   .0150498     0.32   0.751    -.0247199    .0342742
    2015      .006459   .0176337     0.37   0.714    -.0281023    .0410204
    2016    -.0128889   .0160978    -0.80   0.423      -.04444    .0186622
    2017    -.0164484   .0148177    -1.11   0.267    -.0454905    .0125938
    2018      .006521   .0186376     0.35   0.726     -.030008    .0430499
    2019    -.0196788   .0147382    -1.34   0.182    -.0485651    .0092074
    2020    -.0005993   .0215407    -0.03   0.978    -.0428184    .0416198
    2021    -.0249734   .0164056    -1.52   0.128    -.0571279     .007181
    2022    -.0115215   .0297746    -0.39   0.699    -.0698786    .0468356
    
    SIC_WRDS_2 
    13     .0119952   .0265481     0.45   0.651    -.0400381    .0640286
    14    -.0212259   .0199625    -1.06   0.288    -.0603517    .0178998
    20    -.0388021   .0342265    -1.13   0.257    -.1058848    .0282806
    21    -.0651825   .0368441    -1.77   0.077    -.1373957    .0070306
    23    -.0158226     .03285    -0.48   0.630    -.0802073    .0485621
    26    -.0412067   .0384407    -1.07   0.284    -.1165491    .0341358
    27    -.0153482   .0262752    -0.58   0.559    -.0668466    .0361502
    28     -.035293   .0326578    -1.08   0.280     -.099301     .028715
    29     .0121797   .0258391     0.47   0.637     -.038464    .0628233
    34    -.0366601   .0197159    -1.86   0.063    -.0753027    .0019824
    35    -.0329561   .0341038    -0.97   0.334    -.0997984    .0338861
    36    -.0300153    .018292    -1.64   0.101     -.065867    .0058364
    37     -.021545   .0305597    -0.71   0.481     -.081441     .038351
    38    -.0149084   .0191952    -0.78   0.437    -.0525303    .0227134
    39     .1549795   .0171361     9.04   0.000     .1213933    .1885657
    40    -.0268583   .0252582    -1.06   0.288    -.0763634    .0226467
    42    -.0537804   .0152938    -3.52   0.000    -.0837557    -.023805
    45      -.00453   .0423727    -0.11   0.915     -.087579     .078519
    48    -.0118183   .0430402    -0.27   0.784    -.0961755    .0725389
    49    -.0262954   .0324767    -0.81   0.418    -.0899485    .0373577
    50     .0534646   .0202092     2.65   0.008     .0138553     .093074
    51     .0808119   .0178282     4.53   0.000     .0458692    .1157545
    53    -.0340633    .012588    -2.71   0.007    -.0587353   -.0093913
    54     .0167346   .0121019     1.38   0.167    -.0069847    .0404539
    55     .1740546   .0164443    10.58   0.000     .1418244    .2062848
    56    -.0076884   .0195395    -0.39   0.694    -.0459852    .0306084
    58    -.0167598   .0186669    -0.90   0.369    -.0533463    .0198267
    59    -.0850228   .0123317    -6.89   0.000    -.1091925    -.060853
    60    -.0085479   .0262765    -0.33   0.745    -.0600489     .042953
    61     .0418616   .0497663     0.84   0.400    -.0556787    .1394018
    62     .0274917    .038859     0.71   0.479    -.0486705    .1036538
    63     .0035319   .0262013     0.13   0.893    -.0478218    .0548856
    64     .0080424   .0314679     0.26   0.798    -.0536336    .0697184
    70    -.0793502    .020918    -3.79   0.000    -.1203487   -.0383516
    72    -.0364841   .0189971    -1.92   0.055    -.0737178    .0007496
    73    -.0250073   .0214818    -1.16   0.244    -.0671109    .0170963
    80     .0100795   .0360277     0.28   0.780    -.0605335    .0806926
    87    -.0193404   .0225085    -0.86   0.390    -.0634563    .0247755
    99    -.0294638   .0280938    -1.05   0.294    -.0845266    .0255989
    
    _cons    .1137578   .0519667     2.19   0.029     .0119049    .2156106
    
    Underidentification test (Kleibergen-Paap rk LM statistic):             43.876
    Chi-sq(1) P-val =    0.0000
    
    Weak identification test (Cragg-Donald Wald F statistic):              296.811
    (Kleibergen-Paap rk Wald F statistic):        146.292
    Stock-Yogo weak ID test critical values: 10% maximal IV size             16.38
    15% maximal IV size              8.96
    20% maximal IV size              6.66
    25% maximal IV size              5.53
    Source: Stock-Yogo (2005).  Reproduced by permission.
    NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
    
    Warning: estimated covariance matrix of moment conditions not of full rank.
    overidentification statistic not reported, and standard errors and
    model tests should be interpreted with caution.
    Possible causes:
    number of clusters insufficient to calculate robust covariance matrix
    singleton dummy variable (dummy with one 1 and N-1 0s or vice versa)
    partial option may address problem.
    
    Instrumented:         csopresence1
    Included instruments: Firm_Size_w ROA_four_w DCAPEX_w TAX_rate_w KZ_one_w
    DDIVi_w Leverage_w Book_Market_s_w UNION dividends_w
    FREE_CASH_FLOW_w CASH_FLOW_VOLATILITY_w Governance_Score_w
    Fund_Status_w FUNDING_RATIO_w Platn_Size_w
    Pension_contrib_four_w ACTUAL_RETURN_w CSR_Committee
    SustainabilityScore_w 2005.year 2006.year 2007.year
    2008.year 2009.year 2010.year 2011.year 2012.year
    2013.year 2014.year 2015.year 2016.year 2017.year
    2018.year 2019.year 2020.year 2021.year 2022.year
    13.SIC_WRDS_2 14.SIC_WRDS_2 20.SIC_WRDS_2 21.SIC_WRDS_2
    23.SIC_WRDS_2 26.SIC_WRDS_2 27.SIC_WRDS_2 28.SIC_WRDS_2
    29.SIC_WRDS_2 34.SIC_WRDS_2 35.SIC_WRDS_2 36.SIC_WRDS_2
    37.SIC_WRDS_2 38.SIC_WRDS_2 39.SIC_WRDS_2 40.SIC_WRDS_2
    42.SIC_WRDS_2 45.SIC_WRDS_2 48.SIC_WRDS_2 49.SIC_WRDS_2
    50.SIC_WRDS_2 51.SIC_WRDS_2 53.SIC_WRDS_2 54.SIC_WRDS_2
    55.SIC_WRDS_2 56.SIC_WRDS_2 58.SIC_WRDS_2 59.SIC_WRDS_2
    60.SIC_WRDS_2 61.SIC_WRDS_2 62.SIC_WRDS_2 63.SIC_WRDS_2
    64.SIC_WRDS_2 70.SIC_WRDS_2 72.SIC_WRDS_2 73.SIC_WRDS_2
    80.SIC_WRDS_2 87.SIC_WRDS_2 99.SIC_WRDS_2
    Excluded instruments: CSO_Percentage
    .

  • #2
    after that in the warning sign it tell me to use code ( partial ) but when i use it the constant for the regression disappear ,
    HTML Code:
     ivreg2  hard_final_Exact_new   Firm_Size_w   ROA_four_w     DCAPEX_w TAX_rate_w  KZ_one_w    DDIVi_w   Leverage_w   Book_Market_s_w UNION  dividends_w  FREE_CASH_FLOW_w  CASH_FLOW_VOLATILITY_w  Governance_Score_w   Fund_Statu
    > s_w  FUNDING_RATIO_w  Platn_Size_w  Pension_contrib_four_w  ACTUAL_RETURN_w  CSR_Committee  SustainabilityScore_w    i.year    i.SIC_WRDS_2 (csopresence1 = CSO_Percentage )   , partial (i.SIC_WRDS_2  i.year   )   first endog(
    > csopresence1) robust cluster (id)
    
    First-stage regressions
    -----------------------
    
    
    First-stage regression of csopresence1:
    
    Statistics robust to heteroskedasticity and clustering on id
    Number of obs =                   3336
    Number of clusters (id) =          263
    ----------------------------------------------------------------------------------------
                           |               Robust
              csopresence1 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
    -----------------------+----------------------------------------------------------------
            CSO_Percentage |   1.097992   .0907797    12.10   0.000     .9200013    1.275983
               Firm_Size_w |   .0121108     .02667     0.45   0.650    -.0401809    .0644024
                ROA_four_w |  -.1025899   .7043419    -0.15   0.884    -1.483588    1.278408
                  DCAPEX_w |   .8024182   .5033664     1.59   0.111    -.1845285    1.789365
                TAX_rate_w |   .0011333   .0314563     0.04   0.971    -.0605428    .0628094
                  KZ_one_w |   .0479463   .0252224     1.90   0.057    -.0015071    .0973997
                   DDIVi_w |  -4128.335   7197.016    -0.57   0.566    -18239.47    9982.802
                Leverage_w |  -.2111824   .1469058    -1.44   0.151    -.4992196    .0768547
           Book_Market_s_w |  -.0231991   .0605911    -0.38   0.702    -.1419996    .0956014
                     UNION |  -.0992665   .1675468    -0.59   0.554    -.4277743    .2292413
               dividends_w |   1.089643   1.323025     0.82   0.410    -1.504403    3.683689
          FREE_CASH_FLOW_w |   .4497031   .6689588     0.67   0.501    -.8619195    1.761326
    CASH_FLOW_VOLATILITY_w |   1.150295   .8068628     1.43   0.154    -.4317149    2.732305
        Governance_Score_w |  -.0000811   .0006863    -0.12   0.906    -.0014268    .0012646
             Fund_Status_w |   .6693949   .6632205     1.01   0.313    -.6309766    1.969766
           FUNDING_RATIO_w |  -.0515603   .1082133    -0.48   0.634    -.2637333    .1606128
              Platn_Size_w |   .0495668   .0200231     2.48   0.013     .0103076     .088826
    Pension_contrib_four_w |   .1194941   1.410955     0.08   0.933    -2.646956    2.885944
           ACTUAL_RETURN_w |  -.0670515   .0799868    -0.84   0.402    -.2238811    .0897782
             CSR_Committee |   .0889497   .0272679     3.26   0.001     .0354858    .1424136
     SustainabilityScore_w |    .001427   .0009573     1.49   0.136      -.00045     .003304
    ----------------------------------------------------------------------------------------
    F test of excluded instruments:
      F(  1,   262) =   146.29
      Prob > F      =   0.0000
    Sanderson-Windmeijer multivariate F test of excluded instruments:
      F(  1,   262) =   146.29
      Prob > F      =   0.0000
    
    
    
    Summary results for first-stage regressions
    -------------------------------------------
    
                                               (Underid)            (Weak id)
    Variable     | F(  1,   262)  P-val | SW Chi-sq(  1) P-val | SW F(  1,   262)
    csopresence1 |     146.29    0.0000 |      150.37   0.0000 |      146.29
    
    NB: first-stage test statistics cluster-robust
    
    Stock-Yogo weak ID F test critical values for single endogenous regressor:
                                       10% maximal IV size             16.38
                                       15% maximal IV size              8.96
                                       20% maximal IV size              6.66
                                       25% maximal IV size              5.53
    Source: Stock-Yogo (2005).  Reproduced by permission.
    NB: Critical values are for i.i.d. errors only.
    
    Underidentification test
    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)=43.88    P-val=0.0000
    
    Weak identification test
    Ho: equation is weakly identified
    Cragg-Donald Wald F statistic                                     296.81
    Kleibergen-Paap Wald rk F statistic                               146.29
    
    Stock-Yogo weak ID test critical values for K1=1 and L1=1:
                                       10% maximal IV size             16.38
                                       15% maximal IV size              8.96
                                       20% maximal IV size              6.66
                                       25% maximal IV size              5.53
    Source: Stock-Yogo (2005).  Reproduced by permission.
    NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
    
    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(1,262)=       9.20     P-val=0.0027
    Anderson-Rubin Wald test           Chi-sq(1)=      9.45     P-val=0.0021
    Stock-Wright LM S statistic        Chi-sq(1)=     11.12     P-val=0.0009
    
    NB: Underidentification, weak identification and weak-identification-robust
        test statistics cluster-robust
    
    Number of clusters             N_clust  =        263
    Number of observations               N  =       3336
    Number of regressors                 K  =         21
    Number of endogenous regressors      K1 =          1
    Number of instruments                L  =         21
    Number of excluded instruments       L1 =          1
    Number of partialled-out regressors/IVs =         58
    NB: K & L do not included partialled-out variables
    
    IV (2SLS) estimation
    --------------------
    
    Estimates efficient for homoskedasticity only
    Statistics robust to heteroskedasticity and clustering on id
    
    Number of clusters (id) =          263                Number of obs =     3336
                                                          F( 21,   262) =     1.64
                                                          Prob > F      =   0.0402
    Total (centered) SS     =  70.48208283                Centered R2   =  -0.0187
    Total (uncentered) SS   =  70.48208283                Uncentered R2 =  -0.0187
    Residual SS             =  71.79926397                Root MSE      =    .1467
    
    ----------------------------------------------------------------------------------------
                           |               Robust
      hard_final_Exact_new | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
    -----------------------+----------------------------------------------------------------
              csopresence1 |   .0801542   .0264878     3.03   0.002      .028239    .1320694
               Firm_Size_w |  -.0078716   .0055547    -1.42   0.156    -.0187586    .0030154
                ROA_four_w |  -.3641893   .1255164    -2.90   0.004     -.610197   -.1181817
                  DCAPEX_w |   .0200928   .1687929     0.12   0.905    -.3107352    .3509209
                TAX_rate_w |  -.0069881   .0133136    -0.52   0.600    -.0330823    .0191061
                  KZ_one_w |  -.0116238    .009556    -1.22   0.224    -.0303532    .0071057
                   DDIVi_w |   4011.996   4007.044     1.00   0.317    -3841.667    11865.66
                Leverage_w |   .0193079   .0389954     0.50   0.621    -.0571216    .0957374
           Book_Market_s_w |  -.0119774   .0154124    -0.78   0.437    -.0421851    .0182303
                     UNION |   .0093873   .0289523     0.32   0.746    -.0473582    .0661328
               dividends_w |  -.2672219   .4100998    -0.65   0.515    -1.071003    .5365589
          FREE_CASH_FLOW_w |   .2570271   .1226137     2.10   0.036     .0167086    .4973455
    CASH_FLOW_VOLATILITY_w |  -.0511036   .1569072    -0.33   0.745    -.3586361    .2564289
        Governance_Score_w |   .0002583   .0001433     1.80   0.071    -.0000225    .0005392
             Fund_Status_w |  -.3053186   .1467278    -2.08   0.037    -.5928998   -.0177373
           FUNDING_RATIO_w |  -.0054256   .0238981    -0.23   0.820     -.052265    .0414138
              Platn_Size_w |   .0000947   .0041335     0.02   0.982    -.0080069    .0081963
    Pension_contrib_four_w |  -1.295574    .416823    -3.11   0.002    -2.112532   -.4786159
           ACTUAL_RETURN_w |   .0085612   .0451347     0.19   0.850    -.0799012    .0970235
             CSR_Committee |  -.0061234   .0067271    -0.91   0.363    -.0193082    .0070614
     SustainabilityScore_w |   .0000651   .0001901     0.34   0.732    -.0003074    .0004376
    ----------------------------------------------------------------------------------------
    Underidentification test (Kleibergen-Paap rk LM statistic):             43.876
                                                       Chi-sq(1) P-val =    0.0000
    ------------------------------------------------------------------------------
    Weak identification test (Cragg-Donald Wald F statistic):              296.811
                             (Kleibergen-Paap rk Wald F statistic):        146.292
    Stock-Yogo weak ID test critical values: 10% maximal IV size             16.38
                                             15% maximal IV size              8.96
                                             20% maximal IV size              6.66
                                             25% maximal IV 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)
    -endog- option:
    Endogeneity test of endogenous regressors:                               7.532
                                                       Chi-sq(1) P-val =    0.0061
    Regressors tested:    csopresence1
    ------------------------------------------------------------------------------
    Instrumented:         csopresence1
    Included instruments: Firm_Size_w ROA_four_w DCAPEX_w TAX_rate_w KZ_one_w
                          DDIVi_w Leverage_w Book_Market_s_w UNION dividends_w
                          FREE_CASH_FLOW_w CASH_FLOW_VOLATILITY_w Governance_Score_w
                          Fund_Status_w FUNDING_RATIO_w Platn_Size_w
                          Pension_contrib_four_w ACTUAL_RETURN_w CSR_Committee
                          SustainabilityScore_w
    Excluded instruments: CSO_Percentage
    Partialled-out:       13.SIC_WRDS_2 14.SIC_WRDS_2 20.SIC_WRDS_2 21.SIC_WRDS_2
                          23.SIC_WRDS_2 26.SIC_WRDS_2 27.SIC_WRDS_2 28.SIC_WRDS_2
                          29.SIC_WRDS_2 34.SIC_WRDS_2 35.SIC_WRDS_2 36.SIC_WRDS_2
                          37.SIC_WRDS_2 38.SIC_WRDS_2 39.SIC_WRDS_2 40.SIC_WRDS_2
                          42.SIC_WRDS_2 45.SIC_WRDS_2 48.SIC_WRDS_2 49.SIC_WRDS_2
                          50.SIC_WRDS_2 51.SIC_WRDS_2 53.SIC_WRDS_2 54.SIC_WRDS_2
                          55.SIC_WRDS_2 56.SIC_WRDS_2 58.SIC_WRDS_2 59.SIC_WRDS_2
                          60.SIC_WRDS_2 61.SIC_WRDS_2 62.SIC_WRDS_2 63.SIC_WRDS_2
                          64.SIC_WRDS_2 70.SIC_WRDS_2 72.SIC_WRDS_2 73.SIC_WRDS_2
                          80.SIC_WRDS_2 87.SIC_WRDS_2 99.SIC_WRDS_2 2005.year
                          2006.year 2007.year 2008.year 2009.year 2010.year
                          2011.year 2012.year 2013.year 2014.year 2015.year
                          2016.year 2017.year 2018.year 2019.year 2020.year
                          2021.year 2022.year _cons
                          nb: total SS, model F and R2s are after partialling-out;
                              any small-sample adjustments include partialled-out
                              variables in regressor count K
    ------------------------------------------------------------------------------

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