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  • Instrumental Variable - Difference between included and excluded instruments

    Hello all,

    I am trying to run an IV regression with the ivreg2 command
    I want to instument esg with president congress and state_government and als want to add an interaction term between the predicted esg and advertising.
    This is my code and it runs perfectly fine, however I am not sure what included and excluded instruments at the emnd of my output means.
    would be awesome, if you could help me with that.

    Patrick

    Code:
    . ivreg2 firm_beta_w (esg_single c.esg_single#c.advertising_lag1 = president congress state_government c.president#c.advertising_lag1 c.congress#c.advertising_lag1 c.state_govern
    > ment#c.advertising_lag1) diversification_lag1 RnD_lag1 advertising_lag1 leverage_lag1 capex_lag1 cash_lag1 size_lag1 earnings_variability_lag1 state_tax_lag1 cash_flow_lag1 i.i
    > ndustry_key i.year, cluster (double_cluster)
    
    IV (2SLS) estimation
    --------------------
    
    Estimates efficient for homoskedasticity only
    Statistics robust to heteroskedasticity and clustering on double_cluster
    
    Number of clusters (double_cluster) =   5078          Number of obs =     5078
                                                          F( 52,  5077) =     5.92
                                                          Prob > F      =   0.0000
    Total (centered) SS     =  906.7431706                Centered R2   =  -2.2984
    Total (uncentered) SS   =  7018.699109                Uncentered R2 =   0.5739
    Residual SS             =  2990.819343                Root MSE      =    .7674
    
    -------------------------------------------------------------------------------------------------
                                    |               Robust
                        firm_beta_w |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
    --------------------------------+----------------------------------------------------------------
                         esg_single |   3.641782   1.468439     2.48   0.013     .7636933     6.51987
                                    |
    c.esg_single#c.advertising_lag1 |   3.350082   2.830193     1.18   0.237    -2.196995    8.897159
                                    |
               diversification_lag1 |  -.0409026   .0148831    -2.75   0.006    -.0700729   -.0117323
                           RnD_lag1 |   -.790214   .6759942    -1.17   0.242    -2.115138    .5347103
                   advertising_lag1 |  -2.086695   1.305185    -1.60   0.110     -4.64481      .47142
                      leverage_lag1 |  -.2371276   .1306038    -1.82   0.069    -.4931064    .0188511
                         capex_lag1 |  -.1735033   .0502726    -3.45   0.001    -.2720357   -.0749709
                          cash_lag1 |   .0149469   .0095982     1.56   0.119    -.0038652     .033759
                          size_lag1 |  -.3632411   .1132335    -3.21   0.001    -.5851746   -.1413075
          earnings_variability_lag1 |   .0348496   .0107851     3.23   0.001     .0137112    .0559879
                     state_tax_lag1 |  -1.758741   .5530467    -3.18   0.001    -2.842693   -.6747892
                     cash_flow_lag1 |  -1.536057   .4528595    -3.39   0.001    -2.423645   -.6484688
                                    |
                       industry_key |
                                16  |  -1.035736   .3438716    -3.01   0.003    -1.709712   -.3617601
                                19  |  -.0163884   .1882117    -0.09   0.931    -.3852765    .3524997
                                22  |  -1.027894   .2370409    -4.34   0.000    -1.492486   -.5633028
                                25  |  -.7092032   .2650471    -2.68   0.007    -1.228686   -.1897204
                                28  |   -.270681   .1952307    -1.39   0.166    -.6533263    .1119642
                                31  |  -.2162985   .1606167    -1.35   0.178    -.5311016    .0985045
                                34  |  -.6365382   .1855579    -3.43   0.001    -1.000225   -.2728514
                                37  |  -.2419495   .1883621    -1.28   0.199    -.6111325    .1272335
                                40  |  -.5360543   .2120863    -2.53   0.011    -.9517358   -.1203729
                                43  |  -.4280807   .1684857    -2.54   0.011    -.7583065   -.0978548
                                46  |  -1.266207   .2876931    -4.40   0.000    -1.830075   -.7023385
                                49  |  -.4082653    .198143    -2.06   0.039    -.7966184   -.0199122
                                52  |  -.8010831   .3974006    -2.02   0.044    -1.579974   -.0221922
                                55  |  -.7300625   .3022019    -2.42   0.016    -1.322367   -.1377577
                                58  |  -.4206561   .1896787    -2.22   0.027    -.7924196   -.0488926
                                61  |  -.4476334    .232669    -1.92   0.054    -.9036562    .0083895
                                64  |  -.3491936   .3374465    -1.03   0.301    -1.010577    .3121895
                                67  |  -.1514687   .1536733    -0.99   0.324    -.4526629    .1497254
                                70  |  -.7948838   .2461711    -3.23   0.001     -1.27737   -.3123973
                                73  |  -.2534841   .2254281    -1.12   0.261     -.695315    .1883468
                                76  |  -1.216448   .3143974    -3.87   0.000    -1.832656   -.6002409
                                79  |  -.5627339   .2124819    -2.65   0.008    -.9791907    -.146277
                                82  |  -.6367618   .1737174    -3.67   0.000    -.9772417   -.2962819
                                85  |  -.3831806   .1771696    -2.16   0.031    -.7304266   -.0359346
                                    |
                               year |
                              2004  |  -.0751088    .104994    -0.72   0.474    -.2808932    .1306757
                              2005  |  -.1037309   .1263353    -0.82   0.412    -.3513436    .1438817
                              2006  |  -.1009591   .1346585    -0.75   0.453    -.3648848    .1629667
                              2007  |  -.4010997   .1722144    -2.33   0.020    -.7386337   -.0635656
                              2008  |  -.5051028   .2021503    -2.50   0.012    -.9013102   -.1088955
                              2009  |  -.5523198    .229715    -2.40   0.016    -1.002553   -.1020867
                              2010  |  -.6446896   .2584752    -2.49   0.013    -1.151292   -.1380875
                              2011  |  -.6575347   .2649707    -2.48   0.013    -1.176868   -.1382017
                              2012  |  -.6790412   .2618089    -2.59   0.009    -1.192177   -.1659051
                              2013  |  -.6545134   .2603327    -2.51   0.012    -1.164756   -.1442706
                              2014  |  -.6489779   .2600528    -2.50   0.013    -1.158672   -.1392838
                              2015  |   -.778726   .2875821    -2.71   0.007    -1.342377   -.2150755
                              2016  |   -.827802   .3286517    -2.52   0.012    -1.471948   -.1836564
                              2017  |  -.9341321     .34259    -2.73   0.006    -1.605596    -.262668
                              2018  |  -1.048702   .3522091    -2.98   0.003    -1.739019   -.3583846
                              2019  |  -.9575414   .3478008    -2.75   0.006    -1.639218   -.2758643
                                    |
                              _cons |   7.009552   1.756478     3.99   0.000     3.566918    10.45219
    -------------------------------------------------------------------------------------------------
    Underidentification test (Kleibergen-Paap rk LM statistic):             15.402
                                                       Chi-sq(5) P-val =    0.0088
    ------------------------------------------------------------------------------
    Weak identification test (Cragg-Donald Wald F statistic):                2.494
                             (Kleibergen-Paap rk Wald F statistic):          2.611
    Stock-Yogo weak ID test critical values:  5% maximal IV relative bias    15.72
                                             10% maximal IV relative bias     9.48
                                             20% maximal IV relative bias     6.08
                                             30% maximal IV relative bias     4.78
                                             10% maximal IV size             21.68
                                             15% maximal IV size             12.33
                                             20% maximal IV size              9.10
                                             25% maximal IV size              7.42
    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):         4.223
                                                       Chi-sq(4) P-val =    0.3766
    ------------------------------------------------------------------------------
    Instrumented:         esg_single c.esg_single#c.advertising_lag1
    Included instruments: diversification_lag1 RnD_lag1 advertising_lag1
                          leverage_lag1 capex_lag1 cash_lag1 size_lag1
                          earnings_variability_lag1 state_tax_lag1 cash_flow_lag1
                          16.industry_key 19.industry_key 22.industry_key
                          25.industry_key 28.industry_key 31.industry_key
                          34.industry_key 37.industry_key 40.industry_key
                          43.industry_key 46.industry_key 49.industry_key
                          52.industry_key 55.industry_key 58.industry_key
                          61.industry_key 64.industry_key 67.industry_key
                          70.industry_key 73.industry_key 76.industry_key
                          79.industry_key 82.industry_key 85.industry_key 2004.year
                          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
    Excluded instruments: president congress state_government
                          c.president#c.advertising_lag1
                          c.congress#c.advertising_lag1
                          c.state_government#c.advertising_lag1
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