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  • Interpret results from xtabond2

    Dear all,

    I have the results from xtabond2 as follows:
    Code:
    Dynamic panel-data estimation, two-step system GMM
    ------------------------------------------------------------------------------
    Group variable: firmid                          Number of obs      =       370
    Time variable : year                            Number of groups   =        56
    Number of instruments = 40                      Obs per group: min =         2
    F(28, 55)     =     17.64                                      avg =      6.61
    Prob > F      =     0.000                                      max =         9
    ------------------------------------------------------------------------------
                 |              Corrected
         lnTobin |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
    -------------+----------------------------------------------------------------
         lnTobin |
             L1. |   .3589312   .1495623     2.40   0.020     .0592016    .6586608
                 |
           PerFD |  -1.529385   .9790586    -1.56   0.124    -3.491462    .4326921
           After |  -.2640213   .1342461    -1.97   0.054    -.5330566     .005014
         AfterFD |   2.464606   1.261673     1.95   0.056    -.0638425    4.993055
          PerInD |   .4815669   .6739103     0.71   0.478    -.8689795    1.832113
            Dual |  -.0423404   .2274878    -0.19   0.853    -.4982362    .4135553
     lnCEOtenure |    .019317   .0855446     0.23   0.822    -.1521183    .1907522
            FCEO |   .0934513   .3517923     0.27   0.792    -.6115562    .7984589
           bsize |    1.34156   .6865983     1.95   0.056    -.0344134    2.717534
           lnage |  -.0837236   .0475913    -1.76   0.084    -.1790987    .0116515
        Firmsize |  -.0796772   .0762127    -1.05   0.300    -.2324109    .0730566
            blev |   .0898659   .3326785     0.27   0.788    -.5768368    .7565685
           y2001 |   .0924929   .5832582     0.16   0.875    -1.076383    1.261369
           y2002 |  -.0795403   .3058306    -0.26   0.796    -.6924385     .533358
           y2003 |   .2306446   .1815684     1.27   0.209    -.1332266    .5945159
           y2004 |    .232103   .1600517     1.45   0.153    -.0886478    .5528537
           y2005 |   .1602183   .0964058     1.66   0.102    -.0329833    .3534199
           y2006 |   .2876385   .0717168     4.01   0.000     .1439149    .4313621
           y2007 |   .2983802   .0771674     3.87   0.000     .1437333    .4530272
           y2009 |   .2357406   .0857651     2.75   0.008     .0638634    .4076177
           y2010 |   .2821254   .0938799     3.01   0.004     .0939859     .470265
           y2011 |   .2311672   .0806831     2.87   0.006     .0694747    .3928597
           y2012 |    .326781    .086148     3.79   0.000     .1541365    .4994255
           y2013 |   .2673544   .0890159     3.00   0.004     .0889627    .4457462
           y2014 |   .2717915   .1009934     2.69   0.009     .0693961    .4741868
           y2015 |    .174857   .1158495     1.51   0.137    -.0573106    .4070246
           y2016 |   .1760335   .1125244     1.56   0.123    -.0494705    .4015376
           y2017 |   .4763668   .1463013     3.26   0.002     .1831725    .7695611
           _cons |  -1.195517   1.267733    -0.94   0.350    -3.736111    1.345076
    ------------------------------------------------------------------------------
    Instruments for first differences equation
      Standard
        D.(After lnage 2000b.year 2001.year 2002.year 2003.year 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)
      GMM-type (missing=0, separate instruments for each period unless collapsed)
        L2.(AfterFD PerFD PerInD Dual lnCEOtenure FemaleCEO bsize Firmsize blev)
        collapsed
        L(2/3).lnTobin collapsed
    Instruments for levels equation
      Standard
        After lnage 2000b.year 2001.year 2002.year 2003.year 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
        _cons
      GMM-type (missing=0, separate instruments for each period unless collapsed)
        DL.(AfterFD PerFD PerInD Dual lnCEOtenure FemaleCEO bsize Firmsize blev)
        collapsed
        DL.lnTobin collapsed
    ------------------------------------------------------------------------------
    Arellano-Bond test for AR(1) in first differences: z =  -3.06  Pr > z =  0.002
    Arellano-Bond test for AR(2) in first differences: z =  -0.60  Pr > z =  0.547
    ------------------------------------------------------------------------------
    Sargan test of overid. restrictions: chi2(11)   =  12.16  Prob > chi2 =  0.352
      (Not robust, but not weakened by many instruments.)
    Hansen test of overid. restrictions: chi2(11)   =   7.04  Prob > chi2 =  0.796
      (Robust, but weakened by many instruments.)
    
    Difference-in-Hansen tests of exogeneity of instrument subsets:
      GMM instruments for levels
        Hansen test excluding group:     chi2(1)    =   3.88  Prob > chi2 =  0.049
        Difference (null H = exogenous): chi2(10)   =   3.16  Prob > chi2 =  0.977
      gmm(lnTobin, collapse eq(diff) lag(2 3))
        Hansen test excluding group:     chi2(9)    =   6.33  Prob > chi2 =  0.707
        Difference (null H = exogenous): chi2(2)    =   0.71  Prob > chi2 =  0.700
      gmm(lnTobin, collapse eq(diff) lag(2 3)) eq(level) lag(1 1))
        Hansen test excluding group:     chi2(10)   =   6.93  Prob > chi2 =  0.732
        Difference (null H = exogenous): chi2(1)    =   0.11  Prob > chi2 =  0.743
    My interest coefficient is AfterFD. And it is significant at 10%. Also, the AR(2) is not significant and Hansen test of overid restrictions is not significant. it means my regression work through, isn't it?

    In addition, could you please give me interpretation of Difference-in-Hansen test of exogeneity? As far as I understand, it should be insignificant. However, from the table, GMM instruments for levels - Hansen text excluding group: chi2(1) =3.88 Pro>chi2=0.049. Does it matter?

    Thank you very much in advance.

  • #2
    Sebastian Kripfganz Hi, could you please help me?

    Also, I do not know why Difference-in-Hansen test for some instrument subsets disappear.

    Thank you very much in advance.

    Regards,
    Celine

    Comment


    • #3
      The specification tests indeed do not give rise to concern. If everything else if fine, then I would not worry about the marginal rejection of this one Hansen test with a p-value of 0.049.

      Some of the Difference-in-Hansen tests are not shown because they would have negative degrees of freedom. In other words, excluding the respective instruments would lead to an underidentified model but you can only test overidentifying restrictions. The Difference-in-Hansen can be interpreted as a test for the validity of the additional moment conditions implied by the respective instruments, assuming that the model without those additional moment conditions is already correctly specified.

      Comment


      • #4
        Sebastian Kripfganz , Thank you very much for your help. However, honestly, it is quite difficult to understand.

        Here is my code and my result. Could you please have a look and let me know if there is any problems with my regression.

        I have 40 instruments, 56 groups of firms, 370 observations. I use the collapse option for gmm() and equation level for iv() as your suggestion in earlier post. However, one thing I am concerned is that the p-value of Hansen test of overid. restrictions is 0.826 (~1). It is quite high, compared to those in some papers. Does it matter?
        if yes, the reason causing the high p-value is "too many instruments", isn't it?

        Thank you very much in advance.

        I look forward to hearing from you.

        Regards,


        Code:
        xtabond2 lnTobin L.lnTobin PerFD After AfterFD $control y2001-y2017 if year1!=0
        > , gmm(lnTobin, lag(2 3) collapse split) gmm(AfterFD PerFD PerInD Dual lnCEOtenure F
        > CEO bsize,lag(2 2) collapse) gmm(Firmsize blev,lag(2 2) collapse) iv(After lnage i.year,
        >  equation(level)) small two ro

        Code:
         Dynamic panel-data estimation, two-step system GMM
        ------------------------------------------------------------------------------
        Group variable: firmid                          Number of obs      =       370
        Time variable : year                            Number of groups   =        56
        Number of instruments = 40                      Obs per group: min =         2
        F(28, 55)     =      9.37                                      avg =      6.61
        Prob > F      =     0.000                                      max =         9
        ------------------------------------------------------------------------------
                     |              Corrected
             lnTobin |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
        -------------+----------------------------------------------------------------
             lnTobin |
                 L1. |   .3696484    .135212     2.73   0.008     .0986776    .6406192
                     |
               PerFD |  -1.653189   1.003047    -1.65   0.105    -3.663341    .3569624
               After |  -.3258972   .1662289    -1.96   0.055    -.6590274     .007233
             AfterFD |   2.769663   1.223951     2.26   0.028      .316811    5.222515
              PerInD |   .7457029   .7872982     0.95   0.348    -.8320779    2.323484
                Dual |  -.0977969   .2525137    -0.39   0.700    -.6038457    .4082518
         lnCEOtenure |   .0261589   .0963733     0.27   0.787    -.1669775    .2192954
                FCEO |  -.0152825   .3508191    -0.04   0.965    -.7183397    .6877747
               bsize |   1.253761   .6207274     2.02   0.048     .0097957    2.497727
               lnage |  -.1015018   .0525324    -1.93   0.058     -.206779    .0037755
            Firmsize |  -.1020191   .0714924    -1.43   0.159     -.245293    .0412549
                blev |   .1715291   .3489349     0.49   0.625     -.527752    .8708103
               y2001 |    .229439   .5874748     0.39   0.698    -.9478868    1.406765
               y2002 |  -.1244195    .378294    -0.33   0.743    -.8825376    .6336986
               y2003 |   .3094702    .194131     1.59   0.117    -.0795771    .6985175
               y2004 |   .2967379   .2323853     1.28   0.207    -.1689726    .7624484
               y2005 |   .2221926   .1315122     1.69   0.097    -.0413637    .4857489
               y2006 |   .3023192   .0893869     3.38   0.001     .1231839    .4814545
               y2007 |   .2412863   .0900887     2.68   0.010     .0607444    .4218282
               y2009 |   .2466244   .0939943     2.62   0.011     .0582555    .4349933
               y2010 |   .3480248   .1023966     3.40   0.001     .1428174    .5532323
               y2011 |   .3028799   .1021732     2.96   0.004     .0981203    .5076395
               y2012 |   .4023675   .1169464     3.44   0.001     .1680017    .6367334
               y2013 |   .3223182   .1101007     2.93   0.005     .1016715     .542965
               y2014 |   .3314445   .1040471     3.19   0.002     .1229294    .5399596
               y2015 |   .1781131   .1211967     1.47   0.147    -.0647705    .4209967
               y2016 |   .2673366   .1161632     2.30   0.025     .0345403    .5001328
               y2017 |   .5536576   .1869453     2.96   0.005     .1790109    .9283043
               _cons |  -.7342452   1.356923    -0.54   0.591     -3.45358     1.98509
        ------------------------------------------------------------------------------
        Instruments for first differences equation
          GMM-type (missing=0, separate instruments for each period unless collapsed)
            L2.(Firmsize blev) collapsed
            L2.(AfterFD PerFD PerInD Dual lnCEOtenure FemaleCEO bsize) collapsed
            L(2/3).lnTobin collapsed
        Instruments for levels equation
          Standard
            After lnage 2000b.year 2001.year 2002.year 2003.year 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
            _cons
          GMM-type (missing=0, separate instruments for each period unless collapsed)
            DL.(Firmsize blev) collapsed
            DL.(AfterFD PerFD PerInD Dual lnCEOtenure FemaleCEO bsize) collapsed
            DL.lnTobin collapsed
        ------------------------------------------------------------------------------
        Arellano-Bond test for AR(1) in first differences: z =  -3.27  Pr > z =  0.001
        Arellano-Bond test for AR(2) in first differences: z =  -0.67  Pr > z =  0.505
        ------------------------------------------------------------------------------
        Sargan test of overid. restrictions: chi2(11)   =  10.06  Prob > chi2 =  0.525
          (Not robust, but not weakened by many instruments.)
        Hansen test of overid. restrictions: chi2(11)   =   6.66  Prob > chi2 =  0.826
          (Robust, but weakened by many instruments.)
        
        Difference-in-Hansen tests of exogeneity of instrument subsets:
          GMM instruments for levels
            Hansen test excluding group:     chi2(1)    =   2.54  Prob > chi2 =  0.111
            Difference (null H = exogenous): chi2(10)   =   4.12  Prob > chi2 =  0.942
          gmm(lnTobin, collapse eq(diff) lag(2 3))
            Hansen test excluding group:     chi2(9)    =   5.74  Prob > chi2 =  0.765
            Difference (null H = exogenous): chi2(2)    =   0.92  Prob > chi2 =  0.632
          gmm(lnTobin, collapse eq(diff) lag(2 3)) eq(level) lag(1 1))
            Hansen test excluding group:     chi2(10)   =   6.48  Prob > chi2 =  0.773
            Difference (null H = exogenous): chi2(1)    =   0.18  Prob > chi2 =  0.672
          gmm(Firmsize blev, collapse lag(2 2))
            Hansen test excluding group:     chi2(7)    =   5.23  Prob > chi2 =  0.632
            Difference (null H = exogenous): chi2(4)    =   1.44  Prob > chi2 =  0.838
        
        
        .
        end of do-file
        
        .
        Last edited by Celine Tran; 16 Apr 2019, 01:25.

        Comment


        • #5
          The number of instruments is indeed quite high relative to the number of groups (and the high p-value of the Hansen test might indicate that there is a problem, although this is not really clear in your case). Your data set is also heavily unbalanced which does not help either. At the same time, there is not much room to reduce the number of instruments given the large number of estimated coefficients (in particular the time dummies). While you have at most 9 observations per group, the sample appears to span twice as many years. You should ask yourself if you really need to add all of those year dummies or if dummies for particular years (or dummies for periods spanning more than one year) are sufficient. Moreover, it seems that you have assumed that all of your variables are endogenous. This makes the interpretation of your estimates difficult and increases the risk of weak instruments. If possible, I would strongly recommend to simplify your model by allowing some of the regressors to be exogenous.

          Comment


          • #6
            Dear Sebastian Kripfganz

            Thank you very much for your suggestion. I also guess that the really high number of instruments results in the high value of p-value of Hansen test. However, when I try to exclude year dummy, the p-value of Hansen test is still high although the number of instruments drops to 24.

            Here is the result. Please let's have a look.
            Code:
            ------------------------------------------------------------------------------
            Arellano-Bond test for AR(1) in first differences: z =  -2.35  Pr > z =  0.019
            Arellano-Bond test for AR(2) in first differences: z =  -0.91  Pr > z =  0.362
            ------------------------------------------------------------------------------
            Sargan test of overid. restrictions: chi2(11)   =  11.16  Prob > chi2 =  0.430
              (Not robust, but not weakened by many instruments.)
            Hansen test of overid. restrictions: chi2(11)   =   7.26  Prob > chi2 =  0.778
              (Robust, but weakened by many instruments.)
            
            Difference-in-Hansen tests of exogeneity of instrument subsets:
              GMM instruments for levels
                Hansen test excluding group:     chi2(1)    =   1.97  Prob > chi2 =  0.161
                Difference (null H = exogenous): chi2(10)   =   5.29  Prob > chi2 =  0.871
              gmm(lnTobin, collapse eq(diff) lag(2 3))
                Hansen test excluding group:     chi2(9)    =   6.40  Prob > chi2 =  0.699
                Difference (null H = exogenous): chi2(2)    =   0.86  Prob > chi2 =  0.650
              gmm(lnTobin, collapse eq(diff) lag(2 3)) eq(level) lag(1 1))
                Hansen test excluding group:     chi2(10)   =   7.15  Prob > chi2 =  0.711
                Difference (null H = exogenous): chi2(1)    =   0.11  Prob > chi2 =  0.744
              gmm(Firmsize blev, collapse lag(2 2))
                Hansen test excluding group:     chi2(7)    =   4.99  Prob > chi2 =  0.662
                Difference (null H = exogenous): chi2(4)    =   2.28  Prob > chi2 =  0.685
              iv(After lnage, eq(level))
                Hansen test excluding group:     chi2(9)    =   7.25  Prob > chi2 =  0.611
                Difference (null H = exogenous): chi2(2)    =   0.01  Prob > chi2 =  0.994
            In term of endogenous variable, I follow previous papers and most of repressors must be endogenous, except firm age and year dummy ( So, do you any suggestion for me?

            Thank you very much in advance.

            Regards,
            Celine

            Comment


            • #7
              Eventually, such a relatively high p-value of the Hansen test does not necessarily need to be a concern if you are confident that all your assumptions are reasonable. Such a high p-value is certainly possible (and not a bad thing) even if you do not have "too many" instruments. A p-value close to zero would be far more concerning.

              Regarding the classification of regressors as endogenous or exogenous, I am afraid I am unable to give specific advice because I do not know this particular strand of empirical literature.

              Comment

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