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  • Highly significant Hansen statistics after xtabond2

    Hello everyone,

    I have an issue regarding xtabond2 and Hansen statistics and I was wondering if anyone could help me with that.

    Here is my code and what Stata provides:

    Code:
     xtabond2 winv2 wndf wdiv2 wcf  wmtb wtang cage wsalesg wsize l.stdev  l.winv2   y4-y32, gmmstyle(l.winv2 wndf 
    > wdiv2, lag(2 5) collapse) iv( wmtb   wcf wtang l.stdev cage wsalesg wsize y4-y32, eq(level)) iv(wmtb   wcf wta
    > ng l.stdev cage wsalesg wsize, eq(diff)) twostep small robust
    Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
    
    Dynamic panel-data estimation, two-step system GMM
    ------------------------------------------------------------------------------
    Group variable: companyno                       Number of obs      =      4925
    Time variable : datayearfi~l                    Number of groups   =       463
    Number of instruments = 59                      Obs per group: min =         1
    F(39, 462)    =     14.51                                      avg =     10.64
    Prob > F      =     0.000                                      max =        30
    ------------------------------------------------------------------------------
                 |              Corrected
           winv2 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
    -------------+----------------------------------------------------------------
            wndf |   .5197724   .0736962     7.05   0.000     .3749511    .6645937
           wdiv2 |  -.0761525   .0361605    -2.11   0.036    -.1472119    -.005093
             wcf |   .1376568   .0394813     3.49   0.001     .0600716     .215242
            wmtb |   .0065393   .0032135     2.03   0.042     .0002244    .0128543
           wtang |    .031711   .0093283     3.40   0.001     .0133798    .0500421
            cage |  -.0117218   .0047613    -2.46   0.014    -.0210783   -.0023652
         wsalesg |   .0277694    .010588     2.62   0.009     .0069628     .048576
           wsize |   .0029869   .0013757     2.17   0.030     .0002836    .0056903
                 |
           stdev |
             L1. |  -.1754014   .1576928    -1.11   0.267    -.4852853    .1344825
                 |
           winv2 |
             L1. |   .1345404   .0392788     3.43   0.001     .0573531    .2117277
                 |
              y4 |  -.0670014   .0490034    -1.37   0.172    -.1632986    .0292958
              y5 |  -.0764702   .0436855    -1.75   0.081    -.1623172    .0093768
              y6 |  -.0466703    .043778    -1.07   0.287     -.132699    .0393584
              y7 |  -.0535834    .039934    -1.34   0.180    -.1320582    .0248914
              y8 |  -.0046665   .0448924    -0.10   0.917    -.0928851     .083552
              y9 |  -.0310349   .0449769    -0.69   0.491    -.1194196    .0573498
             y10 |  -.0266905   .0421176    -0.63   0.527    -.1094563    .0560752
             y11 |   -.047943   .0454478    -1.05   0.292     -.137253     .041367
             y12 |  -.0457779   .0416776    -1.10   0.273     -.127679    .0361233
             y13 |  -.0440037   .0414834    -1.06   0.289    -.1255232    .0375157
             y14 |  -.0183853   .0432421    -0.43   0.671    -.1033609    .0665902
             y15 |  -.0394861   .0432887    -0.91   0.362    -.1245532    .0455809
             y16 |  -.0272495   .0436253    -0.62   0.533    -.1129781     .058479
             y17 |  -.0428482   .0433147    -0.99   0.323    -.1279664      .04227
             y18 |  -.0159717   .0433348    -0.37   0.713    -.1011294    .0691861
             y19 |  -.0042772   .0432104    -0.10   0.921    -.0891906    .0806361
             y20 |  -.0204746   .0426472    -0.48   0.631    -.1042811    .0633319
             y21 |  -.0016345    .043723    -0.04   0.970     -.087555    .0842861
             y22 |  -.0181546    .042542    -0.43   0.670    -.1017543    .0654451
             y23 |  -.0264723   .0429187    -0.62   0.538    -.1108123    .0578677
             y24 |  -.0299797   .0425649    -0.70   0.482    -.1136245    .0536651
             y25 |  -.0318005   .0421004    -0.76   0.450    -.1145325    .0509314
             y26 |  -.0389249   .0422431    -0.92   0.357    -.1219373    .0440875
             y27 |  -.0237457   .0427874    -0.55   0.579    -.1078278    .0603365
             y28 |    -.02853    .042558    -0.67   0.503    -.1121612    .0551012
             y29 |  -.0178813   .0427483    -0.42   0.676    -.1018865    .0661239
             y30 |  -.0284094   .0426339    -0.67   0.506    -.1121898     .055371
             y31 |  -.0375211   .0422606    -0.89   0.375     -.120568    .0455257
             y32 |  -.0400235   .0424093    -0.94   0.346    -.1233625    .0433156
           _cons |   .0029791   .0440888     0.07   0.946    -.0836603    .0896185
    ------------------------------------------------------------------------------
    Instruments for first differences equation
      Standard
        D.(wmtb wcf wtang L.stdev cage wsalesg wsize)
      GMM-type (missing=0, separate instruments for each period unless collapsed)
        L(2/5).(L.winv2 wndf wdiv2) collapsed
    Instruments for levels equation
      Standard
        _cons
        wmtb wcf wtang L.stdev cage wsalesg wsize y4 y5 y6 y7 y8 y9 y10 y11 y12
        y13 y14 y15 y16 y17 y18 y19 y20 y21 y22 y23 y24 y25 y26 y27 y28 y29 y30
        y31 y32
      GMM-type (missing=0, separate instruments for each period unless collapsed)
        DL.(L.winv2 wndf wdiv2) collapsed
    ------------------------------------------------------------------------------
    Arellano-Bond test for AR(1) in first differences: z =  -6.77  Pr > z =  0.000
    Arellano-Bond test for AR(2) in first differences: z =   0.84  Pr > z =  0.400
    ------------------------------------------------------------------------------
    Sargan test of overid. restrictions: chi2(19)   = 110.06  Prob > chi2 =  0.000
      (Not robust, but not weakened by many instruments.)
    Hansen test of overid. restrictions: chi2(19)   =  32.49  Prob > chi2 =  0.027
      (Robust, but can be weakened by many instruments.)
    
    Difference-in-Hansen tests of exogeneity of instrument subsets:
      GMM instruments for levels
        Hansen test excluding group:     chi2(16)   =  30.31  Prob > chi2 =  0.016
        Difference (null H = exogenous): chi2(3)    =   2.18  Prob > chi2 =  0.536
      gmm(L.winv2 wndf wdiv2, collapse lag(2 5))
        Hansen test excluding group:     chi2(4)    =  17.36  Prob > chi2 =  0.002
        Difference (null H = exogenous): chi2(15)   =  15.14  Prob > chi2 =  0.442
      iv(wmtb wcf wtang L.stdev cage wsalesg wsize, eq(diff))
        Hansen test excluding group:     chi2(12)   =  14.38  Prob > chi2 =  0.277
        Difference (null H = exogenous): chi2(7)    =  18.12  Prob > chi2 =  0.011
    
    .
    Lagged dependent variable, L.winv2, and two other regressors, wdiv2 and wndf, are endogenous variables. I treat the rest as exogenous. As you can see the Hansen test of overid. restrictions comes out highly significant, which is a problem I assume. Given that AR(2) is insignificant, what could cause this and what would a possible solution be? Is there an issue with the code? I am pretty new to xtabond2 and I would appreciate every comment on this.

    Many thanks.

  • #2
    The Difference-in-Hansen test indicates that the instruments in the iv(wmtb wcf wtang L.stdev cage wsalesg wsize, eq(diff)) option might be invalid. The strict exogeneity assumption for those variables might not hold.

    More on GMM estimation of dynamic panel data models:
    https://www.kripfganz.de/stata/

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