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  • #1

    problem in instrumenting endogenous interactive variable in system gmm

    Hi
    I am doing an empirical study on impact of IPRs on income-inequality in developing countries. I am running a regression of income inequality on iprs and other control variables.Since I have a dynamic panel specification, I am using xtabond2 command.My regression eq looks like:
    Income Ineq = b1 +b2. IPRs +b3.lgdp_IPR +b4.controls
    lgdp is log of per capita GDP and lgdp_IPR is an interaction term of IPR and lgdp.IPRs is intellectual property rights index that takes up a value ranging between 1 to 5.
    While estimating the regression eq, I consider IPRs as an endog. variable which is instrumented by its lags while using xtabond2 command.Since i am treating IPRs and log of per capita GDP as endogenous, their interaction is also considered as endogenous.Problem is coefficients of all other explanatory variables become insignificant when i include the interaction term in my specification.
    I have an unbalanced panel of 60 countries.Following are the commands that I am using:
    Code:
    . xi:xtabond2 NetGini l.NetGini  tradeinflow  pol civil  sch_sec FDI lgdp IPR i.year, iv(i.year , equation(level))gmm( sc
> h_sec  pol civil  , lag(1 1)coll) gmm(l. NetGini IPR , lag(3 3)) gmm( lgdp FDI  tradeinflow, lag(2 4) coll) two robust 
> small
i.year            _Iyear_1-7          (naturally coded; _Iyear_1 omitted)
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
_Iyear_6 dropped due to collinearity
Warning: Two-step estimated covariance matrix of moments is singular.
  Using a generalized inverse to calculate optimal weighting matrix for two-step estimation.
  Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: count                           Number of obs      =       318
Time variable : year                            Number of groups   =        60
Number of instruments = 38                      Obs per group: min =         4
F(13, 59)     =     82.70                                      avg =      5.30
Prob > F      =     0.000                                      max =         6
------------------------------------------------------------------------------
             |              Corrected
     NetGini |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     NetGini |
         L1. |   .7507057   .0702816    10.68   0.000     .6100726    .8913388
             |
 tradeinflow |  -.0192333   .0069845    -2.75   0.008    -.0332093   -.0052573
         pol |   .7958731   .3595149     2.21   0.031     .0764854    1.515261
       civil |  -1.130563   .5462879    -2.07   0.043    -2.223682    -.037443
     sch_sec |   1.081968   .7887031     1.37   0.175     -.496223    2.660159
         FDI |   .2054799   .1475252     1.39   0.169    -.0897173     .500677
        lgdp |  -1.658037   .9181514    -1.81   0.076    -3.495254    .1791794
         IPR |  -1.130677   .5105886    -2.21   0.031    -2.152363    -.108992
    _Iyear_2 |  -1.387087   1.284979    -1.08   0.285    -3.958323     1.18415
    _Iyear_3 |   .0444003   1.134693     0.04   0.969    -2.226116    2.314916
    _Iyear_4 |   .6515202   .5685489     1.15   0.256    -.4861436    1.789184
    _Iyear_5 |   .4052887   .3017652     1.34   0.184     -.198542    1.009119
    _Iyear_7 |    .118279   .3462677     0.34   0.734    -.5746012    .8111591
       _cons |   26.64445   8.340958     3.19   0.002     9.954235    43.33467
------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/4).(lgdp FDI tradeinflow) collapsed
    L3.(L.NetGini IPR)
    L.(sch_sec pol civil) collapsed
Instruments for levels equation
  Standard
    _Iyear_2 _Iyear_3 _Iyear_4 _Iyear_5 _Iyear_6 _Iyear_7
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(lgdp FDI tradeinflow) collapsed
    DL2.(L.NetGini IPR)
    D.(sch_sec pol civil) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.62  Pr > z =  0.105
Arellano-Bond test for AR(2) in first differences: z =  -1.41  Pr > z =  0.159
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(24)   =  27.43  Prob > chi2 =  0.285
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(24)   =  24.87  Prob > chi2 =  0.413
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(10)   =  11.01  Prob > chi2 =  0.356
    Difference (null H = exogenous): chi2(14)   =  13.85  Prob > chi2 =  0.461
  gmm(sch_sec pol civil, collapse lag(1 1))
    Hansen test excluding group:     chi2(22)   =  24.43  Prob > chi2 =  0.325
    Difference (null H = exogenous): chi2(2)    =   0.44  Prob > chi2 =  0.802
  gmm(L.NetGini IPR, lag(3 3))
    Hansen test excluding group:     chi2(6)    =  12.09  Prob > chi2 =  0.060
    Difference (null H = exogenous): chi2(18)   =  12.78  Prob > chi2 =  0.805
  gmm(lgdp FDI tradeinflow, collapse lag(2 4))
    Hansen test excluding group:     chi2(12)   =   8.13  Prob > chi2 =  0.775
    Difference (null H = exogenous): chi2(12)   =  16.74  Prob > chi2 =  0.160
  iv(_Iyear_2 _Iyear_3 _Iyear_4 _Iyear_5 _Iyear_6 _Iyear_7, eq(level))
    Hansen test excluding group:     chi2(19)   =  15.83  Prob > chi2 =  0.669
    Difference (null H = exogenous): chi2(5)    =   9.04  Prob > chi2 =  0.107


. xi:xtabond2 NetGini l.NetGini  tradeinflow  pol civil  sch_sec FDI lgdp IPR  lgdp_IPR i.year, iv(i.year , equation(leve
> l))gmm( sch_sec  pol civil  , lag(1 1)coll) gmm(l. NetGini IPR , lag(3 3)coll) gmm( lgdp_IPR lgdp_IPR,lag(2 3)) gmm( lg
> dp FDI  tradeinflow, lag(2 4) coll) two robust small
i.year            _Iyear_1-7          (naturally coded; _Iyear_1 omitted)
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
_Iyear_6 dropped due to collinearity
Warning: Two-step estimated covariance matrix of moments is singular.
  Using a generalized inverse to calculate optimal weighting matrix for two-step estimation.
  Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: count                           Number of obs      =       318
Time variable : year                            Number of groups   =        60
Number of instruments = 42                      Obs per group: min =         4
F(14, 59)     =     47.48                                      avg =      5.30
Prob > F      =     0.000                                      max =         6
------------------------------------------------------------------------------
             |              Corrected
     NetGini |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     NetGini |
         L1. |    .810713    .075913    10.68   0.000     .6588115    .9626146
             |
 tradeinflow |  -.0092124   .0086376    -1.07   0.291    -.0264962    .0080715
         pol |   .9882897   .4575124     2.16   0.035     .0728095     1.90377
       civil |  -1.283232    .606577    -2.12   0.039     -2.49699   -.0694744
     sch_sec |  -.1729401   .6369153    -0.27   0.787    -1.447405    1.101524
         FDI |   .0131383   .1196853     0.11   0.913    -.2263514     .252628
        lgdp |  -.3519632   .6173739    -0.57   0.571    -1.587325    .8833992
         IPR |  -.6190792   .7286319    -0.85   0.399    -2.077068    .8389098
    lgdp_IPR |   2.583593    1.14272     2.26   0.027      .297017     4.87017
    _Iyear_2 |   -1.58519   1.408494    -1.13   0.265     -4.40358      1.2332
    _Iyear_3 |   .1295869   1.252443     0.10   0.918    -2.376546     2.63572
    _Iyear_4 |   1.024117   .7369694     1.39   0.170    -.4505557    2.498789
    _Iyear_5 |    .586456   .4152121     1.41   0.163    -.2443814    1.417293
    _Iyear_7 |  -.0470631   .4969812    -0.09   0.925     -1.04152     .947394
       _cons |   14.15091   5.085775     2.78   0.007     3.974294    24.32752
------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/4).(lgdp FDI tradeinflow) collapsed
    L(2/3).(lgdp_IPR lgdp_IPR)
    L3.(L.NetGini IPR) collapsed
    L.(sch_sec pol civil) collapsed
Instruments for levels equation
  Standard
    _Iyear_2 _Iyear_3 _Iyear_4 _Iyear_5 _Iyear_6 _Iyear_7
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(lgdp FDI tradeinflow) collapsed
    DL.(lgdp_IPR lgdp_IPR)
    DL2.(L.NetGini IPR) collapsed
    D.(sch_sec pol civil) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.77  Pr > z =  0.077
Arellano-Bond test for AR(2) in first differences: z =  -1.97  Pr > z =  0.049
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(27)   =  47.77  Prob > chi2 =  0.008
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(27)   =  36.09  Prob > chi2 =  0.113
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(14)   =  19.49  Prob > chi2 =  0.147
    Difference (null H = exogenous): chi2(13)   =  16.61  Prob > chi2 =  0.218
  gmm(sch_sec pol civil, collapse lag(1 1))
    Hansen test excluding group:     chi2(23)   =  32.99  Prob > chi2 =  0.081
    Difference (null H = exogenous): chi2(4)    =   3.10  Prob > chi2 =  0.542
  gmm(L.NetGini IPR, collapse lag(3 3))
    Hansen test excluding group:     chi2(23)   =  33.57  Prob > chi2 =  0.072
    Difference (null H = exogenous): chi2(4)    =   2.52  Prob > chi2 =  0.641
  gmm(lgdp_IPR lgdp_IPR, lag(2 3))
    Hansen test excluding group:     chi2(11)   =  17.68  Prob > chi2 =  0.089
    Difference (null H = exogenous): chi2(16)   =  18.41  Prob > chi2 =  0.300
  gmm(lgdp FDI tradeinflow, collapse lag(2 4))
    Hansen test excluding group:     chi2(15)   =  20.17  Prob > chi2 =  0.166
    Difference (null H = exogenous): chi2(12)   =  15.92  Prob > chi2 =  0.195
  iv(_Iyear_2 _Iyear_3 _Iyear_4 _Iyear_5 _Iyear_6 _Iyear_7, eq(level))
    Hansen test excluding group:     chi2(22)   =  28.01  Prob > chi2 =  0.175
    Difference (null H = exogenous): chi2(5)    =   8.08  Prob > chi2 =  0.152
    My results become insignificant when i include the interactive term.If I instrument the interactive term with deeper lags, then difference in hansen tests suggests my instruments are invalid..x.My IPR index data changes slowly over period of time.IPR data is like:
    country year gini_net ipr
    Australia 1 28.1872 2.49
    Australia 2 29.0448 2.49
    Australia 3 28.7599 3.28
    Australi 4 29.9817 4.33
    Australia 5 31.1922 4.33
    Australia 6 31.7795 4.33
    Please advise
    Tags: dynamic panel, interactive term, systemGMM, xtabond2
  • #2
    Anybody who can help me out?

    Comment

    • #3
      It is hard to say what exactly causes the behavior you are observing. I have two suggestions for modifications that might help:
      • One of the time dummies is dropped due to collinearity but it appears to be still included in the set of instruments. I recommend to explicitly specify the time dummies for periods 3 to 7 instead of using the i.year factor notation to avoid any undetected collinearity issues among the instruments, i.e.
      Code:
      xi i.year
xtabond2 NetGini l.NetGini ... _Iyear_3-_Iyear_7, iv(_Iyear_3-_Iyear_7, equation(level)) ...
      • Your number of instruments is still large relative to the number of observations. I recommend to use the collapse suboption for all GMM-style instruments.
      • In your second specification, the interaction term lgdp_IPR appears duplicated. I am surprised that this is not detected automatically. Do the results change if you remove the duplicate instrument from the gmm() specification?
      Besides that, I am afraid that there is not much else I can say.
      https://twitter.com/Kripfganz

      Comment

      • #4
        Thank you so much for the suggestions.But my results donot change.
        When I am collapsing all my GMM style instruments after removing the duplicate instrument, almost all my coefficients become insignificant and when I collapse only few GMM style instruments, then interactive term lgdp_IPR is significant but others are rendered insginificant.
        Code:
        . xtabond2 NetGini l.NetGini  tradeinflow  sch_sec FDI lgdp IPR  lgdp_IPR pol civil  _Iyear_3- _Iyear_7, iv( _Iyear_3- _I
> year_7, equation(level)) gmm( sch_sec  pol civil , lag(1 1)coll) gmm(l. NetGini IPR, lag(3 3)coll) gmm( lgdp_IPR,lag(2 
> 3) coll) gmm( lgdp FDI tradeinflow, lag(2 4) coll) two robust small
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: count                           Number of obs      =       318
Time variable : year                            Number of groups   =        60
Number of instruments = 31                      Obs per group: min =         4
F(14, 59)     =     29.60                                      avg =      5.30
Prob > F      =     0.000                                      max =         6
------------------------------------------------------------------------------
             |              Corrected
     NetGini |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     NetGini |
         L1. |   .8680853   .1168698     7.43   0.000     .6342294    1.101941
             |
 tradeinflow |  -.0110798    .010391    -1.07   0.291    -.0318721    .0097124
     sch_sec |   1.235643   .7730513     1.60   0.115    -.3112293    2.782515
         FDI |    .124848   .3108152     0.40   0.689    -.4970918    .7467878
        lgdp |  -1.873107   1.300002    -1.44   0.155    -4.474406    .7281921
         IPR |  -1.020642   .8387611    -1.22   0.229    -2.698999    .6577146
    lgdp_IPR |   1.254342   2.203383     0.57   0.571    -3.154617      5.6633
         pol |   .9667388   .3883779     2.49   0.016     .1895965    1.743881
       civil |   -1.73044   .6580217    -2.63   0.011    -3.047138   -.4137414
    _Iyear_3 |   1.464596   .4991555     2.93   0.005     .4657881    2.463404
    _Iyear_4 |   2.158185     .99396     2.17   0.034      .169276    4.147095
    _Iyear_5 |   1.537832   1.308948     1.17   0.245    -1.081367    4.157031
    _Iyear_6 |   .8916677   1.461313     0.61   0.544    -2.032412    3.815748
    _Iyear_7 |   .8062916   1.667465     0.48   0.630    -2.530299    4.142882
       _cons |   22.63721   14.18796     1.60   0.116    -5.752828    51.02726
------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/4).(lgdp FDI tradeinflow) collapsed
    L(2/3).lgdp_IPR collapsed
    L3.(L.NetGini IPR) collapsed
    L.(sch_sec pol civil) collapsed
Instruments for levels equation
  Standard
    _Iyear_3 _Iyear_4 _Iyear_5 _Iyear_6 _Iyear_7
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(lgdp FDI tradeinflow) collapsed
    DL.lgdp_IPR collapsed
    DL2.(L.NetGini IPR) collapsed
    D.(sch_sec pol civil) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.30  Pr > z =  0.193
Arellano-Bond test for AR(2) in first differences: z =  -1.65  Pr > z =  0.098
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(16)   =  31.49  Prob > chi2 =  0.012
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(16)   =  21.00  Prob > chi2 =  0.178
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(7)    =  10.49  Prob > chi2 =  0.163
    Difference (null H = exogenous): chi2(9)    =  10.52  Prob > chi2 =  0.310
  gmm(sch_sec pol civil, collapse lag(1 1))
    Hansen test excluding group:     chi2(10)   =  17.96  Prob > chi2 =  0.056
    Difference (null H = exogenous): chi2(6)    =   3.04  Prob > chi2 =  0.803
  gmm(L.NetGini IPR, collapse lag(3 3))
    Hansen test excluding group:     chi2(12)   =  16.76  Prob > chi2 =  0.159
    Difference (null H = exogenous): chi2(4)    =   4.24  Prob > chi2 =  0.374
  gmm(lgdp_IPR, collapse lag(2 3))
    Hansen test excluding group:     chi2(13)   =  17.64  Prob > chi2 =  0.172
    Difference (null H = exogenous): chi2(3)    =   3.36  Prob > chi2 =  0.339
  gmm(lgdp FDI tradeinflow, collapse lag(2 4))
    Hansen test excluding group:     chi2(4)    =   5.14  Prob > chi2 =  0.273
    Difference (null H = exogenous): chi2(12)   =  15.86  Prob > chi2 =  0.198
  iv(_Iyear_3 _Iyear_4 _Iyear_5 _Iyear_6 _Iyear_7, eq(level))
    Hansen test excluding group:     chi2(11)   =  12.23  Prob > chi2 =  0.347
    Difference (null H = exogenous): chi2(5)    =   8.78  Prob > chi2 =  0.118


. xtabond2 NetGini l.NetGini  tradeinflow  sch_sec FDI lgdp IPR  lgdp_IPR pol civil  _Iyear_3- _Iyear_7, iv( _Iyear_3- _I
> year_7, equation(level)) gmm( sch_sec  pol civil , lag(1 1)coll) gmm(l. NetGini IPR, lag(3 3)coll) gmm( lgdp_IPR,lag(2 
> 3)) gmm( lgdp FDI tradeinflow, lag(2 4) coll) two robust small
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Warning: Two-step estimated covariance matrix of moments is singular.
  Using a generalized inverse to calculate optimal weighting matrix for two-step estimation.
  Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: count                           Number of obs      =       318
Time variable : year                            Number of groups   =        60
Number of instruments = 42                      Obs per group: min =         4
F(14, 59)     =     47.48                                      avg =      5.30
Prob > F      =     0.000                                      max =         6
------------------------------------------------------------------------------
             |              Corrected
     NetGini |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     NetGini |
         L1. |    .810713    .075913    10.68   0.000     .6588115    .9626146
             |
 tradeinflow |  -.0092124   .0086376    -1.07   0.291    -.0264962    .0080715
     sch_sec |  -.1729401   .6369153    -0.27   0.787    -1.447405    1.101524
         FDI |   .0131383   .1196853     0.11   0.913    -.2263514     .252628
        lgdp |  -.3519632   .6173739    -0.57   0.571    -1.587325    .8833992
         IPR |  -.6190792   .7286319    -0.85   0.399    -2.077068    .8389098
    lgdp_IPR |   2.583593    1.14272     2.26   0.027      .297017     4.87017
         pol |   .9882897   .4575124     2.16   0.035     .0728095     1.90377
       civil |  -1.283232    .606577    -2.12   0.039     -2.49699   -.0694744
    _Iyear_3 |   1.714777   .5673857     3.02   0.004     .5794407    2.850113
    _Iyear_4 |   2.609307   1.025658     2.54   0.014     .5569696    4.661644
    _Iyear_5 |   2.171646   1.262221     1.72   0.091    -.3540526    4.697344
    _Iyear_6 |    1.58519   1.408494     1.13   0.265      -1.2332     4.40358
    _Iyear_7 |   1.538127   1.455809     1.06   0.295    -1.374939    4.451193
       _cons |   12.56572    5.13559     2.45   0.017     2.289424    22.84201
------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/4).(lgdp FDI tradeinflow) collapsed
    L(2/3).lgdp_IPR
    L3.(L.NetGini IPR) collapsed
    L.(sch_sec pol civil) collapsed
Instruments for levels equation
  Standard
    _Iyear_3 _Iyear_4 _Iyear_5 _Iyear_6 _Iyear_7
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(lgdp FDI tradeinflow) collapsed
    DL.lgdp_IPR
    DL2.(L.NetGini IPR) collapsed
    D.(sch_sec pol civil) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.77  Pr > z =  0.077
Arellano-Bond test for AR(2) in first differences: z =  -1.97  Pr > z =  0.049
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(27)   =  47.77  Prob > chi2 =  0.008
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(27)   =  36.09  Prob > chi2 =  0.113
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(14)   =  20.19  Prob > chi2 =  0.124
    Difference (null H = exogenous): chi2(13)   =  15.90  Prob > chi2 =  0.255
  gmm(sch_sec pol civil, collapse lag(1 1))
    Hansen test excluding group:     chi2(22)   =  32.98  Prob > chi2 =  0.062
    Difference (null H = exogenous): chi2(5)    =   3.11  Prob > chi2 =  0.684
  gmm(L.NetGini IPR, collapse lag(3 3))
    Hansen test excluding group:     chi2(23)   =  33.53  Prob > chi2 =  0.072
    Difference (null H = exogenous): chi2(4)    =   2.56  Prob > chi2 =  0.635
  gmm(lgdp_IPR, lag(2 3))
    Hansen test excluding group:     chi2(12)   =  17.87  Prob > chi2 =  0.120
    Difference (null H = exogenous): chi2(15)   =  18.22  Prob > chi2 =  0.251
  gmm(lgdp FDI tradeinflow, collapse lag(2 4))
    Hansen test excluding group:     chi2(15)   =  20.17  Prob > chi2 =  0.166
    Difference (null H = exogenous): chi2(12)   =  15.92  Prob > chi2 =  0.195
  iv(_Iyear_3 _Iyear_4 _Iyear_5 _Iyear_6 _Iyear_7, eq(level))
    Hansen test excluding group:     chi2(22)   =  28.01  Prob > chi2 =  0.175
    Difference (null H = exogenous): chi2(5)    =   8.08  Prob > chi2 =  0.152


.

        Comment

        • #5
          There is one more thing you could try: Are the results also sensitive by that much if you are using only the onstep instead of the twostep estimator? If the onestep estimator delivers much more robust estimates, I would stick to it.

          The advantage of the twostep estimator is asymptotic efficiency, but if the first-step weighting matrix is poorly estimated, then the small-sample performance can be rather poor and sensitive to different specifications of the instruments.
          https://twitter.com/Kripfganz

          Comment

          • #6
            Unfortunately, my all estimates become insignificant when i use one step instead of two step. I feel probably my sample size is small which is creating problems.I have 318 observations for 60 countries.
            Code:
            . xtabond2 NetGini l.NetGini  tradeinflow  sch_sec FDI lgdp IPR  pol civil  _Iyear_3- _Iyear_7, iv( _Iyear_3- _Iyear_7, e
> quation(level)) gmm(sch_sec  pol civil , lag(1 1)coll) gmm(l. NetGini IPR, lag(3 3)coll) gmm( lgdp FDI tradeinflow, lag
> (2 4) coll) robust small
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.

Dynamic panel-data estimation, one-step system GMM
------------------------------------------------------------------------------
Group variable: count                           Number of obs      =       318
Time variable : year                            Number of groups   =        60
Number of instruments = 28                      Obs per group: min =         4
F(13, 59)     =     29.11                                      avg =      5.30
Prob > F      =     0.000                                      max =         6
------------------------------------------------------------------------------
             |               Robust
     NetGini |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     NetGini |
         L1. |   .7298809    .110236     6.62   0.000     .5092992    .9504627
             |
 tradeinflow |  -.0097753   .0091307    -1.07   0.289    -.0280459    .0084952
     sch_sec |   .1645333    1.00053     0.16   0.870    -1.837522    2.166589
         FDI |   .2085587    .163128     1.28   0.206    -.1178597    .5349772
        lgdp |  -.8379406   1.231347    -0.68   0.499    -3.301861     1.62598
         IPR |  -.9536488   .7478062    -1.28   0.207    -2.450005    .5427079
         pol |   .7691928   .3556829     2.16   0.035      .057473    1.480913
       civil |  -.9936412   .6587333    -1.51   0.137    -2.311764    .3244812
    _Iyear_3 |   1.360484   .4878216     2.79   0.007     .3843555    2.336613
    _Iyear_4 |   1.916824   1.004891     1.91   0.061    -.0939595    3.927607
    _Iyear_5 |   1.645847   1.447248     1.14   0.260     -1.25009    4.541783
    _Iyear_6 |    1.21155   1.618499     0.75   0.457    -2.027059     4.45016
    _Iyear_7 |   1.643206    1.76203     0.93   0.355    -1.882607    5.169019
       _cons |   19.71964   12.05318     1.64   0.107    -4.398717    43.83799
------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/4).(lgdp FDI tradeinflow) collapsed
    L3.(L.NetGini IPR) collapsed
    L.(sch_sec pol civil) collapsed
Instruments for levels equation
  Standard
    _Iyear_3 _Iyear_4 _Iyear_5 _Iyear_6 _Iyear_7
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(lgdp FDI tradeinflow) collapsed
    DL2.(L.NetGini IPR) collapsed
    D.(sch_sec pol civil) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.43  Pr > z =  0.154
Arellano-Bond test for AR(2) in first differences: z =  -1.52  Pr > z =  0.129
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(14)   =  22.30  Prob > chi2 =  0.073
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(14)   =  17.64  Prob > chi2 =  0.224
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(6)    =   5.98  Prob > chi2 =  0.426
    Difference (null H = exogenous): chi2(8)    =  11.66  Prob > chi2 =  0.167
  gmm(sch_sec pol civil, collapse lag(1 1))
    Hansen test excluding group:     chi2(8)    =  15.83  Prob > chi2 =  0.045
    Difference (null H = exogenous): chi2(6)    =   1.81  Prob > chi2 =  0.936
  gmm(L.NetGini IPR, collapse lag(3 3))
    Hansen test excluding group:     chi2(10)   =  15.48  Prob > chi2 =  0.115
    Difference (null H = exogenous): chi2(4)    =   2.15  Prob > chi2 =  0.708
  gmm(lgdp FDI tradeinflow, collapse lag(2 4))
    Hansen test excluding group:     chi2(2)    =   2.37  Prob > chi2 =  0.305
    Difference (null H = exogenous): chi2(12)   =  15.26  Prob > chi2 =  0.227
  iv(_Iyear_3 _Iyear_4 _Iyear_5 _Iyear_6 _Iyear_7, eq(level))
    Hansen test excluding group:     chi2(9)    =   5.64  Prob > chi2 =  0.776
    Difference (null H = exogenous): chi2(5)    =  12.00  Prob > chi2 =  0.035

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