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  • #1

    Xtabond, variables choice, model validation

    sebastian Kripfganz
    Thanks for your help, really appreciate.
    You mention in your last post that
    provided that you can assume that your regressors and control variables (besides the lagged dependent variable) are strictly exogenous. If that is a good assumption or not depends on your underlying economic theory. In addition, you would need to check the usual specification tests (Arellano-Bond test, Hansen test).
    .

    1.I read about the assumption regarding the exogenous of the variables but I have to confess that I am not 100 sure about that. Any advice on that?
    2. I checked the specifications tests and obtained the following results. the AR(2) is small can I anyway conclude to the validity of my variables, model choice?

    Many Thanks

    Code:
     xtabond2 L(0/2).fh_polity2 lnQuantity lnQuantity2 lnwdi_gdpcapcur al_ethnic lnross_oil_prod lnwdi_pop tdum4-tdum27, gmmstyle(L.fh_polity2, equation(diff) lag(1 .) collapse) ivstyle(lnQuantity lnQuantity2 lnwdi_gdpcapcur lnwdi_pop lnross_oil_prod al_ethnic, equation(diff)) ivstyle(tdum4-tdum27, equation(level)) twostep robust h(2) 
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, 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: ccode                           Number of obs      =      1069
Time variable : year                            Number of groups   =        52
Number of instruments = 49                      Obs per group: min =         3
Wald chi2(32) =    334.98                                      avg =     20.56
Prob > chi2   =     0.000                                      max =        23
---------------------------------------------------------------------------------
                |              Corrected
     fh_polity2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
     fh_polity2 |
            L1. |    .741296   .2352722     3.15   0.002      .280171    1.202421
            L2. |   -.089446   .0452714    -1.98   0.048    -.1781762   -.0007158
                |
     lnQuantity |          0  (omitted)
    lnQuantity2 |  -.0790774   .2660865    -0.30   0.766    -.6005973    .4424425
lnwdi_gdpcapcur |  -.1744521   .1667085    -1.05   0.295    -.5011947    .1522905
      al_ethnic |   4.508854   5.565101     0.81   0.418    -6.398543    15.41625
lnross_oil_prod |   .0271386   .0810581     0.33   0.738    -.1317323    .1860096
      lnwdi_pop |  -.2055078   .5209358    -0.39   0.693    -1.226523    .8155077
          tdum4 |  -.1254753   .1688911    -0.74   0.458    -.4564958    .2055453
          tdum5 |   .1037048   .1576107     0.66   0.511    -.2052066    .4126161
          tdum6 |   .0731329   .1915654     0.38   0.703    -.3023284    .4485942
          tdum7 |   .1418915   .1983097     0.72   0.474    -.2467883    .5305714
          tdum8 |   .0373409   .2214471     0.17   0.866    -.3966875    .4713693
          tdum9 |    .245128   .1976073     1.24   0.215    -.1421753    .6324312
         tdum10 |    .286853   .2678615     1.07   0.284     -.238146    .8118519
         tdum11 |   .4119268   .2411296     1.71   0.088    -.0606786    .8845322
         tdum12 |   .3155458   .2554646     1.24   0.217    -.1851556    .8162472
         tdum13 |   .3088352   .2112838     1.46   0.144    -.1052734    .7229438
         tdum14 |   .3408329   .2461677     1.38   0.166    -.1416469    .8233126
         tdum15 |   .3912267   .2981041     1.31   0.189    -.1930466       .9755
         tdum16 |   .4814959   .3078377     1.56   0.118    -.1218549    1.084847
         tdum17 |   .3722092   .3573986     1.04   0.298    -.3282792    1.072698
         tdum18 |   .4505485   .3539213     1.27   0.203    -.2431245    1.144222
         tdum19 |   .5127796   .3772751     1.36   0.174    -.2266659    1.252225
         tdum20 |   .5115291   .4016883     1.27   0.203    -.2757656    1.298824
         tdum21 |   .5006258   .4090696     1.22   0.221    -.3011358    1.302387
         tdum22 |   .6272965   .4432503     1.42   0.157    -.2414582    1.496051
         tdum23 |    .566952   .4520146     1.25   0.210    -.3189804    1.452884
         tdum24 |    .563987   .4550702     1.24   0.215    -.3279342    1.455908
         tdum25 |   .5084679   .4822307     1.05   0.292    -.4366869    1.453623
         tdum26 |          0  (omitted)
         tdum27 |          0  (omitted)
          _cons |   4.685599   13.42412     0.35   0.727    -21.62519    30.99638
---------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(lnQuantity lnQuantity2 lnwdi_gdpcapcur lnwdi_pop lnross_oil_prod
    al_ethnic)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(1/26).L.fh_polity2 collapsed
Instruments for levels equation
  Standard
    tdum4 tdum5 tdum6 tdum7 tdum8 tdum9 tdum10 tdum11 tdum12 tdum13 tdum14
    tdum15 tdum16 tdum17 tdum18 tdum19 tdum20 tdum21 tdum22 tdum23 tdum24
    tdum25 tdum26 tdum27
    _cons
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -2.33  Pr > z =  0.020
Arellano-Bond test for AR(2) in first differences: z =  -0.61  Pr > z =  0.545
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(16)   =  13.48  Prob > chi2 =  0.638
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(16)   =  21.38  Prob > chi2 =  0.164
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  iv(lnQuantity lnQuantity2 lnwdi_gdpcapcur lnwdi_pop lnross_oil_prod al_ethnic, eq(diff))
    Hansen test excluding group:     chi2(13)   =  17.45  Prob > chi2 =  0.180
    Difference (null H = exogenous): chi2(3)    =   3.94  Prob > chi2 =  0.269
    Tags: None
  • #2
    It is hard to give specific advice regarding the exogeneity of your variables. You would have to ask this to someone who knows the literature in your applied field.

    Based on your estimation results, the specification is not rejected by the Arellano-Bond AR(2) test and the Hansen test. Both have a p-value larger than conventional significance levels and thus do not reject the respective null hypotheses. That is good news. Also, the second lag of your dependent variable enters the model with statistical significance, confirming the choice of (at least) two lags.

    What is worrying, though, is that there are a couple of omitted variables. Could you please show me the output of the following command when you execute it immediately after xtabond2:
    Code:
    tabulate year if e(sample)
    I suspect that some (3?) of your years are excluded from the estimation because of missing values. That would explain why some dummy variables are dropped. You could also double check the results with my xtseqreg command if the teffects option selects the same number of time dummies or less.
    https://www.kripfganz.de/stata/

    Comment

    • #3
      Dear Sebastian,
      Many thanks.

      1.
      It is hard to give specific advice regarding the exogeneity of your variables. You would have to ask this to someone who knows the literature in your applied field.
      In fact, there might be a feedback of my dependent variable on my independent and control variables. I read that, in such case, I should specify instruments for my regressors but I don't know how to do it.

      2.
      the second lag of your dependent variable enters the model with statistical significance, confirming the choice of (at least) two lags.
      . Do you mean then that my lag specification my be: lag(2 .) (instead of lag(1. .) as it is now?)

      3. the result of:
      Code:
      tabulate year if e(sample)

       Year |      Freq.     Percent        Cum.
------------+-----------------------------------
       2008 |         39       16.39       16.39
       2009 |         39       16.39       32.77
       2010 |         41       17.23       50.00
       2011 |         39       16.39       66.39
       2012 |         39       16.39       82.77
       2013 |         41       17.23      100.00
------------+-----------------------------------
      Total |        238      100.00
      4. Here the results from the xtseqreg command
      Code:
      . xtseqreg L(0/2).fh_polity2 lnQuantity lnQuantity2 lnwdi_gdpcapcur al_ethnic lnross_oil_prod lnwdi_pop tdum4-tdum27, gmmiv(L.fh_polity
> 2, model(diff) lagrange(1 .) collapse) iv(lnQuantity lnQuantity2 lnwdi_gdpcapcur lnross_oil_prod al_ethnic lnwdi_pop, model(diff)) iv
> (tdum4-tdum27, model(level)) twostep vce(robust) wmatrix(independent)                                                                
>            

Group variable: ccode                        Number of obs         =      1069
Time variable: year                          Number of groups      =        52

                                             Obs per group:    min =         3
                                                               avg =  20.55769
                                                               max =        23

                                             Number of instruments =        52

                                     (Std. Err. adjusted for clustering on ccode)
---------------------------------------------------------------------------------
                |              WC-Robust
     fh_polity2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
     fh_polity2 |
            L1. |   .7513084   .1227385     6.12   0.000     .5107454    .9918714
            L2. |  -.0627681   .0548636    -1.14   0.253    -.1702987    .0447626
                |
     lnQuantity |          0  (omitted)
    lnQuantity2 |  -.0448647    .255417    -0.18   0.861    -.5454728    .4557435
lnwdi_gdpcapcur |   .2909337   .5202111     0.56   0.576    -.7286614    1.310529
      al_ethnic |   .7076623   6.993838     0.10   0.919    -13.00001    14.41533
lnross_oil_prod |  -.3826875   .4895483    -0.78   0.434    -1.342185    .5768094
      lnwdi_pop |  -.9005157   1.140704    -0.79   0.430    -3.136255    1.335223
          tdum4 |  -.1236993   .1740843    -0.71   0.477    -.4648982    .2174996
          tdum5 |   .0595028    .134484     0.44   0.658     -.204081    .3230865
          tdum6 |  -.0193784   .2085549    -0.09   0.926    -.4281384    .3893817
          tdum7 |   .1066513   .2417014     0.44   0.659    -.3670748    .5803774
          tdum8 |  -.0030784   .2231264    -0.01   0.989     -.440398    .4342412
          tdum9 |   .2623102    .213425     1.23   0.219    -.1559951    .6806155
         tdum10 |    .319563   .3176661     1.01   0.314    -.3030512    .9421771
         tdum11 |   .4526316    .366217     1.24   0.216    -.2651405    1.170404
         tdum12 |   .3594998   .3513033     1.02   0.306     -.329042    1.048042
         tdum13 |   .5594115    .462866     1.21   0.227    -.3477892    1.466612
         tdum14 |   .5003174   .4947248     1.01   0.312    -.4693254     1.46996
         tdum15 |   .4984977   .5513147     0.90   0.366    -.5820593    1.579055
         tdum16 |   .6054379   .6545619     0.92   0.355    -.6774799    1.888356
         tdum17 |   .4813207   .7013074     0.69   0.493    -.8932164    1.855858
         tdum18 |   .3933586   .7427953     0.53   0.596    -1.062493    1.849211
         tdum19 |   .3782097   .7838292     0.48   0.629    -1.158067    1.914487
         tdum20 |   .4547675   .8085886     0.56   0.574    -1.130037    2.039572
         tdum21 |   .4362111   .8826268     0.49   0.621    -1.293706    2.166128
         tdum22 |   .5281326   .9379268     0.56   0.573     -1.31017    2.366435
         tdum23 |     .50214   .9905782     0.51   0.612    -1.439358    2.443638
         tdum24 |    .497032   1.002608     0.50   0.620    -1.468044    2.462108
         tdum25 |   .4644882   1.016356     0.46   0.648    -1.527534     2.45651
         tdum26 |          0  (omitted)
         tdum27 |          0  (omitted)
          _cons |   20.37665   27.97035     0.73   0.466    -34.44424    75.19753
---------------------------------------------------------------------------------

. 
. . estat overid                                                                                                                       
>   

Hansen's J-test                                        chi2(22)    =   17.0631
H0: overidentifying restrictions are valid             Prob > chi2 =    0.7599

. 
. 
. 
. . estat serial, ar(1/3)

Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1:     z =   -3.3452   Prob > |z|  =    0.0008
H0: no autocorrelation of order 2:     z =   -0.5780   Prob > |z|  =    0.5632
H0: no autocorrelation of order 3:     z =    1.2425   Prob > |z|  =    0.2141
      5. the two tests give different results and also, I was expecting positive signs for the regressor (quantity) that is negative for both of the test.

      Many thanks in advance for your kind help.

      Comment

      • #4
        1. You could use lagged instruments for those variables similar to your dependent variable.
        2. No, I mean that is makes sense that you have L2.fh_polity2 as a regressor in your model.
        3. That's very weird. You told me earlier that your sample ranges from 1990 to 2016. Also, both xtabond2 and xtseqreg report a maximum obs. per group of 23. The tabulate command should thus show at least 23 years and not just the 6 years from 2008 to 2013. I do not understand that. Do you get the same output when you run this tabulate command immediately after the xtseqreg command?
        4. The xtseqreg results are not the same as the xtabond2 results because the default of the iv() option differs. While xtabond2 automatically creates first differences of the respective instruments for the first-differenced equation, xtseqreg does not unless you also specify the suboption difference, i.e.
          Code:
          iv(lnQuantity lnQuantity2 lnwdi_gdpcapcur lnross_oil_prod al_ethnic lnwdi_pop, model(diff) diff)
          Furthermore, could you please rerun the xtseqreg command without manually specifying the time dummies but with the option teffects instead:
          Code:
          xtseqreg L(0/2).fh_polity2 lnQuantity lnQuantity2 lnwdi_gdpcapcur al_ethnic lnross_oil_prod lnwdi_pop, gmmiv(L.fh_polity2, model(diff) lagrange(1 .) collapse) iv(lnQuantity lnQuantity2 lnwdi_gdpcapcur lnross_oil_prod al_ethnic lnwdi_pop, model(diff) diff) teffects twostep vce(robust) wmatrix(independent)
          This should help to identify the time dummies that are really needed.
        5. The test results clearly differ between xtabond2 and xtseqreg because the estimation results are different; see the previous comment about the instruments.
        https://www.kripfganz.de/stata/

        Comment

        • #5
          1.
          That's very weird. You told me earlier that your sample ranges from 1990 to 2016. Also, both xtabond2 and xtseqreg report a maximum obs. per group of 23. The tabulate command should thus show at least 23 years and not just the 6 years from 2008 to 2013. I do not understand that. Do you get the same output when you run this tabulate command immediately after the xtseqreg command?
          Yes the sample range from 1990 to 2016 and no, I do not have the same output when I run the "tabulate year if e(sample)" command immediately after the xterqreg command

          Code:
             xtseqreg L(0/2).fh_polity2 lnQuantity lnQuantity2 lnwdi_gdpcapcur al_ethnic lnross_oil_prod lnwdi_pop tdum4-tdum27, gmmiv(L.fh_polity2, model(diff) lagrange(1 .) collapse) iv(lnQuantity lnQuantity2 lnwdi_gdpcapcur lnross_oil_prod al_ethnic lnwdi_pop, model(diff) diff) teffects twostep vce(robust) wmatrix(independent)

Group variable: ccode                        Number of obs         =      1069
Time variable: year                          Number of groups      =        52

                                             Obs per group:    min =         3
                                                               avg =  20.55769
                                                               max =        23

                                             Number of instruments =        49

                                     (Std. Err. adjusted for clustering on ccode)
---------------------------------------------------------------------------------
                |              WC-Robust
     fh_polity2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
     fh_polity2 |
            L1. |    .741296   .2352722     3.15   0.002      .280171    1.202421
            L2. |   -.089446   .0452714    -1.98   0.048    -.1781762   -.0007158
                |
     lnQuantity |          0  (omitted)
    lnQuantity2 |  -.0790774   .2660865    -0.30   0.766    -.6005973    .4424425
lnwdi_gdpcapcur |  -.1744521   .1667085    -1.05   0.295    -.5011947    .1522905
      al_ethnic |   4.508854   5.565101     0.81   0.418    -6.398543    15.41625
lnross_oil_prod |   .0271386   .0810581     0.33   0.738    -.1317323    .1860096
      lnwdi_pop |  -.2055078   .5209358    -0.39   0.693    -1.226523    .8155077
          tdum4 |  -.1254753   .1688911    -0.74   0.458    -.4564958    .2055453
          tdum5 |   .1037048   .1576107     0.66   0.511    -.2052066    .4126161
          tdum6 |          0  (omitted)
          tdum7 |          0  (omitted)
          tdum8 |          0  (omitted)
          tdum9 |          0  (omitted)
         tdum10 |          0  (omitted)
         tdum11 |   .4119268   .2411296     1.71   0.088    -.0606786    .8845322
         tdum12 |          0  (omitted)
         tdum13 |   .3088352   .2112838     1.46   0.144    -.1052734    .7229438
         tdum14 |   .3408329   .2461677     1.38   0.166    -.1416469    .8233126
         tdum15 |   .3912267   .2981041     1.31   0.189    -.1930466       .9755
         tdum16 |   .4814959   .3078377     1.56   0.118    -.1218549    1.084847
         tdum17 |   .3722092   .3573986     1.04   0.298    -.3282792    1.072698
         tdum18 |          0  (omitted)
         tdum19 |   .5127796   .3772751     1.36   0.174    -.2266659    1.252225
         tdum20 |          0  (omitted)
         tdum21 |   .5006258   .4090696     1.22   0.221    -.3011358    1.302387
         tdum22 |   .6272965   .4432503     1.42   0.157    -.2414582    1.496051
         tdum23 |    .566952   .4520146     1.25   0.210    -.3189804    1.452884
         tdum24 |    .563987   .4550702     1.24   0.215    -.3279342    1.455908
         tdum25 |   .5084679   .4822307     1.05   0.292    -.4366869    1.453623
         tdum26 |          0  (omitted)
         tdum27 |          0  (omitted)
                |
           year |
          1993  |          0  (omitted)
          1994  |          0  (omitted)
          1995  |   .0731329   .1915654     0.38   0.703    -.3023284    .4485942
          1996  |   .1418915   .1983097     0.72   0.474    -.2467883    .5305714
          1997  |   .0373409   .2214471     0.17   0.866    -.3966875    .4713693
          1998  |    .245128   .1976073     1.24   0.215    -.1421753    .6324312
          1999  |    .286853   .2678615     1.07   0.284     -.238146    .8118519
          2000  |          0  (omitted)
          2001  |   .3155458   .2554646     1.24   0.217    -.1851556    .8162472
          2002  |          0  (omitted)
          2003  |          0  (omitted)
          2004  |          0  (omitted)
          2005  |          0  (omitted)
          2006  |          0  (omitted)
          2007  |   .4505485   .3539213     1.27   0.203    -.2431245    1.144222
          2008  |          0  (omitted)
          2009  |   .5115291   .4016883     1.27   0.203    -.2757655    1.298824
          2010  |          0  (omitted)
          2011  |          0  (omitted)
          2012  |          0  (omitted)
          2013  |          0  (omitted)
          2014  |          0  (omitted)
                |
          _cons |   4.685599   13.42412     0.35   0.727    -21.62519    30.99638
---------------------------------------------------------------------------------

. estat overid                                                                                                                       

Hansen's J-test                                        chi2(19)    =   21.3827
H0: overidentifying restrictions are valid             Prob > chi2 =    0.3160

. 
. estat serial, ar(1/3)

Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1:     z =   -2.3320   Prob > |z|  =    0.0197
H0: no autocorrelation of order 2:     z =   -0.6055   Prob > |z|  =    0.5448
H0: no autocorrelation of order 3:     z =    1.1835   Prob > |z|  =    0.2366

. tabulate year if e(sample)

       Year |      Freq.     Percent        Cum.
------------+-----------------------------------
       1992 |         42        3.93        3.93
       1993 |         44        4.12        8.04
       1994 |         43        4.02       12.07
       1995 |         45        4.21       16.28
       1996 |         46        4.30       20.58
       1997 |         47        4.40       24.98
       1998 |         47        4.40       29.37
       1999 |         47        4.40       33.77
       2000 |         47        4.40       38.17
       2001 |         47        4.40       42.56
       2002 |         46        4.30       46.87
       2003 |         47        4.40       51.26
       2004 |         47        4.40       55.66
       2005 |         47        4.40       60.06
       2006 |         48        4.49       64.55
       2007 |         48        4.49       69.04
       2008 |         47        4.40       73.43
       2009 |         47        4.40       77.83
       2010 |         47        4.40       82.23
       2011 |         47        4.40       86.62
       2012 |         49        4.58       91.21
       2013 |         48        4.49       95.70
       2014 |         46        4.30      100.00
------------+-----------------------------------
      Total |      1,069      100.00

          2. I tried out to lagged instruments for the non-exogenous variables as follow, but my AR(2) result is then < 5% and become smaller if I increase the lags.

          Code:
          xtabond2 L(0/2).fh_polity2 lnQuantity lnQuantity2 lnwdi_gdpcapcur al_ethnic lnross_oil_prod lnwdi_pop tdum4-tdum27, gmmstyle(L.fh_pol
> ity2, L.lnwdi_gdpcapcur L.al_ethnic equation(diff) lag(1 .) collapse) ivstyle(lnQuantity lnQuantity2 lnross_oil_prod lnwdi_pop , equa
> tion(diff)) ivstyle(tdum4-tdum27, equation(level)) twostep robust h(2)
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
gmmstyle(L.fh_polity2, L.lnwdi_gdpcapcur L.al_ethnic equation(diff) lag(1 .) collapse) invalid.
r(198);

. 
. . xtabond2 L(0/2).fh_polity2 lnQuantity lnQuantity2 lnwdi_gdpcapcur al_ethnic lnross_oil_prod lnwdi_pop tdum4-tdum27, gmmstyle(L.fh_p
> olity2 L.lnwdi_gdpcapcur L.al_ethnic, equation(diff) lag(1 .) collapse) ivstyle(lnQuantity lnQuantity2 lnross_oil_prod lnwdi_pop , eq
> uation(diff)) ivstyle(tdum4-tdum27, equation(level)) twostep robust h(2)
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Warning: Number of instruments may be large relative to number of observations.
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: ccode                           Number of obs      =      1069
Time variable : year                            Number of groups   =        52
Number of instruments = 93                      Obs per group: min =         3
Wald chi2(32) =    730.59                                      avg =     20.56
Prob > chi2   =     0.000                                      max =        23
---------------------------------------------------------------------------------
                |              Corrected
     fh_polity2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
     fh_polity2 |
            L1. |   .6511516    .282483     2.31   0.021     .0974952    1.204808
            L2. |  -.0695386   .0367554    -1.89   0.059    -.1415778    .0025007
                |
     lnQuantity |          0  (omitted)
    lnQuantity2 |  -.2400393   .2867122    -0.84   0.402    -.8019848    .3219062
lnwdi_gdpcapcur |   .1865474   .3805115     0.49   0.624    -.5592414    .9323362
      al_ethnic |  -.2739179   8.632441    -0.03   0.975    -17.19319    16.64535
lnross_oil_prod |   .0367536   .0640229     0.57   0.566     -.088729    .1622363
      lnwdi_pop |   .4090251   1.304176     0.31   0.754    -2.147113    2.965163
          tdum4 |  -.0607378   .1304037    -0.47   0.641    -.3163244    .1948488
          tdum5 |   .0875442   .1353097     0.65   0.518    -.1776579    .3527464
          tdum6 |    .067788   .1582914     0.43   0.668    -.2424575    .3780334
          tdum7 |   .0600703    .135858     0.44   0.658    -.2062065     .326347
          tdum8 |  -.0443853   .1878557    -0.24   0.813    -.4125757    .3238051
          tdum9 |   .1261298   .2092332     0.60   0.547    -.2839597    .5362194
         tdum10 |   .1646479    .229578     0.72   0.473    -.2853168    .6146125
         tdum11 |   .2473264    .183708     1.35   0.178    -.1127348    .6073875
         tdum12 |   .2083813   .1624491     1.28   0.200     -.110013    .5267756
         tdum13 |   .1492227   .2017969     0.74   0.460    -.2462921    .5447374
         tdum14 |   .1799438   .2371838     0.76   0.448    -.2849278    .6448155
         tdum15 |   .1873821   .2498161     0.75   0.453    -.3022484    .6770126
         tdum16 |   .1712642   .3056707     0.56   0.575    -.4278394    .7703678
         tdum17 |   .0854983    .340212     0.25   0.802     -.581305    .7523016
         tdum18 |   .0076133   .4060675     0.02   0.985    -.7882644    .8034909
         tdum19 |   -.007903   .4448249    -0.02   0.986    -.8797437    .8639377
         tdum20 |   .0502825   .4545515     0.11   0.912    -.8406221    .9411871
         tdum21 |  -.0341587   .4809052    -0.07   0.943    -.9767155    .9083982
         tdum22 |    .004149    .490666     0.01   0.993    -.9575388    .9658367
         tdum23 |  -.0250689   .5146681    -0.05   0.961      -1.0338    .9836619
         tdum24 |  -.0610161   .5200307    -0.12   0.907    -1.080257    .9582254
         tdum25 |  -.1249025   .5336098    -0.23   0.815    -1.170758    .9209536
         tdum26 |          0  (omitted)
         tdum27 |          0  (omitted)
          _cons |    -2.7873   22.12128    -0.13   0.900    -46.14422    40.56962
---------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(lnQuantity lnQuantity2 lnross_oil_prod lnwdi_pop)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(1/26).(L.fh_polity2 L.lnwdi_gdpcapcur L.al_ethnic) collapsed
Instruments for levels equation
  Standard
    tdum4 tdum5 tdum6 tdum7 tdum8 tdum9 tdum10 tdum11 tdum12 tdum13 tdum14
    tdum15 tdum16 tdum17 tdum18 tdum19 tdum20 tdum21 tdum22 tdum23 tdum24
    tdum25 tdum26 tdum27
    _cons
------------------------------------------------------------------------------
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 =  -0.75  Pr > z =  0.455
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(60)   =  67.63  Prob > chi2 =  0.233
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(60)   =  19.28  Prob > chi2 =  1.000
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  iv(lnQuantity lnQuantity2 lnross_oil_prod lnwdi_pop, eq(diff))
    Hansen test excluding group:     chi2(58)   =  19.42  Prob > chi2 =  1.000
    Difference (null H = exogenous): chi2(2)    =  -0.15  Prob > chi2 =  1.000
  iv(tdum4 tdum5 tdum6 tdum7 tdum8 tdum9 tdum10 tdum11 tdum12 tdum13 tdum14 tdum15 tdum16 tdum17 tdum18 tdum19 tdum20 tdum21 tdum22 tdu
> m23 tdum24 tdum25 tdum26 tdum27, eq(level))
    Hansen test excluding group:     chi2(38)   =  23.18  Prob > chi2 =  0.972
    Difference (null H = exogenous): chi2(22)   =  -3.90  Prob > chi2 =  1.000
          the xtseqreg version

          Code:
                xtseqreg L(0/2).fh_polity2 lnQuantity lnQuantity2 lnwdi_gdpcapcur al_ethnic lnross_oil_prod lnwdi_pop tdum4-tdum27, gmmiv(L.fh_polity
> 2 L.lnwdi_gdpcapcur L.al_ethnic, model(diff) lagrange(1 .) collapse) iv(lnQuantity lnQuantity2 lnross_oil_prod lnwdi_pop, model(diff)
>  diff) teffects twostep vce(robust) wmatrix(independent) 

Group variable: ccode                        Number of obs         =      1069
Time variable: year                          Number of groups      =        52

                                             Obs per group:    min =         3
                                                               avg =  20.55769
                                                               max =        23

                                             Number of instruments =        93

                                     (Std. Err. adjusted for clustering on ccode)
---------------------------------------------------------------------------------
                |              WC-Robust
     fh_polity2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
     fh_polity2 |
            L1. |   .6511516    .282483     2.31   0.021     .0974952    1.204808
            L2. |  -.0695386   .0367554    -1.89   0.059    -.1415778    .0025007
                |
     lnQuantity |          0  (omitted)
    lnQuantity2 |  -.2400393   .2867122    -0.84   0.402    -.8019848    .3219062
lnwdi_gdpcapcur |   .1865474   .3805115     0.49   0.624    -.5592414    .9323362
      al_ethnic |  -.2739179   8.632441    -0.03   0.975    -17.19319    16.64535
lnross_oil_prod |   .0367536   .0640229     0.57   0.566     -.088729    .1622363
      lnwdi_pop |   .4090251   1.304176     0.31   0.754    -2.147113    2.965163
          tdum4 |  -.0607378   .1304037    -0.47   0.641    -.3163244    .1948488
          tdum5 |   .0875442   .1353097     0.65   0.518    -.1776579    .3527464
          tdum6 |          0  (omitted)
          tdum7 |   .0600703    .135858     0.44   0.658    -.2062065     .326347
          tdum8 |  -.0443853   .1878557    -0.24   0.813    -.4125757    .3238051
          tdum9 |          0  (omitted)
         tdum10 |   .1646479    .229578     0.72   0.473    -.2853168    .6146125
         tdum11 |   .2473264    .183708     1.35   0.178    -.1127348    .6073875
         tdum12 |          0  (omitted)
         tdum13 |          0  (omitted)
         tdum14 |   .1799438   .2371838     0.76   0.448    -.2849278    .6448155
         tdum15 |   .1873821   .2498161     0.75   0.453    -.3022484    .6770126
         tdum16 |   .1712642   .3056707     0.56   0.575    -.4278394    .7703678
         tdum17 |   .0854983    .340212     0.25   0.802     -.581305    .7523016
         tdum18 |   .0076133   .4060675     0.02   0.985    -.7882644    .8034909
         tdum19 |   -.007903   .4448249    -0.02   0.986    -.8797437    .8639377
         tdum20 |   .0502825   .4545515     0.11   0.912    -.8406221    .9411871
         tdum21 |  -.0341587   .4809052    -0.07   0.943    -.9767155    .9083982
         tdum22 |    .004149    .490666     0.01   0.993    -.9575388    .9658367
         tdum23 |  -.0250689   .5146681    -0.05   0.961      -1.0338    .9836619
         tdum24 |  -.0610161   .5200307    -0.12   0.907    -1.080258    .9582254
         tdum25 |  -.1249025   .5336098    -0.23   0.815    -1.170758    .9209536
         tdum26 |          0  (omitted)
         tdum27 |          0  (omitted)
                |
           year |
          1993  |          0  (omitted)
          1994  |          0  (omitted)
          1995  |    .067788   .1582914     0.43   0.668    -.2424575    .3780335
          1996  |          0  (omitted)
          1997  |          0  (omitted)
          1998  |   .1261298   .2092332     0.60   0.547    -.2839598    .5362194
          1999  |          0  (omitted)
          2000  |          0  (omitted)
          2001  |   .2083813   .1624491     1.28   0.200     -.110013    .5267756
          2002  |   .1492227    .201797     0.74   0.460    -.2462921    .5447374
          2003  |          0  (omitted)
          2004  |          0  (omitted)
          2005  |          0  (omitted)
          2006  |          0  (omitted)
          2007  |          0  (omitted)
          2008  |          0  (omitted)
          2009  |          0  (omitted)
          2010  |          0  (omitted)
          2011  |          0  (omitted)
          2012  |          0  (omitted)
          2013  |          0  (omitted)
          2014  |          0  (omitted)
                |
          _cons |    -2.7873   22.12128    -0.13   0.900    -46.14422    40.56962
---------------------------------------------------------------------------------

. estat overid                                                                                                                       

Hansen's J-test                                        chi2(63)    =   19.2750
H0: overidentifying restrictions are valid             Prob > chi2 =    1.0000

. 
.  estat serial, ar(1/3)

Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1:     z =   -1.7696   Prob > |z|  =    0.0768
H0: no autocorrelation of order 2:     z =   -0.7471   Prob > |z|  =    0.4550
H0: no autocorrelation of order 3:     z =    1.1995   Prob > |z|  =    0.2303

          Comment

          • #6
            1. Please do not combine the teffects option with the tdum variables:
              Code:
              xtseqreg L(0/2).fh_polity2 lnQuantity lnQuantity2 lnwdi_gdpcapcur al_ethnic lnross_oil_prod lnwdi_pop, gmmiv(L.fh_polity2, model(diff) lagrange(1 .) collapse) iv(lnQuantity lnQuantity2 lnwdi_gdpcapcur lnross_oil_prod al_ethnic lnwdi_pop, model(diff) diff) teffects twostep vce(robust) wmatrix(independent)
              The tabulate output shows that you actually do not use data for the years 2015 and 2016. Your estimation sample ends in 2014. That still does not explain why the variable lnQuantity is omitted. Is there anything special about this variable?
            2. With your additional GMM-style instruments for the endogenous variables, the number of instruments (93) becomes (too) large. I would recommend to restrict the maximum lag length, e.g. for xtseqreg:
              Code:
              gmmiv(L.fh_polity2 lnwdi_gdpcapcur al_ethnic, model(diff) lag(1 4) collapse)
              and similar for xtabond2.
            https://www.kripfganz.de/stata/

            Comment

            • #7
              Dear Sebastian,
              Thanks.

              1.
              gmmiv(L.fh_polity2 lnwdi_gdpcapcur al_ethnic, model(diff) lag(1 4) collapse)
              What would be a logic way to obtain this interval?

              2.
              The tabulate output shows that you actually do not use data for the years 2015 and 2016. Your estimation sample ends in 2014. That still does not explain why the variable lnQuantity is omitted. Is there anything special about this variable?
              Quantity is energy household consumption of energy (kWh, Million of Hous.)and I did notice something particular with the time series of this data. When the variable is used as it is, it It is not omitted but when the log is taken, I obtained this omission and I don´t get why.
              Code:
               xtabond2 L(0/2).fh_polity2 Quantity Quantity2 wdi_gdpcapcur al_ethnic ross_oil_prod wdi_popurb tdum4-tdum27, gmmstyle(L.fh_polity2 
> L.wdi_gdpcapcur, equation(diff) lag(2 .) collapse) ivstyle(Quantity Quantity2 al_ethnic ross_oil_prod wdi_popurb, equation(diff)) i
> vstyle(tdum4-tdum27, equation(level)) twostep robust h(2)
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: ccode                           Number of obs      =      2035
Time variable : year                            Number of groups   =        92
Number of instruments = 69                      Obs per group: min =         3
Wald chi2(32) =    338.17                                      avg =     22.12
Prob > chi2   =     0.000                                      max =        23
-------------------------------------------------------------------------------
              |              Corrected
   fh_polity2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
   fh_polity2 |
          L1. |   .5385843   .2824793     1.91   0.057    -.0150649    1.092233
          L2. |   .1272336   .2254383     0.56   0.572    -.3146173    .5690846
              |
     Quantity |   .0004141   .0005019     0.83   0.409    -.0005696    .0013977
    Quantity2 |  -1.23e-09   1.32e-09    -0.93   0.353    -3.81e-09    1.36e-09
wdi_gdpcapcur |   5.75e-06   5.51e-06     1.04   0.297    -5.05e-06    .0000165
    al_ethnic |  -3.941131   8.644647    -0.46   0.648    -20.88433    13.00206
ross_oil_prod |  -9.17e-10   1.69e-09    -0.54   0.588    -4.23e-09    2.40e-09
   wdi_popurb |   .0277273   .0248022     1.12   0.264    -.0208841    .0763388
        tdum4 |  -.2227344   .0976095    -2.28   0.022    -.4140456   -.0314232
        tdum5 |  -.0330069   .1240056    -0.27   0.790    -.2760534    .2100395
        tdum6 |  -.0750574   .1205252    -0.62   0.533    -.3112823    .1611676
        tdum7 |  -.0832793   .1227775    -0.68   0.498    -.3239188    .1573601
        tdum8 |  -.1721146   .1315667    -1.31   0.191    -.4299806    .0857513
        tdum9 |  -.0622459   .1298429    -0.48   0.632    -.3167334    .1922415
       tdum10 |  -.0248061   .1244492    -0.20   0.842     -.268722    .2191098
       tdum11 |   .0021351   .1258773     0.02   0.986    -.2445799    .2488501
       tdum12 |  -.0790016    .126757    -0.62   0.533    -.3274408    .1694376
       tdum13 |   .0095076   .1327168     0.07   0.943    -.2506126    .2696277
       tdum14 |  -.0199106   .1341544    -0.15   0.882    -.2828484    .2430273
       tdum15 |    -.03186   .1352466    -0.24   0.814    -.2969384    .2332184
       tdum16 |   .0018881   .1421934     0.01   0.989    -.2768058     .280582
       tdum17 |  -.0318762   .1436569    -0.22   0.824    -.3134385    .2496861
       tdum18 |  -.1226688   .1591686    -0.77   0.441    -.4346335    .1892959
       tdum19 |  -.1006423    .157964    -0.64   0.524     -.410246    .2089614
       tdum20 |  -.0775193   .1719707    -0.45   0.652    -.4145756     .259537
       tdum21 |  -.1178808   .1800887    -0.65   0.513    -.4708481    .2350865
       tdum22 |  -.0473325   .1752841    -0.27   0.787     -.390883     .296218
       tdum23 |   -.118468   .1943054    -0.61   0.542    -.4992996    .2623636
       tdum24 |  -.0916615   .1856413    -0.49   0.621    -.4555117    .2721887
       tdum25 |  -.1658361   .1949056    -0.85   0.395    -.5478441    .2161719
       tdum26 |          0  (omitted)
       tdum27 |          0  (omitted)
        _cons |   1.547341   6.759539     0.23   0.819    -11.70111    14.79579
-------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(Quantity Quantity2 al_ethnic ross_oil_prod wdi_popurb)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/26).(L.fh_polity2 L.wdi_gdpcapcur) collapsed
Instruments for levels equation
  Standard
    tdum4 tdum5 tdum6 tdum7 tdum8 tdum9 tdum10 tdum11 tdum12 tdum13 tdum14
    tdum15 tdum16 tdum17 tdum18 tdum19 tdum20 tdum21 tdum22 tdum23 tdum24
    tdum25 tdum26 tdum27
    _cons
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.01  Pr > z =  0.310
Arellano-Bond test for AR(2) in first differences: z =  -0.62  Pr > z =  0.538
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(36)   =  10.80  Prob > chi2 =  1.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(36)   =  26.62  Prob > chi2 =  0.873
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  iv(Quantity Quantity2 al_ethnic ross_oil_prod wdi_popurb, eq(diff))
    Hansen test excluding group:     chi2(34)   =  25.02  Prob > chi2 =  0.869
    Difference (null H = exogenous): chi2(2)    =   1.60  Prob > chi2 =  0.449
  iv(tdum4 tdum5 tdum6 tdum7 tdum8 tdum9 tdum10 tdum11 tdum12 tdum13 tdum14 tdum15 tdum16 tdum17 tdum18 tdum19 tdum20 tdum21 tdum22 t
> dum23 tdum24 tdum25 tdum26 tdum27, eq(level))
    Hansen test excluding group:     chi2(14)   =  18.52  Prob > chi2 =  0.184
    Difference (null H = exogenous): chi2(22)   =   8.10  Prob > chi2 =  0.997

              Comment

              • #8
                1. I am not aware of any consensus about a rule of thumb regarding the lag depth. In general, higher-order lags tend to not have a strong correlation with the current values and consequently become weak instruments. If 4 lags is reasonable, I honestly do not know. Ideally, the results should not depend much on whether you choose 3, 4, 5, ... lags. Currently, 69 instruments are still too many.
                2. I cannot say much about the Quantity variable, sorry. Please remove tdum26 and tdum27 from your estimation (both from the set of variables and the set of instruments), i.e. only use tdum4-tdum25.
                https://www.kripfganz.de/stata/

                Comment

                • #9
                  Dear Sebastian,

                  Thanks!

                  How could I reduce the number of the instruments?

                  Comment

                  • #10
                    Originally posted by Nadia Oue View Post
                    How could I reduce the number of the instruments?
                    Please see my advice 2 in my above comment #6 about restricting the maximum lag length. Of course, you choose a different maximum lag length than 4.

                    By the way: In your previous example, you have started with the 2nd lag to form the GMM-style instruments. There is no need to do that, and I would recommend to start with the 1st lag as in your earlier examples.
                    https://www.kripfganz.de/stata/

                    Comment

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