Xtabond2 for system GMM. Please help me for coding

[Khati Zolfaghari]

Dear all,

I am working with the xtabond2 command in Stata to solve the endogeneity problem of my estimation. I read the construction of doing xtabond2 from David Roodman. However, I am still confused that my coding is right or wrong. I appreciate receiving your advice :

*************:
xtabond2 ltotalfertility l.ltotalfertility l(0/2).(pand_res_pt) i.year, ///
iv(i.year, eq(both)) ///
iv(l(0/2).(pand_res_pt), eq(both)) ///
gmm(ltotalfertility, lag(2 .) collapse eq(both))  ///
h(1) ar(3) two cluster(ifscode)

here, by choosing

. xtabond2 ltotalfertility l.ltotalfertility l(0/2).(pand_res_pt) i.year, ///
> iv(i.year, eq(both)) ///
> iv(l(0/2).(pand_res_pt), eq(both)) ///
> gmm(ltotalfertility, lag(2 .) collapse eq(both))  ///
> h(1) ar(3) two cluster(ifscode)
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
1996b.year dropped due to collinearity
1997.year dropped due to collinearity
2009.year dropped due to collinearity
2018.year dropped due to collinearity
2019.year 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: ifscode                         Number of obs      =      3622
Time variable : year                            Number of groups   =       183
Number of instruments = 44                      Obs per group: min =         1
Wald chi2(23) =  69569.39                                      avg =     19.79
Prob > chi2   =     0.000                                      max =        20
                                   (Std. err. adjusted for clustering on ifscode)
---------------------------------------------------------------------------------
                |              Corrected
ltotalfertility | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
----------------+----------------------------------------------------------------
ltotalfertility |
            L1. |   .8861639   .0218916    40.48   0.000     .8432571    .9290708
                |
    pand_res_pt |
            --. |  -.0253932   .0059697    -4.25   0.000    -.0370936   -.0136929
            L1. |  -.0309516    .008387    -3.69   0.000    -.0473897   -.0145134
            L2. |  -.0282224   .0065436    -4.31   0.000    -.0410476   -.0153972
                |
           year |
          1998  |  -.0060163   .0048398    -1.24   0.214    -.0155022    .0034696
          1999  |  -.0054971    .004538    -1.21   0.226    -.0143914    .0033972
          2000  |  -.0053192   .0040945    -1.30   0.194    -.0133442    .0027059
          2001  |  -.0116792    .004663    -2.50   0.012    -.0208184   -.0025399
          2002  |  -.0085614   .0040365    -2.12   0.034    -.0164728     -.00065
          2003  |  -.0082516   .0035831    -2.30   0.021    -.0152744   -.0012288
          2004  |  -.0066783   .0034789    -1.92   0.055    -.0134968    .0001401
          2005  |  -.0094819   .0034326    -2.76   0.006    -.0162097   -.0027541
          2006  |   -.006441   .0031204    -2.06   0.039    -.0125569   -.0003251
          2007  |  -.0062036   .0032063    -1.93   0.053    -.0124879    .0000806
          2008  |   -.006044   .0029945    -2.02   0.044    -.0119131   -.0001749
          2010  |   .0023753   .0019727     1.20   0.229    -.0014911    .0062418
          2011  |  -.0024552   .0013919    -1.76   0.078    -.0051833    .0002729
          2012  |  -.0121593   .0034885    -3.49   0.000    -.0189966    -.005322
          2013  |  -.0177037   .0037538    -4.72   0.000    -.0250609   -.0103465
          2014  |  -.0139368   .0039577    -3.52   0.000    -.0216938   -.0061797
          2015  |  -.0176519   .0041448    -4.26   0.000    -.0257756   -.0095281
          2016  |   -.018251   .0041753    -4.37   0.000    -.0264344   -.0100676
          2017  |  -.0233959   .0044382    -5.27   0.000    -.0320946   -.0146973
                |
          _cons |   .1172786   .0240108     4.88   0.000     .0702183    .1643389
---------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(pand_res_pt L.pand_res_pt L2.pand_res_pt)
    D.(1996b.year 1997.year 1998.year 1999.year 2000.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 2018.year 2019.year)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/23).ltotalfertility collapsed
Instruments for levels equation
  Standard
    pand_res_pt L.pand_res_pt L2.pand_res_pt
    1996b.year 1997.year 1998.year 1999.year 2000.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 2018.year 2019.year
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.ltotalfertility collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -4.49  Pr > z =  0.000
Arellano-Bond test for AR(2) in first differences: z =   0.67  Pr > z =  0.501
Arellano-Bond test for AR(3) in first differences: z =  -1.82  Pr > z =  0.069
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(20)   =  17.39  Prob > chi2 =  0.628
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(20)   =  96.22  Prob > chi2 =  0.000
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(19)   =  70.91  Prob > chi2 =  0.000
    Difference (null H = exogenous): chi2(1)    =  25.31  Prob > chi2 =  0.000
  iv(1996b.year 1997.year 1998.year 1999.year 2000.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 2018.year 2019.year)
    Hansen test excluding group:     chi2(1)    =   0.10  Prob > chi2 =  0.757
    Difference (null H = exogenous): chi2(19)   =  96.12  Prob > chi2 =  0.000
  iv(pand_res_pt L.pand_res_pt L2.pand_res_pt)
    Hansen test excluding group:     chi2(17)   =  90.00  Prob > chi2 =  0.000
    Difference (null H = exogenous): chi2(3)    =   6.21  Prob > chi2 =  0.102


.
end of do-file

the lag(2 .) , but when I use the collapse the Hansen test is not significant.


***also I used the "xtdpdgmm" to get te better results, I did this :

xtdpdgmm L(0/1).ltotalfertility l(0/2).(pand_res_pt) i.year, noserial gmmiv(L.ltotalfertility, collapse model(difference)) iv(l(0/2).(pand_res_pt) i.year, difference model(difference)) twostep vce(robust)

and the results :

. xtdpdgmm L(0/1).ltotalfertility l(0/2).(pand_res_pt) i.year, noserial gmmiv(L.ltotalfertility, collapse model(difference)) iv(l(0/2).(pand
> _res_pt) i.year, difference model(difference)) twostep vce(robust)
note: 1996.year identifies no observations in the sample.
note: 1997.year identifies no observations in the sample.
note: 2017.year omitted because of collinearity.
note: 2018.year identifies no observations in the sample.
note: 2019.year identifies no observations in the sample.

Generalized method of moments estimation

Fitting full model:

Step 1:
initial:       f(b) =  19.115759
alternative:   f(b) =  4.6514905
rescale:       f(b) =  .08442007
Iteration 0:   f(b) =  .08442007  
Iteration 1:   f(b) =  .00083005  
Iteration 2:   f(b) =  .00082701  
Iteration 3:   f(b) =  .00082701  

Step 2:
Iteration 0:   f(b) =  .97149141  
Iteration 1:   f(b) =  .57064682  
Iteration 2:   f(b) =  .56335002  
Iteration 3:   f(b) =   .5633197  
Iteration 4:   f(b) =  .56331884  
Iteration 5:   f(b) =  .56331881  

Group variable: ifscode                      Number of obs         =      3622
Time variable: year                          Number of groups      =       183

Moment conditions:     linear =      43      Obs per group:    min =         1
                    nonlinear =      18                        avg =  19.79235
                        total =      61                        max =        20

                                 (Std. err. adjusted for 183 clusters in ifscode)
---------------------------------------------------------------------------------
                |              WC-Robust
ltotalfertility | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
----------------+----------------------------------------------------------------
ltotalfertility |
            L1. |   1.025479   .0123817    82.82   0.000     1.001211    1.049746
                |
    pand_res_pt |
            --. |   .0027941   .0027985     1.00   0.318    -.0026909    .0082791
            L1. |   .0014515   .0040002     0.36   0.717    -.0063887    .0092917
            L2. |   .0011745   .0039944     0.29   0.769    -.0066543    .0090033
                |
           year |
          1996  |          0  (empty)
          1997  |          0  (empty)
          1998  |  -.0134633   .0039956    -3.37   0.001    -.0212946    -.005632
          1999  |  -.0099362   .0039732    -2.50   0.012    -.0177235   -.0021489
          2000  |  -.0072415   .0039882    -1.82   0.069    -.0150582    .0005752
          2001  |  -.0112745   .0031739    -3.55   0.000    -.0174952   -.0050537
          2002  |  -.0051081   .0031922    -1.60   0.110    -.0113647    .0011486
          2003  |  -.0028348   .0032195    -0.88   0.379    -.0091448    .0034752
          2004  |   .0006642   .0032341     0.21   0.837    -.0056745     .007003
          2005  |  -.0004954    .002737    -0.18   0.856    -.0058598    .0048691
          2006  |    .004047   .0031755     1.27   0.202    -.0021767    .0102708
          2007  |   .0055304   .0032534     1.70   0.089    -.0008462    .0119071
          2008  |   .0068074   .0032675     2.08   0.037     .0004032    .0132115
          2009  |   .0009863   .0024508     0.40   0.687    -.0038171    .0057897
          2010  |   .0030281   .0027427     1.10   0.270    -.0023475    .0084037
          2011  |   .0013373   .0022822     0.59   0.558    -.0031357    .0058103
          2012  |   .0048407   .0023568     2.05   0.040     .0002214    .0094599
          2013  |     .00075   .0015893     0.47   0.637    -.0023651     .003865
          2014  |   .0057334   .0019981     2.87   0.004     .0018172    .0096496
          2015  |   .0034253   .0013914     2.46   0.014     .0006982    .0061525
          2016  |    .003241   .0012295     2.64   0.008     .0008312    .0056508
          2017  |          0  (omitted)
          2018  |          0  (empty)
          2019  |          0  (empty)
                |
          _cons |   -.037772   .0117266    -3.22   0.001    -.0607558   -.0147882
---------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(diff):
   L1.L.ltotalfertility L2.L.ltotalfertility L3.L.ltotalfertility
   L4.L.ltotalfertility L5.L.ltotalfertility L6.L.ltotalfertility
   L7.L.ltotalfertility L8.L.ltotalfertility L9.L.ltotalfertility
   L10.L.ltotalfertility L11.L.ltotalfertility L12.L.ltotalfertility
   L13.L.ltotalfertility L14.L.ltotalfertility L15.L.ltotalfertility
   L16.L.ltotalfertility L17.L.ltotalfertility L18.L.ltotalfertility
   L19.L.ltotalfertility L20.L.ltotalfertility
 2, model(diff):
   D.pand_res_pt D.L.pand_res_pt D.L2.pand_res_pt D.1999bn.year D.2000.year
   D.2001.year D.2002.year D.2003.year D.2004.year D.2005.year D.2006.year
   D.2007.year D.2008.year D.2009.year D.2010.year D.2011.year D.2012.year
   D.2013.year D.2014.year D.2015.year D.2016.year D.2017.year
 3, model(level):
   _cons

.
end of do-file

the results are not the same, Please guide me if is it the right command.

Many thanks in advance for your valuable time and advice.

Regards,

[Sebastian Kripfganz]

You have specified two very different estimators with the two commands. With xtabond2, you have specified a system GMM estimator. With xtdpdgmm, you have specified a difference GMM estimator with the nonlinear Ahn-Schmidt moment conditions.

xtdpdgmm cannot replicate xtabond2 if you specify the eq(both) suboption in the iv() option. However, notice that iv(, eq(both)) is not the same as jointly specifying iv(, eq(level)) iv(, eq(diff)). Unless you know what eq(both) is really doing, you probably want to specify the instruments separately for the two equations.

The following commands should be equivalent:

xtabond2 L(0/1).ltotalfertility l(0/2).(pand_res_pt) i.year, gmmiv(L.ltotalfertility, lag(1 .) collapse eq(diff)) gmmiv(L.ltotalfertility, lag(0 0) collapse eq(level)) iv(L(0/2).(pand_res_pt), eq(difference) mz) iv(L(0/2).(pand_res_pt) i.year, eq(level) mz) twostep robust

xtdpdgmm L(0/1).ltotalfertility l(0/2).(pand_res_pt) i.year, gmmiv(L.ltotalfertility, lag(1 .) collapse model(difference)) gmmiv(L.ltotalfertility, diff lag(0 0) collapse model(level)) iv(L(0/2).(pand_res_pt), diff model(difference)) iv(L(0/2).(pand_res_pt) i.year, model(level)) twostep vce(robust)

You can then adjust the models as needed from this starting point.

If the Hansen test rejects this system GMM estimator, you might have to go back to a difference GMM estimator by removing the instruments for the level model (aside from the time dummies).

More information:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.

[Khati Zolfaghari]

@Sebastian Kripfganz many thanks for your reply. by using both" I wanted to specify the level and diff for IV(and I did wrong).

I follow your assistance , but I receive this error.

 xtabond2 L(0/1).ltotalfertility l(0/2).(pand_res_pt) i.year, gmmiv(L.ltotalfertility, lag(1 .) collapse eq(diff)) gmmiv(L.ltotalfertility,
>  lag(0 0) collapse eq(level)) iv(L(0/2).(pand_res_pt), eq(difference) mz) iv(L(0/2).(pand_res_pt) i.year, eq(level) mz) twostep robust
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
equation(difference) invalid.
r(198);

Many thanks in advance for your valuable time and advice.

regards,

[Sebastian Kripfganz]

Sorry, my mistake. Replace eq(difference) in that command line with eq(diff).

[Khati Zolfaghari]

@Sebastian Kripfganz thanks for your reply, but error is still the same.

. xtabond2 L(0/1).ltotalfertility l(0/2).(pand_res_pt) i.year, gmmiv(L.ltotalfertility, lag(1 .) collapse eq(difference)) gmmiv(L.ltotalfert
> ility, lag(0 0) collapse eq(level)) iv(L(0/2).(pand_res_pt), eq(difference) mz) iv(L(0/2).(pand_res_pt) i.year, eq(level) mz) twostep robu
> st
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
equation(difference) invalid.
r(198);

for the second one :

xtdpdgmm L(0/1).ltotalfertility l(0/2).(pand_res_pt) i.year, gmmiv(L.ltotalfertility, lag(1 .) collapse model(difference)) gmmiv(L.ltotalfertility, diff lag(0 0) collapse model(level)) iv(L(0/2).(pand_res_pt), diff model(difference)) iv(L(0/2).(pand_res_pt) i.year, model(level)) twostep vce(robust)

. xtdpdgmm L(0/1).ltotalfertility l(0/2).(pand_res_pt) i.year, gmmiv(L.ltotalfertility, lag(1 .) collapse model(difference)) gmmiv(L.ltotalf
> ertility, diff lag(0 0) collapse model(level)) iv(L(0/2).(pand_res_pt), diff model(difference)) iv(L(0/2).(pand_res_pt) i.year, model(leve
> l)) twostep vce(robust)
note: 1996.year identifies no observations in the sample.
note: 1997.year identifies no observations in the sample.
note: 2017.year omitted because of collinearity.
note: 2018.year identifies no observations in the sample.
note: 2019.year identifies no observations in the sample.

Generalized method of moments estimation

Fitting full model:
Step 1         f(b) =  .00198467
Step 2         f(b) =  .60731996

Group variable: ifscode                      Number of obs         =      3622
Time variable: year                          Number of groups      =       183

Moment conditions:     linear =      47      Obs per group:    min =         1
                    nonlinear =       0                        avg =  19.79235
                        total =      47                        max =        20

                                 (Std. err. adjusted for 183 clusters in ifscode)
---------------------------------------------------------------------------------
                |              WC-Robust
ltotalfertility | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
----------------+----------------------------------------------------------------
ltotalfertility |
            L1. |   .9620578   .0074356   129.39   0.000     .9474844    .9766313
                |
    pand_res_pt |
            --. |  -.0120369   .0036579    -3.29   0.001    -.0192062   -.0048677
            L1. |  -.0141876   .0053543    -2.65   0.008    -.0246819   -.0036933
            L2. |  -.0173138   .0050407    -3.43   0.001    -.0271935   -.0074341
                |
           year |
          1996  |          0  (empty)
          1997  |          0  (empty)
          1998  |   .0029904   .0027018     1.11   0.268    -.0023051    .0082858
          1999  |   .0051589   .0025662     2.01   0.044     .0001292    .0101886
          2000  |     .00722   .0024117     2.99   0.003     .0024932    .0119468
          2001  |   .0011346    .002387     0.48   0.635    -.0035438     .005813
          2002  |   .0058193   .0020605     2.82   0.005     .0017807    .0098579
          2003  |   .0074605   .0020744     3.60   0.000     .0033948    .0115261
          2004  |    .009511   .0022669     4.20   0.000      .005068     .013954
          2005  |   .0075377   .0018379     4.10   0.000     .0039355    .0111399
          2006  |   .0109501   .0023213     4.72   0.000     .0064004    .0154998
          2007  |    .011599   .0024158     4.80   0.000     .0068641     .016334
          2008  |   .0122399   .0025378     4.82   0.000      .007266    .0172139
          2009  |   .0125501   .0025921     4.84   0.000     .0074697    .0176305
          2010  |   .0132048   .0032966     4.01   0.000     .0067435    .0196661
          2011  |   .0117341   .0027346     4.29   0.000     .0063744    .0170938
          2012  |   .0085155   .0021526     3.96   0.000     .0042963    .0127346
          2013  |   .0028293   .0015655     1.81   0.071    -.0002391    .0058977
          2014  |   .0078911   .0019816     3.98   0.000     .0040072     .011775
          2015  |    .004883   .0014904     3.28   0.001     .0019618    .0078042
          2016  |   .0047944   .0013152     3.65   0.000     .0022166    .0073722
          2017  |          0  (omitted)
          2018  |          0  (empty)
          2019  |          0  (empty)
                |
          _cons |   .0229254    .006648     3.45   0.001     .0098955    .0359552
---------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(diff):
   L1.L.ltotalfertility L2.L.ltotalfertility L3.L.ltotalfertility
   L4.L.ltotalfertility L5.L.ltotalfertility L6.L.ltotalfertility
   L7.L.ltotalfertility L8.L.ltotalfertility L9.L.ltotalfertility
   L10.L.ltotalfertility L11.L.ltotalfertility L12.L.ltotalfertility
   L13.L.ltotalfertility L14.L.ltotalfertility L15.L.ltotalfertility
   L16.L.ltotalfertility L17.L.ltotalfertility L18.L.ltotalfertility
   L19.L.ltotalfertility L20.L.ltotalfertility
 2, model(level):
   D.L.ltotalfertility
 3, model(diff):
   D.pand_res_pt D.L.pand_res_pt D.L2.pand_res_pt
 4, model(level):
   pand_res_pt L.pand_res_pt L2.pand_res_pt 1998bn.year 1999.year 2000.year
   2001.year 2002.year 2003.year 2004.year 2005.year 2006.year 2007.year
   2008.year 2009.year 2010.year 2012.year 2013.year 2014.year 2015.year
   2016.year 2017.year
 5, model(level):
   _cons

.
end of do-file

but the "Hansen test" and "serial correlation":

. estat serial

Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1      z =   -4.6661   Prob > |z|  =    0.0000
H0: no autocorrelation of order 2      z =    0.7144   Prob > |z|  =    0.4750

.

.  estat overid

Sargan-Hansen test of the overidentifying restrictions
H0: overidentifying restrictions are valid

2-step moment functions, 2-step weighting matrix       chi2(23)    =  111.1396
                                                       Prob > chi2 =    0.0000

2-step moment functions, 3-step weighting matrix       chi2(23)    =  147.1723
                                                       Prob > chi2 =    0.0000

also in terms of the number of observation in this model I have doubt.

Many thanks in advance for your valuable time and advice.

regards,

[Sebastian Kripfganz]

@Sebastian Kripfganz thanks for your reply, but error is still the same.

. xtabond2 L(0/1).ltotalfertility l(0/2).(pand_res_pt) i.year, gmmiv(L.ltotalfertility, lag(1 .) collapse eq(difference)) gmmiv(L.ltotalfert
> ility, lag(0 0) collapse eq(level)) iv(L(0/2).(pand_res_pt), eq(difference) mz) iv(L(0/2).(pand_res_pt) i.year, eq(level) mz) twostep robu
> st
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
equation(difference) invalid.
r(198);

You have not replaced eq(difference) by eq(diff).

The serial correlation test is fine, but the Hansen test rejects your model. A likely explanation could be that your level instruments are invalid. You should try a difference GMM estimator first.

[Khati Zolfaghari]

@Sebastian Kripfganz thanks for your reply. I am trying several specifications and following your advice. also, I tried to do a model in terms of the difference-GMM.

• I tried even replacing the eq(difference) by eq(diff) and vs,

mata: mata set matafavor speed, perm
. xtabond2 L(0/1).ltotalfertility l(0/2).(pand_res_pt) i.year, gmmiv(L.ltotalfertility, lag(1 .) collapse eq(diff)) gmmiv(L.ltotalfertility,
>  lag(0 0) collapse eq(level)) iv(L(0/2).(pand_res_pt), eq(diff) mz) iv(L(0/2).(pand_res_pt) i.year, eq(level) mz) twostep robust
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
gmmiv(L.ltotalfertility, lag(1 .) collapse eq(diff)) gmmiv(L.ltotalfertility, lag(0 0) collapse eq(level)) invalid.r(198);

• for the diff-GMM , I estimate:

xi: xtabond2 ltotalfertility l.ltotalfertility l(0/2).(pand_res_pt) i.year, ///

iv(i.year, eq(diff)) ///
iv(l(0/2).(pand_res_pt), eq(diff)) ///
gmm(ltotalfertility, lag(2 2) eq(diff)) ///
h(1) nolev ar(3) cluster(ifscode)

. xi: xtabond2 ltotalfertility l.ltotalfertility l(0/2).(pand_res_pt) i.year, ///
> iv(i.year, eq(diff)) ///
> iv(l(0/2).(pand_res_pt), eq(diff)) ///
> gmm(ltotalfertility, lag(2 2) eq(diff)) ///
> h(1) nolev ar(3) cluster(ifscode)
i.year            _Iyear_1996-2019    (naturally coded; _Iyear_1996 omitted)
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
_Iyear_1997 dropped due to collinearity
_Iyear_1999 dropped due to collinearity
_Iyear_2018 dropped due to collinearity
_Iyear_2019 dropped due to collinearity
Warning: Two-step estimated covariance matrix of moments is singular.
  Using a generalized inverse to calculate robust weighting matrix for Hansen test.
  Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, one-step difference GMM
------------------------------------------------------------------------------
Group variable: ifscode                         Number of obs      =      3439
Time variable : year                            Number of groups   =       182
Number of instruments = 41                      Obs per group: min =         0
Wald chi2(0)  =         .                                      avg =     18.90
Prob > chi2   =         .                                      max =        19
                                   (Std. err. adjusted for clustering on ifscode)
---------------------------------------------------------------------------------
                |               Robust
ltotalfertility | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
----------------+----------------------------------------------------------------
ltotalfertility |
            L1. |   .6417241   .0590909    10.86   0.000     .5259081      .75754
                |
    pand_res_pt |
            --. |   -.002099   .0022695    -0.92   0.355    -.0065472    .0023492
            L1. |  -.0052392   .0034211    -1.53   0.126    -.0119444    .0014659
            L2. |  -.0062662   .0030356    -2.06   0.039    -.0122158   -.0003166
                |
    _Iyear_1998 |   .0028761   .0015311     1.88   0.060    -.0001248    .0058769
    _Iyear_2000 |  -.0015303   .0015071    -1.02   0.310    -.0044842    .0014236
    _Iyear_2001 |  -.0162301   .0031707    -5.12   0.000    -.0224447   -.0100156
    _Iyear_2002 |  -.0156015   .0039573    -3.94   0.000    -.0233576   -.0078454
    _Iyear_2003 |  -.0171492   .0048845    -3.51   0.000    -.0267227   -.0075758
    _Iyear_2004 |  -.0170734    .005531    -3.09   0.002    -.0279139   -.0062328
    _Iyear_2005 |  -.0219861    .006054    -3.63   0.000    -.0338517   -.0101204
    _Iyear_2006 |  -.0194425   .0068225    -2.85   0.004    -.0328143   -.0060707
    _Iyear_2007 |  -.0191756   .0072006    -2.66   0.008    -.0332885   -.0050628
    _Iyear_2008 |  -.0178043   .0079219    -2.25   0.025    -.0333309   -.0022777
    _Iyear_2009 |  -.0251675   .0083649    -3.01   0.003    -.0415623   -.0087726
    _Iyear_2010 |  -.0270057   .0085315    -3.17   0.002    -.0437272   -.0102842
    _Iyear_2011 |  -.0330654   .0086077    -3.84   0.000    -.0499362   -.0161946
    _Iyear_2012 |  -.0328824   .0092524    -3.55   0.000    -.0510168   -.0147481
    _Iyear_2013 |  -.0438404   .0101814    -4.31   0.000    -.0637955   -.0238853
    _Iyear_2014 |  -.0393237   .0105193    -3.74   0.000    -.0599412   -.0187063
    _Iyear_2015 |  -.0451708   .0110972    -4.07   0.000     -.066921   -.0234206
    _Iyear_2016 |  -.0479582    .011823    -4.06   0.000     -.071131   -.0247855
    _Iyear_2017 |  -.0582286   .0125072    -4.66   0.000    -.0827423   -.0337149
---------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(pand_res_pt L.pand_res_pt L2.pand_res_pt)
    D.(_Iyear_1997 _Iyear_1998 _Iyear_1999 _Iyear_2000 _Iyear_2001 _Iyear_2002
    _Iyear_2003 _Iyear_2004 _Iyear_2005 _Iyear_2006 _Iyear_2007 _Iyear_2008
    _Iyear_2009 _Iyear_2010 _Iyear_2011 _Iyear_2012 _Iyear_2013 _Iyear_2014
    _Iyear_2015 _Iyear_2016 _Iyear_2017 _Iyear_2018 _Iyear_2019)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L2.ltotalfertility
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -4.84  Pr > z =  0.000
Arellano-Bond test for AR(2) in first differences: z =   1.68  Pr > z =  0.092
Arellano-Bond test for AR(3) in first differences: z =  -0.37  Pr > z =  0.712
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(18)   = 292.67  Prob > chi2 =  0.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(18)   =  56.32  Prob > chi2 =  0.000
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  iv(pand_res_pt L.pand_res_pt L2.pand_res_pt, eq(diff))
    Hansen test excluding group:     chi2(15)   =  51.89  Prob > chi2 =  0.000
    Difference (null H = exogenous): chi2(3)    =   4.42  Prob > chi2 =  0.219


.
end of do-file

• also , for xtabond2 and diff-GMM , I estimate based on this.

 xtabond2 L(0/1).ltotalfertility l(0/2).(pand_res_pt) i.year, gmm(L.ltotalfertility l(0/2).pand_res_pt , lag(1 3) e(d)) nol r

Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
1996b.year dropped due to collinearity
1997.year dropped due to collinearity
1999.year dropped due to collinearity
2018.year dropped due to collinearity
2019.year dropped due to collinearity
Warning: Two-step estimated covariance matrix of moments is singular.
  Using a generalized inverse to calculate robust weighting matrix for Hansen test.
  Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, one-step difference GMM
------------------------------------------------------------------------------
Group variable: ifscode                         Number of obs      =      3439
Time variable : year                            Number of groups   =       182
Number of instruments = 75                      Obs per group: min =         0
Wald chi2(0)  =         .                                      avg =     18.90
Prob > chi2   =         .                                      max =        19
---------------------------------------------------------------------------------
                |               Robust
ltotalfertility | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
----------------+----------------------------------------------------------------
ltotalfertility |
            L1. |   .7995318   .0285769    27.98   0.000     .7435221    .8555414
                |
    pand_res_pt |
            --. |  -.0051798   .0036244    -1.43   0.153    -.0122835     .001924
            L1. |  -.0078922   .0038674    -2.04   0.041    -.0154722   -.0003122
            L2. |  -.0098069   .0034846    -2.81   0.005    -.0166366   -.0029773
                |
           year |
          1998  |    .002119   .0010274     2.06   0.039     .0001054    .0041327
          2000  |  -.0010319   .0011563    -0.89   0.372    -.0032981    .0012343
          2001  |  -.0099869   .0022407    -4.46   0.000    -.0143786   -.0055952
          2002  |  -.0088589   .0022561    -3.93   0.000    -.0132807   -.0044372
          2003  |  -.0097598   .0026306    -3.71   0.000    -.0149156   -.0046039
          2004  |  -.0094847   .0028779    -3.30   0.001    -.0151253    -.003844
          2005  |  -.0154503   .0032033    -4.82   0.000    -.0217286   -.0091719
          2006  |  -.0139113   .0036764    -3.78   0.000    -.0211169   -.0067056
          2007  |  -.0146629   .0039578    -3.70   0.000      -.02242   -.0069059
          2008  |  -.0145618   .0044231    -3.29   0.001    -.0232309   -.0058926
          2009  |  -.0190504    .004204    -4.53   0.000    -.0272901   -.0108107
          2010  |  -.0214091   .0047103    -4.55   0.000    -.0306412    -.012177
          2011  |  -.0255258   .0048231    -5.29   0.000    -.0349788   -.0160727
          2012  |  -.0271835    .005434    -5.00   0.000     -.037834    -.016533
          2013  |  -.0350847   .0055091    -6.37   0.000    -.0458824    -.024287
          2014  |  -.0302499   .0058633    -5.16   0.000    -.0417418    -.018758
          2015  |    -.03638   .0062337    -5.84   0.000    -.0485978   -.0241621
          2016  |  -.0377174   .0064983    -5.80   0.000    -.0504539   -.0249809
          2017  |   -.045109   .0070333    -6.41   0.000    -.0588939    -.031324
---------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(1/3).(L.ltotalfertility pand_res_pt L.pand_res_pt L2.pand_res_pt)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -4.40  Pr > z =  0.000
Arellano-Bond test for AR(2) in first differences: z =   0.97  Pr > z =  0.332
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(52)   = 286.87  Prob > chi2 =  0.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(52)   =  75.58  Prob > chi2 =  0.018
  (Robust, but weakened by many instruments.)

I do not know if my code is correct. because Hansen test in one is not good and for the second is good but the "Wald chi2(0) = " is not computed.


Many thanks in advance for your valuable time and advice.



regards,