[Eliana Melo]

Dear all,


I have doubts about how to embed predetermined variables in the system GMM. I read Professor Sebastian's presentation and I'm not sure if I'm doing it right. My dependent variable is the percentage of Non-Technical Losses in distribution of electricity (pntbt) or electricity theft. I suspect the endogeneity of two explanatory variable: duration of interruptions in electrical distribution (log_dec)) and electricity price (log_tarid). The other variables are predetermined (I have no evidence to think they are strictly exogenous).

Code:

xtdpdgmm pntbt L.pntbt ob_agre subnormal inadpf log_decapu log_pib log_iasc log_tarid, ///
gmmiv(L.pntbt, lag(2 2) m(d) collapse) ///
gmmiv(L.pntbt, lag(2 2) m(l) diff collapse) ///
gmmiv(log_decapu, lag(2 2) m(d) collapse) ///
gmmiv(log_decapu, lag(3 3) m(l) diff collapse) ///
gmmiv(log_tarid, lag(2 2) m(d) collapse) ///
gmmiv(log_tarid, lag(2 2) m(l) diff collapse) ///
gmmiv(ob_agre subnormal inadpf log_pib log_iasc, lag(0 1) m(d) collapse) ///
gmmiv(ob_agre subnormal inadpf log_pib log_iasc, lag(0 1) m(l) collapse) ///
twostep vce(r) overid

Group variable: id                           Number of obs         =       721
Time variable: ano                           Number of groups      =        61

Moment conditions:     linear =      27      Obs per group:    min =         8
                    nonlinear =       0                        avg =  11.81967
                        total =      27                        max =        12

                                    (Std. Err. adjusted for 61 clusters in id)
------------------------------------------------------------------------------
             |              WC-Robust
       pntbt |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       pntbt |
         L1. |   .8545485   .0980974     8.71   0.000     .6622812    1.046816
             |
     ob_agre |   .0000241   .0002129     0.11   0.910    -.0003931    .0004414
   subnormal |   .2545236   .1650646     1.54   0.123    -.0689971    .5780442
      inadpf |   .0712857   .2658358     0.27   0.789    -.4497428    .5923142
  log_decapu |   .0202332   .0179756     1.13   0.260    -.0149983    .0554647
     log_pib |   .0086632    .008496     1.02   0.308    -.0079886     .025315
    log_iasc |  -.0108519   .0179764    -0.60   0.546    -.0460851    .0243813
   log_tarid |   .0352162   .0273752     1.29   0.198    -.0184383    .0888706
       _cons |  -.2797855   .2705651    -1.03   0.301    -.8100833    .2505124
------------------------------------------------------------------------------

estat serial
estat overid
estat overid, difference

estat serial

Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1:     z =   -3.2453   Prob > |z|  =    0.0012
H0: no autocorrelation of order 2:     z =    1.5184   Prob > |z|  =    0.1289

. estat overid

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

2-step moment functions, 2-step weighting matrix       chi2(18)    =   24.4723
                                                       Prob > chi2 =    0.1402

2-step moment functions, 3-step weighting matrix       chi2(18)    =   30.4614
                                                       Prob > chi2 =    0.0332

. estat overid, difference

Sargan-Hansen (difference) test of the overidentifying restrictions
H0: (additional) overidentifying restrictions are valid

2-step weighting matrix from full model

                  | Excluding                   | Difference                  
Moment conditions |       chi2     df         p |        chi2     df         p
------------------+-----------------------------+-----------------------------
   1, model(diff) |    24.4438     17    0.1079 |      0.0286      1    0.8658
  2, model(level) |    24.4721     17    0.1072 |      0.0002      1    0.9884
   3, model(diff) |    22.0325     17    0.1835 |      2.4398      1    0.1183
  4, model(level) |    24.4103     17    0.1087 |      0.0620      1    0.8033
   5, model(diff) |    22.2540     17    0.1751 |      2.2183      1    0.1364
  6, model(level) |    24.4709     17    0.1072 |      0.0014      1    0.9700
   7, model(diff) |    15.6926      8    0.0470 |      8.7797     10    0.5531
  8, model(level) |     8.6499      8    0.3727 |     15.8224     10    0.1048
      model(diff) |     8.0584      5    0.1530 |     16.4139     13    0.2275
     model(level) |     8.0584      5    0.1530 |     16.4139     13    0.2275

In a last post, prof. Kripfganz mentioned that

It is usually sufficient to consider the overidentification test with the 2-step weighting matrix. The two tests are asymptotically equivalent. If they differ substantially, then this would be an indication that the weighting matrix is poorly estimated.

. In this case, the two overidentification test are differents, what would I do in that case? When is consider that the 2-step and 3-step weighting matrix are substantially different?

Also, I am not sure of interpreting right the Sargan-Hansen difference test. In a general way, the (Difference-in-) Hansen tests do not reject the null hypothesis, then the instruments in all equations are valid. Or is it to be concerned that the in some equations the p values are relatively small?


Thank you so much for any comment!!!

[haiyan lin]

Dear all,

Is there a good way to get bootstrapped confidence intervals after GMM estimation? Great thanks!

Best,
Haiyan

[Sebastian Kripfganz]

I do not have a conclusive answer, but I suspect that the "small" number of clusters relative to the very large number of observations intensifies the differences that result from the different implementations of the Arellano-Bond tests. If you look into the literature on how many clusters you should at least have for reliable inference, you would often find that 57 should be sufficient. However, in my opinion these absolute thresholds are not very meaningful because the performance also depends on how many observations there are within each cluster.

[Reid Taylor]

Sebastian Kripfganz I have 75,204 company-zipcode groupings with observations across a T=10 year panel (so total N=752,050). There are 57 companies in the panel, which are represented by group_code in the code I showed above.

The reason I feel convicted to cluster the standard errors is the yearly treatment variable is common within each company across the zipcodes (x_gt) while observation is (x_igt). Ideally I would cluster at the company-year level, however xtdpdgmm does not allow the clustering to be at the company-year level since the panel id is not contained within the cluster. Therefore, I cluster at the company level.

As you noted, when running the two with unadjusted standard errors and onestep estimation, the two AB z scores match between xtdpdgmm and xtabond2 for both AR(1) and AR(2).

[Sebastian Kripfganz]

Reid Taylor
That is indeed a substantial difference for the AR(2) tests. What are the dimensions of your data set (number of time periods, number of groups, number of clusters)? Do the tests coincide if you do not specify (cluster-)robust standard errors?

Jose Albrecht
Whether the panel is balanced or unbalanced should not be of much relevance here. xtivreg can deal with unbalanced panel data, too. The problem with your data set is rather that the number of groups is very small (20) - usually too small to expect reliable results from standard dynamic panel data GMM estimators. You might want to have a look into estimators for large-T data sets, e.g. those implemented by the community-contributed xtdcce2 command, but that would be a topic for a different thread. But even xtivreg might be good enough given that 35 time periods might be enough to not worry too much about the dynamic panel data (Nickell) bias.

[Reid Taylor]

Sebastian, If I may follow up with your response. The AR results are as follows:

xtdpdgmm yields:
Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1: z = -1.1432 Prob > |z| = 0.2530
H0: no autocorrelation of order 2: z = -0.8983 Prob > |z| = 0.3690

xtabond2:
Arellano-Bond test for AR(1) in first differences: z = -1.19 Pr > z = 0.233
Arellano-Bond test for AR(2) in first differences: z = -6.18 Pr > z = 0.000

As you probably guessed, I am concerned since the xtabond2 model provides strong evidence of AR(2). Does the difference in z scores align with your prior of how much difference there can be between the two processes?

Thanks,
-Reid

[Jose Albrecht]

Dear, Tugrul Cinar ,

Thank you for your comment, what approach do you recommend then? I am aware that my panel data is unbalanced, I have small observations (720) and a common panel data with endogeneity regression (with xtivreg, etc) is mostly used when you have a strongly balanced panel.

By the way, thank you for your time, I am aware that my econometric and Stata level are limited and it would be such a great help to recieve anykind of feedback.

Regards,

José Albrecht

[Tugrul Cinar]

Dear Jose Albrecht

I would not prefer to use xtabond/xtabond2 or even xtdpdgmm in your case since GMM estimation is not a good option for your sample.

If you want to get comprehensive answers to your questions please see the FAQ section for posting rules.

[Sebastian Kripfganz]

xtabond2 and xtdpdgmm use different formulae for the Arellano-Bond test. The results should coincide for the one-step estimator with robust (but not cluster-robust) standard errors, and for the two-step estimator without robust standard errors. They differ for the non-robust one-step estimator because xtdpdgmm always computes the test in a robust way (using an influence function approach in a similar way as the suest command). They differ for the two-step robust estimator because xtdpdgmm accounts for the Windmeijer correction in all terms of the test statistic (while xtabond2 does so only for the main term), and for a similar reason they differ for cluster-robust standard errors. Usually, the differences should not be large.

[Reid Taylor]

I am estimating a model using the difference GMM estimator. I am trying to replicate my results from xtdpdgmm with xtabond2. Results replicate fine (coef. estimates and std.errors). However, the A & B AR tests are vastly different. I saw a comment from Sebastian Kripfganz earlier which stated that the overid tests may vary with the presence of time dummies, but I am not sure if this holds true for the AR tests as well. I am also not sure if this is an issue with the time dummies or the clustering (xtabond2 may not adjust the test for clustering?).

Thanks, and sorry if this is a repeat question.

For reference, the two codes:

 xtdpdgmm log_pols treat rps_treat L1.drought L1.dr  if everfire==0, model(diff) gmm(treat rps_treat, lag(1 3)) iv(drought dr, model(level)) teffects nocons vce(cluster group_code) twostep
xtabond2 log_pols treat rps_treat yr* L1.drought L1.dr if everfire==0, gmmstyle(treat rps_treat, lag(1 3) equation(diff)) ivstyle(yr* drought dr, equation(level) passthru) noconstant cluster(group_code) twostep

[Dario Maimone Ansaldo Patti]

Sebastian Kripfganz thanks a lot. Yes, i am aware of your last comment. The specification is not correct. Bit at the moment I did not pay attention to this. I just wanted to understand the "compatibility" of the two commands. Thanks a lot again.

[Sebastian Kripfganz]

Dario Maimone Ansaldo Patti

You can obtain the same results if you make the following changes to the last two options in your xtabond2 command line:

iv(i.time lnwi, eq(lev)) gmm(wlnyw n g_ef nda, lag(1 1) eq(lev) passt)

Note that xtdpdgmm has no equivalent to the xtabond2 option iv() without an eq() suboption. Also note that with xtabond2 the iv() option without an eq() suboption is not equivalent to the combination of iv(, eq(diff)) iv(, eq(lev)).

As another comment: Specifying lags of wlnyw n g_ef nda as instruments for the level model without a first-difference transformation of the instruments requires that those instruments are uncorrelated with the unit-specific "fixed effects". This assumption is violated by construction for lags of the dependent variable.

[Jose Albrecht]

Hello everyone, I'm doing a dynamic panel data regression to find the effect of corruption and political instability in economic growth for Latin America, the article that Im using as primal reference is Kwabena Gyimah-Brempong & Samaria Muñoz De Camacho's Political Instability, Human Capital, and Economic Growth in Latin America , 1998 (The Journal of Developing Areas). My questions are the following:

1) Im doing a dynamic panel data from 1984 to 2019 (T=35) for 20 countries, that means that I have an unbalanced panel with 720 observations, I got 1 endogenous variable ( GDP % which has unit root so I solve it with first differences ) and 3 independent variables which have endogeneity (corruption, Political instability and total investment % of gdp) and 7 control variables (savings % of gdp, debt service ratio, exports % of gdp, imports % of gdp, tax revenues % of gdp , goverment spendings % of gdp and population %) so I run the xtabond command and the xtdpdgmm command, I do the Sargan test for overidentification of Insturmental varables and of course the test tells me it has overidentification, I know there is an xtabond2 and a xtkr command, but I don´t know how to properly write the whole code for both commands ¿could someone please help me with that? my initial xtabond command was xtabond d.GDP Corruptión PolíticalInstability GovermentSpending TotalInvestment Population Exports Imports Savings debtserviceratio TaxRevenues, lags(3) endog(Corruptión PolíticalInstability TotalInvestment, lagstruct(2,3)) vce(robust) artests(2) and xtdpdsys d.GDP Corruptión PolíticalInstability GovermentSpending TotalInvestment Population Exports Imports Savings debtserviceratio TaxRevenues, lags(3) maxldep(3) maxlags(3) endog(Corruptión PolíticalInstability TotalInvestment, lagstruct(2,3)) artests(3)

2) ¿Could someone help me to formaly construct the equation model? I did it inspiring in the model of the authors I cite at the beginning, but I dont know if this represents formaly what Im trying to find, the equations are (in latex code):

initial equation:

$$gdp= \tau_{0}+\tau_{1}corrup+\tau_{2}pol.insta+\tau_{3} population+\tau_{4}investment+\tau_{5}exports +\tau_{6}govermentspending+\epsilon$$

endogenous variables:

* $$pol.instab= \beta_{0}+\beta_{1}gdp+\beta_{2}corrup+\beta_{3}po pulation+\beta_{4}tax.revenue.+\beta_{5}pol.insta_ {t-1}+\epsilon$$
* $$investment= \gamma_{0}+\gamma_{1}pol.insta+\gamma_{2}corrup+\g amma_{3}gdp+\gamma_{4}imports+\gamma_{5}debtservic eratio+\xi$$
* $$corrup= \delta_{0}+\delta_{1}pol.insta+\delta_{2}populatio n+\delta_{3}tax.revenue+\delta_{4}gdp+\delta_{5}go vermentspending+\psi$$

I know that in GMM by Arellano-Bond (1991) and other methods, the lags are used as Instruments so ¿Is this formaly correct and acuratly represents what Im trying to do with the regression im running?

Thank your very much for the help!

José Albrecht

[Dario Maimone Ansaldo Patti]

Dear All,

I have the following data:

* Example generated by -dataex-. For more info, type help dataex
clear
input float(id pc time wlnyw n g_ef nda lnnda lnwi lnsnda pc2)
 2  1  2         .   3.338289  -.7193089   7.61898 2.0306425         .           .   1
 2  1  3  8.160519   2.944589  2.3303807  10.27497 2.3297107  3.523722    1.194011   1
 2  1  4  8.144518   2.634001  -2.614641   5.01936 1.6133024  3.474745    1.861443   1
 2  6  5  8.070906  2.3827553 -1.5627682  5.819987  1.761298  3.377768   1.6164702  36
 2  6  6  7.988668  -.7692814   9.684753 13.915472  2.633001 3.0445225    .4115212  36
 2  8  7  8.239983  -.7937193   3.120792  7.327073  1.991576  3.457398    1.465822  64
 2  9  8  8.476371  -.8197546   3.746539  7.926785 2.0702474 3.5484214    1.478174  81
 2  9  9  8.750808  -.8475304   4.107702  8.260172 2.1114454  3.347392   1.2359467  81
 2  9 10  8.779557          0   .1755476  5.175548  1.643945 3.2043874   1.5604423  81
 3  1  2 8.7427435   3.129053   2.229619 10.358672  2.337824 3.5484214   1.2105973   1
 3  1  3  8.884125   2.780628   .4705131  8.251142 2.1103516  3.520005   1.4096534   1
 3  1  4  8.911485   4.776382 -1.8550217  7.921361  2.069563  3.479417    1.409854   1
 3  7  5  8.790486  3.0650616   2.604729  10.66979 2.3674164  3.294729    .9273124  49
 3  6  6  8.667766   2.729988   2.612698 10.342686 2.3362796 3.3720055   1.0357258  36
 3  6  7  8.663796  1.6673088  -.9387016  5.728607 1.7454724  3.029032   1.2835593  36
 3  6  8  8.758355   1.562977   5.103999 11.666976  2.456762  3.107734    .6509719  36
 3  6  9  8.804875  2.1752834   .9837627  8.159046 2.0991273 3.5484214    1.449294  36
 3  6 10  8.896683  2.6340485 -1.1135578  6.520491 1.8749496 3.5484214   1.6734718  36
 6  1  2         .  3.1074286          .         .         .         .           .   1
 6  1  3         .  3.6207914   2.584666 11.205458  2.416401         .           .   1
 6  1  4  8.554934   5.296087 -1.4542162  8.841871 2.1794984         .           .   1
 6  1  5  8.581732  2.1752834  4.1983843 11.373668  2.431301         .           .   1
 6  .  6  8.166536    3.85375  1.0764956  9.930246 2.2955854 3.3768466   1.0812612   .
 6  6  7  8.358969   3.338289   2.747208 11.085497  2.405638 2.7116106    .3059728  36
 6  8  8  8.443862   5.578613  -.7392824  9.839331 2.2863877  2.172391  -.11399674  64
 6  8  9  8.829568   3.494024  1.9159198 10.409945 2.3427615 2.6694896    .3267281  64
 6  8 10  8.873868   4.917765  -.9543777  8.963387 2.1931481 2.2567296   .06358147  64
 8  7  2  9.433484  2.0010471  -.5251825  6.475864  1.868082  3.382388   1.5143063  49
 8  1  3  9.512621   1.852703   2.301848  9.154551  2.214251  3.229135    1.014884   1
 8  7  4  9.315701  1.7248154   .2929926  7.017808  1.948451  2.867279    .9188284  49
 8  9  5  9.159047  2.3827553  -.5360782  6.846677 1.9237634  2.638843    .7150797  81
 8  9  6  9.461655  1.4710426   5.310255 11.781298 2.4665134   2.88691    .4203968  81
 8  9  7  9.476044  1.3892174  1.6326785  8.021896 2.0821748 2.7845604    .7023857  81
 8  9  8  9.487972  1.3161182 -1.0530949  5.263023 1.6607057 2.8537424   1.1930367  81
 8  9  9  9.689914   1.250267  .12156963  6.371837 1.8518877    2.8119     .960012  81
 8  9 10  9.706778  1.1906624  -.8750677  5.315595  1.670645 2.7625384   1.0918936  81
 9  1  2         .   2.833223          .         .         .         .           .   1
 9  1  3         .    2.54457          .         .         .         .           .   1
 9  1  4         .  1.5630007          .         .         .         .           .   1
 9  2  5  7.931144  1.4710188          .         .         . 3.5484214           .   4
 9  7  6  7.438384 -2.2403002          .         .         .  2.782168           .  49
 9  8  7  7.673223  -.7937193  4.5565248  8.762806 2.1705163  2.914267     .743751  64
 9  7  8  8.255829  -.8197546  2.1974683  6.377714 1.8528097  3.394344   1.5415342  49
 9  7  9  8.444622  -.8475304   2.624923  6.777392 1.9135925 3.5094416    1.595849  49
 9  7 10  8.612503          0   2.663016  7.663016 2.0364056 3.0259025    .9894969  49
11 10  2 10.661875  1.8526554   1.812625   8.66528 2.1593242 3.2537255   1.0944014 100
11 10  3 10.732767   1.724863   .7021904  7.427053  2.005129  3.274507   1.2693782 100
11 10  4 10.819778  1.6134262   .4446983  7.058125 1.9541794 3.2976685    1.343489 100
11 10  5  10.84707   1.515627   1.209879  7.725506 2.0445273  3.320313   1.2757854 100
11 10  6  10.84707  1.4289856  2.0217419  8.450727 2.1342525 3.2226846   1.0884321 100
11 10  7  10.84707  1.3516426  1.1429667  7.494609  2.014184  3.258004   1.2438202 100
11 10  8  10.84707   1.282358   .5142093  6.796567 1.9164177 3.2966626    1.380245 100
11 10  9  10.84707  2.3827553   .7077575  8.090513 2.0906923  3.322176   1.2314835 100
11 10 10  10.84707  2.1752834  -.2783656  6.896918 1.9310746 3.2829204   1.3518457 100
12 10  2  10.55315   .3311157  1.3487935  6.679909 1.8991044 3.3374195    1.438315 100
12 10  3 10.665627  -.3311157  1.5040874  6.172972 1.8201804  3.309619   1.4894388 100
12 10  4 10.672142   .3311157  .59446096  5.925577  1.779278  3.172916   1.3936377 100
12 10  5 10.819778  .32680035  .12853146  5.455332 1.6965934 3.2362165    1.539623 100
12 10  6  10.84707   .6410599    2.07268   7.71374  2.043003  3.233512   1.1905091 100
12 10  7  10.84707   .3144741  1.2379646  6.552439 1.8798373  3.244481   1.3646438 100
12 10  8  10.84707   .6173134  .25732517  5.874639 1.7706445  3.136133   1.3654886 100
12 10  9  10.84707   .6024361 -.13694763  5.465488 1.6984535  3.070343   1.3718897 100
12 10 10  10.84707    .588274   .3009558   5.88923  1.773125  3.104878    1.331753 100
13  1  2         .  2.2951841  -.0518322  7.243352  1.980084         .           .   1
13  1  3         .   2.102065  .02743602  7.129501 1.9642413         .           .   1
13  1  4         .   1.938963  .02810359  6.967067 1.9411943         .           .   1
13  2  5  8.517193   1.799345  .11470318  6.914048 1.9335554  3.008609   1.0750537   4
13  3  6  7.590207  1.6784668   4.108137 10.786604  2.378305 2.7500556    .3717506   9
13  2  7  7.843464    .955534   8.359504 14.315038  2.661311  3.141429     .480118   4
13  2  8  8.403865  1.2197495  4.2887926 10.508542 2.3521883 3.5484214    1.196233   4
13  2  9  9.006245   2.001071  2.2203028  9.221374  2.221524   2.89959    .6780663   4
13  2 10  9.053771   1.337242  1.4350176   7.77226  2.050561 3.3259456   1.2753847   4
14  .  2 10.071235   2.728295          .         .         .         .           .   .
14  .  3  10.47635   2.728176   .8404911  8.568667 2.1481123 2.7690825    .6209702   .
14  .  4  10.52232  2.7000666  .23694634  7.937013  2.071537  2.866324    .7947867   .
14  .  5 10.518878  2.2059202  .28776526  7.493686 2.0140607   3.24367   1.2296093   .
14  .  6 10.401676   2.220893  1.7398775  8.960771 2.1928563  3.236268   1.0434115   .
14  .  7 10.545793  1.5349865  -.9644091  5.570578 1.7174988  3.254038   1.5365396   .
14  .  8 10.481103   2.502251  -.2521932  7.250057 1.9810094 3.1858194     1.20481   .
14  .  9 10.343328  2.3015738  1.1030972  8.404671 2.1287875  3.179424   1.0506363   .
14  . 10 10.252863  1.7386913   .3578901  7.096581 1.9596132 3.1743386   1.2147254   .
15  1  2         .   5.648899          .         .         .         .           .   1
15  1  3 10.414313   7.471395  .34759045 12.818985  2.550927  3.428089     .877162   1
15  1  4 10.184618  3.7941694   1.346326 10.140495  2.316537 3.5193655   1.2028286   1
15  1  5  10.22391  4.2176247  -.4899025  8.727722 2.1665044  2.940542    .7740376   1
15  1  6 10.360246   3.211951   2.546668  10.75862 2.3757071  2.852295    .4765875   1
15  1  7 10.418768  4.1183233   .8144617  9.932785  2.295841 2.7965736   .50073266   1
15  3  8 10.348213   7.257748  1.5400648 13.797812   2.62451 3.2459655    .6214554   9
15  6  9 10.203553   7.499504  1.0524869  13.55199 2.6065335 3.2598336       .6533  36
15  1 10 10.246432   3.853774 -.10858774  8.745186 2.1685033  3.178483   1.0099797   1
16  1  2  6.432332  2.2072792          .         .         .         .           .   1
16  3  3  6.537382  3.2942295   6.311685 14.605914 2.6814265 2.6699605 -.011466026   9
16  1  4   6.55108   3.453779   .2438903   8.69767 2.1630552  2.761964    .5989087   1
16  2  5  6.584982  4.1970253   4.810601 14.007627  2.639602  2.800854   .16125226   4
16  7  6  6.673355  2.1752834   5.497265 12.672548  2.539438 2.9507244   .41128635  49
16  7  7  6.755739  2.0010471  1.3580143  8.359061  2.123346  3.170047   1.0467007  49
16  7  8  6.884766   1.852703  2.3953736  9.248076 2.2244155  3.251552   1.0271366  49
16  8  9  7.130899  1.7248154  2.2230864  8.947902 2.1914191   3.26754   1.0761211  64
16  6 10  7.282449   1.613474   .6513774  7.264852  1.983048 3.3633814   1.3803335  36
17  .  2         .    .721693   .5018532  6.223546 1.8283398         .           .   .
17  .  3         .   .6024361   .7710993  6.373535 1.8521543         .           .   .
17  .  4         .   .3937006 -.14876127  5.244939 1.6572636         .           .   .
17  .  5  9.954781   .3876209   .3564954  5.744116  1.748176  2.702917     .954741   .
17  .  6  9.868802   .4761934   3.602868 9.0790615 2.2059708  2.436224    .2302532   .
17  .  7  10.03354   .4673004 -1.0186553  4.448645 1.4925996  2.869562   1.3769625   .
17  .  8  10.05377   .3676653  1.4535308  6.821196  1.920035  2.913252    .9932175   .
17  .  9  10.07784  .54154396  .04537106  5.586915 1.7204273  2.547357    .8269298   .
17  . 10  10.07784  .35459995   .5445123  5.899112  1.774802 2.7332175    .9584156   .
18  1  2         .   1.087141          .         .         .         .           .   1
18  1  3         .  .52633286          .         .         .         .           .   1
18  1  4         .  1.0205269          .         .         .         .           .   1
18  2  5  8.456569          0          .         .         . 3.0883114           .   4
18  3  6   8.05017          0          .         .         . 3.2067304           .   9
18  2  7  8.323037          0  4.0236053  9.023605  2.199844 3.2269034   1.0270596   4
18  2  8  8.694528  -.7614613  1.6694963  5.908035 1.7763133  3.277771   1.5014577   4
18  2  9  9.033884  -.5208492   4.118848  8.597999 2.1515296 3.5484214    1.396892   4
18  2 10  9.131559          0   2.901405  7.901405 2.0670407 3.3553035    1.288263   4
19 10  2 10.521285  .25639534   .4892945   5.74569   1.74845 3.2850156   1.5365655 100
19 10  3  10.64988  .25382042   .5866051  5.840425 1.7648036  3.216377    1.451573 100
19 10  4 10.640437          0   .6757379  5.675738 1.7362006   2.93976    1.203559 100
19 10  5  10.80474   .2512455  -.4225969  4.828649 1.5745666 3.1819754   1.6074088 100
19 10  6  10.84707          0  1.1700511  6.170051  1.819707 3.0602365   1.2405293 100
19 10  7  10.84707          0   .9933352  5.993335  1.790648  3.113071   1.3224226 100
19 10  8  10.84707          0   .2231002    5.2231  1.653091  3.098176    1.445085 100
19  7  9  10.84707  2.3827553  .34047365  7.723229 2.0442326 3.0827765   1.0385439  49
19  7 10  10.84707          0  .22324324  5.223243 1.6531185  3.143786   1.4906672  49
20  .  2   8.19165  2.1581888          .         .         .         .           .   .
20  .  3  8.449818   1.986599          .         .         . 3.1199126           .   .
20  .  4  8.303506   3.403306          .         .         .  2.855314           .   .
20  .  5  8.592608  3.2624245 -.31831264  7.944112  2.072431  3.217787   1.1453562   .
20  .  6 8.7816725   2.406907   3.000003  10.40691   2.34247 3.0776486    .7351787   .
20  .  7  8.844236   4.416752   .6585538 10.075306 2.3100874  3.355586   1.0454986   .
20  .  8  8.904082    3.40147  2.7812004  11.18267  2.414365  2.918673   .50430775   .
20  .  9 8.8789835   3.227615  1.0122657 9.2398815  2.223529  2.727212    .5036831   .
20  . 10  8.851792   2.719259  -.4293859  7.289873 1.9864862  3.073133   1.0866468   .
21  1  2  6.964914   3.230286  3.1517804 11.382066  2.432039         .           .   1
21  1  3  7.054359    2.86026  1.8144965  9.674757   2.26952         .           .   1
21  1  4  7.148917  3.7570715   4.816622 13.573693 2.6081336 2.1688707   -.4392629   1
21  .  5  7.090077   3.770566  -1.031524  7.739042  2.046278  2.535402    .4891238   .
21  9  6  7.117476    4.13785   6.661701  15.79955 2.7599816  2.865903   .10592103  81
21  9  7  7.223608   3.914237  1.0650814  9.979319 2.3005147  3.200781    .9002664  81
21  9  8  7.230529  3.6979914   1.377076 10.075068 2.3100638  2.982703    .6726389  81
21  9  9   7.26443   3.494048  3.2622755 11.756324  2.464391 3.1482515    .6838603  81
21  9 10  7.342041  4.4672966  -.1774788  9.289818  2.228919  3.271912   1.0429931  81
23  1  2         .   4.021001    .780499    9.8015 2.2825356         .           .   1
23  1  3  6.649926   3.894544  -.4170954  8.477448 2.1374094 3.4394176    1.302008   1
23  1  4  6.870941  3.3153534  .56893826  8.884292 2.1842847 3.5484214   1.3641367   1
23  1  5  7.288528  3.4917116 -.05614161   8.43557 2.1324573  3.433326   1.3008685   1
23  1  6  7.543744 -1.0457754   .6525278 4.6067524  1.527523 3.5484214   2.0208983   1
23  1  7  7.688704  2.6679754  1.3940692  9.062044 2.2040946 3.5484214   1.3443267   1
23  5  8  7.819058  3.4199476   3.392035 11.811982 2.4691145 3.5484214   1.0793068  25
23  5  9  8.122199  2.5654316  1.9780278  9.543459  2.255856 3.5484214   1.2925653  25
23  8 10  8.275181  1.9481897  4.1246834 11.072873  2.404498 3.5484214    1.143923  64
24  1  2  8.030759  2.6340246   1.556605   9.19063 2.2181845   2.93483    .7166452   1
24  1  3  8.028346   2.833223   1.563984  9.397207 2.2404125  2.828467    .5880544   1
24  9  4  7.830088   2.544546 -.23269057  7.311855  1.989497  2.671635    .6821381  81
24  9  5  7.829437  2.6743174  2.1843553  9.858673 2.2883515  2.530398    .2420461  81
24  9  6  7.870566   2.415657   2.622682  10.03834 2.3064117  2.742999    .4365873  81
24  9  7  7.925142  2.2027016  4.5823455 11.785048  2.466832  2.884102    .4172704  81
24  7  8  8.012637  2.3004532   1.306939  8.607392 2.1526215 2.5642414    .4116199  49
24  7  9  8.128535  2.1065235 -.29264688  6.813877  1.918961 2.8077266    .8887655  49
24  7 10  8.278782   2.634001 -.25732517  7.376676  1.998323 3.0620396   1.0637165  49
25  1  2         .  1.2823343          .         .         .         .           .   1
25  1  3         .  1.2197495          .         .         .         .           .   1
25  1  4         .  1.1630058          .         .         .         .           .   1
25  3  5         .  .56180954          .         .         .         .           .   9
25  .  6  7.146166  -4.226899          .         .         .  2.507035           .   .
25  .  7  8.350139          0   6.834549  11.83455  2.471023  3.022924    .5519011   .
25  .  8  8.660295          0   3.343034  8.343034 2.1214268   3.30064   1.1792133   .
25  .  9  8.785458  -.6667137   2.718425  7.051711 1.9532703    2.8557    .9024295   .
25  . 10  8.881836 -1.3892412   .6289244  4.239683 1.4444885 2.8809555    1.436467   .
26  9  2  7.888905  4.2907476  1.9114017  11.20215  2.416106  3.281415     .865309  81
26  9  3  8.223815   4.783869  .25004148  10.03391 2.3059704  3.541417   1.2354467  81
26  9  4  8.503238  4.5580387   .4899442 10.047983 2.3073719  3.128049    .8206773  81
26  9  5  8.891005   3.853774   .2335787  9.087353 2.2068837 3.4767964   1.2699127  81
26  9  6  8.920953  3.3382654   .4491568  8.787422 2.1733215  3.295007   1.1216855  81
26  9  7  9.059518   1.515627   3.582126 10.097753 2.3123128 3.2245595    .9122467  81
26  9  8   9.11503   2.780628 -.56585073  7.214777 1.9761313  3.232376    1.256245  81
26  9  9 9.2103405  1.2823343   1.241851  7.524185 2.0181224  3.515008   1.4968855  81
26  9 10  9.343872  2.3827553  .56085587  7.943611  2.072368 3.5269544   1.4545865  81
27  2  2  9.406455  3.6651134   .8726835  9.537797 2.2552626  3.193148     .937885   4
27  2  3  9.567016  2.1752834   1.540935  8.716219 2.1651855  3.131237    .9660518   4
27  9  4  9.528794    3.85375   .9817719  9.835522 2.2860005 2.8301735     .544173  81
27  9  5  9.498022  1.7248154 -.52840114  6.196414 1.8239708  3.028209   1.2042384  81
27  9  6  9.546813   1.613474    2.36547  8.978944 2.1948822  3.002678     .807796  81
27  9  7  9.520495   2.944565   1.941043  9.885608   2.29108  2.907147    .6160669  81
27  9  8  9.615806  1.3516903   2.443665  8.795356  2.174224  2.836514    .6622899  81
27  9  9  9.736433   1.282358  1.1907935  7.473152 2.0113168  3.022116   1.0107994  81
27  9 10  9.706778  1.2197495  -.7494569  5.470293  1.699332  2.895155   1.1958226  81
29  .  2  10.84707   5.501556          .         .         .         .           .   .
29  .  3  10.84707  4.5065403          .         .         .         .           .   .
29  .  4  10.84707    3.70605          .         .         .         .           .   .
29  .  5  10.84707     3.5182  1.3557076  9.873907 2.2898955   2.92748    .6375847   .
29  .  6  10.84707   3.422594  2.2959173 10.718512 2.3719723 3.5484214   1.1764491   .
29  .  7  10.84707    2.86026  1.0372818  8.897542  2.185775   2.56169   .37591505   .
29  .  8  10.84707  2.2938728   1.128453  8.422326  2.130886  2.429614     .298728   .
29  .  9 10.837797   1.592064   3.531158 10.123222  2.314832 3.1583314    .8434994   .
29  . 10  10.74414   1.797533   .7746816  7.572215 2.0244856 3.5484214   1.5239358   .
30  1  2         .  .58140755  1.3045967  6.886004  1.929491         .           .   1
30  1  3  8.517193    .568223  1.5277326  7.095956  1.959525  3.341511    1.381986   1
30  1  4  8.642356   .2793312  1.2601078  6.539439 1.8778514   3.27425   1.3963987   1
30  7  5  8.733417  -.8475542 -1.9447505 2.2076952  .7919491   3.05702   2.2650712  49
30  7  6  8.650724   -.877285   4.776955   8.89967 2.1860142  2.727526    .5415118  49
30  7  7  8.699514  -.6024361   3.149223  7.546787  2.021122  2.824677     .803555  49
30  9  8  9.001248 -1.5728474  1.0622859 4.4894385 1.5017277 3.2467284   1.7450007  81
30  9  9 9.2103405  -.9934902  1.6302586  5.636768  1.729311   3.10052   1.3712093  81
30  9 10  9.367526  -.6849766   .9591341  5.274158  1.662819  3.045184   1.3823652  81
31  3  2  6.332391   2.544546   .1516044  7.696151 2.0407202         .           .   9
31  1  3   6.39693  2.3093462  1.2023687  8.511715 2.1414435  2.647571    .5061276   1
31  1  4   6.50229  3.1074286   .9761572  9.083586  2.206469  2.951801    .7453322   1
31  1  5  6.524763   3.338289   1.230657  9.568947 2.2585232 2.8758726    .6173494   1
31  2  6  6.579251   3.195834   2.982259 11.178093  2.413956  3.112617    .6986611   4
31  3  7  6.742241  4.5580387   3.666133 13.224172  2.582046 3.0529675    .4709213   9
31  8  8  6.922354  2.0010948   3.499502 10.500597  2.351432  2.979999     .628567  64
31  8  9  7.025538   5.190945  1.7912567 11.982202  2.483422  3.198747    .7153244  64
31  8 10  7.151952  2.9446125   3.366518  11.31113  2.425787   3.20637    .7805827  64
32  1  2  6.204026  1.3892412    2.44593  8.835172 2.1787405 2.2253973   .04665685   1
32  1  3   6.30162  2.5663614  1.8672407  9.433602  2.244278  2.630867    .3865888   1
32  1  4  6.437752  3.4143925  1.7323494 10.146742 2.3171527  2.660609    .3434565   1
32  1  5   6.50229   3.470898   4.018724 12.489622  2.524898  2.724127     .199229   1
32  .  6  6.348139  2.6340246  2.8668284 10.500853 2.3514564 1.8629942   -.4884622   .
32  6  7  6.214608    1.61345  -1.306969  5.306481  1.668929  1.022861    -.646068  36
32  8  8  6.042758   3.629565  4.2226133  12.85218  2.553513 3.1078415    .5543282  64
32  8  9   6.05334  4.3317795  4.7406616  14.07244 2.6442184  3.418379    .7741604  64
32  6 10  6.054265   3.195834   2.651405  10.84724 2.3839107  2.808052   .42414165  36
34  .  2         .  1.7248392  -.3814995   6.34334 1.8474054         .           .   .
34  .  3         .  -2.819896 .068604946 2.2487092  .8103564         .           .   .
34  .  4         .   3.477812     .49752  8.975332   2.19448         .           .   .
34  .  5         .   3.900123   .6694973   9.56962 2.2585936         .           .   .
34  6  6  6.529689   5.016756   3.449267 13.466023   2.60017  2.633097  .032927036  36
34  8  7  6.654306  2.1752834  8.6847725 15.860056  2.763804 2.9074745    .1436708  64
34  8  8  6.932756  2.0010948   5.677092 12.678186  2.539883  2.938479    .3985963  64
34  8  9  7.108426  1.8526554   2.387899  9.240555 2.2236018  2.784647   .56104517  64
34  6 10  7.377759   3.338289  2.1319926 10.470282  2.348541  3.065025    .7164841  36
35  1  2  7.675011  3.5775185  2.0183444 10.595863 2.3604636  2.796116    .4356523   1
35  1  3  7.801573  3.4214735   1.464224  9.885697  2.291089 2.9970064    .7059174   1
35  1  4  8.168886   3.770566    1.21271  9.983276 2.3009114  2.844328    .5434165   1
35  1  5  7.905392  4.5580387   -2.55574  7.002299 1.9462385  2.852716    .9064775   1
35  6  6   7.62989  2.0010948  2.1203935  9.121489  2.210633  2.985697     .775064  36
35  6  7  7.731264  3.5775185   3.184712  11.76223 2.4648936 2.9774106     .512517  36
35  6  8  7.779594   3.129053  1.5392303  9.668283 2.2688508  3.077294    .8084431  36
35  6  9  7.767957  4.0629864   .4072487  9.470235 2.2481537  3.155638    .9074841  36
35  6 10  7.949209   3.494024   .4433632  8.937387 2.1902432  3.137553    .9473097  36
36 10  2 10.676678  2.2742748    .964725     8.239  2.108879  3.208486    1.099607 100
36 10  3 10.733836  2.0845413  1.4386058  8.523148 2.1427858  3.166782   1.0239964 100
36 10  4 10.808605   .9805202    -.18152     5.799 1.7576855 3.0343566    1.276671 100
36 10  5  10.84707   1.852703   .3649712  7.217674 1.9765328 3.0811346   1.1046017 100
36 10  6  10.84707    .877285  1.8329144  7.710199 2.0425441  2.912671    .8701272 100
36 10  7  10.84707  1.6673088  1.4580607   8.12537 2.0949912   2.97883    .8838391 100
36 10  8  10.84707   .7936954 -.28258562   5.51111  1.706766  3.086829    1.380063 100
36 10  9  10.84707   1.515627   .1657963  6.681423  1.899331  3.157702   1.2583712 100
36 10 10  10.84707   1.428938   .1365304  6.565468  1.881824  3.165057   1.2832333 100
38  1  2  6.994767   2.634001   2.951777 10.585777 2.3595114         .           .   1
38  1  3  6.907755   3.494048  1.4653802  9.959429 2.2985196 1.9384165   -.3601031   1
38  1  4  6.907755  3.0650616   .9599626  9.025024 2.2000012 2.5176885    .3176873   1
38  1  5  6.774224   2.729988 -2.0748317  5.655156 1.7325677  2.469175    .7366077   1
38  7  6  6.656441   3.976607  4.4391394 13.415747  2.596429  2.569087  -.02734208  49
38  7  7  6.620073   2.780652 -.16806126  7.612591 2.0298035 2.4044466    .3746431  49
38  6  8  6.649926  1.8996477  3.5338044 10.433453 2.3450172 2.2793462  -.06567097  36
38  6  9  6.725434   1.765442   1.796019 8.5614605 2.1472707  2.657865   .51059437  36
38  . 10  6.368759  .56180954 -1.1694372  4.392372 1.4798695 2.6335206   1.1536511   .
39  1  2  6.994767   3.251338  2.8879404 11.139278 2.4104774         .           .   1
39  .  3    6.7167  2.3272514 -2.2495449  5.077706 1.6248597         .           .   .
39  1  4  6.981863   3.129077   4.911768 13.040846 2.5680864 1.6406574    -.927429   1
39  1  5  6.974447  4.0629864  -.6284237  8.434563 2.1323378 1.5627886   -.5695492   1
39  3  6  6.907755    3.85375   8.516598 17.370348  2.854765 2.6642516  -.19051313   9
39  6  7  6.882438  4.2586565 -2.8990626  6.359594 1.8499645  3.041733   1.1917683  36
39  6  8  7.446752   4.658222   5.842251 15.500473 2.7408705  3.024893   .28402257  36
39  6  9  7.547792  4.5580387   .4765987 10.034637  2.306043  3.515184   1.2091408  36
39  6 10  7.526794    3.85375  2.2465944 11.100345  2.406976 3.3308144    .9238381  36
41  1  2  8.813039  1.0205269    .810647  6.831174 1.9214965  2.922102   1.0006052   1
41  1  3   9.06837  2.3827553  2.1714509  9.554206 2.2569814  2.875027    .6180456   1
41  2  4  8.926978  2.1752834 -.13941526  7.035868  1.951021 2.8159115    .8648905   4
41  9  5  9.148972  2.0010948   .8217931  7.822888 2.0570538 3.1771994   1.1201456  81
41  9  6  9.476044  1.8526554   3.353596  10.20625 2.3230004  3.248454    .9254537  81
41  9  7  9.546813   1.724863   2.335167   9.06003 2.2038724  3.045836    .8419633  81
41  9  8  9.702817  1.6134262   3.278184   9.89161  2.291687 3.0979595    .8062725  81
41 10  9  9.816476   1.515627   .3207564  6.836383  1.922259 3.0705986   1.1483397 100
41 10 10   9.98353  1.4289856 -.21481514   6.21417 1.8268323  3.162407   1.3355746 100
42  1  2  6.194806  2.8767586  2.9923975 10.869156  2.385929  3.365985    .9800556   1
42  1  3  6.373673  1.5794754  1.1743128  7.753788 2.0481815  3.378829   1.3306475   1
42  1  4  6.746114   2.887821  3.2859325 11.173754 2.4135675  3.442269   1.0287013   1
42  1  5  7.022531          0    4.39322   9.39322  2.239988 3.2013104    .9613223   1
42  1  6  7.536364  2.1752834   5.159652 12.334936  2.512436  3.502185    .9897497   1
42  1  7  7.847035  2.0010471  4.4357004 11.436748  2.436832  3.509573   1.0727415   1
42  1  8  8.250565          0   3.073025  8.073025 2.0885282 3.5484214   1.4598932   1
42  1  9  8.726094          0  .22912025   5.22912  1.654243 3.5484214   1.8941783   1
42  1 10  9.093806   1.852703   .3986716  7.251375  1.981191 3.5484214   1.5672303   1
43  9  2  8.724833    3.19581   .8919835  9.087793  2.206932 2.7281535    .5212214  81
43  9  3  8.804875   2.833223  1.1294007  8.962624  2.193063  2.820271    .6272082  81
43  9  4  8.804875   2.544594  1.1832237  8.727818 2.1665154  2.816247    .6497314  81
43  9  5  8.922658  2.3093224 -.04830956  7.261013 1.9825194 2.8088484     .826329  81
43  7  6  8.965218  2.1139145   3.631264 10.745178 2.3744571  3.108891    .7344341  49
43  7  7  8.896683   1.949072    .228858   7.17793  1.971011 2.6482506    .6772395  49
43  7  8 8.9785385  1.8079758   2.321571  9.129547 2.2115161  2.978876      .76736  49
43  7  9  9.143649  1.6860485     3.1744  9.860449 2.2885318 3.0844114    .7958796  49
43  7 10  9.297352  1.0640144   .6931543  6.757169  1.910604  3.274787   1.3641832  49
44  5  2         .   2.774906          .         .         .         .           .  25
44  1  3  7.431004   4.525614  1.4081955  10.93381   2.39186  3.350872    .9590123   1
44  1  4  7.502841   3.550434   5.244809 13.795243  2.624324 3.3433175    .7189937   1
44  6  5  7.446752   3.722644  -.5507827  8.171862 2.1006968  2.477429    .3767319  36
44  .  6      7.32   3.557277   3.125113  11.68239  2.458083  2.742632   .28454924   .
44  7  7  7.335048   3.298783   2.456176  10.75496  2.375367 2.3361843  -.03918266  49
44  9  8   7.28803   3.036666  1.2051523  9.241818 2.2237387 2.3337543   .11001563  81
44  9  9  7.224795   2.998972   3.254664 11.253635  2.420691 2.3718219  -.04886937  81
44  9 10  7.211115  2.9687166  -.3536463   7.61507 2.0301292  2.912351    .8822215  81
45  1  2  7.558343   3.494024  1.9246995 10.418724 2.3436046 2.6667905    .3231859   1
45  1  3  7.313221  3.0650616   2.712864 10.777925    2.3775  2.176735  -.20076513   1
45  1  4  7.270661  3.5775185   3.823221  12.40074  2.517756  2.411664  -.10609245   1
45  2  5  7.152878   3.853798  -.8175611  8.036237  2.083961  2.552939    .4689782   4
45  .  6  6.635822  4.5580387  1.4540434 11.012082  2.398993  2.267332  -.13166094   .
45  .  7  6.294651  2.8119564  1.0550618  8.867018 2.1823385  2.668498    .4861598   .
45  .  8  6.348139   3.929615   1.505971 10.435586 2.3452218  2.457484   .11226225   .
45  8  9   6.45577  4.1763783   4.973155 14.149533 2.6496816  2.939987   .29030538  64
45  8 10  6.645391   3.908634 -.21011233  8.698522 2.1631532  2.997476    .8343227  64
end

I am going to estimate a SYS-GMM. I previously used xtabond2, but given the limitations it may display, I consider to use xtdpdgmm. I am having an hard time to replicate the estimates with the second command. When using xtabond2, I write:

xtabond2 L(0/1).wlnyw pc pc2 lnwi lnnda i.time, gmm(wlnyw pc pc2 lnsnda, lag(2 4) eq(diff) passt) twos cluster(id) nocon iv(i.time lnwi) gmm(wlnyw n g_ef nda, lag (2 2) eq(lev) passt)

Following the instruction I read from the presentation that Sebastian Kripfganz gave at 2019 Stata conference in London, I thought that the following could match the xtabond2 estimation:

xtdpdgmm L(0/1).wlnyw pc pc2 lnwi lnnda i.time, gmm(wlnyw pc pc2 lnsnda, lag(2 4) m(d)) twos vce (cluster id) iv(i.time lnwi) gmm(wlnyw n g_ef nda, lag (1 1) m(l))

Actually, results are not the same. Does anyone can offer me an hint about I can get the same estimates? By the way, I know that the xtdpdgmm command I am using may not be correct, because I should use teffects rather than i.time and also that the significance of the diagnostic tests could differ, but, at least, I am making some attempts to understand how xtdpdgmm works.

Thanks in advanced for your help.

Dario

[Sebastian Kripfganz]

1. There is admittedly an ambiguitiy in the way the term "exogenous" is used in the context of these dynamic panel models. Conventionally, a variable is said to be strictly exogenous if it is uncorrelated with the idiosyncratic error term from any time period. In the traditional sense, the variable would still be endogenous if it is correlated with the unit-specific effect, which is also part of the combined error term. For iv(x, model(level)), we need x to be truly exogenous in the traditional sense, i.e. it should not be correlated with either component of the error term. If the latter holds, then you would not specify the option in any other way because this way you maximize the correlation between the instrument and the regressor. If the variable is only uncorrelated with the error term but not with the unit-specific effect, then you would need to either specify instruments for a transformed model, or you could specify iv(x, diff model(level)), which would require the additional assumption that the first difference of x is uncorrelated with the unit-specific effect.

2. This statement corresponds to any type of variable. Usually, you would also specify instruments with lags for a transformed model. The additional lags for the level model are then typically redundant. If you specify instruments for the level model only, which is rarely done in the context of dynamic panel models but generally possible, then additional lags might still be useful.

3. See point 2. You need to start with lag 1 because the variable is not strictly exogenous (with respect to the idiosyncratic error component). And you would typically stick to this first lag if you are also using instruments for the transformed model. Note: Most of the time you would again want to add the diff option if you do not want to assume that x is uncorrelated with the unit-specific error component.

4. With gmmiv(x, model(diff) lag(a b)), you are only using the instruments for the differenced model. You would need to add a separate option for the level model if desired. Similarly the other way round. Whether to use a transformation (and if so, which) depends on the arguments in point 1 and further arguments set out in my 2019 London Stata Conference presentation.