[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.

[Prateek Bedi]

1. iv(x, model(level)) requires an even stronger assumption that just strict exogeneity. It also requires that x is uncorrelated with the unobserved unit-specific effects ("fixed effects"), because the level values of x are used as instruments for the level model. The suboption lag() is generally only needed if x is not strictly exogenous. For the level model, usually no lags are used. Even if it is a predetermined or endogenous variable, the conventional use is iv(x, model(level) lag(1 1)) (or equivalently with the gmm() option).

2. Yes, a would typically be 1 for a predetermined and 2 for an endogenous variable with model(diff) or 0 for a predetermined and 1 for an endogenous variable with model(fodev), and provided the idiosyncratic error term (in levels) is serially uncorrelated. b could be the same or a higher number, or a missing value (.) for the maximum possible lag.

Thanks a lot, Prof. Kripfganz. Your answers are so much helpful. Please allow me to ask the following questions.

1. You mention in point #1 that iv(x, model(level)) requires an even stronger assumption of strict exogeneity, However, this assumption is what makes an exogenous variables, exogenous. Is this understanding correct? Also, in what other ways can we define the iv() options for an exogenous variable? I request you to please provide an example.

2. You also mention in point #1 - "For the level model, usually no lags are used.". Does this statement correspond to exogenous variables only?

3. You also mention in point #1 - "Even if it is a predetermined or endogenous variable, the conventional use is iv(x, model(level) lag(1 1))". Why are lags kept at (1 1) here?

4. Considering the fact that system GMM has a level equation and a transformed equation (which effectively involves all variables), how do we decide which model() sub-option (i.e. level/diff/fodev/bodev/mdev) to use each for an exogenous, endogenous and a predetermined variable? I ask this because if (let's say) I put an endogenous variable (say, x) in this way: gmmiv(x, model(diff) lag(a b)), does this mean that I am only using the transformed equation for x (what about the level model, then)? OR if (let's say), I put an exogenous variable (say, p) in this way: iv(p, model(level), lag(c d)), does this mean that I am only using the level equation for x (what about the transformed model, then)?

[Sebastian Kripfganz]

1. iv(x, model(level)) requires an even stronger assumption that just strict exogeneity. It also requires that x is uncorrelated with the unobserved unit-specific effects ("fixed effects"), because the level values of x are used as instruments for the level model. The suboption lag() is generally only needed if x is not strictly exogenous. For the level model, usually no lags are used. Even if it is a predetermined or endogenous variable, the conventional use is iv(x, model(level) lag(1 1)) (or equivalently with the gmm() option).

2. Yes, a would typically be 1 for a predetermined and 2 for an endogenous variable with model(diff) or 0 for a predetermined and 1 for an endogenous variable with model(fodev), and provided the idiosyncratic error term (in levels) is serially uncorrelated. b could be the same or a higher number, or a missing value (.) for the maximum possible lag.

[Prateek Bedi]

Thank you so much, Prof. Kripfganz for such clear and precise answers. Your responses have provided me a better understanding of xtdpdgmm. I have further follow-up questions.

1. For a strictly exogenous variable (x), what does the use of iv(x, model(level)) signify? Does it mean that the level values of the exogenous variable are being used as instrument for it? Is this type of treatment of exogenous variable recommended? In case of this exogenous variable, is there any need to specify the sub-option lag() here i.e. iv(x, model(level) lag(1 2))?

2. In case of an endogenous/predetermined variable (say, p), you said that we need to use the lags of those variables as instruments for the transformed model (say, first-difference). As a sample, is this the correct way to do it in xtdpdgmm: gmmiv(p, lag(a b) model(diff))?

[Sebastian Kripfganz]

1. For the model in first differences, it can be beneficial to also first difference the instrument if the variable is strictly exogenous. You cannot get a stronger instrument for D.x than using D.x itself. With xtdpdgmm, you simply use the iv(x, diff model(diff)) to transform the instrument for the first-differenced model. For a strictly exogenous variable, you could alternatively use the untransformed x as an instrument for the model in mean deviations, i.e. iv(x, model(mdev)), which would also maximize the correlation between the instrument and the regressor. When you have predetermined or endogenous variables, you need to use lags of those variables as instruments for the transformed model (i.e. first differences or forward-orthogonal deviations), and then it is less obvious whether transforming those instruments is beneficial or not. I tend to recommend not to transform the instruments for the transformed model in those cases. Forward-orthogonal deviations are useful when the data has gaps because it retains more information in that case.

2. If the variables are not strictly exogenous, you typically need to specify a lag order with suboption lag() for the level and the transformed models. Please see my 2019 London Stata Conference presentation for applicable lag orders.

3. The maximum lag order depends on the suboptions you choose:

model(level)	T-1
model(level) difference	T-2
model(difference)	T-1
model(difference) difference	T-2
model(fodev)	T-2
model(fodev) bodev	T-3

4. The maximum lag order is always specific to any particular iv() or gmm() option; see point 3.

5. Yes; see again point 3.

[Prateek Bedi]

Thanks, Prof. Kripfganz. In relation to your response, I have the following doubts.

1. When do we need to transform the instruments? How do we decide which transformation to go for? How do we transform the instruments in xtdpdgmm?

2. I suppose that the lag order which we specify in the sub-option lag() is applicable for instruments to be used for both level as well transformed model. Is this correct?

3. If the answer to query #2 is yes, the maximum lag order in the sub-option lag() should allow for a value which is permitted to be used as an instrument in either of the models (level or transformed). Is this correct?.

4. You mentioned in post #295 that for the level model, we need to first difference the instruments, even if we use forward-orthogonal deviations for the transformed model/equation. So, in a model which employs forward-orthogonal deviations for the transformed model, the maximum lag order allowed shall be T-2 only whether we look at it from the perspective of level model or transformed model. Is this understanding correct?

5. In post #293, you mentioned that for a model in which transformed equation has been obtained by taking first-difference, the maximum lag order allowed is T-1. Is this because for the first-differenced model, we can use lags (in levels) starting from t=1 and go on till T-1? (However, we can still only use T-2 lags at max for the level model as you mentioned in point #1 of post #295).

Thanks for your invaluable guidance!!

[Sebastian Kripfganz]

1. If you had strictly exogenous variables, you could also use the first-differenced value from t=4 as an instrument for the level regressors at t=4. Other than that, you are correct. The largest possible lag would be the first-differenced value from t=2 as an instrument for the level regressors at t=4. Thus, the maximum lag order is 4-2=2 (i.e. T-2).
2. You usually cannot use the forward-orthogonally transformed values as instruments for the level model. Due to the subtraction of future information (as opposed to past observation when using first differences), the forward-orthogonal transformation would make these instruments invalid unless the variables are strictly exogenous. xtdpdgmm does not offer a forward-orthogonal transformation of the instruments. For the level model, you would typically still first difference the instruments, even if you used forward-orthogonal deviations for the transformed model/equation.

[Prateek Bedi]

No. Let's look at a simple example. Suppose, you have (untransformed) data for T=4 time periods, t=1,2,3,4. In first differences, the last available observation is for t=4. The largest lag would be to use an instrument from the observation t=1. Thus, the maximum lag order is 4-1=3 (i.e. T-1). In forward-orthogonal deviations, the last available observation is for t=3. The largest lag would still be to use an instrument from the observation t=1. Thus, the maximum lag order is 3-1=2 (i.e. T-2).

Thanks, Prof. Kripfganz. Now, I would like to ask the following questions to enhance my understanding. As per my limited knowledge a system-GMM estimator has two equations - level equation and transformed equation. The transformed equation may be transformed using first-difference transformation or forward orthogonal deviations. Also, the lags of level values serve as instruments for the transformed equation and lags of the transformed values serve as instruments for the level equation. I have the following queries from the perspective of the level equation.

1. Suppose the transformed equation has been obtained using first-difference transformation. Now for the level equation, the first-difference values have to serve as instruments. Assuming T=4 time periods, the first observation of the transformed equation is lost by construction. Hence, the first-differenced values begin from t=2. Now, for the level equation, should not the maximum lag order be T-2? For instance, for the level value at t=4, the lags start from t=2 (because the first-differenced values begin from t=2) and end at t=3 (because the first-differenced value at t=4 cannot be used an instrument for level value at t=4).

2. Suppose the transformed equation has been obtained using forward-orthogonal transformation. Now for the level equation, the forward-orthogonal values have to serve as instruments. Assuming T=4 time periods, the first observation of the transformed equation in this case begins from t=1. Now, for the level equation, should not the maximum lag order be T-1? For instance, for the level value at t=4, the lags start from t=1 and end at t=3 (because the forward-orthogonal value at t=4 cannot be used an instrument for level value at t=4).

Please correct me if my understanding is wrong.