[Mugi Jang]

Dear Sebastian Kripfganz
Could you summarize the option about standard error to get the same value among xtdpd, xtabond2 and xtdpdgmm
Thank you in advance

[Sebastian Kripfganz]

Filip Novinc
Thank you very much for reporting the two bugs with the CU-GMM estimator and the portmanteau test, and for sharing your data with me. I was able to replicate the bugs and implement a fix for them. An update to version 2.6.3 is now available on my personal website:

net install xtdpdgmm, from(http://www.kripfganz.de/stata/) replace

[Sebastian Kripfganz]

(Numbering not consistent with your questions. Not sure what happened with your post above; this appears to be a bug in the forum software.)

1. I would not necessarily be worried by these correlation coefficients; they might be large enought. You could check for potential identification problems with the underid command; see slides 43-47 of my 2019 London Stata Conference presentation.
2. Potentially, yes. It might be enough to simply change the lags for those instruments (i.e. starting with one lag higher).
3. Aside from maybe row 6, your difference-in-Hansen tests look all fine. I would not worry too much about row 6 (which still has a p-value higher than the usual critical values), given the overwhelming evidence for correct specification in the other rows. Regarding the interpretation, taking row 6 again, the test in column "Excluding" is a Hansen test for the model without the instruments in row 6 (see list below the regression output). The test does not provide evidence of model misspecification if those instruments are left out. The column "Difference" then is a test for the validity of the additional instruments in row 6 (assuming validity of all other instruments), which is marginally acceptable here. To check that the difference GMM estimator is fine, I would in the first place just estimate the model with the difference GMM estimator only, i.e. do not include the instruments from row 7 onwards and specify the nolevel option. Then check the Hansen test for that model.
4. All xtdpdgmm postestimation command return results in r(); type return list after a postestimation command to see the full list. These results can then be fed into the usual commands for table generation.
5. Regarding those error messages, would it be possible for you to send me your data set (or a suitable subset of it) by e-mail, so that I can replicate the error messages?
6. These weak instrument procedures are not directly implemented in the xtdpdgmm package. Some might be available with ivreg2 or with other community-contributed commands that work after ivreg2. In that case, replicate the results first with ivreg2, as explained on slides 39-42 of my presentation.
7. I do not have a good answer to the CUE question right now.
8. You could again replicate the results with ivreg2 and then follow the procedure suggested by Baum et al. (2003). If there are problems with instrument relevance, underidentification tests with the underid command might detect them. I generally recommend to routinely carry out these underidentification tests.
9. If there is indication of underidentification, then this would generally imply that your instruments are weak or highly multicollinear. The usual consequences from the weak-instruments literature apply (biased coefficients and test results, large standard errors/confidence intervals, etc.).
10. Without looking into the Blundell and Bond (2000) paper, they might just have obtained predicted firm-specific effects (with option u of the predict command after xtdpdgmm) and then looked at their variance (simply computing summary statistics). Those group-fixed effects are the means of the error term for each firm. While these effects themselves cannot be estimated/predicted consistently, their variance estimate is consistent.
11. Precision problems with the estimate of the weighting matrix typically occur when the cross-sectional sample size N is small, the number of instruments is large, or the instruments are weak. An indication might be large differences in the two versions of the Hansen test reported by estat overid after two-step estimation, or convergence problems of the iterated GMM estimator.
12. If individuals have different starting points, a violation of the system GMM assumption might not be easily seen in the graphs. The best approach would usually be a difference-in-Hansen test, comparing the system GMM estimator with a difference GMM estimator (where the latter might possibly use nonlinear moment conditions as well to avoid weak identification problems). The residuals are already obtained for the model with log dependent variable; no need to apply logs again.

[Filip Novinc]

My apologies for the bigger post. I am trying to rearrange it, but am coming across a bug which doesn't let me edit the post. This is my first time posting on Stata forum. The question numeration is not correct. Questions 5 and 6 are numbered twice, but are two distinct question.

[Filip Novinc]

Dear professor Kripfganz,
Thank you for all the provided information here. I have thoroughly read all the posts related to the xtdpdgmm thread and have thoroughly studied the dynamic panel data estimation for my doctoral disertation but still haven't figured out a couple of questions.
I have a panel of N=500 firms from Croatian manufacturing industry (T=12) and am trying to estimate the impact of unit labour costs (lnulc1) on exports (lnexport3). Other regressors are lagged exports (l.lnxport3) material cost (lnumc), differenced fixed capital assets (dlnreal_K), workers employed (lnL) and intangible fixed assets (Inrealintangible_K). ln means the variable is in natural logarithm. I assume they are all endogenous – there might be unobserved firm characteristics such as quality of management or ownership that can affect behaviour of firms and their exports. I have several questions about my analysis and about xtdpdgmm in general:

1. The correlation coefficient between (some) regressors and their differences is preety small - e.g. for the first available instrument as lnulc1 is treated as endogenous (this applies to longer lags aswell): Corr(d.lnulc1, l2.lnulc1) = -0,1385 ; Corr(lnulc1, d.lnulc1) = 0,1241. Could I be having a weak instrument problem even if diff-in-Hansen test is fine? Or since all instruments instrument all the regressors lead to better estimations so I don't have to worry about these correlations?
2. If diff-in-Hansen test is not satisfying (p<0,1) for only one variable for example in levels, does that mean all the estimated coefficients are biased and inconsistent?
3. Can you help please with diff-in-Hansen test intrepretation?
   

   . xtdpdgmm lnexport3 l.lnexport3 lnulc1 lnL dlnreal_K lnumc l.lnrealintangible_K, ///
   	> model(diff) collapse gmm(lnexport3, lag(2 3)) ///
   	>                      gmm(lnulc1, lag(2 3)) ///
   	>                                          gmm(lnL, lag(2 3)) ///
   	>                                          gmm(dlnreal_K, lag(1 2)) ///
   	>                                          gmm(lnumc, lag(1 2)) ///
   	>                                          gmm(lnrealintangible_K, lag (1 2)) ///
   	>                                          ///
   	>                      gmm(lnexport3, lag(1 1) diff model(level)) ///
   	>                                          gmm(lnulc1, lag(1 1) diff model(level)) ///
   	>                                          gmm(lnL, lag(1 1) diff model(level)) ///
   	>                                          gmm(dlnreal_K, lag(0 0) diff model(level)) ///
   	>                                          gmm(lnumc, lag(0 0) diff model(level)) ///
   	>                      gmm(lnrealintangible_K, lag (0 0) diff model (level)) ///
   	> teffects twostep vce(robust, dc) small overid
   	
   	Generalized method of moments estimation
   	
   	Fitting full model:
   	Step 1         f(b) =  .01217351
   	Step 2         f(b) =  .02229234
   	
   	Fitting reduced model 1:
   	Step 1         f(b) =  .01825629
   	
   	Fitting reduced model 2:
   	Step 1         f(b) =  .01806326
   	
   	Fitting reduced model 3:
   	Step 1         f(b) =  .02210642
   	
   	Fitting reduced model 4:
   	Step 1         f(b) =  .02227238
   	
   	Fitting reduced model 5:
   	Step 1         f(b) =  .01835181
   	
   	Fitting reduced model 6:
   	Step 1         f(b) =  .01389141
   	
   	Fitting reduced model 7:
   	Step 1         f(b) =  .02192478
   	
   	Fitting reduced model 8:
   	Step 1         f(b) =  .02228061
   	
   	Fitting reduced model 9:
   	Step 1         f(b) =   .0193838
   	
   	Fitting reduced model 10:
   	Step 1         f(b) =  .02228957
   	
   	Fitting reduced model 11:
   	Step 1         f(b) =  .01851922
   	
   	Fitting reduced model 12:
   	Step 1         f(b) =  .02220404
   	
   	Fitting reduced model 13:
   	Step 1         f(b) =  .00270867
   	
   	Group variable: id                           Number of obs         =      4402
   	Time variable: year                          Number of groups      =       529
   	
   	Moment conditions:     linear =      29      Obs per group:    min =         1
   	                   nonlinear =       0                        avg =  8.321361
   	                       total =      29                        max =        11
   	
   	                                        (Std. Err. adjusted for 529 clusters in id)
   	------------------------------------------------------------------------------------
   	                  |              DC-Robust
   	        lnexport3 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
   	-------------------+----------------------------------------------------------------
   	        lnexport3 |
   	              L1. |   .5724923   .0602836     9.50   0.000     .4540672    .6909175
   	                  |
   	           lnulc1 |  -.6139368   .1540915    -3.98   0.000    -.9166446   -.3112291
   	              lnL |   .7445906   .1702559     4.37   0.000     .4101284    1.079053
   	        dlnreal_K |   .0816588   .0346772     2.35   0.019     .0135365     .149781
   	            lnumc |  -.4469151   .1617449    -2.76   0.006    -.7646577   -.1291726
   	                  |
   	lnrealintangible_K |
   	              L1. |  -.0093538   .0119297    -0.78   0.433    -.0327893    .0140817
   	                  |
   	             year |
   	            2010  |   .0766462   .0537471     1.43   0.154    -.0289382    .1822306
   	            2011  |   .1398977   .0476322     2.94   0.003     .0463258    .2334697
   	            2012  |    .103861   .0426544     2.43   0.015     .0200678    .1876543
   	            2013  |   .1476749   .0466095     3.17   0.002      .056112    .2392378
   	            2014  |   .2201735   .0483601     4.55   0.000     .1251717    .3151754
   	            2015  |   .2367494   .0529298     4.47   0.000     .1327706    .3407282
   	            2016  |   .2454128   .0546268     4.49   0.000     .1381002    .3527254
   	            2017  |   .2708834   .0549217     4.93   0.000     .1629914    .3787753
   	            2018  |   .2706555   .0580685     4.66   0.000     .1565819    .3847292
   	            2019  |   .2205907   .0591024     3.73   0.000     .1044859    .3366955
   	                  |
   	            _cons |  -3.575295   .8959527    -3.99   0.000    -5.335364   -1.815225
   	------------------------------------------------------------------------------------
   	Instruments corresponding to the linear moment conditions:
   	1, model(diff):
   	  L2.lnexport3 L3.lnexport3
   	2, model(diff):
   	  L2.lnulc1 L3.lnulc1
   	3, model(diff):
   	  L2.lnL L3.lnL
   	4, model(diff):
   	  L1.dlnreal_K L2.dlnreal_K
   	5, model(diff):
   	  L1.lnumc L2.lnumc
   	6, model(diff):
   	  L1.lnrealintangible_K L2.lnrealintangible_K
   	7, model(level):
   	  L1.D.lnexport3
   	8, model(level):
   	  L1.D.lnulc1
   	9, model(level):
   	  L1.D.lnL
   	10, model(level):
   	  D.dlnreal_K
   	11, model(level):
   	  D.lnumc
   	12, model(level):
   	  D.lnrealintangible_K
   	13, model(level):
   	  2010bn.year 2011.year 2012.year 2013.year 2014.year 2015.year 2016.year
   	  2017.year 2018.year 2019.year
   	14, model(level):
   	  _cons
   	
   	.
   	end of do-file
   	
   	. 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) |     9.6576     10    0.4710 |      2.1351      2    0.3439
   	  2, model(diff) |     9.5555     10    0.4803 |      2.2372      2    0.3267
   	  3, model(diff) |    11.6943     10    0.3060 |      0.0984      2    0.9520
   	  4, model(diff) |    11.7821     10    0.2999 |      0.0106      2    0.9947
   	  5, model(diff) |     9.7081     10    0.4665 |      2.0845      2    0.3527
   	  6, model(diff) |     7.3486     10    0.6922 |      4.4441      2    0.1084
   	 7, model(level) |    11.5982     11    0.3946 |      0.1944      1    0.6592
   	 8, model(level) |    11.7864     11    0.3799 |      0.0062      1    0.9372
   	 9, model(level) |    10.2540     11    0.5077 |      1.5386      1    0.2148
   	10, model(level) |    11.7912     11    0.3795 |      0.0015      1    0.9695
   	11, model(level) |     9.7967     11    0.5488 |      1.9960      1    0.1577
   	12, model(level) |    11.7459     11    0.3830 |      0.0467      1    0.8289
   	13, model(level) |     1.4329      2    0.4885 |     10.3598     10    0.4095

   If I got it right, all the model(level) p-values (rows 7 - 13) under column Excluding have to be higher than (let's say) 0,1 to say that difference GMM estimator is fine and we may try the SYS GMM. Then we go to the column Difference where we look for both model(diff) and model(level) rows and all of them need to be fine in order to say that SYS-GMM is ok and we can proceed with the analysis. Is my understanding correct?
4. Is there a way to extract results of Hansen, difference-in-Hansen, underid and AR(2) test from multiple estimations in the same table after applying xtdpdgmm?
5. When I do continuously updated GMM with the following code the error is returned. Could you please help? I am running Stata 14.0 and the xtdpdgmm is up to date (just checked it):

   . xtdpdgmm lnexport3 l.lnexport3 lnulc1 lnL dlnreal_K lnumc l.lnintangible_K, ///
   	> model(diff) collapse gmm(lnexport3, lag(2 5)) ///
   	>                      gmm(lnulc1, lag(2 5)) ///
   	>                                          gmm(lnL, lag(2 5)) ///
   	>                                          gmm(dlnreal_K, lag(2 5)) ///
   	>                                          gmm(lnumc, lag(2 5)) ///
   	>                                          gmm(lnintangible_K, lag (2 5)) ///
   	> ///
   	>                      gmm(lnexport3, lag(1 2) diff model(level)) ///
   	>                                          gmm(lnulc1, lag(1 2) diff model(level)) ///
   	>                                          gmm(lnL, lag(1 2) diff model(level)) ///
   	>                                          gmm(dlnreal_K, lag(1 2) diff model(level)) ///
   	>                                          gmm(lnumc, lag(1 2) diff model(level)) ///
   	>                      gmm(lnintangible_K, lag (1 2) diff model (level)) ///
   	> teffects cu vce(r) overid
   	
   	Generalized method of moments estimation
   	         asarray_keys():  3301  subscript invalid
   	     xtdpdgmm_opt::iv():     -  function returned error
   	   xtdpdgmm_opt::init():     -  function returned error
   	             xtdpdgmm():     -  function returned error
   	                <istmt>:     -  function returned error

6. When I try Jochmans (2020) portmanteau test (after SYS-GMM estimation from the previous point) I get the following error:
   
   

   	. estat serialpm
   	    xtdpdgmm_serialpm():  3200  conformability error
   	                <istmt>:     -  function returned error
   	r(3200);

Bun, M. J., & Windmeijer, F. (2010). The weak instrument problem of the system GMM estimator in dynamic panel data models. The Econometrics Journal, 13Econometric reviews, 19(3), 321-340.


10. Your presentation (2019) slide 94 says: „If there are concerns about the imprecisely estimated optimal weighting matrix, the one-step GMM estimator with robust standard errors might be used instead.“ How can I know if optimal weighting matrix is imprecisely estimated?

11. Blundell-Bond assumption esentially states that devations from long-run means must not be correlated with the fixed effects for SYS-GMM to be valid. First, can I check the assumption by doing a graph where dl.lnexport3 is on the x-axis, and residuals are on y-axis and if there is no correlation between those two (for the first lets say few periods t<5, since my T=12), then the B-B assumption is fine (lnexport3 is my left-hand side variable in an estimated model)? Roodman (2009) makes such graphs on page 146, but states „In sum, for the particular case where individuals have a common starting point, the validity of system GMM is equivalent to all having achieven mean stationarity by the study period.“ Does that mean that these graphs do show the violation/validity of B-B assumption only if the individuals (firms) have a common starting point, i.e. we look at the same time period for all individuals? Lastly, do residuals have to be logged, since lnexport3 is a natural logarithm of exports? Roodman, D. (2009). A note on the theme of too many instruments. Oxford Bulletin of Economics and statistics, 71(1), 135-158.

[Sebastian Kripfganz]

You can use the community-contributed ivreg2 command. Slides 39 to 42 of my 2019 London Stata Conference presentation provide an example of how to replicate xtdpdgmm results with ivreg2. You can then simply amend the latter command to obtain Driscoll-Kraay standard errors (option dkraay()).

[Mugabil Isayev]

Dear Sebastian Kripfganz,

Thank you for the response. Is there any command in Stata where I can incorporate Driscoll Kraay SEs into GMM?

[Sebastian Kripfganz]

These two commands do not compute Driscoll Kraay standard errors, sorry.

[Mugabil Isayev]

Dear Sebastian Kripfganz,

I want to simultaneously take into account cross-sectional dependence and endogeneity problems. Is it possible to incorporate Driscoll Kraay standard errors to xtdpdgmm or xtabond2?

Thanks in advance.

[Sebastian Kripfganz]

The first justification would be that you have endogenous regressors but no suitable external instruments; therefore, you are using internal instruments (lagged transformed regressors).

Compared to the difference-GMM estimator, the justification for the system-GMM estimator would still be that it is more efficient because of the extra instruments it uses. The validity of these extra instruments of course needs to be justified, typically with a difference-in-Hansen test comparing the system-GMM to the difference-GMM estimator. In a nutshell, the arguments are very similar to those for a dynamic model.

The static model is a special case of the dynamic model without the lagged dependent variable. What is good for the more general dynamic model cannot be bad for the restricted static model.

[Sarah Magd]

1. Yes.
2. 2SLS is generally inefficient when using panel data. In any case, "2SLS" is not very informative; you would need to be clear about the instruments you are using. It then becomes a question of whether the instruments used in your sys-GMM estimator are beneficial compared to the instruments used in your 2SLS approach. In the first place, you would need to check whether they might require different assumptions for validity.
3. Reporting serial correlation tests is generally still useful even in static models. For once, they might tell you whether a dynamic model could be reasonable (to account for any serial correlation detected in the static model). If you have predetermined/endogenous variables, serial correlation can still invalidate the instruments in a static model.

Dear Prof. Sebastian Kripfganz
When we use sys-GMM with a static model, how should I justify the selection of this estimator? Do I need to do any further steps or compare it with other estimators?
Or should I use it as a robustness check?
I am just confused about how I should justify the use of sys-GGM to estimate a static model

[Sebastian Kripfganz]

1.1-1.7) I cannot/should not answer those questions without seeing your command line, instruments used, and regression ouput. Eventually, a holistic approach should be used.

1.8-1.9) Assuming that ind and md are time-invariant, the respective instruments for model(md) will be dropped. In that regard, specification A is more reasonable. Other than that, the specifications can be valid.

2) The difference-in-Hansen test can be seen as a test comparing two estimators, one with the instruments under investigation and one without them. You would never consider an estimator without instruments for the time dummies, when such time dummies are included as regressors, because then necessary instruments are missing, which leads to weak identification/underidentification of the model. Therefore, the comparison estimator is rubbish and the test not meaningful. In other words, there is no point testing the validity of time dummy instruments. These are always valid.

3) The test in those rows for the time dummies should always be ignored. It is not meaningful; see 2).

Maybe I should clarify one aspect: When testing for the Blundell-Bond assumption, we need to compare two estimators that both use instruments for the time dummies. We should therefore (for the purpose of this test), use the time dummy instruments in the transformed model, not the level model !!! Once we have done the test, we can then possibly change the specification by including the time dummy instruments for the level model instead.


Please understand that I won't be able to continue my detailed answers in that frequence here on Statalist due to other obligations. Such detailed help would normally require a (paid) consultancy agreement.

[Zainab Mariam]

Dear Professor Sebastian,

Many thanks for your time and hard work. Thank you very much for helping out when I needed it. The support that you show is extremely appreciated, Professor!

Question 1) Suppose the following outcomes of the difference-in-Hansen test.

Table 1

	Excluding			Difference
Moment conditions	chi2	df	p	chi2	df	p
1, model(fodev)	38.4506	17	0.0021	5.6365	3	0.0580
2, model(fodev)	32.2911	17	0.0138	11.7960	3	0.0081
3, model(fodev)	38.2406	17	0.0023	5.8465	3	0.1193
4, model(fodev)	43.0624	17	0.0005	1.0247	3	0.7953
5, model(fodev)	42.8693	17	0.0005	1.2178	3	0.7487
6, model(fodev)	42.9069	17	0.0005	1.1803	3	0.7577
7, model(fodev)	38.2817	17	0.0022	5.8054	3	0.0775
8, model(fodev)	39.2517	17	0.0016	4.8354	3	0.0689
9, model(fodev)	39.2432	17	0.0017	4.8439	3	0.1836
10, model(fodev)	34.1913	17	0.0079	9.8958	3	0.0195
11, model(fodev)	41.1743	19	0.0023	2.9128	1	0.0879
12, model(mdev)	34.6609	19	0.0153	9.4262	1	0.0021
13, model(level)	29.6163	19	0.1070	3.0659	1	0.1087
14, model(level)	0.3539	1	0.1517	43.7332	19	0.0510
model(fodev)	.	-11	.	.	.	.

Table 2 (since the row/line labelled “model(level)” in the difference-in-Hansen test is needed, I kept its findings and deleted the rest).

	Excluding			Difference
Moment conditions	chi2	df	p	chi2	df	p
1, model(fodev)
2, model(fodev)
3, model(fodev)
4, model(fodev)
5, model(fodev)
6, model(fodev)
7, model(fodev)
8, model(fodev)
9, model(fodev)
10, model(fodev)
11, model(fodev)
12, model(mdev)
13, model(level)
14, model(level)	12.0861	7	0.0978	4.1102	2	0.0881
model(diff)	0.0000	0	.	16.1962	9	0.0629
model(level)	8.0920	6	0.0448	8.1042	3	0.0447

Table 3

	Excluding			Difference
Moment conditions	chi2	df	p	chi2	df	p
1, model(fodev)
2, model(fodev)
3, model(fodev)
4, model(fodev)
5, model(fodev)
6, model(fodev)
7, model(fodev)
8, model(fodev)
9, model(fodev)
10, model(fodev)
11, model(fodev)
12, model(mdev)
13, model(level)
14, model(level)	12.0861	7	0.0397	4.1102	2	0.1364
model(diff)	0.0000	0	.	16.1962	9	0.0629
model(level)	8.0920	6	0.0398	8.1042	3	0.1298

Table 4

	Excluding			Difference
Moment conditions	chi2	df	p	chi2	df	p
1, model(fodev)
2, model(fodev)
3, model(fodev)
4, model(fodev)
5, model(fodev)
6, model(fodev)
7, model(fodev)
8, model(fodev)
9, model(fodev)
10, model(fodev)
11, model(fodev)
12, model(mdev)
13, model(level)
14, model(level)	12.0861	7	0.1231	4.1102	2	0.0786
model(diff)	0.0000	0	.	16.1962	9	0.0629
model(level)	8.0920	6	0.1214	8.1042	3	0.0489

Table 5

	Excluding			Difference
Moment conditions	chi2	df	p	chi2	df	p
1, model(fodev)
2, model(fodev)
3, model(fodev)
4, model(fodev)
5, model(fodev)
6, model(fodev)
7, model(fodev)
8, model(fodev)
9, model(fodev)
10, model(fodev)
11, model(fodev)
12, model(mdev)
13, model(level)
14, model(level)	12.0861	7	0.0779	4.1102	2	0.1281
model(diff)	0.0000	0	.	16.1962	9	0.0629
model(level)	8.0920	6	0.1095	8.1042	3	0.1087

I kindly ask you please the following questions!

1.1) Which table(s) of the above findings of the difference-in-Hansen test indicate that the Difference GMM estimator is fine? Which table(s) of the above findings of the difference-in-Hansen test indicate that the instruments for the Difference GMM estimator are valid?

1.2) Which table(s) of the above findings of the difference-in-Hansen test indicate that the variables satisfy/violate the additional Blundell-Bond assumption (sufficient: mean stationarity)?

1.3) Which table(s) of the above findings of the difference-in-Hansen test indicate that I can instrument the variables in the level model?

1.4) Which table(s) of the above findings of the difference-in-Hansen test indicate that I can apply the System GMM estimator?

1.5) Which table(s) of the above outcomes of the difference-in-Hansen test indicate that the Difference GMM estimator is superior to the System GMM estimator?

1.6) Which table(s) of the above outcomes of the difference-in-Hansen test indicate that the System GMM estimator is superior to the Difference GMM estimator? Which of the above findings of the difference-in-Hansen test indicate that the additional instruments for the level model are valid?

1.7) What do the above findings of the difference-in-Hansen test indicate regarding the variables classification whether exogenous, predetermined, or endogenous?

1.8) In case I can apply the System GMM estimator, are the following codes correct to apply the System GMM estimator using your xtdpdgmm command?

A) In this code, I specified ‘model(fod)’ as a separate option in the xtdpdgmm command line, I instrument all the variables (except the dummies) for the differenced model, I instrument all the variables (including the dummies) for the level model, I put ‘model(level)’ in the iv() option for the dummies as follows.

xtdpdgmm L(0/1).y L(0/1).x1 L.x2 L.x3 L.x4 L.x5 L.x6 L.x7 L.x8 L.x9 x10 i.ind mn cf cf*L.x1, model(fod) collapse gmm(y, lag(1 3)) gmm(L.x1, lag(1 3)) gmm(L.x2, lag(0 2)) gmm(L.x3, lag(0 2)) gmm(L.x4, lag(0 2)) gmm(L.x5, lag(0 2)) gmm(L.x6, lag(0 2)) gmm(L.x7, lag(0 2)) gmm(L.x8, lag(0 2)) gmm(L.x9, lag(0 2)) gmm(x10, lag(0 2)) gmm(x10, lag(0 0) model(md)) gmm(cf*L.x1, lag(1 3)) gmm(y, lag(1 1) diff model(level)) gmm(L.x1, lag(1 1) diff model(level)) gmm(L.x2, lag(0 0) diff model(level)) gmm(L.x3, lag(0 0) diff model(level)) gmm(L.x4, lag(0 0) diff model(level)) gmm(L.x5, lag(0 0) diff model(level)) gmm(L.x6, lag(0 0) diff model(level)) gmm(L.x7, lag(0 0) diff model(level)) gmm(L.x8, lag(0 0) diff model(level)) gmm(L.x9, lag(0 0) diff model(level)) gmm(x10, lag(0 0) diff model(level)) gmm(cf*L.x1, lag(1 1) diff(model(level)) iv(i.ind, model(level)) iv(mn, model(level)) iv(cf, model(level)) two small vce(r) overid

B) In this code, I specified ‘model(fod)’ as a separate option in the xtdpdgmm command line, I instrument all the variables (except the dummies) for the differenced model, I instrument all the variables (including the dummies) for the level model, I put ‘model(md)’ in the iv() option for the dummies as follows.

xtdpdgmm L(0/1).y L(0/1).x1 L.x2 L.x3 L.x4 L.x5 L.x6 L.x7 L.x8 L.x9 x10 i.ind mn cf cf*L.x1, model(fod) collapse gmm(y, lag(1 3)) gmm(L.x1, lag(1 3)) gmm(L.x2, lag(0 2)) gmm(L.x3, lag(0 2)) gmm(L.x4, lag(0 2)) gmm(L.x5, lag(0 2)) gmm(L.x6, lag(0 2)) gmm(L.x7, lag(0 2)) gmm(L.x8, lag(0 2)) gmm(L.x9, lag(0 2)) gmm(x10, lag(0 2)) gmm(x10, lag(0 0) model(md)) gmm(cf*L.x1, lag(1 3)) gmm(y, lag(1 1) diff model(level)) gmm(L.x1, lag(1 1) diff model(level)) gmm(L.x2, lag(0 0) diff model(level)) gmm(L.x3, lag(0 0) diff model(level)) gmm(L.x4, lag(0 0) diff model(level)) gmm(L.x5, lag(0 0) diff model(level)) gmm(L.x6, lag(0 0) diff model(level)) gmm(L.x7, lag(0 0) diff model(level)) gmm(L.x8, lag(0 0) diff model(level)) gmm(L.x9, lag(0 0) diff model(level)) gmm(x10, lag(0 0) diff model(level)) gmm(cf*L.x1, lag(1 1) diff(model(level)) iv(i.ind, model(md)) iv(mn, model(md)) iv(cf, model(md)) two small vce(r) overid

Where:
y is the dependent variable;
L.y is the lagged dependent variable as a regressor (L.y is predetermined);
L.x1 is the independent variable (L.x1 is endogenous);
The control variables L.x2, L.x3, L.x4, L.x5, L.x6, L.x7, L.x8, L.x9 are predetermined;
The control variable x10 (firm age) is exogenous;
ind is industry dummies;
mn is country dummies;
cf is a dummy variable that takes the value of 1 for the 3 years 2008, 2009, and 2010;
cf*L.x1 is an interaction between the dummy variable cf and the independent variable L.x1.

1.9) If the previous codes are incorrect to apply the System GMM estimator, what do I have to add, delete, amend in the previous codes to apply the System GMM estimator using your xtdpdgmm command?

Are there other codes which are more appropriate to apply the System GMM estimator using your xtdpdgmm command?

Question 2) Regarding post #514 “Here, it seems that the only instruments specified for the level model are the time dummies. In this case, the difference-in-Hansen test for them is not meaningful. We cannot leave out the instruments for the time dummies. Because the time dummies are the only instruments for the level model, the Blundell-Bond assumption does not apply here.”.

Sorry, I did not get what you mean by that. I kindly ask you please to explain what you mean.

Question 3) Regarding post #520 point 1.1) “You would need to be more specific about which of these difference-in-Hansen tests you are refering to. Each row in the table is a separate test. For example, on page 96, the test in the row labelled "5, model(level)" is not very useful, because removing the instruments for the time dummies (while keeping the time dummies as regressors) does not make much sense and may result in serious weak-instruments problems or even underidentification.”.

Sorry for not being specific there. In all the tables of the difference-in-Hansen test on pages 96, 109, 113, and 123, the row labelled “5, model(level); 8, model(level); 8, model(level); 8, model(level)”, respectively. The respective labels for those rows of the test output are for the time dummies (according to the list of instruments below the regression output). Thus, does that mean the difference-in-Hansen test on pages 96, 109, 113, and 123 is not meaningful? Does that mean the Blundell-Bond assumption does not apply there in those tables on pages 96, 109, 113, and 123?

Your input is so valuable. The work you do is very important and so appreciated. I am very grateful to you for all your patience, help and effort, Professor!

[Sebastian Kripfganz]

Zainab Mariam

1.1) You would need to be more specific about which of these difference-in-Hansen tests you are refering to. Each row in the table is a separate test. For example, on page 96, the test in the row labelled "5, model(level)" is not very useful, because removing the instruments for the time dummies (while keeping the time dummies as regressors) does not make much sense and may result in serious weak-instruments problems or even underidentification.

1.2) I am not sure I understand the question. There is no such minimum number of variables.

2) Yes to all of them.

3) Yes to all of them.

4) The respective labels for the rows of the test output tell you which instruments are being tested; compare with the list of instruments below the regression output.

5.1) Not necessarily. A small estimate of the lagged dependent variable's coefficient might potentially be a consequence of a large bias of the difference GMM estimator if the true coefficient is close to 1. Thus, it is difficult to learn about potential problems of the estimator from actual coefficient estimates. You could again use the difference GMM estimator with additional nonlinear moment conditions, which is less prone to problems under high persistence. If that estimator yields a large estimate of the autoregressive coefficient, this might indicate potential problems of the difference GMM estimator (without such nonlinear moment conditions). And then you can also compare the two estimates; if they are very different, the estimator without the nonlinear moment conditions probably has problematic properties.

5.2) That's the typical application, yes.

5.3) Correct.

5.4) You can still check for correct variable classification with the system GMM estimator. (Essentially, everything you can do with the difference GMM estimator, you can also do with the system GMM estimator). However, this should generally be done first with the difference GMM estimator (ideally also using nonlinear moment conditions), to avoid contamination of the tests with a potential invalidity of the mean stationarity assumption.

5.5) That's the typical application, yes.

[Sebastian Kripfganz]

I specify my model in a static way (i.e., without including the lagged dependent variable as a regressor).

1. Can we still use the sys-GMM to estimate this static regression?
2. How should I justify the use of the sys-GMM to estimate this static regression? (i.e., is it more efficient or robust than the 2SLS regression?)
3. Do I still need to report the Arellano-Bond statistics?[/B]

1. Yes.
2. 2SLS is generally inefficient when using panel data. In any case, "2SLS" is not very informative; you would need to be clear about the instruments you are using. It then becomes a question of whether the instruments used in your sys-GMM estimator are beneficial compared to the instruments used in your 2SLS approach. In the first place, you would need to check whether they might require different assumptions for validity.
3. Reporting serial correlation tests is generally still useful even in static models. For once, they might tell you whether a dynamic model could be reasonable (to account for any serial correlation detected in the static model). If you have predetermined/endogenous variables, serial correlation can still invalidate the instruments in a static model.