[Sebastian Kripfganz]

The underid command with option sw should normally provide you detailed underidentification statistics separately for each regressor. Did you not get those additional statistics? These might tell you for which coefficient there could be an identification problem. Everything else looks good.

Regarding your interaction effect, I believe the categorical variable can take on values 0 or 1, which is why you see separate coefficients. Effectively, you are estimating separate effects for the regressor z when x=0 and when x=1. Your lag specification seems to be alright.

Notice that your example made me aware of a bug in xtdpdgmm that could occur when interaction effects are specified in the list of instruments. I just fixed this bug in a new version that is now available on my personal website. I will make a separate accouncement once it is available on SSC as well.

[Lin Liu]

the code is:
xtdpdgmm L(0/1).slackz munificence complex dynamics area L(0/1).logasset L(0/1).roa agef edu tenure sex agee L(0/1).offideputy offideputy#c.dynamics l.offdepdyn, model(fod) collapse gmm(slackz, lag(1 2)) gmm(munificence, lag(0 1)) gmm(complex, lag(0 1)) gmm(dynamics, lag(0 1)) gmm(area, lag(0 0)) gmm(logasset, lag(1 2)) gmm(roa, lag(1 2)) gmm(agef, lag(0 1)) gmm(edu, lag(0 1)) gmm(sex, lag(0 1) ) gmm (tenure, lag(0 2)) gmm(agee, lag(0 2)) gmm(offideputy, lag(1 2)) gmm(offideputy#c.dynamics, lag(1 2)) gmm(l.offdepdyn, lag(1 2)) gmm(area, lag(0 0) model(md)) gmm(edu, lag(0 0) model(md)) gmm(tenure, lag(0 0) model(md)) gmm( sex, lag(0 0) model(md)) gmm(agee, lag(0 0) model(md)) gmm(slackz, lag(1 1) diff model(level)) gmm(munificence, lag(0 0) diff model(level)) gmm(complex, lag(0 0) diff model(level)) gmm(dynamics, lag(0 0) diff model(level)) gmm(area, lag(0 0) model(level)) gmm( logasset, lag(1 1) diff model(level)) gmm( roa, lag(1 1) diff model(level)) gmm( agef, lag(0 0) diff model(level)) gmm(edu, lag(0 0) model(level)) gmm(tenure, lag(0 0) model(level)) gmm(sex, lag(0 0) model(level)) gmm(agee , lag(0 0) model(level)) gmm(offideputy, lag(1 1) diff model(level)) gmm(offideputy#c.dynamics, lag(1 1) diff model(level)) gmm(l.offdepdyn, lag(1 1) diff model(level)) teffects two vce(r) overid

. xtdpdgmm L(0/1).slackz munificence complex dynamics area L(0/1).logasset L(0/1).roa agef edu tenure sex agee L(0/1).offideputy off
> ideputy#c.dynamics l.offdepdyn, model(fod) collapse gmm(slackz, lag(1 2)) gmm(munificence, lag(0 1)) gmm(complex, lag(0 1)) gmm(dynamics,
> lag(0 1)) gmm(area, lag(0 0)) gmm(logasset, lag(1 2)) gmm(roa, lag(1 2)) gmm(agef, lag(0 1)) gmm(edu, lag(0 0)) gmm(sex, lag(0 0) ) gmm
> (tenure, lag(0 1)) gmm(agee, lag(0 0)) gmm(offideputy, lag(1 2)) gmm(offideputy#c.dynamics, lag(1 2)) gmm(l.offdepdyn, lag(1 2)) gmm(ar
> ea, lag(0 0) model(md)) gmm(edu, lag(0 0) model(md)) gmm( sex, lag(0 0) model(md)) gmm(agee, lag(0 0) model(md)) gmm(slackz, lag(1 1) di
> ff model(level)) gmm(munificence, lag(0 0) diff model(level)) gmm(complex, lag(0 0) diff model(level)) gmm(dynamics, lag(0 0) diff model(
> level)) gmm(area, lag(0 0) model(level)) gmm( logasset, lag(1 1) diff model(level)) gmm( roa, lag(1 1) diff model(level)) gmm( agef, lag(0
> 0) diff model(level)) gmm(edu, lag(0 0) model(level)) gmm(tenure, lag(0 0) diff model(level)) gmm(sex, lag(0 0) model(level)) gmm(ag
> ee , lag(0 0) model(level)) gmm(offideputy, lag(1 1) diff model(level)) gmm(offideputy#c.dynamics, lag(1 1) diff model(level)) gmm(l.offde
> pdyn, lag(1 1) diff model(level)) teffects two vce(r) overid

Generalized method of moments estimation

Fitting full model:
Step 1 f(b) = .14108884
Step 2 f(b) = .07800247

Fitting reduced model 1:
Step 1 f(b) = .06931099

Fitting reduced model 2:
Step 1 f(b) = .07393068

Fitting reduced model 3:
Step 1 f(b) = .06310125

Fitting reduced model 4:
Step 1 f(b) = .07321926

Fitting reduced model 5:
Step 1 f(b) = .07270806

Fitting reduced model 6:
Step 1 f(b) = .06987237

Fitting reduced model 7:
Step 1 f(b) = .07568086

Fitting reduced model 8:
Step 1 f(b) = .07403718

Fitting reduced model 9:
Step 1 f(b) = .07687095

Fitting reduced model 10:
Step 1 f(b) = .07797594

Fitting reduced model 11:
Step 1 f(b) = .0760236

Fitting reduced model 12:
Step 1 f(b) = .07650024

Fitting reduced model 13:
Step 1 f(b) = .06386569

Fitting reduced model 14:
Step 1 f(b) = .05940402

Fitting reduced model 15:
Step 1 f(b) = .05835987

Fitting reduced model 17:
Step 1 f(b) = .07747363

Fitting reduced model 18:
Step 1 f(b) = .07689592

Fitting reduced model 19:
Step 1 f(b) = .07786843

Fitting reduced model 20:
Step 1 f(b) = .07700053

Fitting reduced model 21:
Step 1 f(b) = .07756442

Fitting reduced model 22:
Step 1 f(b) = .07768246

Fitting reduced model 23:
Step 1 f(b) = .07510029

Fitting reduced model 24:
Step 1 f(b) = .07269038

Fitting reduced model 25:
Step 1 f(b) = .07419723

Fitting reduced model 26:
Step 1 f(b) = .07622391

Fitting reduced model 27:
Step 1 f(b) = .07449154

Fitting reduced model 28:
Step 1 f(b) = .07772974

Fitting reduced model 29:
Step 1 f(b) = .0779348

Fitting reduced model 30:
Step 1 f(b) = .07758183

Fitting reduced model 31:
Step 1 f(b) = .0778276

Fitting reduced model 32:
Step 1 f(b) = .07638032

Fitting reduced model 33:
Step 1 f(b) = .0748598

Fitting reduced model 34:
Step 1 f(b) = .06906946

Fitting reduced model 35:
Step 1 f(b) = .03915434

Fitting no-fodev model:
Step 1 f(b) = .00366136

Fitting no-mdev model:
Step 1 f(b) = .06417413

Fitting no-level model:
Step 1 f(b) = .0051203

Group variable: code Number of obs = 1142
Time variable: year Number of groups = 257

Moment conditions: linear = 53 Obs per group: min = 1
nonlinear = 0 avg = 4.44358
total = 53 max = 8

(Std. Err. adjusted for 257 clusters in code)
---------------------------------------------------------------------------------------
| WC-Robust
slackz | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------------+----------------------------------------------------------------
slackz |
L1. | .6218488 .1162067 5.35 0.000 .3940878 .8496098
|
munificence | -.5325147 .7724321 -0.69 0.491 -2.046454 .9814244
complex | -.0403757 .0504071 -0.80 0.423 -.1391718 .0584204
dynamics | 40.72416 82.48774 0.49 0.622 -120.9488 202.3972
area | -.0198439 .2075736 -0.10 0.924 -.4266807 .3869929
|
logasset |
--. | 7.187291 2.761494 2.60 0.009 1.774863 12.59972
L1. | -8.387227 2.801426 -2.99 0.003 -13.87792 -2.896532
|
roa |
--. | -12.11013 6.602533 -1.83 0.067 -25.05085 .8306018
L1. | 6.410398 3.543641 1.81 0.070 -.5350101 13.35581
|
agef | .0583749 .071612 0.82 0.415 -.081982 .1987318
edu | -.0153277 .0769506 -0.20 0.842 -.166148 .1354927
tenure | .0047294 .0374123 0.13 0.899 -.0685974 .0780563
sex | .1996495 .5115984 0.39 0.696 -.8030648 1.202364
agee | .0017578 .0117589 0.15 0.881 -.0212892 .0248048
|
offideputy |
--. | 2.883827 3.854386 0.75 0.454 -4.670631 10.43828
L1. | -2.295162 4.993454 -0.46 0.646 -12.08215 7.491829
|
offideputy#c.dynamics |
1 | -4.082514 195.2103 -0.02 0.983 -386.6876 378.5226
|
offdepdyn |
L1. | -108.3813 231.286 -0.47 0.639 -561.6936 344.931
|
year |
2005 | .3675995 .2461982 1.49 0.135 -.11494 .8501391
2006 | .3671839 .2881837 1.27 0.203 -.1976459 .9320137
2007 | .3655254 .3181113 1.15 0.251 -.2579614 .9890121
2008 | .8464342 .3709715 2.28 0.023 .1193434 1.573525
2009 | .6938291 .3699682 1.88 0.061 -.0312953 1.418953
2010 | .9986676 .3978988 2.51 0.012 .2188003 1.778535
2011 | .8558787 .4232351 2.02 0.043 .0263531 1.685404
|
_cons | 8.629229 3.865083 2.23 0.026 1.053805 16.20465
---------------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(fodev):
L1.slackz L2.slackz
2, model(fodev):
munificence L1.munificence
3, model(fodev):
complex L1.complex
4, model(fodev):
dynamics L1.dynamics
5, model(fodev):
area
6, model(fodev):
L1.logasset L2.logasset
7, model(fodev):
L1.roa L2.roa
8, model(fodev):
agef
9, model(fodev):
edu
10, model(fodev):
sex
11, model(fodev):
tenure L1.tenure
12, model(fodev):
agee
13, model(fodev):
L1.offideputy L2.offideputy
14, model(fodev):
L2.0b.offideputy#c.dynamics L1.1.offideputy#c.dynamics
L2.1.offideputy#c.dynamics
15, model(fodev):
L1.L.offdepdyn L2.L.offdepdyn
17, model(mdev):
edu
18, model(mdev):
sex
19, model(mdev):
agee
20, model(level):
L1.D.slackz
21, model(level):
D.munificence
22, model(level):
D.complex
23, model(level):
D.dynamics
24, model(level):
area
25, model(level):
L1.D.logasset
26, model(level):
L1.D.roa
27, model(level):
D.agef
28, model(level):
edu
29, model(level):
D.tenure
30, model(level):
sex
31, model(level):
agee
32, model(level):
L1.D.offideputy
33, model(level):
L1.D.0b.offideputy#c.dynamics L1.D.1.offideputy#c.dynamics
34, model(level):
L1.D.L.offdepdyn
35, model(level):
2005bn.year 2006.year 2007.year 2008.year 2009.year 2010.year 2011.year
36, model(level):
_cons

. estat serial, ar(1/3)

Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1: z = -2.8390 Prob > |z| = 0.0045
H0: no autocorrelation of order 2: z = -0.5382 Prob > |z| = 0.5905
H0: no autocorrelation of order 3: z = 0.4724 Prob > |z| = 0.6366

.
. estat overid

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

2-step moment functions, 2-step weighting matrix chi2(27) = 20.0466
Prob > chi2 = 0.8288

2-step moment functions, 3-step weighting matrix chi2(27) = 32.1757
Prob > chi2 = 0.2256

.
. 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(fodev) | 17.8129 25 0.8502 | 2.2337 2 0.3273
2, model(fodev) | 19.0002 25 0.7971 | 1.0464 2 0.5926
3, model(fodev) | 16.2170 25 0.9082 | 3.8296 2 0.1474
4, model(fodev) | 18.8173 25 0.8058 | 1.2293 2 0.5408
5, model(fodev) | 18.6860 26 0.8494 | 1.3607 1 0.2434
6, model(fodev) | 17.9572 25 0.8442 | 2.0894 2 0.3518
7, model(fodev) | 19.4500 25 0.7750 | 0.5967 2 0.7421
8, model(fodev) | 19.0276 26 0.8353 | 1.0191 1 0.3127
9, model(fodev) | 19.7558 26 0.8030 | 0.2908 1 0.5897
10, model(fodev) | 20.0398 26 0.7897 | 0.0068 1 0.9342
11, model(fodev) | 19.5381 25 0.7706 | 0.5086 2 0.7755
12, model(fodev) | 19.6606 26 0.8074 | 0.3861 1 0.5344
13, model(fodev) | 16.4135 25 0.9020 | 3.6332 2 0.1626
14, model(fodev) | 15.2668 24 0.9127 | 4.7798 3 0.1886
15, model(fodev) | 14.9985 25 0.9414 | 5.0481 2 0.0801
17, model(mdev) | 19.9107 26 0.7958 | 0.1359 1 0.7124
18, model(mdev) | 19.7623 26 0.8027 | 0.2844 1 0.5938
19, model(mdev) | 20.0122 26 0.7910 | 0.0344 1 0.8528
20, model(level) | 19.7891 26 0.8014 | 0.2575 1 0.6118
21, model(level) | 19.9341 26 0.7947 | 0.1126 1 0.7372
22, model(level) | 19.9644 26 0.7932 | 0.0822 1 0.7743
23, model(level) | 19.3008 26 0.8235 | 0.7459 1 0.3878
24, model(level) | 18.6814 26 0.8496 | 1.3652 1 0.2426
25, model(level) | 19.0687 26 0.8335 | 0.9779 1 0.3227
26, model(level) | 19.5895 26 0.8106 | 0.4571 1 0.4990
27, model(level) | 19.1443 26 0.8303 | 0.9023 1 0.3422
28, model(level) | 19.9765 26 0.7927 | 0.0701 1 0.7912
29, model(level) | 20.0292 26 0.7902 | 0.0174 1 0.8951
30, model(level) | 19.9385 26 0.7945 | 0.1081 1 0.7423
31, model(level) | 20.0017 26 0.7915 | 0.0449 1 0.8321
32, model(level) | 19.6297 26 0.8088 | 0.4169 1 0.5185
33, model(level) | 19.2390 25 0.7855 | 0.8077 2 0.6678
34, model(level) | 17.7509 26 0.8846 | 2.2958 1 0.1297
35, model(level) | 10.0627 20 0.9670 | 9.9840 7 0.1895
model(fodev) | 0.9410 1 0.3320 | 19.1057 26 0.8319
model(mdev) | 16.4928 24 0.8695 | 3.5539 3 0.3138
model(level) | 1.3159 4 0.8587 | 18.7307 23 0.7167

.
. underid, overid underid kp sw noreport

collinearity check...
collinearities detected in [Y X] (right to left): 0o.offideputy#co.dynamics
collinearities detected in [Y X Z] (right to left): __alliv_52 __alliv_51 __alliv_50 __alliv_49 __alliv_48 __alliv_47 __alliv_46 __alliv_41
> __alliv_40 __alliv_38 __alliv_34 0o.offideputy#co.dynamics
collinearities detected in [X Z Y] (right to left): 2011.year 2010.year 2009.year 2008.year 2007.year 2006.year 2005bn.year 0o.offideputy#co
> .dynamics agee sex edu area
warning: collinearities detected, reparameterization may be advisable

Overidentification test: Kleibergen-Paap robust LIML-based (LM version)
Test statistic robust to heteroskedasticity and clustering on code
j= 16.32 Chi-sq( 26) p-value=0.9283

Underidentification test: Kleibergen-Paap robust LIML-based (LM version)
Test statistic robust to heteroskedasticity and clustering on code
j= 34.95 Chi-sq( 27) p-value=0.1400

what's wrong with it? Another question: when the lag of one categorical variable times the lag of another continuous varible, the code is l.x#cl.z(x is categorial, z is continuous), the outcome has two lines of results, line 0 and line 1. What's the meaning? How do I specify the lag of one categorical variable times the lag of another continuous variable?

[Sebastian Kripfganz]

To provide further help, I would need to see your command lines and Stata output (with CODE delimiters) following the advice in the Statalist FAQs?

[Lin Liu]

Thanks. I have some other doubts. Among the serial correlation test, overidentification test, incremental overidentification test, and underidentification test, the former three tests are very easy to pass, however, the underidentification test is very difficult to （even always not）pass,why? What's more，changing the order of the lag of the instruments will lead to largely vary in the underidentification test, but not vary in the former three tests,why?

[Sebastian Kripfganz]

Hello,why the serial correlation test and the overidentificaton test are easy to pass, while the underidentification test is difficult to pass? What are main possible resons?

Notice that for the underidentification test the null hypothesis is that the model is indeed underidentified. Therefore, you actually want to reject the null hypothesis.
For the overidentification test, the null hypothesis is that the model is correctly specified. Therefore, here you do not want to reject the null hypothesis.

If the model is underidentified, then the overidentification tests may not be very reliable because they rely on the maintained assumption that there are at least as many valid instruments available as is needed to identify all coefficients.

[Lin Liu]

Hello,why the serial correlation test and the overidentificaton test are easy to pass, while the underidentification test is difficult to pass? What are main possible resons?

[Tugrul Cinar]

Thank you for your quick reply. I havent think of using an interaction term. That was an enlightening advice.

[Sebastian Kripfganz]

It is correct that xtdpdgmm does not do anything to specifically address cross-sectional dependence. Time dummies can account for cross-sectional dependence due to common shocks assuming homogeneity of the effects of these shocks across units. Any other variables that are constant across units but vary over time become redundant in the presence of time dummies, unless you create interaction terms of these common-shock variables with variables that vary across units. The latter could be away to approximate heterogenous effects of common shocks conditional on observed variables. Obviously, all of this is more restrictive than other approaches for large-N, large-T panel models with common factors / interactive fixed effects, but xtdpdgmm is primarily intended for small-T data.

[Tugrul Cinar]

Dear Sebastian,

I am using xtdpdgmm for my research. As far as i know xtdpdgmm (and gmm estimation in general) does not account for cross sectional dependency.

My data (maybe most of the panel data) suffers from cross sectional dependency and i tried to use extra variables to capture time varying common factors across cross sections to eliminate this problem. But later i realised that we are already using time dummies as regressors with the teffects option (or manually). Since (strong) cross-sectional dependence arise from time varying common shocks, aren't we eliminating it by adding year dummies as regressors? Will any other extra variables to capture time varying common shocks other than time dummies be redundant in this occasion?

Thanks in advance.

[Sebastian Kripfganz]

There is another update of the xtdpdgmm package to version 2.3.0 available on my personal website.

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

This version fixes the problem reported in #221 above, and it adds a new feature for the estimation with nonlinear moment conditions:

Under the assumption of a serially uncorrelated idiosyncratic error term \(u_{it}\), the option nl(noserial) incorporates the following nonlinear moment conditions:
\[E[(\alpha_i+u_{iT}) \Delta u_{it}] = 0\]
for t=1,2,...,T-1.

So far, that is nothing new (see slide 58 of my 2019 London Stata Conference presentation). If we suspect first-order serial correlation of \(u_{it}\), we could still obtain valid nonlinear moment conditions by restricting them to the observations t=1,2,...,T-2. If there is second-order serial correlation, change the upper limit to T-3. This can be achieved with a new lag() suboption, e.g. when we suspect first-order serial correlation we could specify

nl(noserial, lag(2))

When you just specify nl(noserial) without the suboption, the default is lag(1), i.e. no serial correlation. I am grateful to Professor Seung Ahn for proposing this additional feature.

[Sebastian Kripfganz]

As enquired here: https://www.statalist.org/forums/for...2-and-xtdpdgmm, I wonder why I cannot use the estat serial command after xtdpdgmm. I get an error: (r5), not sorted. Would really appreciate if someone could guide me on this and the other question in that post. Thank you.

Please see my response #2 in the topic you have linked.

[Sebastian Kripfganz]

Kristian Szakali
Could you please check whether you have the latest version of xtdpdgmm, which should be 2.2.7. If you do not have the latest version, please update it and try your code again:

adoupdate xtdpdgmm, update

If you still get the same error message with the latest version, would it be possible for you to send me your data set per e-mail? Otherwise it is difficult to replicate the issue.

[Kristian Szakali]

As enquired here: https://www.statalist.org/forums/for...2-and-xtdpdgmm, I wonder why I cannot use the estat serial command after xtdpdgmm. I get an error: (r5), not sorted. Would really appreciate if someone could guide me on this and the other question in that post. Thank you.

[Sebastian Kripfganz]

1. If anything, then only the moment conditions number 7 might be slightly worrying. All the other p-values are definitely fine. A system GMM estimator would produce more efficient / more precise estimates than a difference GMM estimator, at the added risk that it might be stronger biased if the extra instruments are weak or invalid.
2. To check for serial correlation, use the estat serial postestimation command. Out of the top of my head, I am not aware of an easily applicable command for heteroskedasticity testing of the residuals. The only feasible option that comes to my mind is utilizing the nonlinear moment conditions nl(noserial) and nl(iid), where the latter make the additional homoskedasticity assumption, and then to use a generalized Hausman test with estat hausman to test the additional moment restrictions imposed by nl(iid) compared to nl(noserial). See slides 63 to 65 of my 2019 London Stata Conference presentation.
3. You can simply use the test command as you would do after any other estimation command.

[Prateek Bedi]

Dear Prof. Kripfganz,

Your responses are enlightening as always! I got to know some completely new things which I never thought of. Thank you so very much! I have some follow-up queries:

1.I have the following output for the difference-in-Hansen test for my model. Do you think I should stick to system-GMM or switch to difference-GMM?

2-step weighting matrix from full model

                  | Excluding                   | Difference                  
Moment conditions |       chi2     df         p |        chi2     df         p
------------------+-----------------------------+-----------------------------
  1, model(fodev) |    94.4909    106    0.7808 |      0.0107      1    0.9175
  2, model(fodev) |    94.2920    106    0.7851 |      0.2096      1    0.6471
  3, model(fodev) |    94.4466    106    0.7817 |      0.0550      1    0.8146
  4, model(fodev) |    93.8516    104    0.7522 |      0.6500      3    0.8849
  5, model(fodev) |     0.5946      2    0.7428 |     93.9070    105    0.7727
  6, model(fodev) |    94.2131    105    0.7658 |      0.2885      2    0.8657
  7, model(level) |    92.4271    106    0.8235 |      2.0745      1    0.1498
  8, model(fodev) |    94.1725    106    0.7877 |      0.3291      1    0.5662
  9, model(fodev) |    94.4090    106    0.7826 |      0.0926      1    0.7610
 10, model(level) |    83.8859     93    0.7396 |     10.6156     14    0.7159

Moreover, are there any issues if we apply system-GMM estimator when difference-GMM estimator is sufficient for a model?

2. How should we check for heteroscedasticity and serial correlation for our model?

3. How do we check for joint significance tests for multiple coefficients in our model?

Thank you!