[Taka Sakamoto]

3. How many cross-sections is desirable? Also, when researchers find that their cross-sections are too small, what other estimation do they apply?

Thank you again.

Taka

[Taka Sakamoto]

Thank you so much for your response and explanation. May I ask two questions?

1. Re: iv():
What should determine the use of iv() and whether to use difference or level in it? Also, iv() doesn't always have to be used and specified?

2. Re: how different are two step and one step and what should determine which to use?

Thank you your generous and kind help.

Taka

[Sebastian Kripfganz]

1. I cannot see any obvious problem with your specification. However, it is of some concern that you only have 20 groups. It is difficult to obtain reliable results with such a small cross-sectional sample size. If you nevertheless want to do a GMM estimation, you might want to stick to the one-step estimator, which does not require estimation of the optimal weighting matrix. The one-step estimator will be asymptotically inefficient, but with N=20 you are very far away from asymptopia anyway.

2. If your dummy variable varies over time, then you can in principle leave everything as it is. However, there is some risk that lags and/or first differences of dummy variables can be weak instruments. If the dummy variable is time invariant, then you can obviously not first difference it. You might then have to adopt the assumption that this variable is uncorrelated with both the idiosyncratic and the group-specific error component, which might or might not be acceptable, depending on your research question. In this case, you could include the dummy variable without the difference option for the level model.

3. The main concern is about the sample size; see point 1.

[Taka Sakamoto]

Dear Professor Kripfganz:

I would like to ask you to teach me how to apply your xtdpdgmm correctly. I thank you in advance for your kind help. I would like to implement a system-GMM model like the following:

xtdpdgmm lpgrow smei3 labutilpcgr mfppwt rknapcgr hfcegrow l.lrgdpopc if id~=13,gmm(lpgrow  labutilpcgr mfppwt rknapcgr hfcegrow lrgdpopc, lag(2 2) collapse model(diff)) gmm(lpgrow labutilpcgr mfppwt  rknapcgr hfcegrow lrgdpopc, lag(1 1) diff collapse model(level)) iv(smei3,diff model(level)) two vce(cl id) small

And I get the results like this:

. xtdpdgmm lpgrow smei3 labutilpcgr mfppwt rknapcgr hfcegrow l.lrgdpopc if id~=13,gmm(lpgrow  labutilpcgr mfppwt rknap
> cgr hfcegrow lrgdpopc, lag(2 2) collapse model(diff)) gmm(lpgrow labutilpcgr mfppwt  rknapcgr hfcegrow lrgdpopc, lag
> (1 1) diff collapse model(level)) iv(smei3,d model(level)) two vce(cl id) small

Generalized method of moments estimation

Fitting full model:
Step 1         f(b) =    .162683
Step 2         f(b) =  .16926059

Group variable: id                           Number of obs         =       514
Time variable: year                          Number of groups      =        20

Moment conditions:     linear =      14      Obs per group:    min =        12
                    nonlinear =       0                        avg =      25.7
                        total =      14                        max =        28

                                    (Std. err. adjusted for 20 clusters in id)
------------------------------------------------------------------------------
             |              WC-Robust
      lpgrow | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       smei3 |   .0991957    .057027     1.74   0.098    -.0201631    .2185545
 labutilpcgr |  -.3546281   .1410527    -2.51   0.021    -.6498549   -.0594013
      mfppwt |   .6901644   .0872634     7.91   0.000     .5075199    .8728089
    rknapcgr |   .1629855   .0893485     1.82   0.084     -.024023    .3499939
    hfcegrow |   .0271975   .0837204     0.32   0.749    -.1480314    .2024264
             |
    lrgdpopc |
         L1. |  -.7435579   .2764233    -2.69   0.015    -1.322118   -.1649973
             |
       _cons |   8.620034   3.041985     2.83   0.011     2.253086    14.98698
------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(diff):
   L2.lpgrow L2.labutilpcgr L2.mfppwt L2.rknapcgr L2.hfcegrow L2.lrgdpopc
 2, model(level):
   L1.D.lpgrow L1.D.labutilpcgr L1.D.mfppwt L1.D.rknapcgr L1.D.hfcegrow
   L1.D.lrgdpopc
 3, model(level):
   D.smei3
 4, model(level):
   _cons

1. Am I specifying the instrumentation correctly? I'm particularly not confident about specifying the lags in level and difference equations. I would like to make sure I'm doing the right thing.

2. What if I replace the first independent variable "smei3" with "sme" which is a dummy variable? Do I need to change anything inside "iv()"? A difference of a dummy variable is obviously wrong.

3. Is there anything that you notice I'm doing wrong? I would appreciate any suggestion.

Thank you for your generous help.

Best wishes,

Taka

If the results are hard to see, here is a picture that shows the results.

Doc14.docx

[Sebastian Kripfganz]

I would not focus too much on these specific thresholds. Roodman (2009) correctly emphasizes that very large p-values (in extreme situations virtually 1.000) are often an indication of first-stage overfitting - i.e., using too many instruments relative to the sample size. Given your relatively large cross-sectional dimension and moderate time dimension, this should not be a concern in your case. We also should not "accept" the specification right away when the p-value barely exceeds the conventional significance level (say, 5%) because the consequence of incorrectly "accepting" a specification (type-II error) is usually more severe than that of incorrectly rejecting a specification (type-I error).

If you compare the two 2009 papers by Roodman in the Stata Journal and the Oxford Bulletin of Economics and Statistics, they are actually contradicting each other regarding the 0.25 threshold. The Stata Journal article suggests to view values higher than 0.25 as potential signs of concern, while the Oxford Bulletin article recommends that p-values "as high as" (i.e., all p-values lower than) 0.25 as signs of concern. My take: Forget about strict threshold values.

[Neyati Ahuja]

Thank you sir
Actually my doubt was in reference to Roodman (2009) which states p value of sargan hansen test shoul be from 0.10 to 0.25.

[Sebastian Kripfganz]

I am not sure what exactly your question is. The reported p-values for the Hansen test look all fine, and so does the AR(2) test.

[Neyati Ahuja]

Dear Prof. Sebastian

I have a balanced panel dataset of 1,400 MNEs for over 10 years from 2010-20.
My model is dynamic and have also introduced lag of dependant variable as explanatory variable. For the empirical analysis I used System GMM (through xtdpdgmm).

I have a query regarding the post estimation test:

In respect of Sargan Hansen 2 step test few of the p value obtained are 0.52, 0.67, 0.35, 0.48 and so on for different models designed.
No. of moment condition linear range from 25, 27, 35 and so on.

AR(2) Arellano Bond p value is greater that 0.10 around 0.25, 0.27,0.30.

I wanted to check regarding my Sargan Hansen test result. I have read few research articles that report similar p-value for the Sargan Hansen Test.

Thank You.

[Sebastian Kripfganz]

An R-squared is not very meaningful for dynamic panel models with endogenous regressors (or, more generally, any IV/2SLS/GMM estimator); see the following Stata FAQ for context: https://www.stata.com/support/faqs/s...least-squares/

The xtdpdgmm postestimation command estat mmsc provides some criteria that allow you to compare the fit across models (similar to the conventional AIC/BIC criteria).

[Mugi Jang]

Dear Professor Sebastian,
how can we get the
Goodness of fit Panel Data ?
especially for dynamic model?
here is some code some one suggested
xtreg y x, fe i(unit)
add the following lines of code
egen ybar = mean(y) gen y2 = (y - ybar)^2 predict resid, e gen e2 = resid^2 drop resid egen sse = sum(e2) egen sst = sum(y2) gen r2 = 1 - sse/sst sum r2

[Sebastian Kripfganz]

1) Yes.

2) No; the Chudik-Pesaran estimator does not allow for endogenous regressors.

3) initdev is a necessary option for the Chudik-Pesaran estimator.

4) Hayakawa, Qi, and Breitung (2019) do not consider a level model for their estimator. xtdpdgmmfe does not have a nolevel option (only xtdpdgmm does); it automatically decides whether to include instruments for the level model or not, based on the other options specified. If you execute the xtdpdgmmfe command for this estimator, you will see that the nolevel option has been set for the implied xtdpdgmm command line.

5) There is unfortunately no clear guidance about that. As mentioned earlier, with large enough N, it should not matter too much. Personally, I find some value in the vicinity of 4 quite reliable.

6) My personal opinion is that lagging of the regressors is overused in empirical research. If you think that there is indeed no contemporaneous effect, but any effect take some time (1 period) to materialize, then sure: go for it. If it is reasonable to assume that there is a contemporaneous effect, but you lag the variable because of endogeneity concerns, then most likely as a result your model is misspecified. You can then debate whether the resulting misspecification is a smaller or larger problem than the original endogeneity problem. Personally, I think lagging of the regressors often does more harm than good. Endogeneity in the context of GMM should normally be dealt with by using lagged instruments, not lagged regressors.

7) In the light of point 6), in a misspecified model it is very much unclear what happens. The omitted contemporaneous regressors essentially create an omitted-variables bias, which cannot normally be dealt with by using lagged instruments in the usual way. In short, there is no general answer to this question.

8) Again, under model misspecification there is no general answer. You would first need to decide what the assumed timing of the effects is. This gives you the lag structure. Then, again based on economic theory, you can decide whether these variables are endogenous or predetermined. If there is a good theoretical justification for lagging (due to delayed effects), then it is often also easier to assume that those lagged regressors are at least predetermined and not endogenous, because endogeneity would require some kind of anticipation effects (which might still be reasonable depending on the context). In any case, the decision should always be made on economic theory, not a technical argument based on lag orders.

9) Effectively, lags of the dependent variable are predetermined if there is no assumed serial error correlation. If you specify lags with the lags() option, xtdpdgmmfe does this classification automatically for you.

[Zainab Mariam]

Dear Professor Sebastian,

Thank you very much for your swift useful reply. I am very grateful to you for all your support and effort, Professor! If I may follow up with your response, please!

1) Regarding your post #561 point 8) “A variable is classified as endogenous if it is allowed to be correlated with the contemporaneous error term (and all lagged errors). If this is true for L1.x, then L2.x could possibly still be classified as exogenous. L1.x being endogenous means that any show in the current period is anticipated by x in the previous period (because x is lagged). You would then still need to decide, if this shock can even be anticipated by x two periods ahead. It is up to you to make this judgement.…”.

I think you meant endogenous instead of exogenous.

2) Regarding your post #561 point 1.1.A) “… The Chudik-Pesaran estimator does not allow for endogenous regressors! What you get in this case is a first-difference GMM estimator (like Arellano-Bond, but with first-differenced instruments instead of level instruments for the first-differenced model). ...”. And regarding your post #479 point 10) “… the Chudik-Pesaran estimator requires all variables to be either strictly exogenous or predetermined. xtdpdgmmfe "solves" this issue by switching to a specific version of a difference GMM estimator when endogenous variables are present.”. And regarding your post #481 point 2.1) “xtdpdgmmfe automatically selects the appropriate instruments / moment conditions (and therefore the relevant estimator) corresponding to the chosen assumptions.”.

Thus, to check my understanding, the Chudik-Pesaran (2022) estimator can be applied for unbalanced dynamic panel data with at least one endogenous regressor just by using your xtdpdgmmfe command. Am I right?

3) Is it right or wrong not to include the initdev option in the code of the Chudik-Pesaran (2022) estimator?

4) Regarding your post #561 point 6.4.A) “As argued above, you should not include time-invariant dummy variables when there is no level model. …”.

Thus, my question is: How to have a level model when applying Hayakawa, Qi, and Breitung (2019) estimator using your xtdpdgmmfe command? (the code does not include the option nolevel).

5) How to decide the number I should specify in the curtail() option?

6) I read in some research that it is a good idea to lag all explanatory variables one period for endogeneity concerns. Thus, what is your opinion on this idea?

7) If one of the explanatory variables is endogenous, and some of the explanatory variables are predetermined. Then, if all these explanatory variables are lagged one period. Thus, my question is: Does the classification of those lagged explanatory variables still endogenous and predetermined, respectively? Or does the classification of those lagged explanatory variables become predetermined and exogenous, respectively? i.e., Does lagging the variables transform their classification or does lagging the variables have no effect on the variables' classification?

8) Also, I read in some research that when all variables on the right-hand side of the regression model are lagged one-time period, hence, they are assumed to be predetermined rather than endogenous.
Thus, what is your opinion on this idea?

9) When using your command xtdpdgmmfe, should all lags of the dependent variable y be considered predetermined? Can I consider the deep lags of the dependent variable (i.e., L2.y and deeper lags) exogenous?

Even though I may not say it all the time, I do appreciate all that you do, Professor! Much obliged!

[Sebastian Kripfganz]

Mugi Jang

The coefficient estimates in column (3) of Table 4 in Blundell and Bond (1998, Journal of Econometrics) can indeed be replicated with the code you provided. Note that this is a one-step GMM estimator. The "Sargan" test statistic reported in that table is actually not the one-step Sargan test but the two-step Hansen test statistic. To see this, re-estimate the model with xtdpdgmm using the twostep option.

The fact that xtabond2 reports the two-step Hansen test after a one-step estimation is somewhat confusing (even though it follows the appropriate logic that the one-step Hansen test is asymptotically invalid and therefore the two-step Hansen test should be used; but then again the two-step estimator should probably be used in the first place).

[Sebastian Kripfganz]

Zainab Mariam

1.1.A) xtdpdgmmfe has a lags() option, which allows you to directly specify the number of lags of the dependent variable used as regressors. Thus, use option lags(2) and remove L2.y from the list of regressors and the list of predetermined variables. The Chudik-Pesaran estimator does not allow for endogenous regressors! What you get in this case is a first-difference GMM estimator (like Arellano-Bond, but with first-differenced instruments instead of level instruments for the first-differenced model). If your industry dummies and country dummies are time invariant, then you cannot/should not/need not include them in this specification; the unobserved fixed effects (i.e. first-differencing of the model) take care of them.
1.1.B) As before.

1.2) You would need to classify all variables as either exogenous or predetermined in order to use the Chudik-Pesaran estimator.

1.3) Yes; this classification is always your responsibility.

2.1) Yes, but as indicated above these dummies (if time invariant) should really only be included when some instruments refer to the untransformed level model. This is not the case for the Chudik-Pesaran estimator.

2.2) The xtdpdgmmfe command does not offer special treatment for dummy variables; they are treated the same way as any other variable. As the suffix fe of the command suggests, this command takes a fixed-effects approach; this means that coefficients of time-invariant variables cannot be identified. For a more flexible approach, you would need to use the main xtdpdgmm command, but xtdpdgmmfe might give you an idea about how to specify the xtdpdgmm command.

2.3) See 2.2.; whether differenced or level instruments are used depends on other options. In particular, option initdev requires differenced instruments. As always, you can see the full list of instruments and their transformations in the list below the regression output.

3) I do not understand this question.

4) Use option orthogonal.

5) Yes.

6.1) I am not sure I understand this question. xtdpdgmmfe is just a wrapper for xtdpdgmm. Based on your input, xtdpdgmmfe constructs the more complicated command line for xtdpdgmm (which is also displayed above the regression output) and then executes the latter.

6.2) Yes; this is a disadvantage of this estimator.

6.3) No; you can only specify the curtail() option once. If you would like to curtail lag orders differently for different sets of instruments, you would need to use the more flexible xtdpdgmm command.

6.4.A) As argued above, you should not include time-invariant dummy variables when there is no level model. Also, use the lags() option instead of specifying the lags of the dependent variable manually. Endogenous variables can be used here.

6.4.B) As mentioned in 6.3), you cannot include the curtail() option multiple times.

6.5) See 6.4) and 6.3).

7) Whether to transform a variable into natural logs has nothing to do with its classification as endogenous or predetermined.

8) A variable is classified as endogenous if it is allowed to be correlated with the contemporaneous error term (and all lagged errors). If this is true for L1.x, then L2.x could possibly still be classified as exogenous. L1.x being endogenous means that any show in the current period is anticipated by x in the previous period (because x is lagged). You would then still need to decide, if this shock can even be anticipated by x two periods ahead. It is up to you to make this judgement.

[Mugi Jang]

Dear Professor Sebastian,
I hope you're doing well!
with using ab.dta I am replicating the results of Blundell-Bond (1998), Table 4, col. III and IV by xtabond2 and xtdpdgmm

xtabond2 n l.n l(0/1).(w k) yr1978-yr1984, iv(yr1978-yr1984, eq(diff)) gmm(n w k, lag(2 .) eq(diff)) noleveleq h(2) robust


1. I got the following output

some output is dropped

Sargan test of overid. restrictions: chi2(79) = 125.19 Prob > chi2 = 0.001
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(79) = 88.80 Prob > chi2 = 0.211
(Robust, but weakened by many instruments.)

and

xtdpdgmm n l.n l(0/1).(w k) yr1978-yr1984, iv(yr1978-yr1984, model(diff) diff) gmmiv(n w k, lag(2 .) model(diff)) nolevel vce(r) w(ind) overid
estat overid

2. I got the following output

some output is dropped

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

1-step moment functions, 1-step weighting matrix chi2(79) = 125.1925
note: * Prob > chi2 = 0.0007

1-step moment functions, 2-step weighting matrix chi2(79) = 103.4848
note: * Prob > chi2 = 0.0337

* asymptotically invalid if the one-step weighting matrix is not optimal

Here is my question
xtabond2's Sargan test statistic ,chi2(79) = 125.19, matches to xtdpdgmm's 1-step weighting matrix chi2(79) = 125.1925
but xtabond2's hansen test statistic,chi2(79) = 88.80 , does not appear in xtdpdgmm's result
As I understand, under heteroscadasticity hansen test holds and sagan test only under homoscadasticity.
and xtabond2's hansen test statistic,chi2(79) = 88.80 corresponds to that of the paper

then how can I get the hansen test statistic chi2(79) = 88.80 with xtdpdgmm?

Always Thanks lot!