XTABOND2 and unit root test and measure of structural break

[Sabyasachi Tripathi]

Dear Professors,
I am using xtabond2 for my research (System GMM)
My questions are the following;
1. Do I need to test unitroot of the regression variables (dependent+independent variables)
If I test and found that there is unitroot then how can I use variables (i.e., which form) for the analysis.
2. One reviewer suggested me to do structural break test. Then how do I do structural break analysis. If I find there is a structural break then how do I run the model using xtabond2 stata command.

Please help me.

[Sebastian Kripfganz]

The system GMM estimator is usually used for models with a large number of cross-sectional units and a relatively small number of time periods. For such data sets, there is generally no unit-root testing necessary and also hardly possible.

Structural breaks tests for panel data models are not yet well established. If you have a known date at which you suspect the break, you could add dummy variables and their interactions with the other regressors to the model, and then check the significance of the respective coefficients.

More on GMM estimation of linear dynamic panel data models:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.
• XTDPDGMM: new Stata command for GMM estimation of linear (dynamic) panel data models

[Sabyasachi Tripathi]

Dear Prof. Kripfganz

Many Thanks for your kind reply. I have T= 59 and N (no. of countries) =5. Some variables are stationary at level and some of them at first difference and second difference.
In this case what econometrics model I can use. Do you think difference GMM model can be used. I need some model which takes care of endogenity problem and other basic tests.

Thanking you, I am grateful you.

[Sebastian Kripfganz]

I would just use an instrumental variables estimator, for example with ivreg2. This command also provides useful specification tests. Note that with N=5 you should not cluster by country, which is usually done when you employ the familiar panel data GMM estimators.

[Shrimoyee Ganguly]

Respected Professors,
I also have few variables in my data set of 105 countries and 15 years, which are stationary at first difference. But if I insert them in level form in my xtabond2 command, I have noticed in xtanbond2, at the very bottom, the first difference of the exogenous variables and endogenous variables (highlighted in red) are already taken as instruments. So does this take care of the stationarity issue? Or do I have to insert those specific variables as d.var when I write the xtabond2 command? My results worsen drastically if I do that though.
Thanks in advance.

xtabond2 exqua100 l.exqua100 koftrgi infra popusharworld finp comtot mehi reer landlockdum, gmm(l.exqua100 reer comtot mehi, collapse) iv(koftrgi infra popusharworld finp landlockdum) twostep robust artest(2)
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate optimal weighting matrix for two-step estimation.
Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: countrycode Number of obs = 1295
Time variable : year Number of groups = 99
Number of instruments = 65 Obs per group: min = 4
Wald chi2(9) = 118334.27 avg = 13.08
Prob > chi2 = 0.000 max = 14
-------------------------------------------------------------------------------
| Corrected
exqua100 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
exqua100 |
L1. | .5412325 .0288996 18.73 0.000 .4845904 .5978746
|
koftrgi | .1464361 .0239387 6.12 0.000 .0995172 .1933551
infra | 1.38371 .5263381 2.63 0.009 .3521059 2.415313
popusharworld | .1130161 .0631672 1.79 0.074 -.0107895 .2368216
finp | -.0438615 .0405327 -1.08 0.279 -.1233042 .0355813
comtot | 33.50742 7.601673 4.41 0.000 18.60842 48.40643
mehi | .020946 .0361958 0.58 0.563 -.0499964 .0918884
reer | .0132621 .0125523 1.06 0.291 -.0113399 .0378641
landlockdum | .7452212 1.841776 0.40 0.686 -2.864593 4.355035
_cons | -6.150029 7.724754 -0.80 0.426 -21.29027 8.990209
-------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(koftrgi infra popusharworld finp landlockdum)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/14).(L.exqua100 reer comtot mehi) collapsed
Instruments for levels equation
Standard
koftrgi infra popusharworld finp landlockdum
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
D.(L.exqua100 reer comtot mehi) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -2.18 Pr > z = 0.029
Arellano-Bond test for AR(2) in first differences: z = -0.82 Pr > z = 0.414
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(55) = 738.93 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(55) = 78.85 Prob > chi2 = 0.019
(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(51) = 77.29 Prob > chi2 = 0.010
Difference (null H = exogenous): chi2(4) = 1.57 Prob > chi2 = 0.815
iv(koftrgi infra popusharworld finp landlockdum)
Hansen test excluding group: chi2(50) = 74.10 Prob > chi2 = 0.015
Difference (null H = exogenous): chi2(5) = 4.76 Prob > chi2 = 0.446