AR(1) and AR(2) values are missing (xtabond2 command)

[Bryna Meivitawanli]

Hi everyone,

I am using the xtabond2 command to execute system GMM.
My data: n=33, t=6, which satisfies the small t large n dataset required by GMM.
Here are the results that I got from stata 15:

xtabond2 g FDI y SCH TRADE POP FIN INV, gmm(g FDI TRADE FIN, lag(2 2)) iv(l.y SCH POP INV) small robust
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate robust weighting matrix for Hansen test.
Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, one-step system GMM
------------------------------------------------------------------------------
Group variable: ID Number of obs = 44
Time variable : Year Number of groups = 22
Number of instruments = 17 Obs per group: min = 2
F(7, 21) = 3.82 avg = 2.00
Prob > F = 0.008 max = 2
------------------------------------------------------------------------------
| Robust
g | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
FDI | -.000706 .0012351 -0.57 0.574 -.0032745 .0018625
y | -.0000432 .0000305 -1.42 0.171 -.0001066 .0000201
SCH | -.0079411 .1184802 -0.07 0.947 -.2543342 .2384519
TRADE | -23.41223 15.36501 -1.52 0.142 -55.36551 8.541052
POP | -19.36038 8.435523 -2.30 0.032 -36.90301 -1.817747
FIN | 8.016918 2.388503 3.36 0.003 3.049754 12.98408
INV | -22.87045 24.44595 -0.94 0.360 -73.70858 27.96768
_cons | 5.930342 8.015413 0.74 0.468 -10.73862 22.59931
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(L.y SCH POP INV)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L2.(g FDI TRADE FIN)
Instruments for levels equation
Standard
L.y SCH POP INV
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL.(g FDI TRADE FIN)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = . Pr > z = .
Arellano-Bond test for AR(2) in first differences: z = . Pr > z = .
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(9) = 8.65 Prob > chi2 = 0.470
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(9) = 6.44 Prob > chi2 = 0.696
(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(1) = 0.18 Prob > chi2 = 0.674
Difference (null H = exogenous): chi2(8) = 6.26 Prob > chi2 = 0.618
iv(L.y SCH POP INV)
Hansen test excluding group: chi2(5) = 4.10 Prob > chi2 = 0.535
Difference (null H = exogenous): chi2(4) = 2.33 Prob > chi2 = 0.675

As you can see that all Sargan and Hansen test results are well above 5% which means that the estimations are valid.
However I do not know why AR(1) and AR(2) only show .
I have tried to use deeper lags but both AR(1) and AR(2) still show . only.
Any help will be very much appreciated. Thank you.

[Sebastian Kripfganz]

According to the estimation output, there is a maximum of 2 observations (not 6) per group. The lagged differences of just 2 observations do not exist and thus the Arellano-Bond statistics cannot be computed.

[Bryna Meivitawanli]

Thank you so much, I've figured out why :D Sebastian Kripfganz

[Rania Shahine]

I have the same problem of the missing output of the AB test using xtabond2. Here is the output I get, can anyone let me know what am I missing?

.
. xtabond2 L(0/1).gr inf inv govexp op popgr finv, ///
> gmmstyle(L.(gr inf inv govexp op popgr), equation(diff) laglimits(1 1) collapse) ///
> gmmstyle(L.(gr inf inv govexp op popgr), equation(level) laglimits(0 0) collapse) ivstyle
> (finv, equation(level)) robust nocons
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.

Dynamic panel-data estimation, one-step system GMM
------------------------------------------------------------------------------
Group variable: countryid Number of obs = 57
Time variable : year Number of groups = 18
Number of instruments = 13 Obs per group: min = 2
Wald chi2(7) = 34.26 avg = 3.17
Prob > chi2 = 0.000 max = 7
------------------------------------------------------------------------------
| Robust
gr | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
gr |
L1. | -.0215535 .1399065 -0.15 0.878 -.2957652 .2526581
|
inf | -.1002752 .0520624 -1.93 0.054 -.2023155 .0017652
inv | .1016219 .0369339 2.75 0.006 .0292328 .1740111
govexp | .001073 .0019803 0.54 0.588 -.0028083 .0049542
op | -.0010932 .0008578 -1.27 0.202 -.0027744 .0005879
popgr | -.0122443 .1066573 -0.11 0.909 -.2212888 .1968001
finv | .0020188 .0012484 1.62 0.106 -.000428 .0044655
------------------------------------------------------------------------------
Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L.(L.gr L.inf L.inv L.govexp L.op L.popgr) collapsed
Instruments for levels equation
Standard
finv
GMM-type (missing=0, separate instruments for each period unless collapsed)
D.(L.gr L.inf L.inv L.govexp L.op L.popgr) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = . Pr > z = .
Arellano-Bond test for AR(2) in first differences: z = . Pr > z = .
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(6) = 69.78 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(6) = 5.65 Prob > chi2 = 0.464
(Robust, but can be weakened by many instruments.)

[Sebastian Kripfganz]

I would guess that you have a data set with too many gaps. You could try my xtdpdgmm command to double check.

[Rania Shahine]

Thanks Sebastian! I will try it today and keep you posted on how it goes. Much appreciate your time and effort in responding to our questions. Thanks again.

[Rania Shahine]

Dear Sebastian, would you please confirm the equivalence of this model in xtdpdgmm?

xtabond2 L(0/1).gr inf inv govexp op popgr finv, ///
gmmstyle(L.(gr inf inv govexp op popgr), equation(diff) laglimits(1 1) collapse) ///
gmmstyle(L.(gr inf inv govexp op popgr), equation(level) laglimits(0 0) collapse) ivstyle
(finv, equation(level)) robust nocons

[Sebastian Kripfganz]

The syntax for this case should translate in a straightforward way:

xtdpdgmm L(0/1).gr inf inv govexp op popgr finv, ///
    gmm(L.(gr inf inv govexp op popgr), model(diff) lag(1 1) collapse) ///
    gmm(L.(gr inf inv govexp op popgr), diff model(level) lag(0 0) collapse) ///
    iv(finv, model(level)) vce(robust) nocons

Just notice that with xtdpdgmm you need to explicitly specify the diff suboption to request a first-differencing of the instruments for the level model.

Also note that it is unusual and generally not recommended to exclude a constant when it contains instruments for the level model.

[Rania Shahine]

Much appreciated Sebastian, thank you!

[Nida Rahman]

My gmm estimation output does not display AR(2). My T is 4 and N is 31. The estimation output is as follows:
xtabond2 lnbackward_part laglnbackward logfdi lngdp_percapita ln_patents Political_stability rentforresourcesgdp lin
> ershippingconnectivity hdi capitalstoclgdp weightedmfntariffrate tradeopenness, gmm( laglnbackward logfdi lngdp_perc
> apita ln_patents tradeopenness capitalstoclgdp Political_stability , laglimits(2 2) eq(level) collapse) gmm( lnbackw
> ard_part logfdi lngdp_percapita ln_patents tradeopenness capitalstoclgdp Political_stability , laglimits(1 1) eq(dif
> f) collapse) iv( rentforresourcesgdp linershippingconnectivity individualsusinginternet weightedmfntariffrate hdi ,
> eq(level)) twostep robust nodiffsargan
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate optimal weighting matrix for two-step estimation.

Dynamic panel-data estimation, two-step system GMM

Group variable: Country Number of obs = 93
Time variable : year Number of groups = 31
Number of instruments = 19 Obs per group: min = 3
Wald chi2(11) = 76140.84 avg = 3.00
Prob > chi2 = 0.000 max = 3

Corrected
lnbackward_part Coef. Std. Err. z P>z [95% Conf. Interval]

laglnbackward .506341 .3412266 1.48 0.138 -.1624508 1.175133
logfdi .9762495 .5446065 1.79 0.073 -.0911596 2.043659
lngdp_percapita .0478893 .224692 0.21 0.831 -.3924989 .4882776
ln_patents .0281805 .1107136 0.25 0.799 -.1888141 .2451751
Political_stability -.2105374 .4577576 -0.46 0.646 -1.107726 .6866511
rentforresourcesgdp -.0108156 .0439986 -0.25 0.806 -.0970512 .07542
linershippingconnectivity .0019557 .016869 0.12 0.908 -.0311069 .0350183
hdi -2.337256 7.177985 -0.33 0.745 -16.40585 11.73134
capitalstoclgdp .0045885 .4389777 0.01 0.992 -.8557919 .8649689
weightedmfntariffrate -.1803708 .0840757 -2.15 0.032 -.3451561 -.0155855
tradeopenness .0022938 .0039868 0.58 0.565 -.0055202 .0101078
_cons 7.748863 9.103925 0.85 0.395 -10.0945 25.59223

Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L.(lnbackward_part logfdi lngdp_percapita ln_patents tradeopenness
capitalstoclgdp Political_stability) collapsed
Instruments for levels equation
Standard
rentforresourcesgdp linershippingconnectivity individualsusinginternet
weightedmfntariffrate hdi
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL2.(laglnbackward logfdi lngdp_percapita ln_patents tradeopenness
capitalstoclgdp Political_stability) collapsed

Arellano-Bond test for AR(1) in first differences: z = -0.88 Pr > z = 0.377
Arellano-Bond test for AR(2) in first differences: z = . Pr > z = .

Sargan test of overid. restrictions: chi2(7) = 38.26 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(7) = 10.16 Prob > chi2 = 0.179
(Robust, but weakened by many instruments.)

Can anybody suggest a way to get AR(2) and what should be the sargan p value for the estimation to be valid?

[Sebastian Kripfganz]

You need at least 4 time periods for the AR(2) test to be computable. According to the output, you only have 3 time periods. One time period got lost because of the lagged dependent variable.

[HA Borrero]

Hi all. I am facing exactly the same situation. Which is the best way to deal with this circumstance? Are there any alternative serial correlation tests that can be used in the context of system GMM? is it appropriate to just state in the paper that the AR(2) could not be computed? Thank you!!!

[Sebastian Kripfganz]

Please avoid double posting the same question in multiple topics!

Please see my response in the other topic, where I recommend using xtdpdgmm as an alternative to xtabond2: https://www.statalist.org/forums/for...92#post1730392