xtabond2 vs xtdpdgmm

[Abdalla Muktad]

Hello,
I'm trying to study the spillover effect of trading with Arab Spring countries on economic growth for trading partner. I used two-step GMM method.
lngdp = lngdpt-1 + Trade with AS + Trade with non-AS + X
I used both synx
xtabond2 g_realgdp L.g_realgdp ln_inv polstab ln_popgrow ln_k exprt_arab2009 exprt_nonarab2009 i.y, gmm(L.g_realgdp exprt_arab2009 exprt_nonarab2009, collapse) iv(ln_inv polstab ln_popgrow ln_k exprt_arab2009 exprt_nonarab2009 i.y, equation(level)) nodiffsargan twostep robust orthogonal small

My results
Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: id Number of obs = 1361
Time variable : years Number of groups = 106
Number of instruments = 50 Obs per group: min = 2
F(20, 105) = 96.11 avg = 12.84
Prob > F = 0.000 max = 14
-------------------------------------------------------------------------------
| Corrected
g_realgdp | Coefficient std. err. t P>|t| [95% conf. interval]
--------------+----------------------------------------------------------------
g_realgdp |
L1. | .3466934 .0799472 4.34 0.000 .1881728 .505214
|
ln_inv | .0183315 .0081626 2.25 0.027 .0021466 .0345165
polstab | -.0048779 .0012328 -3.96 0.000 -.0073224 -.0024335
ln_popgrow | .0016554 .0009214 1.80 0.075 -.0001716 .0034824
ln_k | -.0009274 .0005903 -1.57 0.119 -.0020977 .000243
exprt_ar~2009 | -.0002798 .0002997 -0.93 0.353 -.000874 .0003145
exprt_no~2009 | .0001107 .0000634 1.75 0.084 -.000015 .0002364
|
years |
2005 | .0053833 .0047511 1.13 0.260 -.0040372 .0148038
2006 | .0108478 .0041824 2.59 0.011 .0025549 .0191408
2007 | .0085987 .0041307 2.08 0.040 .0004083 .0167891
2008 | -.010197 .0052332 -1.95 0.054 -.0205735 .0001794
2009 | -.0357687 .0057003 -6.27 0.000 -.0470713 -.0244662
2010 | .0199983 .0040512 4.94 0.000 .0119655 .028031
2011 | -.0053902 .0039893 -1.35 0.180 -.0133003 .00252
2012 | -.0061589 .0040205 -1.53 0.129 -.0141309 .0018131
2013 | -.0081049 .0050861 -1.59 0.114 -.0181897 .0019798
2014 | -.0013908 .002677 -0.52 0.604 -.0066987 .0039172
2015 | -.0054758 .0027612 -1.98 0.050 -.0109508 -8.56e-07
2016 | -.0088888 .0036413 -2.44 0.016 -.0161089 -.0016688
2018 | -.0057051 .0022761 -2.51 0.014 -.0102182 -.0011919
|
_cons | -.0040318 .0293484 -0.14 0.891 -.0622242 .0541606
-------------------------------------------------------------------------------
Instruments for orthogonal deviations equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/15).(L.g_realgdp exprt_arab2009 exprt_nonarab2009) collapsed
Instruments for levels equation
Standard
ln_inv polstab ln_popgrow ln_k exprt_arab2009 exprt_nonarab2009
2003b.years 2004.years 2005.years 2006.years 2007.years 2008.years
2009.years 2010.years 2011.years 2012.years 2013.years 2014.years
2015.years 2016.years 2017.years 2018.years
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
D.(L.g_realgdp exprt_arab2009 exprt_nonarab2009) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -2.65 Pr > z = 0.008
Arellano-Bond test for AR(2) in first differences: z = -0.82 Pr > z = 0.412
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(29) = 30.13 Prob > chi2 = 0.407
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(29) = 38.07 Prob > chi2 = 0.121
(Robust, but weakened by many instruments.)



Then I used
xtdpdgmm L(0/1).g_realgdp ln_inv polstab ln_popgrow ln_k exprt_arab2009 exprt_nonarab2009, noserial gmmiv(L.g_realgdp, collapse model(difference)) iv(ln_inv polstab ln_popgrow ln_k exprt_arab2009 exprt_nonarab2009, difference model(difference)) twostep vce(robust)

My result is
Generalized method of moments estimation

Fitting full model:

Step 1:
initial: f(b) = .01873944
alternative: f(b) = 2.7782246
rescale: f(b) = .0030811
Iteration 0: f(b) = .0030811
Iteration 1: f(b) = .00032238
Iteration 2: f(b) = .00032225
Iteration 3: f(b) = .00032225

Step 2:
Iteration 0: f(b) = .48682328
Iteration 1: f(b) = .43199136
Iteration 2: f(b) = .43191809
Iteration 3: f(b) = .43191795

Group variable: id Number of obs = 1361
Time variable: years Number of groups = 106

Moment conditions: linear = 20 Obs per group: min = 2
nonlinear = 12 avg = 12.83962
total = 32 max = 14

(Std. err. adjusted for 106 clusters in id)
-------------------------------------------------------------------------------
| WC-Robust
g_realgdp | Coefficient std. err. z P>|z| [95% conf. interval]
--------------+----------------------------------------------------------------
g_realgdp |
L1. | .4840359 .0788513 6.14 0.000 .3294902 .6385816
|
ln_inv | .0156535 .039496 0.40 0.692 -.0617572 .0930641
polstab | .0080878 .0095458 0.85 0.397 -.0106216 .0267972
ln_popgrow | -.007163 .0039151 -1.83 0.067 -.0148364 .0005104
ln_k | .0530058 .0122549 4.33 0.000 .0289866 .077025
exprt_ar~2009 | .0073165 .0015793 4.63 0.000 .0042211 .0104119
exprt_no~2009 | -.0007791 .0001701 -4.58 0.000 -.0011124 -.0004457
_cons | -1.293861 .2752628 -4.70 0.000 -1.833367 -.7543562
-------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(diff):
L1.L.g_realgdp L2.L.g_realgdp L3.L.g_realgdp L4.L.g_realgdp L5.L.g_realgdp
L6.L.g_realgdp L7.L.g_realgdp L8.L.g_realgdp L9.L.g_realgdp L10.L.g_realgdp
L11.L.g_realgdp L12.L.g_realgdp L13.L.g_realgdp
2, model(diff):
D.ln_inv D.polstab D.ln_popgrow D.ln_k D.exprt_arab2009 D.exprt_nonarab2009
3, model(level):
_cons

.
end of do-file

. do "/var/folders/gf/3xtyllt9313gwsb7dd1fqw3h0000gp/T//SD00373.000000"

. estat serial

Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1 z = -3.5876 Prob > |z| = 0.0003
H0: no autocorrelation of order 2 z = -1.1030 Prob > |z| = 0.2700

. estat overid

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

2-step moment functions, 2-step weighting matrix chi2(24) = 45.7833
Prob > chi2 = 0.0047

2-step moment functions, 3-step weighting matrix chi2(24) = 48.3531
Prob > chi2 = 0.0023

.
My question is: Which result is better??

[Sebastian Kripfganz]

You are comparing quite different specifications with each other:

• Your xtabond2 specification yields a system GMM estimator with time effects and forward-orthogonal deviations for the transformed model. All the variables specified in the iv() option are implicitly assumed to be uncorrelated with the unobserved group-specific effect, which is similar to a random-effects assumption.
• Your xtdpdgmm specification does not include time effects, and it yields an difference GMM estimator with additional nonlinear moment conditions. (Note that the option noserial is depreciated and was replaced by option nl(noserial) in newer versions of the command.)

In general, time effects tend to be important and should not be omitted. In your case, some of them are statistically significant in the first regression. The rejection of the Hansen test in the second specification might possibly be a consequence of omitted time effects. With xtdpdgmm, you can use the option teffects to include them.
A system GMM estimator requires additional assumptions which may not be satisfied. It usually makes sense to also specify the instruments in the iv() option for the transformed model. Their untransformed inclusion in the level model may be difficult to justify.