Dear statalists,

I'm learning how to use the command xtabond2, but I'm not sure about a few things in the results which I couldn't understand. I read parts of the famous article of Roodman of 2009 but I didn't solve the issues.
From a technical point of view I didn't understand why sometimes the difference in Hansen test is not present - my idea is that it can't be done but I'm not able to explain technically why

I post one model as an example to show my result

Code:
 xtabond2 LECI L.LECI LGCF LP LSFI LPA LHC LTO LFDI LGC , gmm(L.LECI, lag(1 6) collapse ) iv( LGCF LP LSFI LPA LHC LTO LFD
> I LGC ) robust twostep
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: Code Number of obs = 1038
Time variable : year Number of groups = 93
Number of instruments = 16 Obs per group: min = 1
Wald chi2(9) = 651.63 avg = 11.16
Prob > chi2 = 0.000 max = 16
------------------------------------------------------------------------------
| Corrected
LECI | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
LECI |
L1. | .345666 .126138 2.74 0.006 .0984402 .5928919
|
LGCF | -.157589 1.114522 -0.14 0.888 -2.342012 2.026834
LP | 1.420067 .6380981 2.23 0.026 .1694178 2.670716
LSFI | -2.405806 .8000958 -3.01 0.003 -3.973965 -.8376465
LPA | .3219948 .2495487 1.29 0.197 -.1671116 .8111011
LHC | 5.588163 2.899331 1.93 0.054 -.0944215 11.27075
LTO | 3.191879 1.300292 2.45 0.014 .6433525 5.740405
LFDI | .2704359 .3048973 0.89 0.375 -.3271518 .8680236
LGC | 1.893409 1.265654 1.50 0.135 -.5872276 4.374046
_cons | -37.55127 15.16168 -2.48 0.013 -67.26762 -7.834926
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(LGCF LP LSFI LPA LHC LTO LFDI LGC)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/6).L.LECI collapsed
Instruments for levels equation
Standard
_cons
LGCF LP LSFI LPA LHC LTO LFDI LGC
GMM-type (missing=0, separate instruments for each period unless collapsed)
D.L.LECI collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -3.13 Pr > z = 0.002
Arellano-Bond test for AR(2) in first differences: z = 0.22 Pr > z = 0.829
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(6) = 24.85 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(6) = 6.34 Prob > chi2 = 0.386
(Robust, but can be weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(5) = 6.33 Prob > chi2 = 0.276
Difference (null H = exogenous): chi2(1) = 0.01 Prob > chi2 = 0.909
furthermore I'm not sure if I have to use both the suboptions equation(level) and equation(diff) in the option ivstyle in order to use instruments in the level model and in the transformed model. Third question is what kind of result I obtain with none of two suboptions in ivstyle.

Any help is appreciated.