Different results obtained in the heterogeneity test using the GMM model

[Febrian Yalisman]

I am currently conducting research on the effects of budget revisions (rebudgeting) on expenditure realization using panel data consisting of +/- 15,000 units/observations over 20 periods (quarterly), using the generalized method of moments. I have performed various exercises and found a model that, in my opinion, makes sense with the result of (1) significant lag dependent variable, (2) significant VoI, (3) meets AR1, AR2, and Hansen Test criteria.
However, when I conduct a heterogeneity test by separating data between central and non-central area, the results obtained are as follows:
Units on Central Area:
(1) significant lag dependent variable, (2) significant VoI, (3) meets AR1, AR2, and Hansen Test criteria
Units on Non Central Area:
(2) insignificant lag dependent variable, (2) insignificant VoI, (3) meets only AR2 and Hansen Test criteria.

Questions:
1. With the differences in signifcancy, autocorrelation test results (AR1 and AR2) and validity (Hansen test) in the heterogeneity test, is the developed main model still valid? Are there any potential model misspecification issues?
2. How do we interpret the heterogeneity test between Central Area and Non-Central Area?

[Febrian Yalisman]

Here is the command on the main model

  
xtabond2 y1 L(1/3).y1 L(0/1).x1a L(0/2).x2a c1b c2b c3 dummyc7 c8 dummyc9_statuspaguKL  dummyc10_kw dummy12c_statkabkota L(0/2).c13_lnpagu c14b i.ta if dummy12a_pulau==0, gmm(L1.y1 , collapse) iv (x2a c8 dummyc10_kw  dummy12c_statkabkota c13_lnpagu c14b) nodiffsargan twostep robust orthogon

Result

Here is the command for the heterogeneity - Units on Central Area

xtabond2 y1 L(1/3).y1 L(0/1).x1a L(0/2).x2a c1b c2b c3 dummyc7 c8 dummyc9_statuspaguKL  dummyc10_kw dummy12c_statkabkota L(0/2).c13_lnpagu c14b i.ta if dummy12a_pulau==1, gmm(L1.y1 , collapse) iv (x2a c8 dummyc10_kw  dummy12c_statkabkota c13_lnpagu c14b) nodiffsargan twostep robust orthogon

Result

Here is the command for the heterogeneity - Units on Non Central Area

xtabond2 y1 L(1/3).y1 L(0/1).x1a L(0/2).x2a c1b c2b c3 dummyc7 c8 dummyc9_statuspaguKL  dummyc10_kw dummy12c_statkabkota L(0/2).c13_lnpagu c14b i.ta if dummy12a_pulau==0, gmm(L1.y1 , collapse) iv (x2a c8 dummyc10_kw  dummy12c_statkabkota c13_lnpagu c14b) nodiffsargan twostep robust orthogon

Result