When reproducing this code to explain the growth relationship, it drops both period 1 and period 4 dummies, and the sargan test seems to reject the null. What can I improve in the coding to avoid period 4 to be dropped and how should I interpret the results as most of them are not significant which is worrying me.

my regression is Growthit=GDPi,t-1+Ginii,t-1+PPPIi,t-1+countrydummies*i+Perioddummiest+eit
with 69 countries and t=5....

xtabond2 l.Growth L.(GINI logGDP EDUCATION PPPI) _IPer*, iv(_IPer*) gmm(L.(EDUCATIO
> N PPPI GINI logGDP)) two small nol robust
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed,
> perm.
_IPeriod_4 dropped due to collinearity
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate optimal weighting matrix for two-step estim
> ation.
Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step difference GMM
------------------------------------------------------------------------------
Group variable: country1 Number of obs = 139
Time variable : Period Number of groups = 51
Number of instruments = 27 Obs per group: min = 0
F(0, 51) = . avg = 2.73
Prob > F = . max = 3
------------------------------------------------------------------------------
| Corrected
L.Growth | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
GINI |
L1. | -.0004038 .001774 -0.23 0.821 -.0039652 .0031575
|
logGDP |
L1. | -.0144806 .0576446 -0.25 0.803 -.1302069 .1012456
|
EDUCATION |
L1. | .0658534 .0283553 2.32 0.024 .0089278 .122779
|
PPPI |
L1. | -.0310512 .026564 -1.17 0.248 -.0843807 .0222783
|
_IPeriod_2 | .0099311 .013796 0.72 0.475 -.0177655 .0376278
_IPeriod_3 | .0065741 .0084682 0.78 0.441 -.0104266 .0235748
_IPeriod_5 | .0006271 .0080175 0.08 0.938 -.0154687 .0167229
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(_IPeriod_2 _IPeriod_3 _IPeriod_4 _IPeriod_5)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/4).(L.EDUCATION L.PPPI L.GINI L.logGDP)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -2.30 Pr > z = 0.022
Arellano-Bond test for AR(2) in first differences: z = 0.04 Pr > z = 0.970
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(20) = 37.41 Prob > chi2 = 0.010
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(20) = 25.23 Prob > chi2 = 0.193
(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
iv(_IPeriod_2 _IPeriod_3 _IPeriod_4 _IPeriod_5)
Hansen test excluding group: chi2(17) = 21.38 Prob > chi2 = 0.210
Difference (null H = exogenous): chi2(3) = 3.85 Prob > chi2 = 0.279