Dear all
I need help to minimize the instrument count in my dynamic panel model estimation using difference and system GMM method. Can anyone please point out my mistake in writing the code/suggest minimizing instrument count with xtabond2 command.

I am using xtabond2 command in Stata 16, have in total 14 independent variables covering years from 1976-2017, total group is 78. All the variables are logged.

Have the plan to run regressions as below
a) Regression 1: use 13 independent variables covering years 1976-1990
b) Regression 2: use 13+1 independent variables covering years 1991-2005 (Because the institutional variables are only available from 1996)
c) Regression 3: use 13+1 independent variables covering years 2006-2017

I have run regression 1 with xtabond2 using the following command.

. xtabond2 lngrate_mx l.lngrate_mx $endo2 $pre6 yr1976-yr1984 if year<=1990, gmm(l.lngrate_mx l2.$endo2 l1.$pre6, collapse) iv(yr1976-yr1990) noleveleq nodiffsa
> rgan robust
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Warning: Number of instruments may be large relative to number of observations.
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate robust weighting matrix for Hansen test.

Dynamic panel-data estimation, one-step difference GMM
------------------------------------------------------------------------------
Group variable: cnt Number of obs = 189
Time variable : year Number of groups = 39
Number of instruments = 178 Obs per group: min = 0
Wald chi2(18) = 97.74 avg = 4.85
Prob > chi2 = 0.000 max = 15
------------------------------------------------------------------------------
| Robust
lngrate_mx | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lngrate_mx |
L1. | -.2979105 .0732073 -4.07 0.000 -.4413942 -.1544268
|
lnfdif_mx | -.0496543 .0345899 -1.44 0.151 -.1174493 .0181408
lnaid | -.0077373 .1264407 -0.06 0.951 -.2555565 .2400819
lninftel_mx | -.4036854 .4649351 -0.87 0.385 -1.314941 .5075707
lntrd_mx | .9904507 .6384156 1.55 0.121 -.2608209 2.241722
lnexreal_mx | -.217682 .2607278 -0.83 0.404 -.7286991 .2933352
lngcf | -.0503376 .5228976 -0.10 0.923 -1.075198 .9745228
lninfgdp | -.1821023 .1134625 -1.60 0.109 -.4044847 .0402802
lnprenr | -1.694952 1.023869 -1.66 0.098 -3.701697 .3117942
yr1976 | .0499593 .2039131 0.25 0.806 -.3497029 .4496216
yr1977 | -.1087436 .2819799 -0.39 0.700 -.6614141 .4439269
yr1978 | .1015337 .2823504 0.36 0.719 -.4518629 .6549304
yr1979 | -.2403875 .2630821 -0.91 0.361 -.756019 .275244
yr1980 | -.0665753 .3839448 -0.17 0.862 -.8190933 .6859428
yr1981 | .1880516 .2475811 0.76 0.448 -.2971984 .6733016
yr1982 | -.3936692 .2194516 -1.79 0.073 -.8237863 .036448
yr1983 | -.862448 .2664371 -3.24 0.001 -1.384655 -.3402408
yr1984 | -.6206123 .2557127 -2.43 0.015 -1.1218 -.1194245
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984 yr1985
yr1986 yr1987 yr1988 yr1989 yr1990)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/.).(L.lngrate_mx L2.lnfdif_mx lnaid L.lninftel_mx lntrd_mx lnexreal_mx
lngcf lninfgdp lnprenr) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -1.47 Pr > z = 0.141
Arellano-Bond test for AR(2) in first differences: z = -1.75 Pr > z = 0.079
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(160) = 229.69 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(160) = 17.73 Prob > chi2 = 1.000
(Robust, but can be weakened by many instruments.)



****Here $endo2=lnfdi_mx & lnaid, $pre6=lngcf lntrd_mx lnexreal_mx lninftel_mx lninfgdp lnprenr).
****Other variables are 4 financial development variables and 1 index of institutional variable
***$endo2 and l.lngrate are considered endogenous; $pre6, 4 financial development variables and institutional index are considered predetermined variables.
The regression returns results with 39 groups and instrument count 178.

My questions are;
1. How to restrict the instrument count to be less than the number of groups to validate the Hansen test of overidentification restrictions (Chi square value is always 1.00 but Arellano-Bond test for AR(2) in first differences is quite ok)? The same problem is faced with xtdpd and xtdpdsys command as well.

2. How can ensure the same groups to be used in every regression for consistency and validity of results? It seems if the instrument count is fixed,it will be managed whatever difference or system GMM.
Regards
Habibul Hasan