Dear Statalist users.

I am using the xtabond2 to draw advantage of the twostep System GMM approach in order to estimate my dynamic panel data model. I am considering two groups of countries: The European Union (28 countries) and the Central and Eastern Europe (10 countries) both groups from 1990 - 2014 with an unbalanced dataset. Hence, N1 = 700, N2 = 250 and T = 25.

The point is to estimate the effect of investments in renewable energy for the two groups of countries on (ln) of gross domestic product pr. capita. Since I assume that the model is dynamic I also use the first three lags of ln GDP pr. capita as independent variables. My linear regression model takes the form:
LnGDPc,t = β1RECc,t + β2LnGDPc,t-1 + β3LnGDPc,t-2 + β3LnGDPc,t-3 + αc + µt + ɛc,t,
RECc,t is gross inland renewable energy consumption and my coefficient of interest.

To estimate this model I run the following code:
Code:
 xtabond2 L(0/3).LnGDP REC tdum4-tdum25, ///
    gmm(L.LnGDP, lag(1 4) collapse equation(diff)) ///
    gmm(REC, lag (1 2) collapse equation(diff)) ///
    ivstyle(tdum4-tdum25, equation(level)) twostep robust
where tdum are yearly time dummies for each of the years from 1993 to 2014.

I hereby instrument by two lags of REC as first-difference and four lags of the first lagged dependent variable as first-difference. This works well when I estimate the model for the European Union countries (N=28). However, when I run the same regression for the Central and Eastern European countries (N=10) I obtain the following output:
Code:
Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: country1                        Number of obs      =       220
Time variable : year                            Number of groups   =        10
Number of instruments = 28                      Obs per group: min =        22
Wald chi2(25) =  2.01e+07                                      avg =     22.00
Prob > chi2   =     0.000                                      max =        22
------------------------------------------------------------------------------
             |              Corrected
       LnGDP |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       LnGDP |
         L1. |    1.06558   .0589094    18.09   0.000     .9501197     1.18104
         L2. |          0  (omitted)
         L3. |  -.0614096    .059251    -1.04   0.300    -.1775394    .0547201
             |
         REC |  -2.52e-06   1.69e-06    -1.49   0.135    -5.82e-06    7.87e-07
       tdum4 |   -.044087    .010539    -4.18   0.000    -.0647431   -.0234308
       tdum6 |   .0105556   .0108727     0.97   0.332    -.0107544    .0318657
       tdum7 |   -.008127   .0136221    -0.60   0.551    -.0348258    .0185717
       tdum8 |          0  (omitted)
       tdum9 |          0  (omitted)
      tdum10 |   -.028836   .0148624    -1.94   0.052    -.0579658    .0002938
      tdum11 |          0  (omitted)
      tdum12 |          0  (omitted)
      tdum13 |          0  (omitted)
      tdum14 |          0  (omitted)
      tdum15 |          0  (omitted)
      tdum16 |          0  (omitted)
      tdum17 |          0  (omitted)
      tdum18 |   .0298336   .0065639     4.55   0.000     .0169685    .0426987
      tdum19 |  -.0188079   .0147789    -1.27   0.203    -.0477741    .0101583
      tdum20 |          0  (omitted)
      tdum21 |          0  (omitted)
      tdum22 |   -.057359   .0440904    -1.30   0.193    -.1437746    .0290566
      tdum23 |          0  (omitted)
      tdum24 |          0  (omitted)
      tdum25 |          0  (omitted)
       _cons |          0  (omitted)
------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(1/2).REC collapsed
    L(1/4).L.LnGDP collapsed
Instruments for levels equation
  Standard
    tdum4 tdum5 tdum6 tdum7 tdum8 tdum9 tdum10 tdum11 tdum12 tdum13 tdum14
    tdum15 tdum16 tdum17 tdum18 tdum19 tdum20 tdum21 tdum22 tdum23 tdum24
    tdum25
    _cons
The problem is that many of the coefficients are omitted. My best guess is that this relates to problem of instrument proliferation when I have too few degrees of freedom when considering a lower number of countries. If I run the regression without year dummies the coefficient on the lagged dependent variable is no longer omitted. However, according to Roodman (2009) simply removing the time dummies never seems as the best practise.
My question: How do I come around this problem in Stata? I have read threads like https://www.statalist.org/forums/for...m-time-dummies[\URL] but I cannot find the answer here.

Any help is appreciated. Thank you in advance.
Best regards,
Emil F. Mahler.