Non-Dynamic System-GMM

[Fillipe Soares]

Dear all,

I am working on my dissertation project that is aimed to estimate an econometric model to find the determinants of CO2 emissions for Brazilian states between 2005-2015, except 2008 (N=27, T=10). According to the literature, my variables are likely to be endogenous so I decided to use the System-GMM approach due to its good properties in small samples when compared to other panel data estimators.

Firstly I estimated a dynamic model with the lagged dependent variable in the right-hand side of the equation and as a result, I found different outcomes in terms of the expected signs and statistical significance of coefficients. Then I run additional tests in my variables which showed a strong multicollinearity between the lagged dependent variable and some regressors which can bias my estimates.

Due to the issue described above, I dropped out the lagged dependent variable and run the model without the dynamic term and the result was more reasonable according to the specific literature. However, I am not confident whether my equation is well specified and specification tests are acceptable.

The estimated equation follows:

 xtabond2  I P Arpc V QR year2 year3 year5-year11, gmm(P Arpc  V QR, laglimits(1 2) collapse equation(diff)) gmm(P Arpc V  QR, laglimits(1 1) collapse eq(level)) ivstyle(year2 year3 year5-year11, eq(level)) twostep small robust orthog

My results:

.  
Dynamic panel-data estimation, two-step system GMM

Group variable: Ufs                             Number of obs      =       270
Time variable : AnoStata                        Number of groups   =        27
Number of instruments = 22                      Obs per group: min =        10
F(13, 26)     =     84.30                                      avg =     10.00
Prob > F      =     0.000                                      max =        10

Corrected
I       Coef.   Std. Err.      t    P>t     [95% Conf. Interval]

P         .810655   .1350605     6.00   0.000     .5330342    1.088276
Arpc    .8631221   .1800172     4.79   0.000     .4930914    1.233153
V         .1794541   .2069648     0.87   0.394     -.245968    .6048763
QR      .2443307   .1923399     1.27   0.215    -.1510296     .639691
year2   -.1213536    .050725    -2.39   0.024    -.2256202   -.0170869
year3   -.0953036    .103279    -0.92   0.365    -.3075966    .1169895
year5    -.216924     .20192    -1.07   0.293    -.6319765    .1981284
year6   -.2111071    .247421    -0.85   0.401    -.7196882    .2974741
year7   -.2329856   .2552947    -0.91   0.370    -.7577515    .2917802
year8    -.178021    .262647    -0.68   0.504    -.7178996    .3618576
year9   -.1452306   .2614932    -0.56   0.583    -.6827376    .3922764
year10   -.1175916   .2612318    -0.45   0.656    -.6545612     .419378
year11   -.1408464   .2415388    -0.58   0.565    -.6373365    .3556437
_cons   -2.782019   1.229473    -2.26   0.032    -5.309237   -.2548011

Instruments for orthogonal deviations equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/2).(P Arpc V QR) collapsed
Instruments for levels equation
Standard
year2 year3 year5 year6 year7 year8 year9 year10 year11
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL.(P Arpc V QR) collapsed

Arellano-Bond test for AR(1) in first differences: z =  -0.41  Pr > z =  0.685
Arellano-Bond test for AR(2) in first differences: z =   1.31  Pr > z =  0.190

Sargan test of overid. restrictions: chi2(8)    =  14.20  Prob > chi2 =  0.077
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(8)    =   4.75  Prob > chi2 =  0.784
(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group:     chi2(4)    =   2.15  Prob > chi2 =  0.709
Difference (null H = exogenous): chi2(4)    =   2.60  Prob > chi2 =  0.626
gmm(P Arpc V QualidadeRodovias, collapse eq(diff) lag(1 2))
Hansen test excluding group:     chi2(0)    =   0.18  Prob > chi2 =      .
Difference (null H = exogenous): chi2(8)    =   4.57  Prob > chi2 =  0.803
gmm(P Arpc V QualidadeRodovias, collapse eq(level) lag(1 1))
Hansen test excluding group:     chi2(4)    =   2.15  Prob > chi2 =  0.709
Difference (null H = exogenous): chi2(4)    =   2.60  Prob > chi2 =  0.626

My questions are:

1) Is my equation correctly specified?
1) Aside from the fact that the interpretation of my results is now reasonable, considering only the specification results of the model (AR(1), AR(2), Hansen and Diff-Hansen) is it possible to assume that I have consistent estimates?
2) Considering that my dataset is composed of 270 observations does the non-dynamic system-gmm estimation really take all into consideration?

Any help would be welcome.

Regards,

[Sebastian Kripfganz]

The clear non-rejection of the Arellano-Bond AR(1) test is problematic. No serial correlation in the first differenced error term indicates that the error term in levels is a random walk process. This in turn indicates that your model is misspecified. A dynamic model might be preferable or, alternatively, the estimation of a static model in first differences.

[Fillipe Soares]

The clear non-rejection of the Arellano-Bond AR(1) test is problematic. No serial correlation in the first differenced error term indicates that the error term in levels is a random walk process. This in turn indicates that your model is misspecified. A dynamic model might be preferable or, alternatively, the estimation of a static model in first differences.

Thank you, Sebastian. I really appreciate your help.

About my third question, does this non-dynamic system-gmm approach really take all observations in a dataset into consideration as it happened in this case?

[Sebastian Kripfganz]

I do not see a reason why it should not.