Dear all,

I'm currently investigating the relationship between carbon emissions and socioeconomic variables for Brazilian states. My data has 27 individuals (states) and 6 years (5-year interval 1990-2015). According to the literature review my regressors are likely to be endogenous then I've decided to run the system GMM estimator by using the program xtabond2. However, as a new Stata user, I'm not convinced if I'm doing it correctly due to the unusual output I have.

My variables are: I = carbon emissions, P = population, Arpc = per capita GDP and T = technology. I've also included year fixed effects.

According to the above output, we can't reject the null hypothesis of the validity of the overidentifying restrictions, the values reported for the Diff-in-Hansen test are the p-values for the validity of the additional moment restrictions necessary for system GMM. Again, we do not reject the null that the additional moment conditions are valid. On the other hand, there is evidence for second-order autocorrelation and my lagged dependent variable is the only regressor which has statistical significance.

All comments and suggestions are very welcome and valuable.

Best regards,

I'm currently investigating the relationship between carbon emissions and socioeconomic variables for Brazilian states. My data has 27 individuals (states) and 6 years (5-year interval 1990-2015). According to the literature review my regressors are likely to be endogenous then I've decided to run the system GMM estimator by using the program xtabond2. However, as a new Stata user, I'm not convinced if I'm doing it correctly due to the unusual output I have.

My variables are: I = carbon emissions, P = population, Arpc = per capita GDP and T = technology. I've also included year fixed effects.

Code:

xtabond2 L(0/1).I P Arpc T i.AnoStata, gmmstyle( L.(I P Arpc T), laglimits(1 2) collapse equation(diff)) gmmstyle( L.(I P Arpc T > ), laglimits(0 0) collapse eq(level)) ivstyle(i.AnoStata, eq(level)) twostep robust Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm. Warning: Two-step estimated covariance matrix of moments is singular. Using a generalized inverse to calculate optimal weighting matrix for two-step estimation. Difference-in-Sargan/Hansen statistics may be negative. Dynamic panel-data estimation, two-step system GMM Group variable: Ufs Number of obs = 135 Time variable : AnoStata Number of groups = 27 Number of instruments = 17 Obs per group: min = 5 Wald chi2(10) = 2.00e+06 avg = 5.00 Prob > chi2 = 0.000 max = 5 Corrected I Coef. Std. Err. z P>z [95% Conf. Interval] I L1. .7259731 .206855 3.51 0.000 .3205448 1.131401 P .2356326 .2079675 1.13 0.257 -.1719761 .6432413 Arpc .08098 .2533465 0.32 0.749 -.4155699 .57753 T .051556 .2607521 0.20 0.843 -.4595087 .5626208 Ano 1990 0 (empty) 1995 1.93051 1.654896 1.17 0.243 -1.313027 5.174047 2000 2.019052 1.712828 1.18 0.238 -1.338029 5.376133 2005 1.83546 1.831226 1.00 0.316 -1.753678 5.424598 2010 1.981132 1.858962 1.07 0.287 -1.662367 5.624631 2015 1.997801 1.917377 1.04 0.297 -1.760188 5.75579 _cons 0 (omitted) Instruments for first differences equation GMM-type (missing=0, separate instruments for each period unless collapsed) L(1/2).(L.I L.P L.Arpc L.T) collapsed Instruments for levels equation Standard 1990b.Ano 1995.Ano 2000.Ano 2005.Ano 2010.Ano 2015.Ano _cons GMM-type (missing=0, separate instruments for each period unless collapsed) D.(L.I L.P L.Arpc L.T) collapsed Arellano-Bond test for AR(1) in first differences: z = -2.23 Pr > z = 0.026 Arellano-Bond test for AR(2) in first differences: z = 1.97 Pr > z = 0.049 Sargan test of overid. restrictions: chi2(6) = 23.71 Prob > chi2 = 0.001 (Not robust, but not weakened by many instruments.) Hansen test of overid. restrictions: chi2(6) = 7.12 Prob > chi2 = 0.310 (Robust, but weakened by many instruments.) Difference-in-Hansen tests of exogeneity of instrument subsets: GMM instruments for levels Hansen test excluding group: chi2(2) = 4.11 Prob > chi2 = 0.128 Difference (null H = exogenous): chi2(4) = 3.01 Prob > chi2 = 0.557 gmm(L.I L.P L.Arpc L.T, collapse eq(level) lag(0 0)) Hansen test excluding group: chi2(2) = 4.11 Prob > chi2 = 0.128 Difference (null H = exogenous): chi2(4) = 3.01 Prob > chi2 = 0.557 iv(1990b.Ano 1995.Ano 2000.Ano 2005.Ano 2010.Ano 2015.Ano, eq(level)) Hansen test excluding group: chi2(2) = 5.94 Prob > chi2 = 0.051 Difference (null H = exogenous): chi2(4) = 1.18 Prob > chi2 = 0.882

According to the above output, we can't reject the null hypothesis of the validity of the overidentifying restrictions, the values reported for the Diff-in-Hansen test are the p-values for the validity of the additional moment restrictions necessary for system GMM. Again, we do not reject the null that the additional moment conditions are valid. On the other hand, there is evidence for second-order autocorrelation and my lagged dependent variable is the only regressor which has statistical significance.

All comments and suggestions are very welcome and valuable.

Best regards,

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