# Governance and Dynamic Efficiency with Network Structure in the Brazilian Natural Gas Utilities
## 3 Results
### Econometric Model Analysis  
From the analysis carried out in the previous section regarding the overall and divisional efficiency of the companies in the piped gas sector in Brazil, this final stage gathers evidence of the impact on overall efficiency of factors indicated in the literature, such as regional indicators, production, and the implementation of control systems like corporate governance, in order to meet specific objective III. The results presented in this section demonstrate the impact of the level of adoption of corporate governance and other factors on the overall efficiency of piped gas companies in Brazil. The results obtained also point to the influence of other factors on the efficiency of the companies in the researched sector. The model proposed in Equation (5) was estimated using pooled, fixed effects, and random effects models. According to [PERSON] (2019) [81], in the panel model with fixed effects, the attributes (variables) of each company, which are unobserved and constant over time, are potentially correlated with the other independent variables that vary over time, conferring a heterogeneity bias due to this relationship. Thus, it is necessary to exclude the variables that are constant over time, which, in this model, are the geographic region dummies and the ownership dummy. The random effects model, still according to [PERSON] (2019) [81], assumes that the unobservable and time-constant characteristics for each company are not correlated with the independent variables. Thus, the fixed effects are not removed from the analysis. After estimating the mentioned models, tests were conducted to determine the most appropriate model for the data. The Chow test, Breusch-Pagan LM test, and Hausman test were performed for model selection. First, the Chow test indicated that the data analysis in the panel data model with fixed effects was superior to the estimation of the model by pooled OLS, clustered, and robust. Finally, the Hausman test was performed, through which it was found that the null hypothesis could not be rejected at the 99% probability level, defining the random effects model as the better model compared to the fixed effects model. The choice to estimate the clustered models was due to the presence of serial correlation, through which it was observed that the error term is correlated between different periods for the same company. Thus, the models were estimated to allow correlation within the group. Consequently, the models estimated with robust standard errors to cluster, allowing the observations to be independent between the groups, but not necessarily within the groups, considering that each piped gas company in Brazil represents a group, or a cluster. The applied models and results in this section, of fixed and random effects, were estimated with robust and clustered standard errors. The results of the panel data model estimations are presented in Table 7.  
In general, the results of the models estimated based on Equation (5) provide estimates to verify all the hypotheses of this study. The result of the random effects model indicates that the governance index (ICG) does not influence the overall efficiency of the companies in the piped gas sector in Brazil. Regarding the location effect indicators, it can be observed based on the random effects model result that there is a positive influence between being located in the northern region of Brazil and the efficiency of piped gas companies in Brazil, at the 5% probability level. Thus, companies located in the northern region tend to be 0.2552 more efficient than companies located in the central-western region of Brazil. No influence, either positive or negative, was noted for the other geographical regions.