# Governance and Dynamic Efficiency with Network Structure in the Brazilian Natural Gas Utilities
## 4 Discussion  
The efficiencies revealed 75 efficient scores and 51 inefficient scores, with the overall score showing ten efficient companies and eleven inefficient ones. From the results, it is possible to observe that most distributors do not present continuous results over the periods, exhibiting fluctuations in their efficiency scores, indicating that the segment is still evolving. The results obtained from the estimations of the frontiers made it possible to determine the efficiency range in which the DMUs operate, showing the overall efficiency scores of each distributor under evaluation, ranging from a score of 0.0646 to 1. In this analysis, only the distributors with an overall efficiency score of 1 (\(\theta_{\circ}^{*}=1\)) qualify as efficient. In the analysis of the frontiers for each period, considering the inter-temporal trajectory, 48% of the companies are on the efficiency frontier, which represents a segment with low excellence in terms of efficiency. In previous research using the DNSBM model for other segments, the Spearman correlation analysis pointed to a weak relationship between divisional efficiencies [82; 83]. However, our research revealed a positive and statistically significant correlation between the efficiency of DIV TO, that of DIV EF, and overall efficiency, corroborating the findings of [PERSON] (2017) [32], who used the model for his study. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & **Pooled** & **Fixed Effect** & **Random Effect** \\ \hline ICG & \(-\)0.3648 & 0.6283 & 0.2886 \\ Northeast & 0.0011 & & \(-\)0.0457 \\ North & 0.2102 ** & & 0.2552 ** \\ South & \(-\)0.1782 & & \(-\)0.3030 \\ Southeast & 0.1035 & & \(-\)0.0541 \\ Pub & \(-\)0.2339 *** & & \(-\)0.1998 * \\ DensPop & 0.0000 *** & 0.0006 *** & 0.00001 *** \\ Constant & 1.2004 *** & 0.0866 & 0.8040 \\ Quantity of Observations & 126 & 126 & 126 \\ R2 & 0.2379 & 0.0230 & \\ R2\_O & & 0.0209 & 0.2093 \\ R2\_B & & 0.0257 & 0.2603 \\ R2\_w & & 0.0230 & 0.0144 \\ Sigma\_u & & 0.9928 & 0.2819 \\ Sigma\_e & & 0.1499 & 0.1499 \\ rho & & 0.9777 & 0.7795 \\ \hline \hline \end{tabular} Legend: *** Significant at 1%, ** Significant at 5%, * Significant at 10%. Source: Prepared by the author with research data.  
\end{table} 
Table 7: Results of Panel Data Applied for Analysis of the Relationship between Governance and Ownership on the Efficiency of Piped Gas Distributors. In general, it can be argued that, being positioned in a market with a natural monopoly, where the state monopoly prevails, with each federation entity granting the activity, these distributors had to improve their economic and financial efficiency to compensate for the increasing costs of each individualized regulation. This finding corroborates the finding of [PERSON] and [PERSON] (1999) [84], which shows that'regulatory distortions' can be corrected through benchmarking and market opening, encompassing a broader set of regulatory measures. This discovery may have been due to the DNSBM model employed or the short study period (2014-2019), as, given the characteristics of each distributor and the market in which they operate, costs similarly affect the vast majority of distributors. Our results may provide evidence that confirms [PERSON] and [PERSON]'s (2008) [23] hypothesis, whose findings suggest a strong need for regulatory rules that can reproduce competitive conditions for gas distributors. According to Table 7, it is not possible to confirm hypothesis H\({}_{1}\), which predicted a positive relationship between corporate governance and efficiency, moving in the opposite direction to the studies by [PERSON] and [PERSON] [85], [PERSON] and [PERSON] [71], [PERSON] et al. [86], [PERSON] and [PERSON] [87], [PERSON] et al. [88], and [PERSON] et al. [89]. The results of the estimated models show that there are statistically significant indications in this study to support hypothesis H\({}_{2}\).