# Governance and Dynamic Efficiency with Network Structure in the Brazilian Natural Gas Utilities
## 3 Results
Of the ten distributors that reached the overall efficiency frontier, five are located in the southeast, three in the center-west, one in the northeast, and one in the north. For DIV TO, COPERGAS reached the efficiency frontier, adding an efficient distributor to the northeast division. For DIV EF, all the distributors maintained the same characteristic found in the overall score. Among the public and private properties, 100% of the private distributors are on the efficiency frontier, while only 39% of public distributors are. The evaluation of Table 4 and Figure 3 reinforces the importance of delving deeper into the discussion of solid and comprehensive regulation, with the possibility of opening the market to other distributing companies, allowing for evolution in the criteria and production aspects that provide a better position on the efficiency frontier. As can be observed in Table 5, the efficiency of DIV EF shows a stronger relationship with overall efficiency (overall score), whereas DIV TO, despite having a close relationship, is the division that presents the possibility of improvement for natural gas distributors. The density distribution of the efficiency scores for the two divisions based on the overall score is shown in Table 6, respectively, below. Figure 3: Overall and Divisional Efficiency Level of Natural Gas Distributors. Source: Own elaboration. The main advantage of using a DNSBM model is the possibility of exploring divisional efficiencies by period, examining more scores than those generated by DEA models without dynamic network structures. As mentioned in this study, the production process is divided into two divisions (DIV TO and DIV EF). The efficiency scores per period of the two divisions are listed in Figures 4 and 5, where we can visualize a comparison of overall efficiency versus DIV TO and DIV EF, respectively. It is possible to individually identify the effects of each distributor's performance over each studied period, and due to the DNSBM structure, a non-radial slacks-based model, it is possible to analyze each slack individually and identify the sensitivity of each distributor in its trajectory towards the efficiency frontier. The findings of the period-divisional efficiency (\(\rho_{\text{ok}}^{\text{t}}\)) are demonstrated in the divisional analysis below: \begin{table}
\begin{tabular}{c c c} \hline  & **Overall Score** & **DIV TO** & **DIV EF** \\ \hline Overall Score & 1.0000 & \\ DIV TO & 0.9635 * & 1.0000 \\ DIV EF & 0.9753 * & 0.9605 * & 1.0000 \\ \hline \end{tabular} Legend: *Significant at the 1% level. Source: Own elaboration.  
\end{table} 
Table 6: Spearman Correlation between Overall and Divisional Efficiency Scores of Natural Gas Distributors. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Region** & **UF** & **Acronym** & **Overall Score** & **DIV TO** & **DIV EF** \\ \hline North (N) & AM & CIGAS & Yes & Yes & Yes \\ \hline \multirow{6}{*}{Northeast (NE)} & MA & GASMAR & No & No & No \\  & CE & CEGAS & No & No & No \\  & RN & POTIGAS & No & No & No \\  & PB & PBGAS & No & No & No \\  & PE & COPERGAS & No & Yes & No \\  & AL & ALGAS & Yes & Yes & Yes \\  & SE & SERGAS & No & No & No \\  & BA & BAHIAGAS & No & No & No \\ \hline \multirow{6}{*}{Southeast (SE)} & MG & GASMIG & Yes & Yes & Yes \\  & ES & BR-DIST.PBR & Yes & Yes & Yes \\  & RJ & CEG GAS & Yes & Yes & Yes \\  & SP & COMGAS & Yes & Yes & Yes \\  & SP & GAS BRASILIANO & Yes & Yes & Yes \\ \hline \multirow{3}{*}{South (S)} & PR & COMPARGAS & No & No & No \\  & SC & SCGAS & No & No & No \\  & RS & SULGAS & No & No & No \\ \hline \multirow{3}{*}{Midwest (CO)} & DF & CEBGAS & Yes & Yes & Yes \\  & GO & GOAISGAS & Yes & Yes & Yes \\ \cline{1-1}  & MS & MSGAS & No & No & No \\ \cline{1-1}  & MT & MTGAS & Yes & Yes & Yes \\ \hline \end{tabular} Source: Own elaboration.  
\end{table} 
Table 5: Characteristics of Efficient Distributors.