# Governance and Dynamic Efficiency with Network Structure in the Brazilian Natural Gas Utilities
## 2 Materials and Methods
### Hypothesis Development  
There are numerous records in the literature of studies whose main objective is to empirically confirm that the adoption of corporate governance practices influences the efficiency of companies. However, despite the extensive range of research, there are still inconsistencies in the results. This is due to the limitation of the lack of a consolidated theoretical framework or conclusive empirical evidence on how (and whether) governance mechanisms influence efficiency, as well as how these mechanisms relate to each other, either as complements or as substitutes [69].  
As it presents some interesting lines of investigation, the topic is considered controversial, especially due to the distinct approaches and application of different theoretical frameworks [70]. Several authors have addressed the advantages obtained by companies that adopt good corporate governance practices. For example, the relationship between the corporate governance system and technical efficiency in the Italian industry motivated the study by [71], showing that both dimensions of governance proved to have a positive impact on efficiency.  
Corporate governance provides a mechanism to direct a company to develop its activities efficiently [72], as it deals with the rules on how to govern rights and responsibilities in various scenarios, aiming to prevent corporate failures. Regarding the pipeline gas segment, there are no studies in the literature that examine the impact of governance on the efficiency of distribution companies. Thus, we formulate the following hypothesis:  
H\({}_{1}\) : There is a positive association between corporate governance and the efficiency of pipeline gas distributors in Brazil.  
The myth of an independent ownership role for better efficiency can no longer be debated, as the lack of a strong control mechanism gives management the freedom to pursue its own goals, which may not be aligned with those of shareholders. Thus, it is widely recognized that ownership concentration is the primary determinant of the governance mechanism, as it directly affects the company's efficiency [73]. Ownership concentration is the most important factor in shaping the corporate governance system of any company.  
Managers of a public company may not have the autonomy to make decisions for optimal management. In contrast, private ownership provides the company with decision-making autonomy but often faces high capital costs (i.e., high operating costs). According to [PERSON] and [PERSON] [74], the relationship between ownership concentration and governance can have a positive or negative effect, directly impacting efficiency. The issue of ownership has long been discussed as a corporate governance problem [75].  
Conversely, there are studies that argue that less radical methods, such as managerial incentive contracts, market deregulation, and internal and external governance reform, are effective substitutes for full privatization [76; 77; 78]. Therefore, it is essential to understand how ownership concentration influences the efficiency of pipeline gas distributors. Thus, the second hypothesis is as follows:  
H\({}_{2}\) : There is a significant positive association between ownership concentration and the efficiency of pipeline gas distributors in Brazil.