## Efficiency Estimation

**Know where your company stands in the ranking of the most efficient!**

The goal of BenchSmart is to **estimate the cost efficiency** of each company. To do so, it is estimated the distance between the real cost of each company and the frontier costs, that is, the minimum possible costs defined based on all the companies in the study, using **stochastic frontier techniques**.

These results indicate the cost reduction margin of each company, that is, if the efficiency of the company is 80%, then it has a reduction margin of 20% to be located in the frontier.

#### Models Run

Several econometric models were run using **stochastic frontier techniques with panel data **and including different variables to explain OPEX.

#### Robust Models

Then, the **models with varying efficiency in the estimated time for true fixed effects** are selected. These purify the efficiency error of the effects, which reflect own characteristics of the companies that are not necessarily associated with inefficient practices.

**Estimated Models**

Model |
Supplies |
Products |
Heteroscedasticity sigma v |

1 |
OPEX | Customers | Constant |

2 |
OPEX | Costumers, Sales | Constant |

3 |
OPEX | Costumers, Sales | Density |

4 |
OPEX | Costumers, Sales | Network |

5 |
OPEX | Network | Network |

6 |
OPEX | Network, Network squared | Density |

7 |
OPEX | Customers, Network per Customers | Constant |

8 |
Labour force, CMSO | Customers | Density |

9 |
Labour force, CMSO | Customers, Customers squared, Network per Customers | Density |

10 |
Labour force, CMSO | Costumers, Sales | Network per Costumer |

11 |
Labour force, CMSO | Customers, Network | Constant |

** CMSO*

*CMSO stands for Cost of Materials, Services and Others*

##### Selected Models for Residential

**Model 3** controls customers and sales with a heteroscedasticity correction by network density. In that sense, this model is superior to the 1, 2 and 7 that are homoscedastic and the models 5 and 6 that only include the network length. In this way, the efficient OPEX is explained by the customers, the driver of commercial costs and sales, the driver of costs associated with the system capacity.

**Model 9** is explained by customers and by the joint effect of customers and network length. It is also heterogeneous with respect to network density and considers the number of employees and the CMSO as inputs. The model includes a quadratic term to capture the economies of scale associated with customers. In general, it captures the size of the companies in the sample.

##### Selected Models for Non-Residential

For companies characterized as “Non-Residential” that present relatively few clients compared to other distribution companies, the customer variable is not relevant to explain the frontier. On the contrary, the maintenance of the networks is significant.

**Models 5 and 6**, which define the stochastic frontier with the network, are those that best represent the reality of industrial distribution companies