# Are Frontier Efficiency Methods Adequate to Compare the Efficiency of Water Utilities for Regulatory Purposes?

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## Abstract

**:**

## 1. Introduction

- Partial efficiency measures;
- Average efficiency measures;
- Econometric frontier efficiency methods;
- Non-parametric frontier efficiency methods.

## 2. Methods

_{n}where n = 1, …, N to generate a set of outputs y

_{m}, where m = 1, …, M. The linear programming model is written as follows:

_{j}) in the sample is then calculated as ${\mathrm{CE}}_{\mathrm{j}}=\mathrm{exp}\left({\mathrm{u}}_{\mathrm{j}}\right).$ In this study the volume of water delivered, the number of connections, and the length of mains are used as proxies for density. Additional cost drivers are used to capture the quality of service, such as volume of water loss and the number of water service interruptions. Similar variables were also employed in Murwirapachena et al. [22] in the context of water and in Kuosmanen [25] and Jamsbab et al. [26] in the electricity sector.

#### Description of the Sample

^{3}/year), service interruptions (number/year), volume of produced water (m

^{3}/year), and number of households covered by the water service (No.). The description of each variable can be found in the ERSAR Technical Guide [30]. Table 1 summarizes the use of these variables in each model.

## 3. Impacts of Data Quality and Uncertainty

#### 3.1. General Considerations

#### 3.2. Data Envelopment Analysis Model

^{4}) DEA scenarios were run with different combinations of values for variables. The three are the alternatives which correspond to the situations considered for each utility (DMU): favorable, unfavorable, and original. The number four are the possible combinations of inputs and outputs were used for the analyzed utility. These are inputs and outputs for the analyzed DMU and inputs and outputs for the remaining DMUs. Thus, the best case scenario for the evaluated utility is has the lowest values for inputs and the highest for outputs.

#### 3.3. Stochastic Frontier Analysis Model

## 4. Further DEA and SFA Limitations

#### 4.1. Limitation of the Number of Variables

#### 4.2. Other Limitations of Frontier Efficiency Methods for Regulatory Uses

## 5. Consistency Check of DEA and SFA Models

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Variables | Parameter | Coefficient | Standard Error | T-Statistic | p-Value |
---|---|---|---|---|---|

Constant | β_{0} | 4.165 | 0.864 | 4.823 | 0.000 |

Water delivered | β_{1} | 0.789 | 0.111 | 7.098 | 0.000 |

Connections | β_{2} | 0.287 | 0.108 | 2.650 | 0.008 |

Network length | β_{3} | 0.145 | 0.053 | 2.718 | 0.007 |

Service interruptions | β_{4} | 0.003 | 0.024 | 0.117 | 0.907 |

Water losses | β_{5} | −0.285 | 0.064 | −4.486 | 0.000 |

Log-likelihood | −31.839 | ||||

Theta | 4.020 | 0.749 | 5.366 | 0.000 | |

Sigmav | 0.228 | 0.029 | 7.848 | 0.000 |

Variables | Parameter | Coefficient | S.E. | T-Statistic | p-Value |
---|---|---|---|---|---|

Constant | β_{0} | 4.420 | 0.926 | 4.775 | 0.000 |

Water delivered | β_{1} | 0.800 | 0.117 | 6.832 | 0.000 |

Connections | β_{2} | 0.303 | 0.112 | 2.693 | 0.007 |

Network length | β_{3} | 0.167 | 0.057 | 2.951 | 0.003 |

Service interruptions | β_{4} | −0.002 | 0.026 | −0.075 | 0.940 |

Water losses | β_{5} | −0.305 | 0.068 | −4.468 | 0.000 |

Log-likelihood | −42.116 | ||||

Theta | 3.473 | 0.667 | 5.207 | 0.000 | |

Sigmav | 0.241 | 0.036 | 6.738 | 0.000 |

Variables | Parameter | Coefficient | S.E. | T-Statistic | p-Value |
---|---|---|---|---|---|

Constant | β_{0} | 4.037 | 0.848 | 4.762 | 0.000 |

Water delivered | β_{1} | 0.780 | 0.109 | 7.122 | 0.000 |

Connections | β_{2} | 0.286 | 0.107 | 2.667 | 0.008 |

Network length | β_{3} | 0.138 | 0.052 | 2.631 | 0.009 |

Service interruptions | β_{4} | 0.004 | 0.023 | 0.155 | 0.877 |

Water losses | β_{5} | −0.276 | 0.062 | −4.418 | 0.000 |

Log-likelihood | −29.887 | ||||

Theta | 4.094 | 0.751 | 5.450 | 0.000 | |

Sigmav | 0.224 | 0.028 | 8.010 | 0.000 |

## References

- Posner, R.A. Natural Monopoly and Its Regulation. Stanf. Law Rev.
**1969**, 21, 548. [Google Scholar] [CrossRef] [Green Version] - Shleifer, A. A Theory of Yardstick Competition. RAND J. Econ.
**1985**, 16, 319. [Google Scholar] [CrossRef] - Coelli, T.; Walding, S. Performance measurement in the Australian water supply industry: A preliminary analysis. In Performance Measurement and Regulation of Network Utilities, 1st ed.; Edward Elgar Publishing Limited: Cornwall, UK, 2006. [Google Scholar]
- Ferro, G.; Lentini, E.; Romero, C.A. Eficiencia y su Medición en Prestadores de Servicios de Agua Potable y Alcantarillado. Available online: http://hispagua.cedex.es/sites/default/files/hispagua_documento/documentacion/documentos/eficiencia_agua_potable_alcantarillado.pdf (accessed on 10 December 2019).
- Abbott, M.; Cohen, B. Productivity and efficiency in the water industry. Util. Policy
**2009**, 17, 233–244. [Google Scholar] [CrossRef] - Ferro, G.; Lentini, E.J.; Mercadier, A.C.; Romero, C.A. Efficiency in Brazil’s water and sanitation sector and its relationship with regional provision, property and the independence of operators. Util. Policy
**2014**, 28, 42–51. [Google Scholar] [CrossRef] - CEPA (Cambridge Economic Policy Associates Ltd.). OFWAT: Cost Assessment—Advanced Econometric Models. Available online: https://www.ofwat.gov.uk/wp-content/uploads/2015/11/rpt_com201301cepacostassess.pdf (accessed on 20 May 2017).
- Forsyningssekretariatet. Total Economic Benchmarking—Determination of Individual Efficiency Requirements in the Financial Framework for 2018–2019 for Water and Wastewater Companies; Forsyningssekretariatet: Copenhagen, Denmark, 2017. [Google Scholar]
- Cabrera, E., Jr. The need for the regulation of water services. Key factors involved. In Regulation of Urban Water Services. An Overview; Marcet, E.C., Cabrera, E., Jr., Eds.; IWA Publishing: London, UK, 2016; p. 218. [Google Scholar]
- Cooper, W.W.; Seiford, L.M.; Zhu, J. Handbook on Data Envelopment Analysis; Springer: Berlin/Heidelberg, Germany, 2011. [Google Scholar]
- ISO. Activities Relating to Drinking Water and Wastewater Services—Guidelines for the Assessment and for the Improvement of the Service to Users; ISO Copyright Office: Geneva, Switzerland, 2007. [Google Scholar]
- Byrnes, J.; Crase, L.; Dollery, B.; Villano, R.A. The relative economic efficiency of urban water utilities in regional New South Wales and Victoria. Resour. Energy Econ.
**2010**, 32, 439–455. [Google Scholar] [CrossRef] - Thanassoulis, E. The use of data envelopment analysis in the regulation of UK water utilities: Water distribution. Eur. J. Oper. Res.
**2000**, 126, 436–453. [Google Scholar] [CrossRef] - Yekta, A.P.; Kordrostami, S.; Amirteimoori, A.; Matin, R.K. Data envelopment analysis with common weights: The weight restriction approach. Math. Sci.
**2018**, 12, 197–203. [Google Scholar] [CrossRef] [Green Version] - De Witte, K.; Marques, R.C. Influential observations in frontier models, a robust non-oriented approach to the water sector. Ann. Oper. Res.
**2010**, 181, 377–392. [Google Scholar] [CrossRef] [Green Version] - Berg, S.; Marques, R.C. Quantitative studies of water and sanitation utilities: A benchmarking literature survey. Hydrol. Res.
**2011**, 13, 591–606. [Google Scholar] [CrossRef] [Green Version] - Worthington, A.C. A review of frontier approaches to efficiency and productivity measurement in urban water utilities. Urban Water J.
**2013**, 11, 55–73. [Google Scholar] [CrossRef] - Aigner, D.; Lovell, C.; Schmidt, P. Formulation and estimation of stochastic frontier production function models. J. Econ.
**1977**, 6, 21–37. [Google Scholar] [CrossRef] - Meeusen, W.; Broeck, J.V.D. Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error. Int. Econ. Rev.
**1977**, 18, 435. [Google Scholar] [CrossRef] - Cullmann, A. Benchmarking and firm heterogeneity: A latent class analysis for German electricity distribution companies. Empir. Econ.
**2010**, 42, 147–169. [Google Scholar] [CrossRef] - Ferro, G.; Mercadier, A.C. Technical efficiency in Chile’s water and sanitation providers. Util. Policy
**2016**, 43, 97–106. [Google Scholar] [CrossRef] - Murwirapachena, G.; Mahabir, J.; Mulwa, R.; Dikgang, J. Efficiency in South African Water Utilities: A Comparison of Estimates from DEA, SFA and StoNED; Economic Research Southern Africa (ERSA): Cape Town, South Africa, 2019. [Google Scholar]
- Saal, D.S.; Parker, D.; Weyman-Jones, T. Determining the contribution of technical change, efficiency change and scale change to productivity growth in the privatized English and Welsh water and sewerage industry: 1985–2000. J. Prod. Anal.
**2007**, 28, 127–139. [Google Scholar] [CrossRef] - Molinos-Senante, M.; Porcher, S.; Maziotis, A. Impact of regulation on English and Welsh water-only companies: An input-distance function approach. Environ. Sci. Pollut. Res.
**2017**, 24, 16994–17005. [Google Scholar] [CrossRef] - Kuosmanen, T. Stochastic Semi-Nonparametric Efficiency Analysis of Electricity Distribution Networks: Application of the StoNED Method in the Finnish Regulatory Model. SSRN Electron. J.
**2011**, 34, 2189–2199. [Google Scholar] [CrossRef] - Jamasb, T.; Orea, L.; Pollitt, M. Estimating the marginal cost of quality improvements: The case of the UK electricity distribution companies. Energy Econ.
**2012**, 34, 1498–1506. [Google Scholar] [CrossRef] [Green Version] - ERSAR. ERSAR—Relatório Anual dos Serviços de Águas e Resíduos em Portugal. 2015. Available online: http://www.esgra.pt/ersar-relatorio-anual-dos-servicos-de-aguas-e-residuos-em-portugal/ (accessed on 16 June 2017).
- Marques, R.C.; Berg, S.V.; Yane, S. Nonparametric Benchmarking of Japanese Water Utilities: Institutional and Environmental Factors Affecting Efficiency. J. Water Resour. Plan. Manag.
**2014**, 140, 562–571. [Google Scholar] [CrossRef] [Green Version] - Pinto, F.S.; Costa, A.S.; Figueira, J.R.; Marques, R.C. The quality of service: An overall performance assessment for water utilities. Omega
**2017**, 69, 115–125. [Google Scholar] [CrossRef] - ERSAR. Guide for the Assessment of the Quality of Water and Waste Services, 3rd Generation of the Assessment System; ERSAR: Lisbon, Portugal, 2011. [Google Scholar]
- ISO. Water Meters for Cold Potable Water and Hot Water—Part 1: Metrological and Technical Requirements; ISO Copyright Office: Geneva, Switzerland, 2018. [Google Scholar]
- Arregui, F.; Cabrera, E.; Cobacho, R.; García-Serra, J. Key factors affecting water meter accuracy. In Proceedings of the Specialised Conference of the IWA, Halifax, NS, Canada, 12–14 July 2005; pp. 1–10. [Google Scholar]
- Matos, R.; Cardoso, M.; Duarte, P.; Ashley, R.; Molinari, A.; Schulz, A. Performance indicators for wastewater services—Towards a manual of best practice. Water Supply
**2003**, 3, 365–371. [Google Scholar] [CrossRef] - Alegre, H.; Baptista, J.; Cabrera, E.; Cubillo, F.; Duarte, P.; Hirner, W.; Merkel, W.; Parena, R. Performance Indicators for Water Supply Services: Third Edition. Water Intell. Online
**2016**, 15. [Google Scholar] [CrossRef] - Cabrera, E.; Estruch-Juan, E.; Molinos-Senante, M. Adequacy of DEA as a regulatory tool in the water sector. The impact of data uncertainty. Environ. Sci. Policy
**2018**, 85, 155–162. [Google Scholar] [CrossRef] - Molinos-Senante, M.; Donoso, G.; Sala-Garrido, R. Assessing the efficiency of Chilean water and sewerage companies accounting for uncertainty. Environ. Sci. Policy
**2016**, 61, 116–123. [Google Scholar] [CrossRef] - Picazo-Tadeo, A.J.; Fernandez, F.J.S.; González-Gómez, F. Does service quality matter in measuring the performance of water utilities? Util. Policy
**2008**, 16, 30–38. [Google Scholar] [CrossRef] [Green Version] - Marques, R.C.; Contreras, F.H.G. Performance-based potable water and sewer service regulation: The regulatory model. Cuad. Adm.
**2007**, 20, 283–298. [Google Scholar] - Dubouskaya, A. Relative Performance of DEA and SFA in Response to Multicollinearity and Measurement Error Problems. Master’s Thesis, National University “Kyiv-Mohyla Academy”, Kiev, Ukraine, 2006. [Google Scholar]
- IWA. The Lisbon Charter; IWA Publishing: London, UK, 2015. [Google Scholar]
- OFWAT. Delivering Water 2020: Our Final Methodology for the 2019 Price Review; OFWAT: London, UK, 2017.
- OFWAT. Setting price limits for 2010-15: Framework and Approach; OFWAT: London, UK, 2008.
- Kumbhakar, S. A Critique of Ofwat’s Cost Assessment Models; Southern water: Worthing, UK, 2014. [Google Scholar]
- Berg, S.; Lin, C. Consistency in performance rankings: The Peru water sector. Appl. Econ.
**2008**, 40, 793–805. [Google Scholar] [CrossRef] - Ferro, G.; Romero, C.A. Setting performance standards for regulation of water services: Benchmarking Latin American utilities. Hydrol. Res.
**2011**, 13, 607–623. [Google Scholar] [CrossRef] - Molinos-Senante, M.; Maziotis, A. Productivity growth and its drivers in the Chilean water and sewerage industry: A comparison of alternative benchmarking techniques. Urban Water J.
**2019**, 16, 353–364. [Google Scholar] [CrossRef] - Corton, M.L.; Berg, S.V. Benchmarking Central American water utilities. Util. Policy
**2009**, 17, 267–275. [Google Scholar] [CrossRef] [Green Version]

**Figure 2.**Minimum, maximum, and original data envelopment analysis (DEA) results for the reduced sample [36].

**Figure 3.**Minimum, maximum, and original stochastic frontier analysis (SFA) results for the reduced sample.

**Figure 4.**Comparison of the efficiency scores from the reduced sample for SFA and DEA models: (

**a**) efficiency results for both SFA and DEA models: (

**b**) differences in the ranking positions between both methods.

**Table 1.**Configuration of the variables for the data envelopment analysis (DEA) and stochastic frontier analysis (SFA) models.

Variables | DEA Model | SFA Model |
---|---|---|

Network length (km) | Input | Independent/Output |

Total expenses (€/year) | Input | Dependent |

Volume of real water losses (m^{3}/year) | Input | Independent/Environmental |

Service interruptions (number/year) | Input | Independent/Environmental |

Volume of produced water (m^{3}/year) | Output | Independent/Output |

Number of households covered by the water service (number/year) | Output | Independent/Output |

Variables | Unit | Mean | Standard Deviation | Minimum | Maximum |
---|---|---|---|---|---|

Volume of water produced | m^{3}/year | 3,994,778 | 8,971,219 | 133,259 | 107,304,807 |

Number of households covered by the water service | nr/year | 22,161 | 36,715 | 1157 | 308,986 |

Network length | km | 448 | 479 | 7 | 3960 |

Total expenses | €/year | 3,777,639 | 7,114,562 | 0.001 | 72,270,048 |

Volume of real water losses | m^{3}/year | 751,023 | 975,151 | 8000 | 5,694,343 |

Service interruptions | nr/year | 15 | 31 | 0.001 | 233 |

Observations | 194 |

ID Utility | Original Simulation | Simulation 1 | Simulation 2 | Max ΔPosition | ||
---|---|---|---|---|---|---|

Ranking Position | Ranking Position | ΔPosition | Ranking Position | ΔPosition | ||

49 | 34 | 30 | 4 | 55 | −21 | 25 |

15 | 24 | 43 | −19 | 19 | 5 | 24 |

39 | 20 | 39 | −19 | 18 | 2 | 21 |

26 | 8 | 25 | −17 | 6 | 2 | 19 |

Gas | Electricity | Drinking Water/Wastewater |
---|---|---|

Continuity | Continuity | Continuity |

Suitable rates | Suitable rates | Suitable rates |

Correct customer management | Correct customer management | Correct customer management |

Suitable voltage/current | Suitable pressure/flow rate | |

Drinkability | ||

No taste | ||

No smell | ||

No residual flooding | ||

Minimum environmental impact |

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**MDPI and ACS Style**

Estruch-Juan, E.; Cabrera, E., Jr.; Molinos-Senante, M.; Maziotis, A.
Are Frontier Efficiency Methods Adequate to Compare the Efficiency of Water Utilities for Regulatory Purposes? *Water* **2020**, *12*, 1046.
https://doi.org/10.3390/w12041046

**AMA Style**

Estruch-Juan E, Cabrera E Jr., Molinos-Senante M, Maziotis A.
Are Frontier Efficiency Methods Adequate to Compare the Efficiency of Water Utilities for Regulatory Purposes? *Water*. 2020; 12(4):1046.
https://doi.org/10.3390/w12041046

**Chicago/Turabian Style**

Estruch-Juan, Elvira, Enrique Cabrera, Jr., María Molinos-Senante, and Alexandros Maziotis.
2020. "Are Frontier Efficiency Methods Adequate to Compare the Efficiency of Water Utilities for Regulatory Purposes?" *Water* 12, no. 4: 1046.
https://doi.org/10.3390/w12041046