Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A metastochastic frontier analysis for technical efficiency comparison of water companies in England and Wales

  • 46 Accesses

  • 1 Citations


Evaluating the performance of water companies is of great importance for both water utilities and water regulators. This paper explores comparative levels of technical efficiencies and technology gap ratios with the metafrontier concept by estimating an input distance function using stochastic frontier techniques. The metafrontier framework is employed in the water services of water and sewerage companies (WaSCs) and water-only companies (WoCs) in England and Wales. The results show that the English and Welsh water industry is an efficient industry, with WaSCs more efficient than WoCs. On average, a water company can increase its technical efficiency by operating in more densely populated areas and by investing in technology to reduce bursts in water mains. We also link the efficiency results with the regulatory cycle to assess the impact of regulation on the efficiency levels of water companies.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3


  1. 1.

    For English and Welsh water companies, considering the time period analysed in this study, water price was reviewed by Ofwat in 1994, 1999, 2004 and 2009.


  1. Battese GE, Rao DSP (2002) Technology gap, efficiency, and a stochastic Metafrontier function. Int J Bus Econ 1(2):870–930

  2. Battese GE, Rao DP, O’Donnell CJ (2004) A metafrontier production function for estimation of technical efficiencies and technology gaps for firms operating under different technologies. J Prod Anal 21(1):91–103

  3. Berg S, Marques R (2011) Quantitative studies of water and sanitation utilities: a literature survey. Water Policy 13(5):591–606

  4. Bottasso A Conti M (2003) Cost inefficiency in the English and welsh water industry: an heteroskedastic stochastic cost frontier approach. Economics discussion paper 575. University of Essex, Department of Economics

  5. Bottasso A, Conti M (2009) Scale economies, technology and technical change: evidence from the English water only sector. Reg Sci Urban Econ 39(2):138–147

  6. Bottasso A, Conti M, Piacenz M, Vannoni D (2011) The appropriateness of the poolability assumption for multiproduct technologies: evidence from the English water and sewerage utilities. Int J Prod Econ 130(1):112–117

  7. Carvalho P, Marques RC (2011) The influence of the operational environment on the efficiency of water utilities. J Environ Manag 92(10):2698–2707

  8. Carvalho P, Marques RC (2014) Computing economies of vertical integration, economies of scope and economies of scale using partial frontier nonparametric methods. Eur J Oper Res 234(1):292–307

  9. CEPA (2014) Cost assessment—advanced econometric models. Cambridge Economic Policy Associates Ltd, Report prepared for Ofwat

  10. Cherchye L, Demuynck T, De Rock B, De Witte K (2014) Non-parametric analysis of multi-output production with joint inputs. Econ J 124(577):735–775

  11. Coelli T, Rao P, O’Donnell CJ, Battese G (2005) An introduction to efficiency and productivity analysis, 2nd ed. Springer, New York

  12. De Witte K, Marques RC (2009) Capturing the environment, a metafrontier approach to the drinking water sector. Int Trans Oper Res 16(2):257–271

  13. De Witte K, Marques RC (2010) Designing performance incentives, an international benchmark study in the water sector. CEJOR 18:189–220

  14. Ferro G, Mercadier AC (2016) Technical efficiency in Chile’s water and sanitation provides. Util Policy 43:97–106

  15. Fried HO, Knox Lovell CA, Schmidt SS (2008) The measurement of productive efficiency and productivity change, pp. 1-641

  16. Garrido-Baserba M, Vinardell S, Molinos-Senante M, Rosso D, Poch M (2018) The economics of wastewater treatment decentralization: a techno-economic evaluation. Environ Sci Technol 52(15):8965–8976

  17. Giustolisi O, Laucelli D, Berardi L (2013) Operational optimization: water losses versus energy costs. J Hydraul Eng 139(4):410–423

  18. Guerrini A, Romano G, Leardini C (2018) Economies of scale and density in the Italian water industry: a stochastic frontier approach. Util Policy 52:103–111

  19. Hayami Y (1969) Sources of agricultural productivity gap among selected countries. Am J Agric Econ 51(3):564–575

  20. Honma S, Hu J-L (2018) A meta-stochastic frontier analysis for energy efficiency of regions in Japan. J Econ Struct 7(1):21

  21. Huang CJ, Huang TH, Liu NH (2014) A new approach to estimating the metafrontier production function based on a stochastic frontier framework. J Prod Anal 42:241–254

  22. Joskow PL (2014) Incentive regulation in theory and practice: electricity distribution and transmission networks, chapter in NBER book economic regulation and its reform: what have we learned?

  23. Kumbhakar SC (2013) Specification and estimation of multiple output technologies: A primal approach. Eur J Oper Res 231:465–743

  24. Kumbhakar SC, Wang H-J, Horncastle A (2015) A practitioner’s guide to stochastic frontier analysis using STATA. Cambridge University Press

  25. Li H-Z, Kopsakangas-Savolainen M, Xiao X-Z, Lau S-Y (2017) Have regulatory reforms improved the efficiency levels of the Japanese electricity distribution sector? A cost metafrontier-based analysis. Energy Policy 108:606–616

  26. Marques RC (2011) Regulation of water and wastewater services: an international comparison. IWA Publisking, London

  27. Marques RC, Berg S, Yane S (2014) Nonparametric benchmarking of Japanese water utilities: institutional and environmental factors affecting efficiency. J Water Resour Plan Manag 140(5):562–571

  28. Maziotis A, Saal DS, Thanassoulis E, Molinos-Senante M (2015) Profit, productivity and price performance changes in the water and sewerage industry: an empirical application for England and Wales. Clean Techn Environ Policy 17(4):1005–1018

  29. Maziotis A, Saal DS, Thanassoulis E, Molinos-Senante M (2016) Price cap regulation in the English and Welsh water industry: a proposal for measuring performance. Util Policy 41:22–30

  30. Mbuvi D, De Witte K, Perelman S (2012) Urban water sector performance in Africa: A step-wise bias-corrected efficiency and effectiveness analysis. Util Policy 22:31–40

  31. Mellah T, Ben Amor T (2016) Performance of the Tunisian Water Utility: An input-distance function approach. Util Policy 38:18–32

  32. Molinos-Senante M, Maziotis A (2018a) Flexible versus common technology to estimate economies of scale and scope in the water and sewerage industry: an application to England and Wales. Environ Sci Pollut Res 25(14):14158–14170

  33. Molinos-Senante M, Maziotis A (2018b) Assessing the influence of exogenous and quality of service variables on water companies´ performance using a true-fixed stochastic frontier approach. Urban Water J 15(7):682–691

  34. Molinos-Senante M, Sala-Garrido R (2016a) Cross-national comparison of efficiency for water utilities: a metafrontier approach. Clean Techn Environ Policy 18(5):1611–1619

  35. Molinos-Senante M, Sala-Garrido R (2016b) Performance of fully private and concessionary water and sewerage companies: a metafrontier approach. Environ Sci Pollut Res 23(12):11620–11629

  36. Molinos-Senante M, Maziotis A, Sala-Garrido R (2014) The Luenberger productivity indicator in the water industry: an empirical analysis for England and Wales. Util Policy 30:18–28

  37. Molinos-Senante M, Maziotis A, Sala-Garrido R (2015) Assessing the relative efficiency of water companies in the English and welsh water industry: a metafrontier approach. Environ Sci Pollut Res 22(21):16987–16996

  38. Molinos-Senante M, Maziotis A, Sala-Garrido R (2017a) Assessing the productivity change of water companies in England and Wales: a dynamic metafrontier approach. J Environ Manag 197:1–9

  39. Molinos-Senante M, Porcher S, Maziotis A (2017b) Impact of regulation on English and Welsh water-only companies: an input distance function approach. Environ Sci Pollut Res 24(20):16994–17005

  40. Nguyen TPT, Nghiem SH, Roca E, Sharma P (2016) Efficiency, innovation and competition: evidence from Vietnam, China and India. Empir Econ 51(3):1235–1259

  41. O’Donnell CJ, Rao P, Battese GE (2008) Metafrontier frameworks for the study of firm-level efficiencies and technology ratios. Empir Econ 34:231–255

  42. Ofwat (2003) A further consultation on incentive mechanisms: rewarding future outperformance and handling under-performance of regulatory expectations – a consultation paper. Office of Water Services, Birmingham

  43. Ofwat (2004) Future water and sewerage charges 2005–10: final determinations. Office of Water Services, Birmingham

  44. Ofwat (2005) Levels of service for the water industry in England & Wales 2004-2005 report. Office of Water Services, Birmingham

  45. Paramesh V, Arunachalam V, Nikkhah A, Das B, Ghnimi S (2018) Optimization of energy consumption and environmental impacts of arecanut production through coupled data envelopment analysis and life cycle assessment. J Clean Prod 203:674–684

  46. Pinto FS, Simões P, Marques RC (2017) Water services performance: do operational environment and quality factors count? Urban Water J 14(8):773–781

  47. Pollitt M (2005) The role of efficiency estimates in regulatory price reviews: Ofgem’s approach to benchmarking electricity networks. Util Policy 13:279–288

  48. Porcher S, Maziotis A, Molinos-Senante M (2017) The welfare costs of non-marginal water pricing: evidence from the water only companies in England and Wales. Urban Water J 14(9):947–953

  49. Portela MCAS, Thanassoulis E, Horncastle A, Maugg T (2011) Productivity change in the water industry in England and Wales: application of the meta-Malmquist index. J Oper Res Soc 62(12):2173–2188

  50. Roefs I, Meulman B, Vreeburg JHG, Spiller M (2017) Centralised, decentralised or hybrid sanitation systems? Economic evaluation under urban development uncertainty and phased expansion. Water Res 109:274–286

  51. Saal DS, Parker D (2001) Productivity and Price performance in the privatized water and sewerage companies in England and Wales. J Regul Econ 20(1):61–90

  52. Saal DS, Parker D (2006) Assessing the performance of water operations in the English and welsh water industry: a lesson in the implications of inappropriately assuming a common frontier. In: Coelli T, Lawrence D (eds) Performance measurement and regulation of network utilities. Edward Elgar, Cheltenham

  53. Saal DS, Arocena P, Maziotis A (2011) The cost implications of alternative vertical configurations of the English and Welsh water and sewerage industry. ACCIS Working Paper, No. 8. Aston University

  54. Stone and Webster Consultants (2004) Investigation into evidence for economies of scale in the water and sewerage industry in England and Wales; Final Report, Report prepared for and published by Ofwat

  55. Suárez-Varela M, de los Ángeles García-Valiñas M, González-Gómez F, Picazo-Tadeo AJ (2017) Ownership and performance in water services revisited: does private management really outperform public? Water Resour Manag 31(8):2355–2373

  56. Torres M, Morrison P (2006) Driving forces for consolidation or fragmentation in the US water utility industry: a cost function approach with endogenous outputs. J Urban Econ 59:104–120

  57. UN (2019) Sustainable Development Goals by United Nations. Available at:

  58. Wang Q, Zhang H, Zhang W (2013) A Malmquist CO2 emission performance index based on a metafrontier approach. Math Comput Model 58(5–6):1068–1073

  59. Worthington AC (2014) A review of frontier approaches to efficiency and productivity measurement in urban water utilities. Urban Water J 11(1):55–73

Download references

Author information

Correspondence to María Molinos-Senante.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Responsible editor: Philippe Garrigues

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Molinos-Senante, M., Maziotis, A. A metastochastic frontier analysis for technical efficiency comparison of water companies in England and Wales. Environ Sci Pollut Res 27, 729–740 (2020).

Download citation


  • Technical efficiency
  • Metafrontier
  • Stochastic frontier analysis (SFA)
  • Input distance function
  • Water industry