Innovative Applications of O.R.
Evaluating the water sector in Italy through a two stage method using the conditional robust nonparametric frontier and multivariate adaptive regression splines

https://doi.org/10.1016/j.ejor.2011.02.003Get rights and content

Abstract

The aim of this paper is to assess the efficiency of the integrated water service in Italy in recent years, through a robust and flexible methodology. This paper, from a methodological point of view, enhances a ”two stage” method, based on ideas suggested by Florens and Simar (2005), which estimates the efficiency frontier through conditional robust models and bypasses, at the same time, the choice of a specific functional form in the second stage; the MARS (Multivariate Adaptive Regression splines) method, in fact, provides for approximate production function using linear splines without any assumption of a functional form.

Applying this specific two stage method, despite poor assumptions of the production function form, we provide an estimate for the Italian water companies; we have found spatial and dimensional patterns, especially in metropolitan vs. low density areas.

Introduction

The purpose of this article is to present an original methodology that complements to classical ones, for the estimation of productive efficiency in public services, and in particular in a natural monopoly sector like water sector. The more common approaches in this field are based on nonparametric methods, such as, for example, the Data Envelopment Analysis (Charnes et al., 1978) or the Free Disposal Hull (Deprins et al., 1984) which offer several advantages, such as, for example, the absence of specification of the functional form in the relationships between input and output in multi-dimensional spaces, the measure of efficiency relating to an efficiency frontier and the non-necessity of some theoretical benchmarks.

Such methods in not identifying a precise functional form, do not grant the possibility of a generalization of the results attained; for this reason and to have tools at hand that allow for subsequent simulations, some researchers (see e.g. Curram et al., 2004) have proposed alternative nonparametric regression methods, such as for example artificial neural networks.

This paper presents an original productive efficiency estimation method that uses the Multivariate Adaptive Regression Splines (Friedman, 1991); it is a regression technique that in adopting a divide and conquer type computational strategy on different subgroups of data establishes the relationship between input and output thanks to a set of coefficients and to basis functions that are completely data driven, thereby attaining for each subgroup a regression line or, more generally, an hyperplane.

The Italian public utilities are undergoing a phase of radical change. The innovations introduced regard multiple aspects of the sector, including: the regulatory framework, the legal and economic nature of the subjects involved, the structure and the dimensions of the markets. The concept of productive efficiency acquires special significance in the water sector in Italy; this is the sector in which the economic variable in question, that is the proceeds, is subject to regulation.

More specifically, Italian legislation with the Galli law (Law No. 36, dated the 5th of January 1994) later repealed and supplemented with the Legislative Decree No. 156, dated the 3rd of April 2006 and subsequent amendments and supplements thereto intended to regulate, in a structured way, the local public services and more specifically the water services. The pricing system for such service is defined by the Ministerial Decree dated 1/8/96, noted also as a Standardized Method to determine the cost components and to determine the fees in question.

Although the introduction of the fee calculated on the basis of the Standardized Method occurred slowly, until today it can be observed that the integrated water service implements an industrial model, that is applying a service fee that sustains production costs and finances the investments, for 79.2% of the population (Utilitatis, 2008).

The highlighted aspects constitute only some of the major legal changes in the reforms of the water service, even if some difficulties related to their effective implementation may be observed. Legislators and legislation do not always obtain positive results due to both the complexity of the industrial situation in which the reform takes place and the weaknesses of the planned regulation model when the reform is implemented.

In Italy, the governing system of regulation in the water sector is based, in fact, on two levels: central and local. The main body is represented by the Supervisory Board for Water Resources (Co.Vi.Ri.) that operates within the Ministry of the Environment, which has functions of control and orientation. The local government is organized in territorial areas where borders are established by regions and defined on the basis of hydrographic criteria (catchment areas) of contiguity, of positioning of the supplies and/or destination of the sewage, with the aim of creating territorial dimensions whose economic and technical management attains efficiency and affordability.

Each territorial area refers to its own Authority of the Optimal Territorial Area (“ATO”, because it is an Italian abbreviation for “Ambito Territoriale Ottimale”) which has a legal character and has the task of organizing the integrated water service.

To assess the relative productive efficiency and the cost structures of a unit in the relevant literature, different analysis techniques have been used since the first study carried out by Ford and Warford (1969).

Efficiency studies have been carried out from different perspectives (for a more complete literature, see Gonzalez and Rubio, 2008) to analyze whether it was a more efficient management of water cycle when assigned to a single company or several companies, to better investigate the economies of scale in a natural monopoly, for comparing public or private management and to identify and quantify the environmental factors in terms of explaining differences in efficiency.

Since the 1990s, thanks to the methodological improvements in parametric (SFA) and in nonparametric (FDH/DEA) analysis, most of the studies carried out make use of frontier techniques.

In particular, for the economic analysis of the water sector, it is worth noting works by Byrnes, 1985, Lambert et al., 1993, Cubbin and Tzanidakis, 1998 that use the DEA methodology, although the first works in this specific field mostly concentrated on the econometric estimate of the cost function.

Stewart (1993), for example, estimated a cost function for a sample of water companies in the United Kingdom. As explanatory variables, he considered the volume of water supplied, the length of the network, the amount of water supplied for non domestic aims and other dimensional factors.

Lynk (1993) used the analysis of the stochastic frontier to evaluate the efficiency of both the water sector alone and the water sector and the sewage network together in England and Wales; he used data related to the labour costs, to the water supplied on a daily basis, and to the sewage network, estimated though the volumes of water that flow through the network daily, in conjunction with two dummy variables, one temporal and one regional.

Optimization analyses of costs and sources of inefficiency in the water sector have been carried out by Bhattacharyya et al. (1995) as well.

For about 10 companies observed from 1989 to 1997 in the English market, Ashton (1999) analyzed the water and sewage sector through a translog type cost frontier. As output he choose the number of families connected to the distributive system, while he considered as input the cost of work, materials of consumption (defined as the relationship between the expense level for consumable goods, among which are the electric costs, materials, taxes and duties and direct costs and the level of assistance and fixed costs) and the cost of capital.

Also Garcia and Alban (2001) analyzed the cost structure of French water companies through a translog cost function.

In recent years, the econometric approach has left room for analytical methods that mainly focus on efficiency.

Estache and Rossi (2002), for example, used the stochastic frontiers to estimate a cost function for a sample of companies in Asia and the Pacific region; as explanatory variables they considered the number of clients, the daily production, the density of the population in the area served, the percentage of water from surface sources, pay levels of the personnel, the number of hours of availability of water and the relationship between the residential sales and the total sales in cubic meters.

Thanassoulis (2000), instead, in a study on a particular period of the regulations of British water services, such as that of modifying the criteria of calculating fees which took place in 1994 by the regulator of the water sector (OFWAT), estimated, through a DEA analysis, the savings in the operational costs of the water distribution.

Cardoso et al. (2000) used the DEA method applying it to the Portuguese water sector that is characterized by management that is partly entrusted to the local authorities and partly to private entities.

Among the more recent works to be mentioned is that of Shih et al. (2006) in which the technical efficiency and the economies of scale in the municipal water services in the USA have been measured, thereby focusing on the services managed by companies of small or very small dimensions; as we shall also see in the water sector in Italy, the small dimension of the companies may represent an obstacle to the efficiency of the service making diseconomies of scale emerge, due to the elevated costs of production and to the difficulty of achieving financial, technical and managerial capacities.

As far as regards the Italian market, recent studies conducted on Italian companies have demonstrated the existence of economies of scale in the water sector, but such integration proceeds extremely slowly given the conflicts of or among the local authorities. In particular, the current regulatory framework, in most cases, leads to outsourcing with no public competition for contracts and the creation of a highly fragmented system of management among different companies within an ATO.

Among the more interesting studies, it is worth noting the work by Pigliapoco (1997) where an analysis is made of the cost function that presents as output the quantity of water supplied while the input is presented as labour costs, materials, services and electrical energy used.

Antonioli and Filippini (2001) estimate a multivariate variable cost function in a SFA framework in order to analyze the cost structure of a panel data sample of Italian water distribution companies, demonstrating the importance of explanatory variables such as price of labor, water loss and service area characteristics.

Fraquelli focuses on both on the Italian peculiarities in determining fees (Fraquelli and Fabbri, 1997) and on the analyses of efficiency of Italian companies (see in particular Fraquelli and Giandrone, 2003, Fabbri and Fraquelli, 2000, Fraquelli and Moiso, 2005). He concludes that “the presence of relevant scale economies suggests that the situation could be improved by a reduced fragmentation at the local level”.

In particular the aim of our paper, although essentially methodological, is to investigate the effects of consumer density (density of inhabitants per km2) incorporating this environmental factor in a more consistent framework (conditional order-m approach, see Section 2.1) and, at the same time, to obtain an estimation of the functional relationships between inputs and output on the efficient frontier in a nonparametric way (MARS approach).

It is worth noting, finally, that Italy presents another difficulty in the efficiency analysis due to the lack of reliable, complete and verified databases, since the data collection is not entrusted to a Public Central Administration.

The present work is structured as follows: in the second section the two stage methods and MARS models are briefly outlined; the results are presented in the third section and the conclusive observations in the fourth section.

Section snippets

Two stage methods

Nonparametric estimators are very appealing because they rely on very few assumptions for the shape of the frontier; however this flexibility and generalization do not provide for easier and better economic interpretation of the production frontier.

In 2005, Florens and Simar (2005) proposed a two stage method for estimating the parametric model in an individual way overcoming most drawbacks of the classical approaches; they first proposed to plot the cloud of data points on a nonparametric

Data

Data used for our analyses derived from Plans for the Area, drafted by ATO, whose systematic collection of information is the basis for the monographic study “Blue Book – i dati sul servizio idrico integrato in Italia” (Utilitatis, 2008) which reports the planning of 82 ATOs that are the source for 91 Plans for the Area (the numbers do not correspond because some ATOs were divided into sub-areas).

The advantage of using this information lies in the fact that it may help overcome the information

Conclusions

In the present article we have estimated the efficiency levels in the water sector in Italy aimed at testing an original methodology to complement the classical ones; such estimates, which were carried out starting with official data that is not yet public at the disaggregate level, base their validity on the robustness and flexibility of the model and the absence of hypotheses a priori.

The results demonstrate how the MARS techniques may be used in a complementary way to the classic estimate

Acknowledgements

The author thanks Dr. Rita Mileno (Utilitatis) for support and making avalaible Italian water basic data. Thanks are due to two referees for their valuable comments, too.

References (36)

  • Cardoso, J., Soares, C. Martins, J., 2000. Application of data envelopment analysis to the portuguese water sector,...
  • Curram, S., Athanassopoulos, A., Antreas, A. Shale, B., 2004. A frontier based neural network for assessing the...
  • C. Daraio et al.

    Introducing environmental variables in nonparametric frontier models: a probabilistic approach

    Journal of Productivity Analysis

    (2005)
  • C. Daraio et al.

    Advanced Robust and Nonparametric Methods in Efficiency Analysis: Methodology and Applications

    (2007)
  • C. Daraio et al.

    Conditional nonparametric frontier models for convex and non convex technologies: a unifying approach

    Journal of Productivity Analysis

    (2007)
  • Deprins, D., Simar, L., Tulkens, H., 1984. The performance of public enterprises: Concepts and Measurements. In:...
  • A. Estache et al.

    How different is the efficiency of public and private water companies in Asia?

    The World Bank Economic Review

    (2002)
  • P. Fabbri et al.

    Costs and structure of technology in the italian water industry

    Empirica

    (2000)
  • Cited by (0)

    View full text