Measuring the Environmental Pressure of Portuguese Water and Waste Utilities: A Composite Indicator Approach

(1)

Measuring the Environmental Pressure

of Portuguese Water and Waste Utilities:

A Composite Indicator Approach

candidate: Anna Mergoni

Supervisor: professor Laura Carosi

Master of Science in Economics

University of Pisa and S.Anna School of Advanced Studies

Department of Economics and Management

(2)

to

(3)

Acknowledgements

My first heartfelt thanks for my supervisor, Professor Laura Carosi; for the time she de-voted to review my thesis, for the patience in listening and clarifying my doubts, for the kindness in correcting my mistakes, for having demanded me more than what I was able to do and above all, for the affection in doing all this.

Then I have to thank Giovanna and all the other professors, since without whose help it would not have been possible to realize this thesis. I thank Giovanna for the commitment in taking care of guiding me in this work and in particular for the time she spent reviewing my thesis and for her enlightened advice on the Robust and Con-ditional analysis, for her help with the code, for the frankness in the discussions. I thank Professor Giulia Romano for directing me in the database search and for her use-ful reading suggestions regarding the literature on the water utilities. I have to thank also Professor Caterina Giusti and Professor Stefano Marchetti, for having supported and encouraged me a lot. Thank you professor Giusti for having guided me through the preliminary steps to writing the code and for having discussed with me the possi-ble ways to impute the missing values of the database. Thank you professor Marchetti for the very useful advice regarding the kernel estimation and the implementation of the function on R, for lending me the book of Li and Racine 2004. In particular I have to thank Stefano and Caterina for the availability, the kindness and the commitment in listening and answering to my doubts and for the trust you have given me since the first day we met. I then thank Professor Angela Parenti for having introduced me to the the-ory of the kernel estimation, for the suggested readings, for the time spent in listening to and clarifying my questions, for all the encouragements. Finally, I thank Professor Caterina Giannetti and her sunny and comforting smile. Thank you for haveing been

(4)

iv

the first person to which I have repeated my thesis. Thank you for the attention and the curiosity in listening to me, for the supports and the advice.

I need also to address a special thanks to my colleagues who have made these two years of master a wonderful walk in the mountains. You have enriched my knowledge with your intelligence, your curiosity and your willing in sharing with me these years. Thank you for sharing your doubts with me, for listening to mine, for trusting me, for always pushing me to improve and to do better. To Francesca, without you probably R, for me, would be only the letter after the Q. To Sofia and her advice, her support and trust; to her being, after all, the greatest. To Chiara and Elena for having hosted me over and over again, for having been always by my side, for having spent precious time on my thesis. To Chiara for never having reacted to my punches, for the wise ad-vice (for LA_{TEX and for life). To Elena for the ’deep’ discussions before sleeping, for the}

unconditional and unmeasurable trust. Thanks to Marco and Tommaso, with whom I shared practically every step of this journey, with whom I have prepared almost ev-ery exams. Thank you for having share your doubts with me since the vev-ery first day of class, thanks for having always been close to me in the studying. Thank you Tommy for having shared with me the train journeys on the Wednesday evenings after the in-terminable lessons of statistics (and for the Wednesday evenings dinners!). Thanks for being my first reviewer of every applications (and not only), for correcting my english, for the encouragements, the advice and the discussions. Thanks to Marco, to his tire-less curiosity, to the tenacity in trying to answer every doubt of anyone of us. Thank you for the passion in dedicating yourself to study. Thank you for convincing me to go in Eramsus, for having been close to me in every possible group work (in Pisa and Coimbra!), and, most of all, thanks for having never left me alone.

Finally, thanks to Marco, the man of goodbyes. Thank you for always assuming that we could do it, for your incurable optimism and for all the good memories we shared, the trip to Rome, the mountain outings, the exhausting relaxing walks, the moped trips, the piano pieces you refuse to learn, the songs in the endless car trips in Portugal and many other unspeakable adventures.

(5)

v

An other important thank is for Anna, my room/soul mate in Coimbra. Thank you for having shared with me your experiences, for having been my mentor (and student of statistics), my spiritual guide, my sister. For the mini-marathon we ran together, for the cakes and the pizzas we cooked, for making me feeling at home.

Infine mi piacerebbe ringraziare alcune le persone che hanno dato colore e allegria alla mia vita. Vorrei ringraziare quindi miei amici di sempre: Chiara, Jacopo, Francesca, Sofia, Rossella e Rachele, per essermi stati vicini nonostante lo studio abbia rubato molto tempo alla nostra compagnia. In particolare vorrei esprimere il mio ringrazia-mento a Rachele, che mi è stata vicina per tutto il percorso scolastico dai primi anni di scuola fino alla maturità. La persona più diligente e sveglia che io conosca, la prima che mi ha insegnato che studiare significa aprire il libro e non solo il quaderno.

Non può mancare poi un ringraziamento sincero e profondo a Zia Silvan e alla sua amicizi. Per essere stata mia ’compagna di banco’ dalla terza media fino ad ora, per i pomeriggi passati insieme a tradurre versioni, per tutte le discussioni, per tutti i rimproveri, per la sua incredibile capacità di interpetare la realtà, per non avermi mai nascosto la verità, per conoscermi meglio di quanto mi conosca io stessa, per esserci stata sempre.

Un ringraziamento speciale infine alla mia famiglia: a Domenico e ai miei genitori. A mio padre, per avermi svegliata e accompagnata alla stazione praticamente tutte le mattine di questi ultimi cinque anni e per l’ immancabile sorriso con cui mi ha sempre accolta al ritorno. A mia madre, per l’instancabilità con cui continua a darmi consigli (nonostante rimangano inascoltati) e per essere stata capace di avermi lasciato andare. A Domenico, perchè riesce a farsi voler bene nonostante sia la persona più robotica, razionale, egocentrica e testarda che possa esistere al mondo, per la serietà e l’impegno che mette in ogni discussione assieme, per l’energia con cui cerca sempre di tirare fuori il meglio da me.

(6)

Introduction

The aim of this thesis is the construction of a composite indicator able to compare the environmental performance of Portuguese Water and Waste Utilities. Sustainability and sustainable development became common concepts after the World’s first Earth Summit in Rio in 1992. In 2015, Agenda 2030 with goal 6 (ensure availability and sus-tainable management of water and sanitation for all) and target 12.5 (by 2030, sub-stantially reduce waste generation through prevention, reduction, recycling and reuse) highlighted the importance of water and waste sectors for reaching a sustainable de-velopment. In this thesis we focus on the environmental impact of the utilities which manage water and waste in Portugal and specifically, on the environmental pressure of these entities (following the definition of Smeets and Weterings [1999]).

In particular it is presented a literature review over some different non-parametric (DEA-like) models that can be used to construct composite indicators with both de-sirable and undede-sirable output. Then the use of the directional distance BoD Com-posite Indicator, proposed in the paper of Zanella et al. [2015], is deepened. Their ap-proach can be seen as the conjunction point between the Composite Indicator based on the Benefit of the Doubt (BoD) of Cherchye et al. [2007] and the models for measur-ing efficiency originatmeasur-ing from the directional distance approach of Shephard [1970] and Chung et al. [1997]. In particular, the directional distance BoD (as Rogge et al. [2017] calls it), is a BoD composite indicator, which is able to take care for undesirable output. It is a directional distance model, which is able to evaluate the performances (and not just the efficiency of the production process) like a Composite Indicators. To be more specific, the DDBoD approach allows for the accommodation of undesirable sub-indicators in their original form and overcomes some limitations associated with the approach of Chung et al. [1997], for example it avoids downward-sloping segments

(9)

Contents 2

in the frontier, that is, it avoids negative trade-offs between desirable and undesirable outputs. A Robust order - m analysis (following Cazals et al. [2002]) and a Conditional analysis (following Daraio and Simar [2007]) is also conducted, in order to add com-plementary insights to the Composite Indicator scores and to search for a ‘common pattern’. The importance of the robust analysis comes from the fact that our DDBoD CI is very sensitive to extremes and outliers, since it envelops all the observations in the analysis; order -m analysis overcomes this since it calculates the score using an order m frontier that envelops just m observations and therefore is less sensitive to extreme points and to outliers. Conditional analysis provides insights on the environmental variables that could impact the frontier (and so the relative values of the Composite Indicators). The methodology has been applied to the case study of the environmen-tal pressure exerted by Portuguese Water and Waste utilities. Specifically, the overall performance of the utilities is assessed along five dimensions: 1. treated water 2. re-cycled water 3. consumption of energy 4. real water losses 5. gas emissions, where the last three represent undesirable features that should be lowered to denote a better performance.

The obtained results show an average score for the CI of 0.784 which indicates that, if all the entities would perform along the dimensions under analysis as the best per-forming utilities, they could, on average, increase their CI scores by 21.6%. We check the robustness of our result running the Robust Analysis: choosing m = 65 andτ = 0.5 just 6 units are classified as ‘super-performing’. Finally we implemented also a condi-tional analysis, to identify the influence of some specific environmental variables on the values of the CIs. The conditional analysis shows that the size, as well as being located in a rural area, has a positive influence on the performance of the units, in-stead being in the north and having some ‘environmental certificates’ have a negative influence.

A non parametric regression (following Daraio and Simar [2007] p. 113) is used to test the significance of these influences, the result is a strong p-value just for the variables ‘area of activity’.

(10)

Contents 3

Summary for the readers :

In the first chapter you can find a motivation of the work and a discussion over the framework in which this thesis wants to be settled. Here it is stressed the importance of the two sectors under analysis in the contest of the sustainable development. A brief review of common adopted sub-indicators is also presented. In the second chapter water and waste management utilities in Portugal are described in a nutshell. Data used for the analysis are also presented. In the third chapter, the main one, some ap-proaches to construct CI are discussed. Here you can have an idea on the literature regarding the DEA-like Composite Indicators, in particular the ones able to manage undesirable outputs. In the fourth chapter results are shown and commented. In the end a brief conclusion.

To help the readers to go into the subject, some crucial aspects are treated in the Appendix, for example in Appendix B you can find a brief review over the kernel den-sity estimation. Besides, you can find complementary information such as how we imputed the missing values and a more detailed table of results (Appendix A and C).

(11)

Chapter 1 Sustainability, water and waste

Sustainability and sustainable development became common concepts after the World’s first Earth Summit in Rio in 1992. According to the Working group of the UNESCO In-ternational Hydrologycal Programme, guided by Loucks and Gladwell [1999], the rapid diffusion of the concept was due to the growing awareness that in a globalized world local economic activities may be associated with large scale and global environmental effects; this awareness gave rise to the necessity of rethinking the management of nat-ural resources in order to pursue an economic development that is not in contrast with a higher quality of life for everybody. However giving a definition of sustainability is a difficult task and finding a widely accepted method to measure the relative degree to which some actions or policies contribute to a sustainable improvement in social wel-fare is almost impossible. These difficulties are mainly due to the fact that the concept of sustainability is holistic and regards many aspects at the same time.

The Brundtland Commission’s report Our Common Future, Brundtland [1989], de-fined sustainable the development which meets the need of the present without com-promising the ability of future generations to meet their own needs.

Bruce [1992] tried to be more specific and stated that

First, development must not damage or destroy the basic life support system of our planet earth: the air, the water and the soil, and the biological sys-tems. Second, development must be economically sustainable to provide a continuous flow of goods and services derived from the Earth’s natural re-sources, and thirdly it requires sustainable social systems, at international,

(12)

Chapter 1. Sustainability, water and waste 5

national, local and family levels, to ensure the equitable distribution of the benefits of the goods and services produces, and of sustained life supporting system

Some years later, Loucks and Gladwell [1999] added that sustainable development refers to a process in which the economy, environment and ecosystem of region develops in harmony and in a way that will improve over time, admitting that sustainability is related to various economic, environmental, ecological, social and physical goals and objectives and thus it must be analyzed in a multi-disciplinary way. In particular it was understood that it is necessary to include in the debate as many people as possible, giving a special attention to the opinion of those who will be affected the most by the current management decisions, that is to future generations.

Sustainability, in fact, is related also to the problem that short and long run goals may be in contrast sometimes, so actions that seem to improve quality of life today may significantly damage resources for future human beings. This is why muliti-disciplinariety should be complemented with a sort of multi-temporal approach, to find the right trade off between the different stakeholders (Kuhlman and Farrington [2010]).

For these reasons it is easy to understand why water and waste are two fundamen-tal sectors to be considered in relation to sustainability. This is confirmed also by the stress that UN posed on these sectors in 2015, implementing the 2030 Agenda for Sus-tainable Development (UNGA [2015]). In fact, among the 17 SusSus-tainable Development Goals and the 169 associated targets announced by UN, Goal 6 is focused on water (the goal is to ensure availability and sustainable management of water and sanitation for all) and Goal 12 is somehow focused on waste (the goal is to ensure sustainable consumption and production patterns and in particular target 12.5 consists of this dec-laration: by 2030, substantially reduce waste generation through prevention, reduction, recycling and reuse). Nevertheless, it seems that the growing awareness is not yet trans-lated in practical actions, not even in the scientific attention of the scholar world. For these reasons we decided to focus our thesis on the Environmental Impact of Water and Waste Utilities. We choose to study the Portuguese case since I spent the win-ter semeswin-ter of this year in Coimbra, this allowed me to manage the research of the database; morover, data on Portuguese water and waste utilities are freely availability

(13)

1.1. Selecting the sub-Indicators 6

on the ERSAR website.

1.1 Selecting the sub-Indicators

In Marques et al. [2015] we find a brief review of the criteria used in the literature to evaluate the sustainability of Urban Water Services (UWS). The common feature of all of these papers is that to asses sustainable level in water systems it is necessary to ac-count for several aspects. In particular Marques et al. [2015] present the paper by Hell-ström et al. [2000], which analyses the sustainability of urban water systems in Sweden and discusses the (MISTRA) "Sustainable Urban Water Management" program and its five main objectives (that can be extended to any urban infrastructure): 1. moving towards a nontoxic environment 2. improving health and hygiene 3. saving human re-sources 4. conserving natural rere-sources 5. saving financial rere-sources. Balkema [2003] implemented the methodology of MISTRA focusing on the sustainability assessment of waste water treatment systems, they were inspired by the idea that ‘environmen-tal problems have become the reverse salient components of current large-scale sys-tems’. Within the same framework, Lundin [2003] investigates deeply two assessment tools for measuring the sustainability of urban water systems: LCA (life cycle assess-ment, which takes into account the environmental impacts of products during the all arch of their life) and SI (sustainability indicators). Within the framework of sustain-able indicators she presents also some different perspectives, distinguishing in par-ticular among indicators which stresses the link between generated services and used resources (as in Nilsson and Bergström [1995]), indicators which focus on the link be-tween human activities and the environment (as in Holmberg [1995]) and indicators which highlights the pressure from human activities, through emissions and usage of natural resource, on the environment (as in OECD [1998]).

As for the waste sector den Boer et al. [2007] deepen the use of life cycle assessment tools for the development of integrated waste management strategies for cities and regions with rapid growing economies. Zurbrugg et al. [2012] describe an approach to assess typical success or failure factors in waste management, but they do not consider the environmental aspect. The method covers just issues such as (i) social

(14)

mobiliza-1.1. Selecting the sub-Indicators 7

tion and acceptance (social element), (ii) stakeholder, legal and institutional arrange-ments, responsibilities and management functions (institutional element); (iii) finan-cial and operational requirements, as well as cost recovery mechanisms (economic ele-ment). Ramachandra and Varghese [2003] instead explore the sustainable options that conserve both natural and man-made resources and avert ecological risks. Integrated waste management system is proposed as an option, which include collection, trans-port and processing of wastes in an environmentally sound way.

However about the choice of indicators, we adapted the ones suggested by Pinto et al. [2017]. They developed a system of performance indicators for the quality of wa-ter utilities services which included indicators about three macro areas: 1. protection of user interests 2. operator sustainability (economic, infrastructural and physical pro-ductivity) and 3. environmental sustainability. We decided to focus only on this last aspect. This was due to the fact that the environmental aspect is usually neglected by the literature on the assessment of performance in water and waste sectors; besides there was the necessity of choosing a quite objective and specific phenomenon to be measured. Indicators used by Pinto et al. [2017] to measure the environmental sus-tainability are the following: 1. water losses 2. fulfillment of the water intake licensing 3. standardized energy consumption 4. sludge disposal. Inspired by these indicators, in this thesis the used indicators are the followings: 1. real water losses 2. consump-tion of energy 3. treated water 4. recycled waste and 5. gas emission (for an accurate description of these sub-indicators, see 2.3).

In particular we tried to measure the pressure exerted by water and waste utilities on the environment, constructing a Pressure Indicator, that is an indicators which fo-cus on the release of substances and in the use of resources, as Smeets and Weterings [1999] defined it (see chapter 3).

(15)

Chapter 2 Water and Waste Utilities in Portugal

2.1 Water and Waste Sector Activities

The urban water cycle encompasses all phases referred to water supply and waste wa-ter sanitation activities, from wawa-ter abstraction to final waste wawa-ter rejection in nature. Generally the water sector can be divided in two branches in accordance with the pro-vided services, water supply for human consumption or urban waste water drainage:1

- the public water supply service includes the activities of capturing (extraction of raw water in the surface or underground) , treatment (correction of the physical, chemical and microbiological characteristics of water in order to make it suitable for human consumption), elevation (lifting water in order to circulate it under pressure and overcome orographic barriers), transport (transport of treated wa-ter from the production zone to the areas of consumption), storage (storage of treated water to ensure continuity of supply), distribution (distribution to users of water in quantity and pressure appropriate to the needs);

- the urban wastewater sanitation activity comprises the discharge, drainage (col-lection of waste water produced), elevation (elevation of wastewater produced for the purpose of overcoming orographic barriers), transport and treatment of waste water of urban origin (correction of physical, chemical and

microbiolog-1_{see RASSARP VOL 1 and VOL 2}

http://www.ersar.pt/pt/site-publicacoes/Paginas/edicoes-anuais-do-RASARP.aspx|

(16)

2.1. Water and Waste Sector Activities 9

ical characteristics of wastewater taking into account the characteristics of the receiving medium), as well as its rejection in the water environment or through reutilization (reuse of treated waste water for uses consistent with its quality (ur-ban and non-ur(ur-ban)) or through processing of sludge (treatment of sludge gen-erated in waste water treatment) to final destination (forwarding of sludge to suitable final destination (agriculture, landfill, among others)). This activity is fundamental to guarantee the safeguarding of the quality of the water since it is determinant in the conditioning of the other uses of the water (domain), namely the capture of water for human consumption.

The urban waste management service is provided on the basis of a complex techno-logical system, which includes the collection (indifferentiated and selective), transport, sorting (selection of recoverable waste), recovery (operations that make it possible to monetize the waste treatment process through the production of recycled materials, including organic compost, electricity or heat) and disposal (routing of the fraction of waste resulting from the treatment and recovery operations destined for confinement) of waste of householders and other types of waste which, by their nature or compo-sition, are similar to residues from housing. Waste management systems encompass two major flows depending on the type of collection: undifferentiated or selective. The undifferentiated collection corresponds to the collection of urban waste without prior selection, for this activity the service em baixa are responsible. The selective collection instead, the one which maintains the waste stream by type and nature, in order to fa-cilitate specific treatment, is carried out, in most systems, by em alta services (see also subsection 2.2.1).

In terms of waste flows, the above steps differ between systems according to the technological options adopted to comply with the general principles of waste manage-ment. Nevertheless, the main driver is the principle of waste hierarchy, giving priority to recycling recovery and, as a last resort, landfill disposal.

Market Structure

From the point of view of the market structure, the water sector is a typical case of the network industry, both at the level of high and low systems, configuring the

(17)

man-2.2. Classification of water service entities 10

agement of these infrastructures as a situation of natural monopoly; the scale of the monopolies is regional, as far as the geographical coverage of each network. An other characteristic that facilitates the water sector to be a natural monopoly is the high level of resource absorption; the sector in fact is capital-intensive and with long periods of return on investment. This characterization is justified by the high investment needed in the initial phase, and the fact that return only occurs in the long term, with the soft-ening of the applied tariffs over the useful life of the infrastructures. Also the urban waste management service reflects this feature: high investments are required at an early stage. However municipal waste management service is not a network industry, it is a national strategic option to provide the service under a legal monopoly regime, in order to ensure that there is a single provider for each geographical area, minimizing environmental problems resulting from this activity.

2.2 Classification of water service entities

2.2.1 ‘Em alta’ (High) and ‘Em baixa’ (Low) systems

Supply water service, waste water treatment service and waste management service have been classified in ’em alta’ and ’em baixa’ systems according to the activities of the management entities. Respectively, are called ’em alta’ systems those which deal with wholesale activities and ’em baixa’ systems those specialized in retail activities. This distinction, introduced with the Decree-Law No. 379/93, of November 5, was at the heart of the creation of multi-municipal systems, mainly responsible for high sys-tems, and municipal syssys-tems, mainly responsible for low systems. This structure of the sector has led to advantages in terms of economies of scale and has simultaneously led to the division of the value chain taking into account the phases of the production pro-cess.

In Portugal (continental) there are 9 management entities for the ’em alta’ service of water supply and 256 entities for the ’em baixa’ service. The population served is 9.6 million (data from 98 % of EG), equivalent to 96 % of houses (98 % of EG). As for the wastewater treatment service there are 9 management entities for the ’em alta’ service and 257 EG for the ’em baixa’ service; for a total of 8,4 million of inhabitants served

(18)

2.2. Classification of water service entities 11

with drainage (over 97 % of the EG) equal to the 83 % of the houses (97 % das EG) and 8,32 million of inhabitants served with treatment with adequate destination (by 97 % of the EG) equivalent to the 82 % of the houses (97 % das EG).

The differences among this two type of systems are summarized in the tables 2.1. The presented numbers refer only to the managing entities subject to the system of evaluation of the quality of the service provided to the users.2

Table 2.1:Entities ’em alta’ and ’em baixa’

Alta Baixa

AA

Water abstracted 582 million (m3/year) 217 million (m3/year) Real losses 23 million (m3/year) 166 million (m3/year) Energy consumption 217 million (kWh/year) 247 million (kWh/year) Own staff 863 + Outsourcing staff: 363 7 545 + Outsourcing staff: 628 Energy production 1,0 % of the whole energy

con-sumed

3,3 % of the whole energy con-sumed

AR

Waste water collected 573 million (m3/year) 678 million(m3/year)

re-used treated water 1,2 % of the whole treated water 0,7 % of the whole treated water Energy consumption 283 million (kWh/year) 106 million (kWh/year) Own staff 636 + outsourcing staff 1 106 4 309 outsourcing staff 535 Energy Production 7,9 % of the whole energy

con-sumed

2,0 % of the whole energy con-sumed

RU

Waste entered 4,65 million (t) Energy consumption 83 (g Wh/year)

Own staff 2 932 + Outsourcing staff: 946 6 510 + Outsourcing staff: 2 923 CO2 Emission from vehicles

for selective collection

11 290 (t of CO2/year) 6 383 (t of CO2/year)

(19)

2.3. Database 12

2.3 Database

The data used to implement the analysis have been taken from ERSAR website3, they refer to the year 2016. The database contains information about all the water and waste utilities in Portugal, but only the entities active in each of the three sectors (water sup-ply (AA), water treatment (AR) and waste (RU)) have been selected. So among the 371 entities only 178 entered in our initial sample. This choice is due to the requirement of homogeneity among the entities under analysis. The reason lying under this require-ment is the fact that the methodology we implerequire-ment makes a series of homogeneity assumptions as reported in p. 247 of Dyson et al. [2001]. In particular, according to them, homogeneity has a triple meaning: 1. firms are undertaking similar activities, so that they share a common set of outputs 2. a similar range of resources is available to all the units and 3. unwritten assumptions units are operating in similar environ-ment since the external environenviron-ment generally impacts upon the overall performance units. While our set of entities respects the first and the second assumptions, the last one can hardly be made. So to overcome the problems that follow as a consequence of not respecting this requirement, a conditional analysis is implemented (see chapter 3, section 3.2.2 to have more details on the conditional analysis).

The sub-indicator disposable in the data set were 169, 64 relative to the activity of water supply, 69 for the water treatment activity and 35 for the waste management. Among these, 5 sub-indicators have been selected to measure the pressure on the en-vironment from water and waste utilities: 1) water loss 2) consumption of energy 3) treated water 4) recycled waste 5) gas emission. The description of this indicators fol-lows in table 2.3

(20)

Table 2.2: ESDAR sub-indicators

Sub Indicator Definition

Real water losses the volume of actual losses per unit length of conduit in a day,

mea-sured in volume of loss / conduit in a day.

Consump. of Ener. standardized average energy consumption of the whole waste water

treatment plant, measured in kWh per year.

Treated water calculated as the ratio between the volume of sludge from collective

sewage treated in the plant and the volume of waste-water received in the treatment plant decreased by the volume of sludge sent to be treated by another management entity, per year.

Recycled waste ratio among the tonne of waste recycled and the total tonne of waste

entering the infrastructures of the management entity in the year.

Gas Emissions total amount of CO2 emissions from undifferentiated collection

ve-hicles per tonne of waste collected in the management area of the management body.

Table 2.3: Descriptive Statistics of the Sub Indicators

Indicator NA Min 1st Qu. Median Mean 3rd Qu. Max. CV water loss (l/(ramal.day)) 25 0.8 78.5 133 143.7 186.8 535 0.7 energy consum. (kWh/year) 28 0 11370 39560 190800 135000 7766000 3.78 treated water (m3/year) 7 0 0.1267 1 0.7073 1 3.034 0.707 recycled waste (%) 0 0.02001 0.06793 0.08691 0.0961 0.1144 0.4562 0.537 gas emissionkg (CO2/t) 4 6 16 19 20.5 24 51 0.375

note: to see how we imputed the missing values check Appendix A

To conduct the conditional analysis other sub-indicators have been selected as en-vironmental variables: 1) geographical position 2) intervention area 3) certificates of environmental quality 4) volume of water suppliedd. The control variables are de-scribed in table 2.3 and the descriptive statistics are presented in table 2.4.

(21)

Table 2.4: Control Variables

Control Variable Definition

geograph. position Portugal is divided into 5 macro regions: the region of the north, the region of the centre, the region of Lisbon, Alentejo and Algarve. We consider just three macro domains: the north, equivalent to the region of the north, the center,equivalent to the region of the center plus the Lisbon district and the south,composed by Alentejo and Algarve. In this thesis the categorical variable geographical position has value 1 if the considered entity is located in the south, 2 for the entities located in the center and 3 for the entities located in the north.

intervention area We considered the typology of areas according to the definition of the De-liberations n. 488/98 and n. 2717/2009, followed also by the Portuguese national institute of Statistics. In this thesis it is assigned the value 1 to the predominantly rural areas, 2 to the medium urban areas and 3 to the pre-dominantly urban areas.

certificates This categorical variables is constructed assigning one point for each of the following certificates that ESDAR assign to the entities: ’Certification of en-vironmental management systems’ (for the three activity), ’Energetic certi-fication’ and ’Energy Efficiency Plan’, 0 point if no certificates is owned Volume of activity Volume of water (in m3) supplied in a year

Table 2.5: Descriptive Statistics for the Categorical Control Variables

0 1 2 3

Geographical position: 0 67 (37.64%) 46 (25.84 %) 65 (36.52%)

Intervention area : 0 140 (78.65%) 29 (16.29%) 9 (5.06%)

Certificates : 167 (93.82%) 1 (056%) 3 (1.69%) 7 (3.93%)

Table 2.6: Descriptive Statistics for the Variables Volume

Min. 1st Qu. Median Mean 3rd Qu. Max. cv Volume 80940 281000 518100 1311000 1117000 19740000 1.911379

(22)

Chapter 3 Methodology

According to Smeets and Weterings [1999] indicators should promote information ex-change regarding the issue they want to address, and communication demands sim-plicity [p5]. Environmental indicators communicate those aspects that are critical or typical for the complex interrelation between natural species and abiotic components of the environmental system. In relation to policy-making, environmental indicators are used for three major purposes:

1. to supply information on environmental problems, in order to enable policy-makers to value their seriousness;

2. to support policy development and priority setting, by identifying key factors that cause pressure on the environment;

3. to monitor the effects of policy responses.

In addition the indicators may be used as a powerful tool to raise public awareness on environmental issues.

Smeets and Weterings [1999] also stated that to evaluate environmental perfor-mance a wide variety of indicators is available, the most common are the one within the framework of system analysis indicators (DPSIR)1, that is indicators which try to explain the relations between the environmental system and the humans. They start

1_{Driver, Pressures, State, Impact, Responses}

(23)

Chapter 3. Methodology 16

from the assumption that social and economic developments exert pressures on the environment and the State of the environment changes as a consequences of these pressures. This may lead to Impacts on human health, ecosystems and resources avail-ability and may elicit a societal Response that feeds back on the Driving forces. The Eu-ropean Environment Agency (EEA) indicators, which belong to the class of DPSIR can be further divided into four types, according to the questions that they try to answer: type A or Descriptive Indicators. What is happening to the environment and to humans? type B or Performance Indicators. Does it matter?

type C or Efficiency Indicators. Are we improving?

type D or Total Wealfare Indicators. Are we on the whole better off?

Within the framework of Descriptive Indicators, we can distinguish among 1. Driving Forces Indicators (population growth and developments in the needs and activities of individuals), which describe the social, demographic and economic developments in societies and the corresponding changes in life styles, overall levels of consumption and production patterns. 2. Pressure Indicators, which describe the pressures exerted by society on the environment, in particular the indicators describe developments in the release of substances (emissions) and in the use of resources. 3. State indicators give a description of the quantity and quality of physical, biological and chemical phe-nomena in a certain area. 4. Response Indicators, which refer to responses by groups (and individuals) in society, as well as government attempts to prevent, compensate, ameliorate or adapt to changes in the state of the environment.

In this thesis a Composite Descriptive Pressure Indicators is developed, to collect information on the impact that the water and waste utilities may have on the environ-ment.

The use of composite indicators is quite consolidated in literature when dealing with phenomena characterized by multiple variables, and, in particular, when dealing with environmental issues (see Nardo et al. [2005], Cherchye et al. [2008], Zanella et al. [2013], Zanella et al. [2015] for example). As stated by Nardo et al. [2005] a composite

(24)

indicator, saying it in a nutshell, synthesizes the information included in a selected set of indicators and variables. The output is a set of scores indicating the relative perfor-mance of the entities under analysis. A composite indicators thus is a measure of sim-ilarity, p. 1. Pros and Cons of using a composite indicators were collected by Saisana and Tarantola [2002], the most significative aspects are reported in table 3.1. In the paper they refer in particular to CI for the evaluation of country performances.

Table 3.1: Pros and Cons of using CI

Pros Cons

- Can summarize complex or

multi-dimensional issues in view of support-ing decision-makers

- May send misleading policy messages if they are poorly constructed or misinter-preted

- Easier to interpret than trying to find a trend in many separate indicators

- May invite simplistic policy conclusions - Facilitate the task of ranking the

coun-tries on complex issues in a benchmark-ing exercise

- May be misused, e.g., to support a de-sired policy, if the construction process is not transparent and lacks statistical or conceptual principles

- Reduce the size of a set of indicators or include more information within the ex-isting size limit

- The selection of indicators and weights could be the target of political challenge. - Place the issues of country performance

and progress at the centre of the policy arena

- May disguise serious failings in some di-mensions and increase the difficulty of identifying proper remedial action - Facilitate communication with general

public (i.e. citizens, media, etc.) and promote accountability

- May lead to inappropriate policies if di-mensions of performance that are diffi-cult to measure are ignored.

The Handbook on Constructing Composite Indicators: Methodology and User Guide by Nardo et al. [2005] tried to cope with the presented issues. The book presents and discusses the steps that must be followed in order to construct a composite indicator as well as the popular methodologies already in use. The steps suggested are the fol-lowing:

step 1 A description of the theoretical framework to provide the basis for the selection and combination of single indicators into a meaningful composite indicator. step 2 Selection of data on the basis of their analytical soundness, measurability,

coun-try coverage, relevance to the phenomenon being measured and relationship to each other.

(25)

step 3 Imputation of missing data.

step 4 Multivariate analysis, to investigate the overall structure of the indicators and to assess the suitability of the data set and explain the methodological choices. step 5 Normalization of indicators to render them comparable

step 6 Weighting and aggregation according to the underlying theoretical framework. Correlation and compensability issues among indicators need to be considered and either to be corrected for or treated as features of the phenomenon under analysis.

step 7 Robustness and sensitivity analysis to assess the robustness of the composite in-dicator in terms of, e.g., the mechanism for including or excluding single indi-cators, the normalization scheme, the imputation of missing data, the choice of weights and the aggregation method.

step 8 Back to the real data, to ensure transparency and fit with their underlying indi-cators or values.

step 9 Links to other variables attempting to correlate the composite indicator with other published indicators, as well as to identify linkages through regressions. step 10 Presentation and Visualization.

In this thesis the steps suggested by Nardo et al. [2005] are considered and re-adapted in the following way: step 1 is covered in chapter 1 and 2, where the problem of sustainability is defined, a brief review of the sustainable indicators is presented and the situation of water and waste sector in Portugal is described. Step 2, 3, 4, 5, 6 and 7 will be covered in chapter 2 and 3 (and in Appendix A and B) where the database will be presented, as well as the techniques for the imputation of the missing values and the choice of the variables used to construct the composite indicator. Step 8, 9 and 10 in chapter 4, where results are presented.

To construct an environmental performance indicator, many methods are avail-able. In the framework of performance evaluation of water and waste utilities, the variety of methodologies is maintained: De Gisi et al. [2014], Marques et al. [2015], among others, use a MCDA approach and in particular Pinto et al. [2017] uses Electre TRI-nC; Romano and Guerrini [2011] and Molinos-Senante et al. [2017] are example for approaches based on DEA methodologies.

The composite indicator implemented in this thesis is the one presented by Zanella et al. [2015]. It is based on the directional distance of Chung et al. [1997], a method

(26)

3.1. Data Envelopment Analysis and Composite Indicator 19

that has its root in the Shephard distance function and it is developed to take into ac-count the undesirable output in the efficiency evaluation. Zanella et al. [2015] adapt the model to use it in the framework of composite indicators (departing the production world). An other way to see the model of Zanella is as a directional BOD2model, that has its root in the DEA model, but it is tuned to take in consideration for undesirable output using the transformation function proposed by Koopmans [1951] ( f (U ) = −U ) and expressing it in a more general term: f (U ) = −gu . Rogge et al. [2017] defined the

methods as a directional distance version of the Benefit-of-the-Doubt (BoD), p. 20. Some of the advantages and disadvantages of using technique based on BOD are summarized in table 3.2, from Nardo et al. [2005], pag 99.

Table 3.2: Pros and Cons of using CI

Advantages Disadvantages

- The indicator is sensitive to decision makers priorities, in that the weights are endogenously determined by the ob-served performances

- It may happen that there exists a multi-plicity of solutions making the optimal set of weights undetermined (likely to happen when CI=1)

- The benchmark is not based upon theo-retical bounds, but on a linear combina-tion of observed best performances

- The index is likely to reward the status quo, since for each country the maxi-mization problem gives higher weights to higher scores

- Policy-makers could not complain

about unfair weighting: any other

weighting scheme would have gener-ated lower composite scores

- The best performer (that with a compos-ite equal to one) will not see its progress reflected in the composite (which will remain stacked to 1). This can be solved by imposing an external benchmark - Weights, by revealing information about

the priorities, may help to define trade-offs, overcoming the difficulties of linear aggregations

3.1 Data Envelopment Analysis and Composite Indicator

As reported by Cherchye et al. [2008], the original question that DEA-literature tries to answer is how one could measure each decision making unit’s3relative efficiency,

2_{Benefit of the Doubt of Cherchye et al. [2007]}

3_{As S. Ray suggests in Ray [2004], Charnes, Cooper and Rodhes coined the phrase decision making}

(27)

given observations on input and output quantities in a sample of peers, when no reli-able information on prices are availreli-able. The conceptual similarity between that orig-inal problem and the one of constructing CIs is immediate. To construct CIs, in fact, quantitative sub-indicators for overall benchmarking are available, but, in most cases, there is only disparate expert opinion available about the appropriate weights to be used in an aggregator function. The DEA methodology allows to overcome this prob-lem, looking for endogenous weights/shadow prices, yielding an overall score that de-picts the analyzed decision making unit in its best possible light relative to the other observations. This quality explains a major part of the appeal of DEA-based CIs in real settings.

A brief overview on DEA

As explains Ray [2004], Data Envelopment Analysis is a non parametric method to mea-sure the efficiency of a decision making unit (DMU). It is a method that uses mathe-matical programming rather than regression. This is a double edged weapon. On the one hand, being non parametric allows DEA to overcome the problem of specifying an explicit form for the production function, making only a minimum number assump-tions about the underlying technology and constructing a benchmark technological frontier from the observed input-output bundles of the DMU in the sample. On the other hand, being non deterministic in nature, the linear programming solution pro-duces no standard errors and leaves no rooms for hypothesis testing. The pioneers of DEA models are Charnes Cooper and Rhodes, who presented a model that was only applicable to technologies characterized by constant return to scale (Charnes et al. [1978]). Banker, Charnes and Cooper overcame the problem to accommodate tech-nologies that exhibit variables return to scale (Banker et al. [1984]). Since then many other models have been developed (see for all Emrouznejad et al. [2008], Liu et al. [2016], Zhou et al. [2018], and references therein)

(28)

Charnes, Cooper and Rhodes 1978

According to Charnes et al. [1978], p. 669 a DMU will be characterized as efficient if and only if neither (i) nor (ii) are true:

(i) Output Orientation: A Decision Making Unit is not efficient if it is possible to aug-ment any output without increasing any input and without decreasing any other output.

(ii) Input Orientation: A DMU is not efficient if it is possible to decrease any input without augmenting any other input and without decreasing any other output. So the efficiency of DMU0is defined as the value h0∗ which is obtained from the

following maximization problem:

max h0= Ps r =1uryr 0 Pm i =1vixi 0 (3.1.1) s.t .                Ps r =1uryr j Pm i =1vixi j ≤ 1; j = 1,...,n ur ≥ 0; r = 1,..., s vi≥ 0; i = 1,...,m

where xj = (x1 j, ..., xm j) and yj = (y1 j, ..., ys j) represent respectively the input and

output values for the jt h DMU. All of the outputs and inputs are assumed to be ob-served as positive values and all the DMU are assumed to produce the same outputs given the same inputs, in (generally speaking) different amounts. The n constraints Ps

r =1uryr j

Pm

i =1vixi j

≤ 1 ensure that no DMU can achieve an efficiency rating which will exceed unity when the weights obtained from the maximization for the DMU0are attributed.

The result of the optimization problem are a set of ur* and yi* which generate an

opti-mal h0∗. 0 ≤ h0∗ ≤ 1 and h0∗ = 1 if and only if the DMU is efficient in the sense of (i)

and (ii).

Banker, Charnes and Cooper 1984

Banker et al. [1984] operates a fine tuning of the model presented in Charnes et al. [1978], the objective is to characterize a production possibility set and to determine

(29)

an ’efficient’ subset based on the observed data. The production possibility set (T ) is defined in page 1081, as well as the postulates used by Charnes et al. [1978].4

1. Convexity. If (Xj, Yj) ∈ T, j = 1,...,n and λj≥ 0 are non negative scalars such that

Pn j =1λj= 1 then ( Pn j =1Xjλj, Pn j =1λjYj) ∈ T .

2. Inefficiency Postulate a) if (X , Y ) ∈ T and ¯X ≥ X , then ( ¯X , Y ) ∈ T . b) if (X , Y ) ∈ T and ¯Y ≤ Y , then (X , ¯Y ) ∈ T .

3. Ray Unboundedness if (X , Y ) ∈ T then (k X ,kY ) ∈ T for any k > 0.

4. Minimum Extrapolation T is the intersection set of all ˆT satisfying Postulates 1-3 and subject to the condition that each off the observed vectors (Xj, Yj) ∈ ˆT , j =

1, ..., n.

The model presented is the following, it avoids the assumption of the third postu-late (so it allows for variables return to scale).

max s X r =1 uryr 0− u0 (3.1.2) s.t .                        Pm i =1vixi 0= 1 Ps r =1uryr j− Pm i =1vixi j− u0≤ 0; j = 1,...,n ur≥ 0; r = 1,..., s vi≥ 0; i = 1,...,m

u0is unconstrained in sign and its sign is fundamental to determine the return to scale

(i) increasing returns to scale ⇐⇒ u0∗ < 0

(ii) constant returns to scale ⇐⇒ u0∗ = 0

(iii) decreasing returns to scale ⇐⇒ u0∗ > 0

4_{The symbolization of Banker et al. [1984] is reported here: T = {(X ,Y )|Y ≥ 0 can be produced from}

X _{≥ 0}; L(Y ) = {Y |(X , Y ) ∈ T } the input possibility set; P (X ) = {X |(X , Y ) ∈ T } the output possibility set.} L(X ) and P (X ) are defined following Shephard (1970, p 179)

(30)

Dea and Undesirable Output

In the production processes, usually, udesirable outputs are an inevitable complement to desirable ones, so when evaluating the performance of producers it makes sense to credit them for their provision of desirable outputs and penalize them for their provision of undesirable outputs (Färe et al. [1993a], p. 90). However this joint production has been ignored for a long time in traditional measures of productivity, since “prices” are typically unavailable for bad outputs, as reported by Chung et al. [1997].

To threat undesirable output there are two main approaches in the literature, as reported in Zanella et al. [2015]:

- direct approaches, which allow to treat output in their original form

- indirect approaches, which transform the values of undesirable outputs to allow treating them as normal output in traditional DEA

In the first case the output are treated in their original form, that is, no modification of scale is required, in the second case instead the values of undesirable output are trans-formed in order to threat them as normal output in traditional DEA models. Following the review of Zanella et al. [2015] the presented approaches are summarized in table 3.3 .

Table 3.3: Approaches to Deal with Undesirable Output

Direct Indirect Pittman [1983] Scheel [2001]

Färe et al. [1993b] Golany and Roll [1989] Färe et al. [1993a] Seiford and Zhu [2002] Chung et al. [1997] Cherchye et al. [2011]

As for the direct approaches they use original output values but modify the assump-tions about the structure of technology set in order to treat the undesirable output ap-propriately Scheel [2001]. These kind of models have usually their root in the Multilat-eral Productivity Approaches of Caves et al. [1982] and try to overcome the drawback

(31)

of this model, that is the specification of the price information for undesirable output. Pittman [1983] expanded the model of Caves et al. [1982], by introducing the estima-tion of shadow prices. Färe et al. [1993b] proposed an alternative model to estimate shadow prices using linear programming, based on Shephard distance function, Shep-hard [1970]. Färe et al. [1993a] proposed a hyperbolic output efficiency unit approach. The model was adapted from Färe et al. [1985], who introduced it to treat outputs and inputs asymmetrically when measuring technical efficiency in the sense of Farrell [1957]. The hyperbolic measure was adapted in Färe et al. [1993a] to yield a variety of efficiency measures that allow to treat desirable and undesirable outputs asymmetri-cally. These efficiency measures provide the basis for making multilateral productivity comparisons conditioned on different assumptions about the undesirable outputs.

Chung Fare Grosskopf 1997

Among the direct methods we present the one of Chung et al. [1997], which proposed a directional distance function approach to allow the expansion of the desirable output and the simultaneous reduction of the undesirable ones. The model has been rewrote by Zanella et al. [2015] in the following way:

max β (3.1.3) s.t . _                       Pn j =1xi jλj≤ xr j0− βgx i = 1,...,m Pn j =1bi jλj= br j0− βgb k = 1,...l Pn j =1yi jλj≥ yr j0+ βgy r = 1,..., s λj≥ 0 j = 1,...,n

In this modelβ is a measure of the inefficiency of the DMU under analysis. It mea-sures how much is possible to simultaneously reduce inputs and undesirable outputs, and increasing desirable outputs. In particular the model assumes strong disposability for the desirable outputs and the inputs5and just a weak disposability for the

unde-5_{that is, if (x, y, b) ∈ T , then ( ¯x, y,b) ∈ T if ∃ ¯}_x

(32)

sirable output6. This features come from the fact that the model has its root in the production theory.

As for the indirect approaches, they are based on monotone decreasing transfor-mation function ( f ) of undesirable outputs, such that the transformed data can be included as ‘normal’ desirable outputs in the technology set.

Scheel 2001

In Scheel [2001], as well as in Zanella et al. [2015], three main transformations are iden-tified , as reported in table 3.4. Data so transformed can be put in the DEA model 3.1.1 as well as in model 3.1.2 and their further extensions.

Table 3.4: Approaches to Deal with Undesirable Output

Transformation Papers

f (U ) = −U Koopmans [1951]

f_ik(U ) = −uk_i + βi Ali and Seiford [1990] and Seiford and Zhu [2002] f_ik(U ) = 1/u_ik Golany and Roll [1989]

The function suggested by Koopmans [1951] is f (U ) = −U (where U denotes the matrix of undesirable output) As stated in Scheel [2001], it generates the same technol-ogy set as incorporating undesirable outputs U as inputs, with the only difference in the sign. The classification of efficient or inefficient DMU is the same.

The results are preserved if the values of undesirable outputs are translated through f_ik(U ) = −u_ik+ βi, whereβiis a sufficiently large scalar such that f_ik(U ) are positive for

each DMU k; as suggested by Ali and Seiford [1990] and then revisited by Seiford and Zhu [2002]. It is Pastor [1996] that stated the invariance of efficiency classification with respect to the translation vectorβ, and it is maybe for this reason that it is the most frequently used transformation in the literature according to Zanella et al. [2015].

An other function that allows to incorporate undesirable output as ‘normal’ out-put is the one proposed by Golany and Roll [1989], and applied, among the others, in

(33)

Lovell et al. [1995] and in in Athanassopoulos [1995]. In this methodology f_ik(U ) = 1/uk_i (multiplicative inverse). If a DMU is efficient using this approach, then it is efficient as well according to the other presented approaches. As Zanella et al. [2015] suggest, the method of Golany and Roll [1989] has been criticized by Dyson et al. [2001] since it would destroy the ratio or interval scale of the data. However Cook et al. [2014], p. 3, stated that a mixture of ratios/percentiles and raw data is permissible in DEA applica-tions, considering also the examples by Cooper et al. [2007] it seems that there is not a justification for not using ratio and raw data simultaneously, but just a call for attention when doing it (particularly when choosing the return to scale).

DEA model for CI

Papers mentioned above do not address the modeling of undesirable factors in the construction of composite indicators (CIs). As reported before, the Handbook pro-vided by the OECD and EU Commission Nardo et al. [2005] on the construction of composite indicator indicates DEA (and in particular the ‘Benefit of the Doubt’ model of Melyn and Moesen [1991], then developed by Cherchye et al. [2007]) as an inter-esting weighting and aggregation procedure to reduce the subjectivity associated with the specification of weights. As Cook et al. [2014] says in p. 2, DEA can be viewed as a multiple-criteria evaluation methodology where DMUs are alternatives, and DEA in-puts and outin-puts are two sets of performance criteria where one set (inin-puts) is to be min-imized and the other (outputs) is to be maxmin-imized. As Zanella et al. [2015] reports Cook and Kress [1990] have been the first to use DEA for performance assessment focus-ing only on achievements. Then application in different fields have developed, for ex-ample Lovell et al. [1995] for the evaluation of macroeconomic performance of OECD countries.

Cherchye, Moesen, Rogge and Van Puyenbroeck 2007

Cherchye et al. [2007] tried to overcome some shared criticism of CI, in particular: i) the lack of a standard methodology to construct them; ii) the subjectivity inherent to the choice of the methodology; iii) the difficult interpretation of the weights in case of aggregation; iv) the fact that composite indicators are not usually well-defined in a

(34)

mathematical sense, that is, they are not meaningful when the resulting order of the entities under evaluation changes if original data are transformed in such a way that the information content in the data is not fundamentally altered. They depart from the articles of Melyn and Moesen [1991], developing the idea of the ‘Benefit of the Doubt’.

The idea behind this approach is that a good relative performance of an entity in one particular sub-indicator dimension indicates that the specific evaluated unit con-siders that political dimension as relatively important. The CI is thus constructed in the following way

C Ic maxwc,i Pm i =1wc,iyc,i maxyj ,i Pm i =1wc,iyj ,i (= 1) (3.1.4) s.t .        Pm i =1wc,iyj ,i ≤ 1 j = 1,...,n wc,i ≥ 0 i = 1,...,m

The CI is expressed as the ratio between the aggregated performance of the entity (‘DMU’) under evaluation and a benchmark obtained from the other existing observa-tions rather than with external references (if a DMU acts as its own benchmark, then it has the maximal value of the CI, that is 1). The value of the performance is obtained aggregating all the sub-indicators values, weighting them in the most convenient way for the entity under analysis, subject to two constraints: 1) the weights have to be posi-tive and, 2) using these weights for evaluating any other entity, no one of the entities in the sample can reach a certain threshold (usually fixed at 1). So every DMU is granted with the ‘benefit of the doubt’. The selection of the specific benchmark for entity c is operated through a maximization process too: it is selected the entity that, with the maximizing weight of entity c, obtains the maximal value among the others entities. So it can be said that the CI is the value obtained specifying as weights the ones which maximize the ratio, and as benchmark entity, the one which minimizes the value of the CI. So the weights, as well as the benchmark, are endogenously determined. The perspective is strongly data oriented.

This formulation is equivalent to the original input oriented DEA model of Charnes et al. [1978], with the sub-indicators considered as outputs and a dummy input equal to

(35)

one for each DMU. However Zanella et al. [2013] proposes to use the output oriented approach (in the dual version) 3.1.5. Both 3.1.5 and 3.1.4 assume constant return to scale, therefore the performance scores are the same. The advantage of using an output oriented model is that it leads to a more direct estimation of targets (page 519 of Zanella et al. [2015]) min v s.t .                        Ps r =1uryr j0= 1 Ps r =1uryr j0− v ≤ 0, j = 1,...,n ur ≥ 0 r = 1,..., s v ≥ 0 (3.1.5)

Zanella, Camanho, Dias 2015

Zanella et al. [2015] propose an alternative formulation for the composite indicator model in the presence of undesirable outputs p. 523. The formulation is based on the di-rectional distance function model of Chung et al. [1997], presented before in equation 3.1.3, using a unitary level of inputs and setting the directional vector as g = (−gb, gy),

which allows to simultaneously contract undesirable output and expand the desirable outputs, keeping the inputs fixed (Pn

j =1λj ≤ 1). Chung et al. [1997] max γ (3.1.6) s.t .                        Pn j =1bk jλj= bk j0− γgb, k = 1,...,l Pn j =1yr jλj ≥ yr j0+ γgy, r = 1,..., s Pn j =1λj ≤ 1 λj ≥ 0, j = 1,...,n Zanella et al. [2015] max γ (3.1.7) s.t .                        Pn j =1bk jλj≤ bk j0− γgb, k = 1,...,l Pn j =1yr jλj≥ yr j0+ γgy, r = 1,..., s Pn j =1λj = 1 λj ≥ 0, j = 1,...,n

(36)

si-3.1. Data Envelopment Analysis and Composite Indicator 29

multaneous maximal feasible expansion of desirable and contraction of undesirable outputs. When g = (−gb, gy) = (−bk j0, yr j0) is chosen, the directional distance function is comparable to the Shephard’s output distance function and thus the output oriented efficiency measure is given by 1

1 + γ∗, which belongs to (0, 1].

In the model of Chung et al. [1997] desirable output are assumed to be strongly disposable (Pn

j =1yr jλj ≥ yr j0+ γgy), while the undesirable output are assumed to be weakly disposable (Pn

j =1bk jλj = bk j0− γgb). Weak disposability says that if (b, y) be-longs to the possibility set P , then (θb,θy) ∈ P if 0 ≤ θ ≤ 1, but ( ¯b, y) may not belongs even if ¯bi > bi. Roughly speaking, a reduction of undesirable output can be “paid" by

a reduction of the desirable one. Besides imposingPn

j =1λj ≤ 1 hides the assumption

of strong disposability of inputs. This is a residual of the fact that the model of Chung was developed in a ‘production environment’, but in the case of a CIs we can not talk about inputs and outputs. We have just sub-indicators of the performance of our enti-ties (or DMU). So Zanella et al. [2015] modify the model of Chung et al. [1997] with two features:

• replace ‘Pn

j =1bk jλj = bk j0−γgb’ with ‘ Pn

j =1bk jλj≤ bk j0−γgb’. This ensures that an entity can be classified as efficient if no further simultaneous improvement in outputs (desirable and undesirable) are possible.

• replacePn

j =1λj≤ 1 with

Pn

j =1λj = 1, considering in this way that exists a sort of

’unitary inputs’ behaving as a ’helmsman’ underlying every DMU.

The result is a redesign of the efficient frontier to avoid downward-sloping segments, with negative trade-offs between desirable and undesirable outputs, (p.523 of Zanella et al. [2015]).

The model implemented in this thesis is the dual of problem 3.1.7, with g = (−gb, gy) =

(−bk j0, yr j0) and is reported in 3.1.8 mi n β = − s X r =1 yr j0ur+ l X k=1 bk j0pk+ v (3.1.8)

(37)

3.2. Robust and Conditional Analysis 30 s.t .                              Ps r =1yr j0ur+ Pl k=1bk j0pk= 1 −Ps r =1yr jur+Pl_k=1bk jpk+ v ≥ 0, j = 1,...,n v ∈ ℜ ur≥ 0 r = 1,..., s pk≥ 0 k = 1,...,l β∗ _{= mi n} ₋Ps r =1yr j0ur+ Pl

k=1bk j0pk+ v . β∗is a measure of inefficiency, is the

maximal feasible improvement to the desirable and undesirable outputs that can be achieved simultaneously. In this modelβ∗belongs to (0, +∞). The value of the CI is

then defined as 1

1 + β∗. This formulation allows to ‘standardize’ the value of theβ

∗_{, so}

the value of the CI belongs to (0, 1]. The higher the value of the CI, the nearer the DMU under analysis is to the frontier. DMUs on the frontier assume a CI = 1 .

3.2 Robust and Conditional Analysis

In addition to the disadvantages listed in table 3.2, from Nardo et al. [2005], Daraio and Simar [2007] highlight other traditional limitations related to the use of a non para-metric approach, and so, to the use of the Directional Distance BOD of Zanella et al. [2015]. In particular, the deterministic nature of the CI obtained in this way, the dif-ficulty in making statistical inference (since it is assumed that all the deviations from the frontier are due to inefficiencies), the sensitivity to outliers and to the sample size. To overcome these problems Aigner et al. [1977] and Hall and Simar [2002], among many others, tried to consider approaches which assume a parametric function for the frontier; Simar and Wilson [1998] and Simar and Wilson [2000] instead proposed the application of the bootstrap, using asymptotic results. In this thesis however it is followed the line of De Witte and Rogge [2011] that has its root in the papers by Cazals et al. [2002], Daraio and Simar [2005] and Daraio and Simar [2007]. In this line, a robust and a conditional Directional Distance BOD model is implemented.