• Benefit of the Doubt
• Composite Indicator
• Data Envelopement Analysis
• Directional Distance Function
• Robust and Conditional Analysis
• Water and Waste Utilities

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 2105, Agenda 2030 with goal 6 (ensure availability and sustainable management of water and sanitation for all) and target 12.5 (by 2030, substantially reduce waste generation through prevention, reduction, recycling and reuse) highlighted the importance of water and waste sectors for reaching a sustainable development.
In this thesis we focused on the environmental impact of the utilities who 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 desirable and undesirable output. Then the use of the directional distance BoD Composite Indicator, proposed in the paper of Zanella, Camanho and Dias (2015), is deepened. Their approach 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 measuring efficiency originating from the directional distance approach of Shepard (1970) and Chung et al. (1997). In particular, the directional distance BoD (as Rogge 2017 calls it), is a BoD composite indicators, which is able to take care for undesirable output and 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, Färe, and Grosskopf (1997), for example it avoids downward-sloping segments in the frontier, that is, it avoids negative trade-offs between desirable and undesirable outputs.
A Robust order - m analysis (following Cazals, Florens and Simar (2002)) and a Conditional analysis (following Daraio and Simar (2007)) is also conducted, in order to give credibility to the Composite Indicator and to search for '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 envelop 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 provide 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 environmental pressure exerted by Portuguese Water and Waste utilities.

Results obtained show an average score for the CI of 0.784 which indicates that, if all the entities would perform on the five sub-indicators as well as the best performing entities, they could, on average, increase their CI scores by 21.6%. We check the robustness of our result running the Robust Analysis. What we discovered is that choosing m = 65 and t = 0.5 just 6 units are classified as super-performing. Finally we implemented also a conditional analysis, to identify the influence of some specific environmental variable on the values of the CIs. The conditional analysis shows that the size has a negative influence on the performance of the units, as well as being in a rural area, instead being in the north and having some `environmental certificates' have a negative influence. A non parametric regression (following Daraio and Simar (2007) p. 113) was used to test the significance of these influences, the results is a strong p-value just for the variables 'area of activity'.