Productivity of wastewater treatment plants in the Valencia Region of Spain

Utilities Policy xxx (2017) 1e13

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Productivity of wastewater treatment plants in the Valencia Region of Spain*
ndez-Sancho b R. Fuentes a, *, T. Torregrosa-Martí a, F. Herna a b

Department of Applied Economic Analysis, University of Alicante, Spain Department of Applied Economics II, University of Valencia, Spain

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 December 2015 Received in revised form 21 April 2017 Accepted 21 April 2017 Available online xxx

This study analyses the evolution of productivity over the 2008e2012 period for a homogenous set of 199 wastewater treatment plants that are located in the Valencia Region of Spain and utilize the same treatment technology, using the smoothed bootstrap Malmquist productivity index based on Data Envelopment Analysis (DEA). The results reveal a negative trend in productivity that is mainly the result of resource management rather than an inappropriate level of innovation or use of new technologies. In addition, the effect of exogenous factors on productivity is analysed using the Kruskal-Wallis (KW) test, finding that productivity levels were affected by the quality of the influent water and the size of the plants, but not by the other factors considered. © 2017 Elsevier Ltd. All rights reserved.

Keywords: Malmquist index Bootstrap Wastewater treatment plants Productivity

1. Introduction The capacity of water bodies to process the ever-increasing pollutant charges from expanding urban, industrial and agricultural water uses is increasingly limited. The adverse impact of anthropogenic pollution on the environment is also on the rise (Lazarova et al., 2012). This situation is further worsened by the increasingly frequent and lengthy periods of drought attributed to €ssling et al., 2012; Hof and climate change (Eurostat, 2009; Go Schmitt, 2011). Concerns about water supply and quality as well as the severe conditions of water stress found in many regions of the world are expected to escalate. In this context wastewater reuse is becoming an effective method of reclaiming a percentage of scarce water sources. Since the early 1980s, the general approach has been to treat the wastewater and then either discharge it into the environment, where it mixes with freshwater flows and is indirectly reused downstream, or to use the resulting effluent for agricultural, urban,
ndez-Sancho or industrial purposes (BIO by Deloitte, 2015; Herna

* It is important to point out that this study could not have been carried out without the assistance we received from the Entidad Pública de Saneamiento de Aguas Residuales (EPSAR), who provided the necessary information, nor the
. invaluable help of Professor Lluís Torro * Corresponding author. E-mail address: [email protected] (R. Fuentes).

et al., 2011c; Lazarova et al., 2012; WWAP, 2012). Although wastewater treatment does not always involve water reuse, this evolving use is becoming widespread (TYPSA, 2013). In addition to these considerations, there are a number of other justifications for analysing the performance of wastewater treatment plants (WWTPs). Not only can reuse help address the adequacy and ecological status of water masses, as laid down in article 4 of the Framework Water Directive (European Union, 2000), it also has enormous economic potential. Furthermore, one of the principal benefits of wastewater treatment is that it avoids the costs of redressing pollution and the downstream risk of municipalities, industries, farmers, and the tourism industry using contaminated water (WWAP, 2012). From this perspective, it is clear that environmental improvement is one of the factors that justify the importance of analysing the efficiency and productivity of wastewater treatment plants (WWTPs) (De Jong et al., 2000; Laukkanen and Huhtala, 2008; Van der Veeren and Tol, 2001). The aim of this paper is to study the productivity of wastewater treatment plants using rigorous methods backed by previously published literature. We analyse the influence of both technological changes and the efficiency of processes itself, in an attempt to explain productivity behaviour in a plant over an extended period. Given the potential economic and environmental impact of reuse, we expect the results to be useful to both public managers and private companies in areas facing severe water shortages. The structure of this report is as follows. A literature review of

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previous research is carried out in section 2. In section 3, the statistical model is explained and described. In section 4, the data used in the study are presented. The results obtained are further explained and discussed in section 5. The conclusions suggest ideas to improve the productivity of the wastewater treatment plants analysed.

2. Literature review In this section we review previously published papers that analyse both the efficiency and the productivity of WWTPs in order to identify the statistical variables and methods used. Not only have we centred on papers that analyse the productivity of plants, but also on those that analyse efficiency; since the former is merely an evolution of the latter, the variables used in both types of papers should be taken into account, even if the aim of this study is essentially related to productivity. Many previously published studies have addressed wastewater treatment from a variety of perspectives. However, studies referring exclusively to wastewater treatment productivity and efficiency are scarce. Upon reviewing all the available literature on the subject, we find that only a few have been published on this subject, in Spain. See, for example, Molinos-Senante et al. (2014a,b,c, 2015,
ndez-Sancho et al. 2016), Lorenzo-Toja et al. (2015), Herna
ndez-Sancho (2011a,b,c), Sala-Garrido et al. (2011, 2012a,b), Herna and Sala-Garrido (2005, 2009). At the international level, mention should also be made of the research carried out by Mahmoudi et al. (2012) in Iran and by De Jong et al. (2000) and Kemp (1998) in Dutch WWTPs. As regards methods, the articles by Abbott et al. (2012), Abbott and Cohen (2009), Covelli et al. (2010), or Ferro et al. (2011) argue that, given how little is known about the production function in the wastewater sector, the most commonly-used methods are those based on nonparametric frontier estimations. Most of those involved in the treatment field use a Data Envelopment Analysis (DEA) approach, although with variations of the models. For example, Molinos-Senante et al. (2014b) use DEA with non
ndez-Sancho et al. (2011b) and Molinosdesirable output, Herna Senante et al. (2014c) use a non-radial DEA model, and SalaGarrido et al. (2012a) use a DEA approach with tolerances. Molinos-Senante et al. (2015, 2016) used the Metafrointier Malmquist productivity index (MMPI) and the Hicks-Moorsteen Productivity Index, respectively. Other studies use the influence of more specific aspects, such as the effect of contextual factors on the calculation of economic-environmental efficiency ratios (LorenzoToja et al., 2015; Molinos-Senante et al., 2014a,b; Fuentes et al.,
ndez-Sancho et al., 2011c; Sala2015), or seasonal influences (Herna Garrido et al., 2012b). As we analyse the internal structure of these studies, we see that only the samples used vary significantly. They range from 338
ndez-Sancho and Sala-Garrido (2005, WWTPs in the study by Herna 2009), to the 45 WWTPs in the study by Sala-Garrido et al. (2012a), depending on homogenous subgroups, using a specific technology or treatment process, or referring to a specific area (most of them in
ndez-Sancho the Valencia Region). With the exception of Herna et al. (2011a) and Molinos-Senante et al. (2016), where a 6-year period is considered, and Molinos-Senante et al. (2015), using a 3-year period, almost all of the studies refer to a specific year. A comparison of the variables used on the papers shows similar conclusions. The inputs used vary in terms of aspects ranging from technical data, such as the water mass treated in cubic metres, to purely economic data measured in euros per year, such as operation and maintenance costs, staffing, chemical reagents, or energy costs.
ndez-Sancho et al. (2011a,b,c), Herna
ndezThe studies by Herna

Sancho and Sala-Garrido (2005, 2009), Molinos-Senante et al. (2014a,b,c, 2015, 2016), Sala-Garrido et al. (2011, 2012a,b), LorenzoToja et al. (2015) and Fuentes et al. (2015) include the elimination of contaminants from treated water as output, calculated on the basis of entry and output levels of solids in suspension (SS in mg/l) and on the entry and output levels of organic material expressed as a chemical demand for oxygen (COD, in mg/l) or nitrogen. Some also take into consideration non-desirable outputs such as noise, odour and visual impact levels (Molinos-Senante et al., 2014a,b; Lorenzo
ndez-Sancho Toja et al., 2015). Some studies (for example, Herna et al., 2011a,b; Sala-Garrido et al., 2011, 2012b; Fuentes et al., 2015) use contextual variables, like the characteristics of the effluent, the age or the size of the plant, or the treatment technology. Table 1 and Fig. 1 present the literature on WWTP efficiency and productivity. Table 1 summarizes the recent studies and Fig. 1 summarizes the variables and models used in the studies.

3. Method As seen from the literature review, most previous studies carried have either analysed the efficiency or the productivity of WWTPs using non-parametric models, such as the Data Envelopment Analysis model (DEA) or the Free Disposal Hull (FDH), in one of their various forms. These models have important advantages over parametric models: there is no need to establish the form of the production function; they allow for analysis processes involving various inputs to generate multiple outputs at the same time; they allow the comparison of the activity of each unit (Decision Making Unit DMU) with the rest (since it is based on an efficient production frontier that includes DMUs, which show higher levels of efficiency); and it is not necessary to make adjustments in situations where the prices of factors and products are either unknown or difficult to calculate. Until now, these models have been used to evaluate the efficiency and/or productivity of WWTPs while trying to incorporate advances with which to fine-tune the estimates made in this respect, but there is still room for improvement with regard to possible alternatives. Specifically, as proposed in this paper, it is possible to evaluate the productivity of WWTPs over a period in order to observe how it evolves and obtain results using the bootstrap method. That allows us to validate values found, which in general go beyond merely specific information on the sample used as well as build confidence intervals, which makes it possible to contrast the statistical significance of productivity improvements in WWTPs. Given these advantages and the fact that the majority of the previous studies used DEA to analyse the evolution of WWTP productivity, we also chose to conduct a productivity analysis of the plants using DEA and calculate the DEA-based Malmquist Productivity Index (Malmquist, 1953). DEA allows the units analysed to be organised hierarchically in terms of efficiency levels, whilst the Malmquist index makes it possible to estimate changes in productivity throughout the entire time period of the sample. In terms of input-oriented evaluation processes, a decisionmaking unit (DMU) is considered to be efficient when it uses the minimum input empirically observable for any examined DMU, given its output vector (Charnes et al., 1981). In other words, a DMU is inefficient when it cannot use the minimum input level to obtain the maximum output production (Cooper et al., 2004). DEA is a non-parametric method, where it is not necessary to impose any functional form on the production function and, since it is not stochastic either, it must not be assumed that the non-

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Table 1 Studies on productivity and efficiency in wastewater treatment sector. Authors

Characteristics of the sample

Kemp (1998)

Variables of the Threshold not avalaible (n/a) Diffusion Model: Total costs of using technology, savings in pollution taxes, other benefits derived from using technology (improved image of the company due to environmental awareness…). Variables relating to the use of biological WWTPs: taxes paid for dumping, total costs, annual unit cost of using a WWTP, efficiency of cleaning device control (different if the technology employed is aerobic or anaerobic), the uncertainty factor. Inefficiency in Wastewater Theoretical model proposal n/a treatment plants using one based on utility, cost and public WWTP and polluting revenue functions. private companies. Year of sample unavalaible.

De Jong et al (2000)

Inputs

Outputs and contextual variables

Analysis of the efficiency of biological WWTPs in the Dutch food and beverage industry, covering 93 companies. Year 1991


ndez- Technical efficiency in 338 Staff, maintenance, waste Eliminated contaminants Herna management and other Sancho WWTPs. 2004. costs. and SalaContextual variables: size of Garrido plant. (2005)


ndez- Technical efficiency in 338 Energy, staff, maintenance, Herna waste management and Sancho WWTPs. Year 2004 other costs. and Sala(Reagents and capital Garrido, amortisation). (2009)

Solids in Suspension (SS), chemical oxygen demand (COD) and bio chemical oxygen demand (BOD).

Method

Country/ Region

The Threshold Model / Kolmogorov-Smirnov test/ Netherlands The logistic model/ Gompertz model/

Main results Investments made by the food and beverage industry in biological WWTPs were efficient given the nature of the effluent (homogenous and practically all organic). Relatively high efficiency of control at a low cost. Relative efficiency of levies or charges for pollution in the use of biological WWTPs.

The Subsidies might in part Netherlands compensate for the lack of private sector investment, given the decreasing returns to scale in a context of Zero Profit and cost minimisation. Great efficiency in the larger Valencia DEA / CRS (constant WWTPs maintenance and returns to scale)/IO (input region waste management costs (Spain) orientation) ANOVA being the most important factors explaining differences in the efficiency of WWTPs Maintenance and waste DEA/CRS/IO / Cost analysis Valencia management costs are the region most important factors (Spain) explaining the differences between WWTPs from an efficiency standpoint. Not adapting the facilities to Valencia DEA / CRS/IO/ technological improvement region Malmquist Productivity explains the drops in (Spain) Index/CRS/IOKruskalefficiency and productivity Wallis test levels in the period under analysis. WWTPs with improved productivity are those with lower energy consumption. The size of the plant, the Non-radial DEA/CRS/IO Valencia amount of organic material region eliminated and the type of (Spain) bio-reactor explain the differences in efficiency. Decision Making model under a Zero Profit constraint


ndez- Technical and productivity Herna Sancho efficiency in 196 WWTPs, Years 2003 and 2008. et al. (2011a)

Solids in Suspension (SS), Energy, staff, reagent, chemical oxygen demand maintenance, waste (COD). management costs Contextual variables: age of the plant, size, equivalent population. Technology.


ndez- Energy efficiency in 177 Herna Sancho WWTPs, Year 2009. et al. (2011b)

Solids in Suspension (SS), Energy, staff, reagent, chemical oxygen demand maintenance, waste (COD) management and other costs (laboratory and office expenses,…).Factors affecting energy consumed: size of plant, nature of effluent treated (grams of COD per m3), type of aeration in bio-reactor.


ndezHerna Sancho et al. (2011c)

Seasonal influences in 76 WWTPs, 44 with EA technology and 32 with Activated Sludge (AS) technology.

Energy, staff, reagent, maintenance, waste management and other costs

Solids in Suspension (SS), chemical oxygen demand (COD), Nitrogen (N) and phosphate (P)

Free disposal hull (FDH) VRS (Variable returns to scale)/IO

Valencia region (Spain)

SalaGarrido et al. (2011)

Technology in use at 99 WWTPs. Year 2009

Running and maintenance costs. Technology used.

Solids in Suspension (SS), chemical oxygen demand (COD), Nitrogen (N).

DEA/VRS/OO(Output oriented) TGRs Metafrontier approach (technological gap ratios)

Valencia region (Spain)

Plants with seasonal variations are less efficient in terms of costs than those which show no seasonal behaviour, this being most evident in those using AS technology As regards efficiency, no significant differences are noted, the four technology types analysed being, on average, similar. According to the TGRs, operating using (continued on next page)

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Table 1 (continued ) Authors

Characteristics of the sample

Inputs

Outputs and contextual variables

Method

DEA/VRS/IO with tolerances

Country/ Region

Valencia region (Spain)

SalaGarrido et al. (2012a)

Uncertainty in 45 WWTPs, Running and maintenance Year 2009. costs.

Solids in Suspension (SS), chemical oxygen demand (COD). Nitrogen (N).

SalaGarrido et al. (2012b)

Efficiency in 272 WWTPs, Year 2008.

Energy, staff, reagent, maintenance, waste management and others costs (all in euros/year).

Valencia SS and COD as (gr/year) and, DEA/VRS/IO with scaled variable performances and region as contextual variables: (Spain) Mann-Whitney Test. Seasonality, activated sludge and extended aeration (EA).

MolinosSenante et al. (2014a)

Analysis of 7 different technologies for secondary treatment in small WWTPs. 11 research group, 29 relevant water companies and 14 public entities related to water management, and real data from a sample of Spanish WWTPs. Years of sample unavalaible. Analysis of efficiency in 60 WWTPS, Year 2009.

Investment, running and maintenance costs, energy consumption, elimination of solids, nitrogen, phosphorus

Contextual variables: surface area required for the facilities’ noise levels, odour levels, visual impact and public acceptance.

Compound socioeconomic and environmental model to evaluate the plants’ sustainability.

Spain

Total costs including energy, staff, reagents, waste management and maintenance.

Total quantity of pollutants removed: suspended solids (SS), oxygen demand (COD), total nitrogen (N) and total phosphorus (P). Also, as non-desirable outputs: GHG emissions (Kg of CO2 equivalent).

Environmental performance indicators and DEA/VRS/UOO (undesirable output oriented) with nondesirable outputs in two stages to construct an index of overall performance.

Valencia region (Spain)

MolinosSenante et al. (2014c)

Efficiency in 192 WWTPs. Years of sample unavalaible.

Energy, staff costs, reagents, SS and COD removed. maintenance, waste management and other costs.

MolinosSenante et al. (2015)

Productivity assessment of Energy, labour, reagent, waste management and 99 WWTPs. maintenance costs. 2007 & 2009

MolinosSenante et al. (2014b)

COD, N, P.

Valencia Non-radial DEA/VRS/IO, Total Improvement Index region (Spain) (TII), and Relative Improvement Index (RII), Kruskal-Wallis nonparametric test.

Catalonia Metafrontier Malmquist productivity index (MMPI) (Spain) OO, (unspecified returns to scale).

Main results sludge technology is the optimum method. The input variability is lower than the output variability. Broad scope for reducing running costs if the number of efficient plants changes when using values with tolerances instead of the originals. Seasonality has an adverse effect on the efficiency of the WWTPs, and this factor has a greater effect on WWTPs with AS technology than on those with EA technology. Lower sustainability of intensive technologies from an environmental standpoint, although the cost is lower.

The best results from an environmental standpoint came from the WWTPs based on anaerobic digestion for sewage sludge. Given that only 7% of the treatment plants examined were identified as efficient, there is clearly broad scope for improvement of global efficiency and also for energy consumption or reducing GHG (greenhouse gas) emissions. Economies of scale did not affect environmental efficiency. They isolated the specific inputs on which to act in order to save costs. The highest efficiency score was for energy costs, while the lowest was for staff costs. Taking into account that staff costs account for around half of the total cost, it is vital to increase the efficiency of this cost item in order to control costs and improve the competitiveness of the WWTPs The MMPI indicates that, over the period analysed, the productivity rose by 0.9% and 0.3% for Activated Sludge (AS) and Biological Contractor (BC) technologies respectively, whilst for the Aerated Lagoon (AL) and Trickling Filter (TF) processes, the productivity decreased by 0.5% and 2.2% respectively

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Table 1 (continued ) Authors

Characteristics of the sample

Inputs

Outputs and contextual variables

LorenzoToja et al. (2015)

Analysis of efficiency in 113 Electric power WWTPs in various regions consumption, chemical components and sludge of Spain. Year 2011. production.

Life Cycle Assessment and Spain input oriented DEA/CRS/IO SBM (Slacks-based measure) and Assurance Region Models.

Fuentes et al. (2015)

Efficiency in 199 homogeneous WWTPs. Year 2012.

FDH (Free Disposal Hull) Conditional order-m efficiency CRS/IO

Valencia region (Spain)

MolinosSenante et al. (2016)

Productivity assessment of Energy, staff, reagents, maintenance, waste 204 WWTPs. management and other Years 2003 & 2008. costs.

DEA-Based/VRS/ simultaneous IO and OO Hicks-Moorsteen Productivity Index

Spain

Quality of the treated water as the difference between contamination entering and exiting. Kg of suspended solids removed, cubic metres of treated water or kg of PO4 -3 removed. Energy, staff and other costs SS and COD removed. Contextual variables: level (reagents, maintenance, waste management, offices, of suspended solids, level of COD, plant size, type of gardens, laboratories...) aeration and age.

COD removed and SS.

calculated efficiency follows some kind of probabilistic distribution. Apart from this, it can be used to evaluate the behaviour of DMUs in sectors where multiple inputs and outputs are involved in the production process, without requiring any information on prices (Charnes et al., 1997). However, it is not entirely without disadvantages; these are usually related to the homogeneity of the units being compared and the fact that the reliability of the results depends on the relationship between the number of DMUs and the number of variables being considered. In this respect, Cooper et al. (2007) recommend that the number of units should be at least the max {(s$r), 3$(s þ r)} (where s and r are the number of outputs and inputs, respectively); otherwise the hierarchy based on the efficiency levels of the units under evaluation might be questionable. Furthermore, DEA does not offer the possibility of testing the stability of the results obtained. This is due to the fact that it modifies the variables (inputs or outputs) involved. Therefore, these variables must be carefully selected beforehand according to experts' opinions and their availability, and subjected to an exhaustive literature review (Barros, 2005). Lastly, as the samples used by the DEA method are finite, the estimation of their efficiency might vary from sample to sample (Simar and Wilson, 1998). All of these drawbacks were taken into account and overcome in this study by choosing units which were perfectly homogenous, by adhering to the required relationship between the number of DMUs

Method

Country/ Region

Main results Key factors in detecting inefficiencies: contamination load of influent water, change of climate zone, treatment complexity level. Smaller WWTPs could improve with constant supervision. The quality of the influent water and also the size and age of the plants had a significant influence on their efficiency levels. In particular, an inverse relationship between the quality of the influent water and the efficiency of the WWTPs. Also, a smaller size and more modern installations showed a positive influence. Finally, the average efficiency levels observed turned out to be higher than those reported in previous studies. Total Factor Productivity (TFP) decreased over WWTPs and years analysed, primarily due to increased energy and staff costs; Efficiency changes (ECH) were largely responsible for the decline in TFP, whilst technical changes (TCH) exhibited a positive trend; and TFP increased in 12.8% of the WWTP assessed, indicating that, overall, the facilities require substantial improvements in performance.

and the number of variables, by carrying out an exhaustive review of literature and by using an effective method to avoid the productivity results varying from sample to sample (smoothed bootstrap), which also eliminates the problem of the deterministic nature of the estimations due to the non-stochastic characteristic of € thgren and Tambour, 1999), as explained below. DEA (Lo Considering all of the above, a DEA-based measurement of any change in the unit's productivity over time will be calculated using the Malmquist Productivity Index (M) (Malmquist, 1953). In accordance with F€ are et al. (1994), the central idea is that changes in productivity can be the result of enhanced efficiency, but sometimes they can be caused by technological improvements, and M allows changes in productivity to be divided into two initial factors referring to technical efficiency (E) and technological change (T). This index is based on the calculation of distance functions. A generic input-oriented distance function can be defined as:

n o Dt ðXt; YtÞ ¼ inf q*Rþ : ðq*Xt; YtÞ2Pt

(1)

where q represents the lowest factor by which the input vector in year t can be decreased when the output vector and the technology for year t is used; Y is a vector of outputs; X is a vector of inputs; and Pt represents the feasible production set given the technology in period t, which is defined as:

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Fig. 1. Synthesis of the variables used above in the analysis of the productivity and efficiency of WWTPs.

Pt ¼ fYt : Xt can produce Ytg

(2)

With regard to the above, the input-oriented Malmquist index (M) between time periods t and tþ1 would be defined as:

    Dt ðXtþ1 ; Ytþ1 Þ Dtþ1 ðXtþ1 ; Ytþ1 Þ ð1=2Þ Mt;tþ1 Xtþ1; Ytþ1; Xt ; Yt ¼ Dt ðXt ; Yt Þ Dtþ1 ðXt ; Yt Þ (3) As previously mentioned, this index can initially be broken down into two components: technological change (T) and technical efficiency change (E). The breakdown is as follows:

Mt;tþ1 ðXtþ1 ; Ytþ1 ; Xt ; Yt Þ ¼

output vector and technology (previous studies, such as
ndez-Sancho et al., 2011a; also selected this orientation). Herna

1 ¼ minql q Dk0 ;t ðXtþ1 ; Ytþ1 Þ K P k;t k0 ;tþ1 s:a: l $Xk;t ;c r r  qXr 

K P k¼1

k¼1

(5) 0

k ;tþ1 lk;t $Yk;t ;c s s  Ys

lk;t  0; c k where q denotes an efficiency score for a particular DMU (DMUk'

    Dtþ1 ðXtþ1 ; Ytþ1 Þ Dt ðXtþ1 ; Ytþ1 Þ Dt ðXt ; Yt Þ ð1=2Þ $ Dt ðXt ; Yt Þ Dt ðXt ; Yt Þ Dtþ1 ðXt ; Yt Þ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl ffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} T

(4)

E

The first ratio (E) represents changes in technical efficiency between two periods (t and tþ1). The second ratio (T) is a measure of technological progress between the same periods evaluated. E and T are also known as the catch-up effect and frontier-shift effect, respectively. The four different distances shown in equation (3) can be achieved using mathematical programming (see equation (5)). In particular, an input-oriented approach is used to estimate the Malmquist Productivity Index because the principal objective of WWTPs is to use the minimum level of inputs given a specific

with k:1, …,K - the sub-index k' shall be used to name the DMU under analysis-); Xk,t r , represents the rth input respectively observed at DMUk in year t (with r:1, …,R and t:1, …,T); Yk,t s , is the sth output respectively observed at DMUk in year t (s:1, …,S); and lk,t, is a coefficient that shows the proportion of DMUk used to evaluate DMUk' in year t. Constant scale returns are assumed in equation (5) for three reasons. First, under variable returns the Malmquist index does not give a true reflection of the variation in productivity (F€ are and Grosskoppf, 1996; Molinos-Senante et al., 2014c). Second, this assumption was previously made in other studies, within the same
ndez-Sancho et al., 2011a). Lastly, for all the years sector, (Herna

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within the 2008e2012 period, the existence of constant returns to scale (CRS) technology was tested using the bootstrap procedure proposed by Simar and Wilson (2002). The test based on the mean of ratios, involving distances assuming constant returns, divided by those based on variable returns was utilized. The C*a values obtained for each year (0.024, 0.028, 0.034, 0.034 and 0.05 for 2008 to 2012, respectively) indicated that the CRS hypothesis was not rejected for any one of those years. Given the input orientation used and the adopted definition of distances adopted, values for M (E or T) lower than 1 would indicate an improvement in productivity (technical efficiency or techno€re et al. logical progress), and vice versa, in accordance with Fa (1994). Since non-parametric DEA estimators are based on a finite sample of observations, it is necessary to use a method capable of analysing the sensitivity of the productivity results to changes in the data (Simar and Wilson, 1998). Furthermore, DEA cannot offer any information regarding uncertainty in the estimates of the ef€ thgren and Tambour, 1999). Fortunately, the ficiency of each unit (Lo bootstrap is a statistical procedure capable of eliminating these two drawbacks of the DEA. This technique, introduced by Efron (1979), is based on the idea of simulating the data-generating process (DGP) to obtain a new estimate for each simulated sample. In this way, the estimates obtained would mimic the distribution of the real population estimator (Simar and Wilson, 1998). For example, it is possible to obtain confidence intervals for the estimates of the efficiency parameters, enabling us to determine whether the efficiency levels of the DMUs, initially obtained by DEA, are statistically significant (Tortosa-Ausina et al., 2008; Fuentes, 2011; Fuentes and Lillo~ uls, 2015). Ban This study will follow the method described by Simar and Wilson (1999) (smoothed bootstrap). This method improves the estimates obtained when we resample directly using the original data, unlike naive bootstrap, which provides a poor estimate of the DGP. Furthermore, it incorporates the reflection method described by Silverman (1986), which avoids estimate problems derived from the fact that the efficiency parameters of the input-oriented model's upper limit is equal to one. For the DEA approach, the smoothed bootstrap algorithm follows the steps described below (Simar and Wilson, 1999):

when their values are organised in ranks (Conover, 1999). We chose this method for two reasons. First, like the Malmquist technique, it is non-parametric. And second, as there is no reason to assume the existence of any type of underlying probability distribution in productivity levels or the variables whose potential relationship is being analysed, the conditions are ideal for this model to be effective in analysing the hypothesis (Sheskin, 2000). Furthermore, this test is more powerful than other non-parametric alternatives such as the median test (Conover, 1999) and it has also
ndezbeen used in previous studies with similar objectives (Herna Sancho et al., 2011a). In addition, by using KW, it is possible to avoid the problems caused by the correlation that exists among the DEA estimations (Simar and Wilson, 2007). The test is based on the calculation of a value usually called T, as follows:

1. Compute the Malmquist productivity index _ M t;tþ1 ðXtþ1 ; Ytþ1 ; Xt ; Yt Þ for each DMU by solving the linear programming _ models_(5) to obtain the estimations of E and T shown in (4) (E and T ). 2. Obtain a pseudo dataset (X*t, Y*t) for each DMU and t to construct the reference bootstrap technology, by using bivariate kernel density estimation and the reflection method. 3. Calculate the bootstrap estimate of the Malmquist index for _ *kb each DMU, M t;tþ1 ðXtþ1 ; Ytþ1 ; Xt ; Yt Þ using the sample obtained in step 2. 4. Repeat steps 2e3 B times to obtain a set of estimates _ *kb M t;tþ1 ðXtþ1 ; Ytþ1 ; Xt ; Yt Þ. Simar and Wilson (2000) recommend a value of B ¼ 2000. 5. Obtain confidence intervals for the Malmquist index and its components, after obtaining the first 2000 estimates from the pseudo-samples generated.

In any case, prior to commencing the analysis of the data using the methods described so far, the Wilson (1993) outlier detection method is applied to detect and eliminate any observations that could potentially be influenced by measurement errors and/or an atypical behaviour of specific DMUs in order to eliminate the bias that such observations might introduce in the sample subject to analysis, the results and the final conclusions obtained. In the event of the number of outputs (s) being equal to or greater than one (s  1), this method is based on a statistical computation of the following type:

In addition to the Malmquist and smoothed bootstrap techniques, the Kruskal-Wallis test (KW) is used to analyse the influence of specific contextual variables on the plants' productivity. The KW test is based on the idea that the relationship that could potentially exist among three or more variables may be revealed

T¼

M X ½Ri  ð1=2Þpi ðP þ 1Þ2 12 PðP þ 1Þ i¼1 pi

where P is P ¼

(6)

PM

i¼1 pi denotes the total number of observations, M P RðZij Þ i ¼ 1; 2; …; M the total independent samples and Ri ¼ pi i¼1 the sum of rank assigned to the ith sample, Zij represents the j element of the ith sample and R(Zij) the rank assigned to Zij. The lack of significant differences among the samples analysed is not rejected with a level of significance a (Ho not rejected) when the value of T is lower than or equal to the 1- a quantile of a chisquare with k-1 degrees of freedom (Conover, 1999), in other words, when a level of statistical significance (p) higher than 0.05 is obtained. Otherwise, the null hypothesis (Ho) is rejected. However, this test is not without limitations:

a) When a set of data is transformed into a rank, part of the information is lost. However, if the original data is important, as in an ordinal comparison (which is the case with Malmquist estimates), this is not a problem (Conover, 1999). b) Non-parametric tests are designed merely to test statistical hypotheses, not to estimate parameters. However, this is not a problem because the aim is to inform of the existence of a relationship between the productivity of the agencies and the variables studied.

h i ðiÞ ðiÞ ðiÞ RL ðW*Þ ¼ RL ðWÞ DL ðjUjÞ jUj1

(7)

where W is the input matrix including a column vector of ones ðiÞ

(Wk,rþ1), W*¼(W'Z), Z being the output matrix (Zk,s), DL ðεÞ represents the value calculated from a set of observations K-L with K¼(1, …,k) where L M K and ε is a value computed from the total set of observations K, U represents the matrix of products of ordinary least squares regression residuals of Zh and Zj over W and, lastly, ðiÞ

RL ðW*Þ is the statistic representing the proportion of volume in space [(rþ1)þs] spanned by a subset of data obtained by eliminating i observations from the total set (K). Subsets of data (L)

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R. Fuentes et al. / Utilities Policy xxx (2017) 1e13

eliminated from the total set (K) that generate small values for ðiÞ

RL ðW*Þ are considered to be outliers. In particular, such small

2i max ðiÞ values are identified by computing values of RL ðX*Þ i (imax being the size of the subset of observations to be eliminated) ðiÞ

and then selecting the minimum value of RL ðX*Þ among them. The results obtained using the four methods that have been explained in this section (input-oriented DEA Malmquist productivity indices, smoothed bootstrap, Kruskal-Wallis test and Wilson (1993) outliers detection method) are reported and discussed below. 4. Data and variables From the moment wastewater enters the plant, the treatment process comprises several stages, both physical and biochemical. Such treatment stages or levels are divided into preliminary, primary, secondary (with or without elimination of nutrients), and tertiary stages. The aim of the first, or preliminary stage, is to condition the polluted water to facilitate subsequent treatments, thus avoiding erosion and obstruction. At this stage, gross solids, small pieces of stone, sand and non-miscible solids, with lower density than water, are eliminated. After the preliminary stage and during the primary treatment stage, wastewater undergoes a sedimentation process to remove both floating materials and sediment or settleable materials. Thereafter, during secondary treatment, the elimination process of organic material and nutrients (nitrogen and/or phosphorus) begins. However, not all the treatment plants with secondary treatment include this nutrient-related procedure. Finally, during the tertiary treatment, a high-quality effluent is obtained by removing other pathogens and substances that were not eliminated in the earlier stages. This is mainly achieved through chlorination and ultraviolet radiation. Preliminary and primary treatments are usually similar in the different WWTPs. The same, however, is not true for secondary treatments. Secondary treatments vary depending on the wastewater treatment technology implemented (mainly activated sludge, aerated lagoon, trickling filter, and rotating biological contractor or biodisk) (Sala-Garrido et al., 2011). For this research, the most numerous homogenous subgroup of all the WWTPs in the Valencia Region (using the same treatment technology and identical methods of pollutant elimination) is analysed. This has the twofold aim (1) respecting the basic requirements of the DEA model with regard to the homogenous nature of the units to be procured and (2) ensuring that there is a high number of DMUs, which in turn ensures the best possible degree of nesting. Specifically, this involves the productivity of 199 WWTPs treating domestic wastewater, whose treatment was based on activated sludge using prolonged aeration without eliminating nutrients. The data used in this study was kindly supplied by Entidad Pública de Saneamiento de Aguas Residuales (EPSAR) in the Valencia Autonomous Region (Spain) and refers to 199 WWTPs operating in the Valencia Region during the period 2008e2012 (the most recent period for which it was possible to obtain figures). With regard to inputs, these include the cost of energy used, including the fixed part (power term) and the variable component (consumption) (Hern
andez-Sancho and Sala-Garrido, 2005, 2009;
ndez-Sancho et al., 2011a,b,c; Sala-Garrido et al., 2012a,b; Herna Molinos-Senante et al., 2014a,b,c, 2015, 2016; Lorenzo-Toja et al., 2015; Fuentes et al., 2015), total staffing costs (including salaries,
ndez-Sancho and taxes and social security contributions) (Herna
ndez-Sancho et al., 2011a,b,c; Sala-Garrido, 2005, 2009; Herna Sala-Garrido et al., 2012a,b; Molinos-Senante et al., 2014a,b,c, 2015,

2016; Fuentes et al., 2015) and other costs, including maintenance costs for treatment facilities and infrastructure, such as equipment and machinery (even their replacement), waste and sludge management, as well as other costs relating to other items such re
ndez-Sancho and agents, offices, laboratories, gardens etc... (Herna
ndez-Sancho et al., 2011a,b,c; Sala-Garrido, 2005, 2009; Herna Sala-Garrido et al., 2011, 2012a,b; Molinos-Senante et al., 2014a,b,c, 2015, 2016; Lorenzo-Toja et al., 2015; Fuentes et al., 2015). All input costs were deflated (price changes over time do not affect the results) and expressed in euros/m3 (using 2008 as the baseline). The variables used for the outputs were the level of elimination of suspended solids (ESS) and the elimination of chemical oxygen demand (ECOD), both measured in mg/l. These concepts are normally used by WWTPs and previous studies to measure the quality
ndez-Sancho and Sala-Garrido, 2009; of treated water (Herna
ndez -Sancho et al., 2011a,b,c; Sala-Garrido et al., 2011, Herna 2012a,b; Molinos-Senante et al., 2014a,b,c, 2015, 2016; LorenzoToja et al., 2015; Fuentes et al., 2015). Suspended solids (SS) represents the total amount of particles of solid pollutant remaining in suspension in water. Given a specific quality level of the influent, the greater the amount of SS eliminated, the greater the improvement of the water quality. In turn, the chemical oxygen demand (COD) is the amount of oxygen that is consumed by oxidisable materials (organic and a small quantity of inorganic matter). Degrading the organic material present in the water consumes oxygen and the level of oxygen consumption indicates the degree of pollution present in the wastewater; therefore, the lower the COD level, the higher the water quality. Statistical information on the variables for the years 2008 through 2012 is summarised in Table 2. 5. Results The data mentioned in the above section was analysed, using the FEAR 1.15 package running on R 2.12.2, to obtain the productivity results (M) broken down into its two factors (E and T) as described in equations (3)e(5), and the smoothed bootstrap algorithm of Simar and Wilson (1999). As explained in section 3 (Method), the Wilson (1993) outlier detection method was first applied to detect observations resulting from measurement or recording errors and/or an atypical behaviour that for this reason are likely to alter real productivity results. This procedure obviously reduced the size of the original samples for each year of the period analysed. The number of original DMUs from 2008 to 2012 was 179, 182, 190, 195 and 199, respectively. After the outlier detection the size of the samples was 173, 168, 177, 185 and 189 (always respecting the reasonable proportion of units to be left out given by pffiffi k , where k is the original number of DMUs in the sample) (Barnett k and Lewis, 1995). The disparity of the DMUs, for each period, is dealt with by restricting the calculations to the DMUs in common between periods, hence the number of DMUs finally included in the analysis is 166. Table 6 (see appendix) shows the results for M, E and T for each WWTP, for the 2008e2012 period as a whole. These results indicate that the average productivity for the period under consideration was 1.215, indicating a 21.5% drop (1.215e1) in the level of productivity over the study period; this result was statistically significant at the 95% confidence level. The bootstrap methodology enables us to confirm the null hypothesis of no productivity change by calculating confidence intervals. The asterisked figures shown in Table 6 (95% confidence) indicate that the null hypothesis is rejected and therefore it is not ruled out that changes occurred. In other words, only the statistically significant figures suggest a real change in the level of productivity of the corresponding DMUs. In

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R. Fuentes et al. / Utilities Policy xxx (2017) 1e13

9

Table 2 Sample description: 2008e2012. Years

2008

2009

2010

2011

2012

Statistics Description

Inputs

Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum

Outputs

Energy V/m3

Staffing V/m3

Others V/m3

ESS mg/l

ECOD mg/l

0.100 0.070 0.015 0.459 0.117 0.076 0.013 0.495 0.117 0.080 0.012 0.427 0.106 0.070 0.014 0.447 0.106 0.077 0.014 0.458

0.386 0.299 0.046 1.705 0.408 0.325 0.058 1.940 0.436 0.379 0.047 2.251 0.437 0.367 0.044 2.114 0.458 0.401 0.043 1.984

0.248 0.208 0.034 1.306 0.264 0.227 0.041 1.485 0.271 0.220 0.033 1.273 0.316 0.294 0.020 1.927 0.333 0.282 0.020 1.544

259.503 160.210 32.000 1201.000 284.600 178.144 65.000 1276.000 251.452 131.820 17.000 877.000 239.144 119.684 34.000 743.000 247.889 158.663 49.000 1072.000

556.480 290.982 87.000 1771.000 609.059 341.715 106.000 2613.000 561.763 260.853 54.000 1442.000 576.989 254.738 85.000 1710.000 569.735 273.855 91.000 1603.000

*SD stands for standard deviation. Source: EPSAR

productivity levels dropped for the whole time period under consideration, despite the use of better innovation and new technologies (T), due to the plants' resource management (E). However, on the basis of the results obtained, it is not possible to be more specific. Therefore, it would be advisable for the authorities responsible for management to concentrate on detecting the factors that might have led to this situation. As regards the year-on-year trend, the average results are shown in Table 3. Unfortunately, the frequent lack of significance in the average levels, on a year-on-year basis, means it is not possible to make any statements based thereon. Nevertheless, as can be seen from the average values of the plants with significant values (second row of Table 3) there is a reduction in M levels, because its values were always greater than one. However, the trends in technical efficiency change (E) and in technological change (T) were quite different, with highs and lows during the period analysed. With regard to the values for E, there was clear improvement at the beginning of the period (2008/2009 and 2009/2010), followed by a strong decline in the last two sub-periods. The values for T showed the opposite trend, with the worst values in the two first sub-periods and the best in the later periods. In other words, the reasons for obtaining inappropriate M levels changed throughout the 2008e2012 period. At first, resource management (E) improved the value of M, while the effect of the levels of innovation and adoption of new technologies (T) worsened it. At the end of the period, the influences of E and T were opposing. It seems that the efforts made to correct the

this regard, 103 out of the 129 units with significant results for M experienced drops in productivity levels, while only 26 showed improvements in productivity and the average of their M values was 1.364. In general terms, this implies a decrease in their level of productivity over the 5 years analysed. As explained in section 3 on the methodology, M can be broken down into two factors. The results of the first factor (technical efficiency change -E), for the 2008e2012 period, are shown in columns 3 and 7 of Table 6. Its average value reaches the significant level of 1.328 and therefore indicates a 32.8% drop in productivity level, which can be attributed to worse management of the resources used by the treatment plants. This trend is confirmed by the result of the average value for the significant DMUs (1.720) and the fact that six out of the total 97 plants showed improvements, while 91 showed the opposite trend. The results for the second of the factors into which M can be broken down (T), obtained for the five-year period from 2008 to 2012, are shown in columns 4 and 8 of Table 6. The non-significant average value reached was 0.914 and the significant average value was 0.807, both indicating technological (T) improvement over the study period. In addition to this, the six units with significant averages improved their T levels. Therefore, both in terms of the average results and the number of units with significant improvements, it can be observed that there seems to be an increase in the levels of innovation and adoption of new technologies over the period under consideration. To summarize, the results point to the fact that WWTPs

Table 3 Year-on-year trend in results of M, E and T. 2008/2009

Geometric mean Geometric mean of significant Significant Significant improving Significant worsening a

2009/2010

2010/2011

2011/2012

M

E

T

M

E

T

M

E

T

M

E

T

1.051 1.152 117 38 79

0.945 0.915 74 41 33

1.113 1.308 36 0 36

1.123a 1.132 154 57 97

0.961 0.915 95 54 41

1.169 1.353 56 0 56

1.021 1.021 149 66 83

1.357a 1.528 123 16 107

0.752a 0.741 150 150 0

1.059 1.113 145 54 91

1.095 1.282 81 31 50

0.968 0.879 39 24 15

Implies a 95% significance.

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R. Fuentes et al. / Utilities Policy xxx (2017) 1e13

initially inappropriate trend of T correspond to worsening values of E. In summary, regarding the entire five-year period under consideration, it can be seen that the lower productivity levels were due to the evolution in the level of technical efficiency change (E). However, from a year-on-year perspective, both E and T were responsible for the negative trend of M. Having calculated the productivity ratios for the WWTPs we next analyse whether there is any type of relationship between their significance levels and a group of exogenous variables, using the KW test, as explained in section 3. The choice of variables was based on the literature review presented in section 2 above, along with expert opinions, and considering data availability. From this perspective, the contextual factors considered were: the levels of solids in suspension in the influent water (SS), its chemical oxygen demand (COD), the type of aeration (TA), the age of the plants (Age), and the volume of water treated (VWT). To conduct the KW test, the R 2.12.2 software environment was used. The various levels into which the values of each variable were divided are shown in Table 4, and were selected according to both: levels usually used by
ndez-Sancho EPSAR and previous studies on the same issue (Herna et al., 2011a,b). The results of the tests are shown in Table 5. As seen from the results shown in Table 5, only two of the contextual variables significantly influenced the productivity levels of the WWTPs: SS and VWT. The rest of the values of the KW test were greater than 0.05, not rejecting the null hypothesis of no influence. Therefore, the productivity of the treatment plants during the period under study showed a relationship with the quality of the influent water (measured by SS) and their own size (VTW). However, neither the age of the WWTPs, their level of COD, nor their type of aeration seemed to have influenced their level of productivity. In addition, with regard to the size of the plants, it is possible to observe that the median value of the VWT in the ten most productive plants was 112.272 m3. This size is different from the median value of the whole sample (56.113 m3) and points to the idea of reorienting the size of the sample to the level of the most productive WWTPs. The results obtained in this work differ substantially from previous results obtained in other studies carried out to analyse the performance of WWTPs in Spain. Of the 17 previous studies (see
ndez-Sancho et al., 2011a; MolinosTable 1), only three (Herna Senante et al., 2015, 2016), set out to analyse WWTP productivity as we did here. The other fourteen studies analyse efficiency, and therefore differ diametrically from this work. Our findings differ from the three previous analyses that similarly estimate WWTP productivity using appropriate and accepted methods. We offer the following explanations. First, in none of these three cases is a comparable sample used in terms of time period, plant location, or specific plant characteristics. In particular, the sample used by the previous studies referred to only two years

Table 5 P-values of KW test. Kruskal-Wallis test SS COD TA Age VWT

0.015 0.062 0.410 0.683 0.038

(2003 and 2008 or 2007 and 2009), compared with more inclusive five years of this analysis (2008e2012). Furthermore, although the location of the WWTPs only coincides in one case (Hern
andezSancho et al., 2011a) the sample used in that study included plants with a different treatment technology, whereas the sample used in our work focuses on treatment with activated sludge, using prolonged aeration without eliminating nutrients, in order to make the sample as homogenous as possible. Our work also applies statistical methods that differ from those used in previous studies, allowing outlier WWTPs to be eliminated (thus avoiding bias in calculations) and making it possible to check the existence of constant scale returns (which provides the appropriate context for computing the Malmquist productivity index with added accuracy of results). In addition, calculating the index using the smoothed bootstrap technique allows the extrapolation of results to the future while at the same time allowing their statistical significance to be contrasted. Our results thus do not fully coincide with those of previous studies. The different sample sizes, time periods, the types of WWTPs considered, and the statistical methods used give rise to dissimilar results. We estimate a 21.5% reduction in productivity over the period analysed, compared to between 0.5% and 2.2% (Molinos-Senante et al., 2015), 5.4% (Molinos-Senante et al., 2016),
ndez-Sancho et al., 2011a). Similarly, the factors and 14% (Herna explaining productivity trends do not coincide. In particular, previous papers attributed the negative trend to energy and/or staffing
ndez-Sancho et al., 2011a; Molinos-Senante et al., costs (Herna
ndez-Sancho et al., 2011a), to 2016), to the size of the plant (Herna technological progress (T) (Hern
andez-Sancho et al., 2011a), to efficiency change (ECH) (Molinos-Senante et al., 2016), or to the type of treatment technology used (Molinos-Senante et al., 2015). Only this last work quantified a rise in productivity in some of the WWTPs (those with technologies based on activated sludge and aerated lagoon). In our work, decreasing productivity results were also obtained over time, but the results put forward here focus on a homogeneous sample of WWTPs using a single type of technology (activated sludge), identifying inappropriate management in the use of resources (E) as a key influential and predominant factor, although both this factor and the influence of technological change (T) had an alternating negative effect throughout the period analysed. Moreover, the quality of the influent water (measured by SS)

Table 4 Division of the levels of exogenous variables. Exogenous variable

Levels

Exogenous variable

Levels

SS (mg/l)

<150 150e250 >250

Age

<8 8e18 >18

COD (mg/l)

<400 400e800 >800

VWT (103 m3/year)

<100 100e250 >250

TA

2 ¼ Blowers 1 ¼ Turbines 3 ¼ Aerators 4 ¼ Rotors

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R. Fuentes et al. / Utilities Policy xxx (2017) 1e13

and the size of the WWTPs (VWT) were also determining factors.

6. Conclusions From a policy point of view, improving the productivity levels of WWTPs is an important way to mitigate the environmental strain on water resources as well as to reduce costs, thereby encouraging greater investment levels and ultimately resulting in improved water quality and service. In order to reduce the negative aspects of water stress, the re-use of water from treatment plants is promising as an alternative source of water. Thus there should be greater interest in analysing these plants' productivity and the operations. In this regard, our research complements previous studies with similar aims by bootstrapping the DEA-based Malmquist productivity index, thus making the results more generally applicable and statistically significant. Additionally, the KW test enabled us to confirm the influence of certain contextual variables on the productivity values. The results obtained clearly show that productivity in the plants decreased over the period studied (2008e2012) due to an evolution in the level of technical efficiency change (E). However, the year-onyear analysis revealed that this trend was associated with both E and T on an alternating basis. Regarding the contextual variables, we can conclude that the influent water quality (SS) and plant size (VWT), influence their productivity. However, neither the quality of the influent water measured by COD, the age of the treatment plants, nor the type of aeration had any effect on the values of M. In light of our findings, it would seem logical to attempt to maintain the levels of innovation and of new technology adoption (T) implemented over the last part of the period, while resource

11

management (E) should be improved. In particular, in terms of measures to improve the plants' productivity, it would be advisable for the relevant authorities to invest in renovating and improving the facilities. Moreover, more control and supervision may be needed in the management of the facilities. Implementing stricter performance criteria and incentives for plant managers could be beneficial. Furthermore, implementing measures to reduce SS levels in influent water would lead to improvements in plant productivity, given the significant importance of this variable. The significant results obtained, in terms of the influence of VWT, seem to point to the fact that the size of plants should be reoriented to the size that seems to be the most productive. The median value of the VWT in the ten most productive plants was 112.272 m3. This study is limited by two factors. First, it would be useful to increase the time period under consideration to fine-tune the analysis and increase the general applicability of the results obtained. Second, statistical analysis techniques allowing the calculation of productivity levels while taking into account exogenous variables, thereby avoiding the need for a separate second stage, would contribute to the study's aim. Despite these particular limitations, which stem mainly from data availability, we believe that the results obtained are sufficiently conclusive to persuade the relevant authorities to consider improvements to treatment process management. Lastly, incorporating other contextual variables would help to broaden the action guidelines for improving the productivity of WWTPs. Unfortunately, although the plant managers were very helpful to this study, constraints on their time and the limited availability of records precluded this possibility and thus the scope of our study.

Appendix Table 6 Results for M, E and T between 2008 and 2012. WWTPs

M

E

T

WWTPs

M

E

T

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

0.904 1.691* 0.925 1.031* 0.638* 0.833 0.895* 1.229* 1.593* 2.136* 1.175 0.556* 0.869* 0.628* 1.378* 8.080* 2.314* 1.718* 1.427* 1.113* 0.725* 0.750 1.077* 1.377* 0.981 1.820* 1.137* 1.107* 1.151*

0.928 1.757* 1.012 1.077 0.655 0.869 0.950 1.293* 1.746* 2.254* 1.271 0.603* 1.082 0.666* 1.448* 8.541* 2.496* 1.955* 1.555* 1.201* 0.771* 0.795 1.163* 1.430* 1.091 2.062* 1.278 1.238* 1.351*

0.975 0.963 0.914 0.957 0.974 0.959 0.942 0.950 0.912 0.948 0.924 0.923 0.803* 0.943 0.952 0.946 0.927 0.878 0.917 0.926 0.941 0.944 0.926 0.963 0.899 0.883 0.890 0.894 0.852

87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115

1.196* 3.029* 1.632* 1.206* 1.278* 1.368* 1.436* 1.325* 0.895* 1.565* 1.232* 0.655* 1.018 1.358* 0.971 1.203* 1.892* 0.923* 2.228* 2.640* 1.152* 1.462* 0.996 0.687* 0.582 1.867* 1.334* 0.316 1.707*

1.252* 3.244* 1.727* 1.284* 1.361 1.509* 1.500* 1.398* 1.023 1.617* 1.420* 0.718* 1.073 1.680* 1.175 1.284* 2.020* 0.993 2.354* 2.788* 1.262 1.729* 1.050 0.736 0.647 2.000* 1.412* 0.338 1.997*

0.955 0.934 0.945 0.940 0.939 0.906 0.957 0.948 0.875 0.968 0.867 0.913 0.949 0.808* 0.827 0.937 0.937 0.929 0.946 0.947 0.913 0.845 0.949 0.933 0.899 0.934 0.945 0.934 0.855

(continued on next page)

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R. Fuentes et al. / Utilities Policy xxx (2017) 1e13

Table 6 (continued ) WWTPs

M

E

T

WWTPs

M

E

T

30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86

2.822* 1.113* 0.871* 0.702* 1.420* 1.256* 0.503* 1.821* 0.865 1.732* 1.256* 0.513* 1.165* 1.144* 3.680* 1.182* 1.408* 1.445* 0.920 0.937 0.929 0.766 2.791* 0.954 1.407* 0.829* 0.880* 0.510* 1.265* 0.618* 1.401* 1.146* 1.824* 0.966 1.124 0.832* 0.994 5.744* 2.364* 1.493* 1.339* 1.522* 1.539* 0.821* 3.605* 1.110* 1.173* 0.452 1.805* 1.810* 5.337* 2.089* 2.595* 1.335* 1.346* 1.617* 0.612

2.919* 1.204 0.975 0.746* 1.652* 1.561* 0.541 1.913* 1.000 1.891* 1.337* 0.566 1.444* 1.214 3.726* 1.250* 1.616* 1.572* 1.101 1.100 0.981 0.818 2.903* 1.016 1.483* 0.890 0.920 0.605* 1.347* 0.721 1.463* 1.207* 1.979* 1.172 1.325* 0.976 1.173 6.063* 2.494* 1.756* 1.415* 1.632* 1.629* 1.029 3.733* 1.180 1.252* 0.478 1.948* 1.958* 5.591* 2.226* 2.750* 1.425* 1.477* 1.736* 0.628

0.967 0.925 0.892 0.941 0.860 0.804* 0.930 0.952 0.865 0.916 0.939 0.906 0.806* 0.942 0.988 0.946 0.872 0.919 0.835 0.852 0.947 0.937 0.961 0.939 0.949 0.932 0.957 0.843 0.939 0.856 0.958 0.949 0.921 0.824 0.849 0.853 0.848 0.947 0.948 0.850 0.946 0.933 0.945 0.798 0.966 0.941 0.937 0.946 0.927 0.924 0.955 0.938 0.944 0.937 0.911 0.932 0.975

116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166

1.711* 1.703* 0.937 4.116* 1.129* 1.136* 1.231* 1.492* 1.078* 1.453* 2.575* 0.767 2.501* 0.753 0.547* 1.259* 0.790 4.537* 0.728* 1.192 0.620 0.736 1.210* 1.496* 0.360 1.335* 0.925* 1.272* 1.637* 0.867 1.328* 0.285* 1.164* 3.139* 2.554* 0.917* 1.494* 1.103* 0.640 0.835 1.000 1.481* 1.109* 1.300* 1.071* 1.079 1.083* 0.718 0.692* 2.105* 0.839

1.969* 1.997* 0.960 4.376* 1.139 1.188* 1.346* 1.571* 1.099* 1.581* 2.645* 0.806 2.672* 0.822 0.613 1.329* 0.791 4.779* 0.809 1.286* 0.715 0.772 1.276* 1.583* 0.415 1.449* 0.964 1.390* 1.721* 1.063 1.453 0.306 1.302* 3.660* 2.641* 1.138 1.583* 1.240 0.798 1.000 1.175 1.472 1.363 1.327 1.266* 1.241 1.289 0.853 0.809 2.285* 0.963

0.869 0.853 0.976 0.941 0.992 0.956 0.915 0.950 0.981 0.919 0.974 0.951 0.936 0.917 0.893 0.948 0.999 0.949 0.900 0.927 0.867 0.954 0.949 0.945 0.866 0.922 0.960 0.915 0.951 0.816* 0.914 0.930 0.893 0.857 0.967 0.806* 0.944 0.890 0.802 0.835 0.852 1.006 0.814 0.980 0.846 0.869 0.840 0.841 0.856 0.921 0.871

Geometric Mean (GM) Significant GM of significant Significant improving Significant worsening

1.215* 129 1.364 26 103

1.328* 97 1.720 6 91

0.914 6 0.807 6 0

Note: * implies a 95% significance.

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Please cite this article in press as: Fuentes, R., et al., Productivity of wastewater treatment plants in the Valencia Region of Spain, Utilities Policy (2017), http://dx.doi.org/10.1016/j.jup.2017.04.004