“Evaluating the efficiency of public expenditure in municipal waste collection: A comparative study of Portuguese municipalities”

Effective waste management is fundamental to sustainable development and the well-being of societies. This study focuses on the financial efficiency of urban waste collection in Portuguese municipalities, with the aim to analyze the effects of the allocation of public resources in the waste management sector. The main objective is to analyze the relationship between public spending and waste collection over a five-year period. Through the application of the classic data envelopment analysis model (DEA), the study seeks to observe the existence of benchmarking patterns, identify possible inef-ficiencies, and determine opportunities for improvement in urban waste management and collection practices. The results suggest substantial variations in waste collection efficiency between municipalities and a positive correlation between public spending and the volume of waste collected. The results emphasize the need for a strategic allocation of financial resources in order to promote sustainable waste management practices. The paper highlights the importance of municipalities reassessing their strategies for allocating financial resources to ensure a better balance between funding and efficiency in the use of resources. The conclusions offer valuable practical implications for defining strategies and managing municipal waste collection services in Portugal and other countries with similar contexts.


INTRODUCTION
The efficiency of municipal waste collection is an essential area of research due to its environmental, economic, and social implications.Waste management is one of the crucial aspects of society, since the growing amount of waste produced and the need to adopt sustainable management practices are increasingly essential for reducing environmental effects.
Governments need to optimize the allocation of financial resources to the growing collection of urban waste.Defining a balance between environmental needs and budgetary constraints requires academia to have a greater understanding of the dynamics of how public resources are allocated.It is crucial to address the relationship between public spending and waste collection results.By elucidating this relationship, the results can contribute to the perception of waste collection efficiency levels and assist in the public decision-making process through the implementation of public policies that promote the practice of more efficient collection processes.

LITERATURE REVIEW AND HYPOTHESES
Efficiency in the collection of municipal urban waste is currently one of the most relevant areas of research for the development of the theoretical field of territorial management and public administration (Rodrigues, 2016).Observing efficiency involves assessing the processes, methods, and practices used by municipalities to collect municipal waste (Phillips & Thorne, 2013).This helps one identify benchmarking practices and opportunities to optimize the financial resources allocated to public services (Simões & Marques, 2009).
For financial theory, one of the main metrics for analyzing the efficiency of public spending is the relationship between the financial resources allocated and the results obtained by public services (Aquino, 2011).Thus, analyzing the efficiency of public services, regardless of their substance and purpose, includes the costs associated with the remuneration of employees, the equipment assigned to the service, as well as the time and costs associated with carrying out operations (Rocha, 2020).In a broader analysis, it is also possible to consider the relationship between the quality of the public service provided and the level of public spending carried out for the purposes of pursuing the financial public interest (Inês, 2014).
Fonseca (2016) emphasizes the importance of comparing private and public management models and operational structuring processes in the municipal waste collection sector, particularly in terms of efficiency.The techniques adopted to measure efficiency levels alternate between parametric (stochastic frontier model) and non-parametric (DEA model) systems.However, according to Zhu (2001), due to the sensitivity of the results, the analysis can significantly affect the reliability of the efficiency assessment.Accordingly, the efficiency of municipalities in municipal waste collection should be analyzed from the perspective of the super-efficiency model approach.
The theory allows the most efficient municipalities to be identified among the most efficient (Bruno & Erbetta, 2013).
Rogge and Jaeger (2012), Afonso and Fernandes (2005) This study analyzes the efficiency of urban waste collection in Portuguese municipalities between 2018 and 2022, looking at the level of correlation between public spending on collection and the amount of waste collected.The paper aims to assess the efficiency of Portuguese municipal waste management in order to estimate the effectiveness of strategies for allocating public financial resources to the urban services provided.
To this end, the following hypotheses were established: H1: Municipal spending on municipal waste collection services is not related to the tons collected with an efficiency equal to 1 (eλ = 0).
H2: Municipal expenses associated with municipal waste collection services have some level of relationship with the tons collected of efficiency equal to 1 (0 > eλ < 1).
H3: Municipal spending on municipal waste collection services has a perfect relationship with the tons collected with an efficiency equal to 1 (eλ = 1).

METHODS
This analysis is based on a case study.Statistical data from 308 Portuguese municipalities were analyzed relating to public spending (on waste collection) and the quantities of waste collected (tons declared by municipal services) from 2018 to 2022.The expenditure and tonnage databases were obtained from the official websites of Banco de Portugal and PORDATA.
The statistical information from the municipalities was distributed in a matrix and arranged into decision-making centers (DMUs), inputs (public spending), and outputs (undifferentiated, selective, and total collection).For each type of collection, the weight of the inputs (actual public expenditure) and their relationship with the outputs (tons of waste) were assessed.
The paper applies the non-parametric DEA methodology, in which a direct relationship between inputs and outputs is not defined.The efficiency of public expenditure (inputs) in relation to the total amount of municipal waste collected is assessed using an index (Paço & Pérez, 2013), in which the municipality is more efficient when it is able to collect the greatest number of tons with the lowest level of financial resources allocated to carry out the public service (Carvalho & Rizzo, 1994).
Waste collection efficiency varies between 0 (inefficient) and 1 (efficient) and is measured by the distance between the inefficient DMU and the most efficient DMU (Jahanshahloo & Afzalinejad, 2006).The methodology selected for analyzing the results was the input-oriented model, where efficiency is described using the following expression (Vincová, 2005): where U r = weight of tons of municipal waste collected; Y r = the level of tons of municipal waste; V i = weight of actual public expenditure associated with municipal urban waste collection; X i = the level of effective public expenditure; s = number of sectors related to the tons of municipal waste collected; and m = number of sectors related to actual public expenditure.
The procedure adopted assesses the efficiency of the allocation of public financial resources (actual public expenditure) in each of the Portuguese municipalities.The numerator (∑ s r=1 U r Y r ) measures the total amount of tons of municipal waste (out-puts) generated by the municipalities, weighted by the weights associated with each sector of municipal waste collected.The denominator (∑ m i=1 V i X i ) evaluates the total amount of actual public spending by municipalities, weighted by the weights associated with each sector of public spending by municipalities.
The efficiency of the allocation of public resources in municipal waste collection is obtained by dividing the tons of municipal waste collected by the total weighted efficiency of actual public spending on municipal waste collection.The results obtained provide a practical perspective on the level of efficiency in the allocation of public spending on the collection of waste produced in each of the political and geographical areas, bearing in mind the respective limitations and theoretical reservations of the DEA model (Lins et al., 2007).
The efficiency levels of each municipality were measured using Excel software.The DEA model was selected as a tool for measuring municipal urban waste collection due to its high degree of flexibility in defining the input-output matrix.In addition, it allows for selecting the model's orientation, since the preference of the analysis is to maintain levels of effective public spending (inputs) and increase the efficiency of municipal urban waste collection (outputs).

RESULTS
The results provide a new perspective on the levels of efficiency between the ratio of actual public expenditure in each of the 308 municipalities and the amount of municipal waste collected each year.Table 1 and Figure 1 show municipalities that are the most and least efficient in allocating public spending on municipal waste collection by district and autonomous region.
In relation to the autonomous regions of Madeira and the Açores, the most efficient municipalities in allocating public spending to waste collection in 2018 were Câmara de Lobos and Vila da Praia da Vitória, respectively.
With regard to the autonomous regions, Table 1 and Figure 1 show that the least efficient municipalities were Porto Moniz, with 21.2599% (Madeira), and Vila do Porto, with 9.7021% (Açores).
In the autonomous regions, the results suggest that the most efficient cities in the collection of selective and undifferentiated waste were Câmara de Lobos (Madeira) and Calheta (Açores).
As far as the autonomous regions are concerned, the results show that the least efficient cities in the allocation of public expenditure for the management of municipal waste collection were Porto Moniz, with 21.6058% (Madeira), and Vila do Porto, with 11.7833% (Açores).
As for the autonomous regions, the most efficient municipalities in allocating public funds to the waste collection service were Câmara de Lobos (Madeira) and Calheta (Açores).
In the autonomous regions, the estimated data show that the least efficient municipalities when it comes to allocating public resources to municipal waste collection were Porto Moniz, with 18.8914% (Madeira), and Vila do Porto, with 10.5876% (Açores).
In terms of the autonomous regions, the municipalities of Santana (Madeira) and Vila da Praia da Vitória (Açores) had the highest levels of efficiency in the ratio between public spending and municipal waste collection.
With regard to the autonomous regions, the data suggest that the least efficient municipalities in terms of the ratio between public spending and municipal waste collection were São Vicente, with 25.0122% (Madeira) and Lajes do Porto, with 9.5928% (Açores).
As for the autonomous regions in 2022, the results suggest that the most efficient cities in allocating public financial resources to waste collection were Ribeira Brava (Madeira) and Calheta (Açores).
As far as the autonomous regions are concerned, the results show that the least efficient municipalities in terms of the ratio between public spending and ton of waste collected were Porto Moniz, with 12.3370% (Madeira), and Lajes do Pico, with 4.6685% (Açores).Table 1 shows that the results on the efficiency of municipal waste collection in Portugal by district reject hypotheses 1 (eλ = 0), 2 (0 > eλ < 1), and 3 (eλ = 1).The data suggest that there is some relationship between public spending and the quantities of municipal waste collected, i.e., the level of spending has contributed in some way to the efficiency of municipal waste collection (selective and undifferentiated) in Portuguese municipalities.
The results of the average efficiency of public spending on municipal waste collection are irregular (Table 1), which allows the hypotheses defined to be validated and rejected simultaneously.
In 2018, hypothesis 1 was rejected, hypothesis 2 was confirmed in 251 municipalities, and hypothesis 3 was validated in 57 municipalities.In 2019, hypothesis 1 was rejected, hypothesis 2 was confirmed in 244 municipalities, and hypothesis 3 was accepted in 64 municipalities.For 2020, hypothesis 2 was accepted in 251 municipalities and hypothesis 3 in 57 municipalities; hypothesis 1 was rejected.
As for 2021, hypothesis 1 was rejected, hypothesis 2 was confirmed in 250 municipalities, and hypothesis 3 was confirmed in 58 municipalities.Finally, in 2022, hypothesis 1 was rejected, hypothesis 2 was confirmed in 244 municipalities, and hypothesis 3 was validated in 64 municipalities.

DISCUSSION
Analyzing the efficiency of public spending on municipal waste collection services is fundamental for understanding the efficiency levels of municipal collection services and, on the other hand, for defining the best strategies for allocating financial resources to ensure that municipal waste collection services are provided in an appropriate and sustainable manner (Ferreira et al., 2020).The efficiency of public spending plays a decisive role in the effectiveness and sustainability of municipal waste collection services.In Portugal, by prioritizing the adoption of more efficient and transparent financial management (Magalhães et al., 2023), municipalities can and should define operational strategies together with citizens in order to increase the quality of public services (Humphreys, 1998), promote more responsible environmental practices (Keles et al., 2023), and meet the needs and expectations of citizens (Meirinhos et al., 2022).
The results corroborate the need for municipalities to increase the efficiency of public expenditure allocated to waste collection and for public decisionmakers to adopt high-performance management models with low levels of expenditure (Bevilacqua et al., 2010).The data are in line with the conclusions of the aforementioned studies.
The results stress the need for Portuguese municipalities to re-evaluate decisions on the allocation of public financial resources in terms of expenditure on municipal urban waste collection services.Due to inefficiencies and the emergence of a private sector, Nepal et al. (2022) state that municipalities have been forced to reform their waste management strategies.On the other hand, the results suggest a correlation between the efficiency of public spending and the quality and effectiveness of waste collection services.In other words, municipalities with higher levels of efficiency in municipal waste collection tend to have better levels of management of available resources (Volsuuri et al., 2023).
The study defends the relevance of measuring the various levels of performance of municipalities in the collection of urban waste, especially in terms of the expenditure allocated to the pur-suit of the public interest.In line with the conclusions of Rogge and Jaeger (2012) and Afonso and Fernandes (2005), the levels of efficiency of municipalities in allocating public expenditure to waste collection and, consequently, the level of productivity of public resources are necessary to consider.On the other hand, Camanho et al. ( 2024) note advantages to selecting and applying the DEA model to assess the efficiency of public service expenditure, especially in terms of operational activities.However, the results obtained do not support the conclusions, as the efficiency of Portuguese municipalities is clearly higher than that of Flemish municipalities.This is mainly due to the low levels of public revenue allocated to urban waste collection services in Belgium.
As As for the hypotheses, the data mostly point to the validation of hypothesis 2, since the majority of municipalities do not have a technical efficiency ratio equal to 1, but rather a ratio between public spending and tons of municipal waste collected greater than 0 and less than 1.
addition to analyzing the efficiency levels of municipal services, a pertinent question for future research is to study the effects of adopting artificial intelligence in defining possible routes, managing the various types of municipal waste, and promoting the circular economy.

CONCLUSION
The study analyzed the financial efficiency of municipal waste collection in Portugal over five years using data envelopment analysis.The aim was to provide evidence-based public policy on municipal waste collection to improve the sustainability and effectiveness of waste management.
The results suggest that the level of expenditure made has contributed in some way to the efficiency of waste collection.There is a notable disparity in levels of technical efficiency between the 308 Portuguese municipalities.The data confirm a positive correlation between realized expenditure and the quantities of municipal waste collected.
The paper shows that municipalities with higher levels of public funding tend to exhibit higher levels of efficiency in waste collection.However, efficiency is not only determined by the amount of expenditure made; it is also affected by political rationality, which tends to override economic logic.
The results suggest that Portuguese municipalities need to re-evaluate and adjust their strategies for allocating financial resources to waste collection in order to ensure a better balance between the levels of funding required and the efficient use of available resources.The analysis highlights the importance of municipalities promoting social awareness and environmental education among citizens in order to encourage active participation in achieving efficiency gains in municipal waste collection.
The findings emphasize the importance of efficiency in the operational management of municipal waste, the need to draw up more effective environmental policies, the existence of adequate levels of funding, and the involvement of the community in the process of continuous improvement.However, this study has some limitations.It only covers a five-year period, which may not be enough time to observe all the variations and trends over time.It is solely focused on Portuguese municipalities, which may limit the application and generalization of the results to other geographical contexts.Finally, efficiency is based on the relationship between public spending and the amount of waste collected and disregards other factors that may also affect efficiency.
Regardless of the identified limitations, the study presents a perspective on the efficiency of the allocation of public resources to municipal urban waste collection services, highlighting the need to continue improving the performance of the public service .

Figure 1 .
Figure 1.The more (green) and less (red) efficient municipalities by districts and autonomous regions, 2018-2022

Table 1 (
cont.).Results by districts and autonomous regions(2018)(2019)(2020)(2021)(2022) Hoang et al., 2024).The existence of high levels of efficiency in the collection of urban waste, in fact, contributes to reducing the costs related to waste treatment and relieving pressure on public resources.