Spatio-temporal modelling of municipal waste management systems’ meta-efficiency scores

ABSTRACT

This paper describes an approach to measure the intensity and the territorial dispersion of spatial proximity effects, which affect efficiency scores obtained through data envelopment analysis in the field of municipal waste management systems (MWMSs). In particular, we show that these analyses cannot be conducted by relying on efficiency scores that are not comparable over time and treated as cross-sectional data, as is done in most previous studies. Instead, the use of panel data is a key element to obtain reliable results. We used a meta-frontier approach to obtain meta-efficiency scores comparable over time and a modified conditional autoregressive (CAR) model to provide an estimation of the intensity of spatial proximity effects. This approach was applied to data on 277 MWMSs located in the Italian region of Abruzzo. Our method provides useful information for policymakers. In particular, the areas in which stagnating and suboptimal performance can be expected over time can be identified by plotting over the regional territory the posterior medians of the random effects obtained by the spatial component of the CAR model together with the highly efficient municipalities. To improve efficiency, these areas require an active intervention by levels of government higher than the municipal level.

KEYWORDS:

• Municipal waste management systems
• meta-frontier analysis
• CAR model
• spatial-temporal analysis
• spatial interdependence

Disclosure of conflicts of interest Statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Notes

¹ Given that a producer belongs to only one group, they will receive a unique within-group efficiency score that will be calculated measuring its distance from its relative group frontier.

² A meta-efficiency score for each producer is calculated measuring its distance from the (unique) meta-frontier.

³ This approach is not without flaws. The deterministic nature of the meta-efficiency measures thus calculated makes them sensitive to sample characteristics. Many empirical studies have opted to use partial frontiers (e.g. order-m or order-α robust estimators) to avoid potential bias in the estimations (see, for example, Tzeremes and Tzeremes 2021). Unfortunately, none of the studies which have proposed the use of currently available robust Malmquist indexes can be taken as a reference in our research because the proposed indexes are not circular and, therefore, efficiency scores on which they are based are not comparable over time.

⁴ For the general case, letting ${\theta }_{jt}^m$ be the meta-efficiency score of DMU j observed in sub-period t, and ${\theta }_{jt+1}^m$ be the meta-efficiency score of DMU j observed in sub-period t + 1, the MMI to measure the productivity change between t and t + 1 is defined as follows: $MM{I}_{jt}^{t+1}={\theta }_{jt+1}^m/{\theta }_{jt}^m$. When ${\mathrm{M}\mathrm{M}\mathrm{I}}_{\mathrm{j}\mathrm{t}}^{\mathrm{t}+1}$ is greater than 1, the productivity of DMU j has increased from period t to t + 1. Productivity decline has occurred in the converse situation.

⁵ There are several possible options which can be used to deal with undesired outputs in a DEA framework. One of the most popular methods is based on the use of the directional distance function (DDF). Generally, the DDF approach is used when the undesirable output is a by-product arising from the production process under investigation (for example, fossil fuel electricity generation produces electricity as the ‘good’ output and carbon dioxide, or CO₂, as the ‘bad’ output). When this occurs, free or strong disposability cannot be assumed because the good and the bad are jointly produced. Consequently, the bad outputs are avoidable only if there is no production. The use of DDFs is advised in these cases because the function proposes to maximize the expansion of good outputs while contracting bad outputs. In our study, however, the relationship between the desired and the undesired outputs does not match the description just given. For this reason, the approach proposed by Scheel (2001) and Seiford and Zhu (2005, 2002) has been preferred over the DDF.

⁶ Data on metric tons of sorted and unsorted waste for the year 2014 were not available for 42 municipalities. To avoid an excessive shrinkage of the sample, these missing data have been replaced with estimated data. Specifically, the average of the values of the previous and the following year has been used.