Ecological Efficiency Based Ranking of Cities: A Combined DEA Cross-Efficiency and Shannon’s Entropy Method

Corrado Lo Storto

doi:10.3390/su8020124

Abstract

In this paper, a method is proposed to calculate a comprehensive index that calculates the ecological efficiency of a city by combining together the measurements provided by some Data Envelopment Analysis (DEA) cross-efficiency models using the Shannon’s entropy index. The DEA models include non-discretionary uncontrollable inputs, desirable and undesirable outputs. The method is implemented to compute the ecological efficiency of a sample of 116 Italian provincial capital cities in 2011 as a case study. Results emerging from the case study show that the proposed index has a good discrimination power and performs better than the ranking provided by the Sole24Ore, which is generally used in Italy to conduct benchmarking studies. While the sustainability index proposed by the Sole24Ore utilizes a set of subjective weights to aggregate individual indicators, the adoption of the DEA based method limits the subjectivity to the selection of the models. The ecological efficiency measurements generated by the implementation of the method for the Italian cities indicate that they perform very differently, and generally largest cities in terms of population size achieve a higher efficiency score.

Highlights

In the last decade, cities have gained a greater centrality in the economic and social growth of nations
Even performing cross-efficiency analysis, any single Data Envelopment Analysis (DEA) model has limited discriminatory power to generate an effective ranking of cities and, it is useful to combine the results provided by several models integrating the different rankings of DMUs
As it has been emphasized in the second section of this paper, the Sole24Ore index has a large amount of subjectivity determined by the arbitrary choice of the set of weights utilized to combine and group 25 indicators of environmental quality into seven macro-indicators that are aggregated to get an individual index of environmental quality by adopting a further set of weights

Summary

Introduction

Cities have gained a greater centrality in the economic and social growth of nations. The recent report delivered by the Brookings Institution indicates that in 2014 the economies of the 300 largest metropolitan areas accounted for 47% of global gross domestic product (GDP) and 38% of GDP growth [1]. According to recent estimates provided by Seto et al [2], more than 80% of the national gross domestic product (GDP) is generated in urban areas. More than half of the human population over the world is living in cities and towns, and, in the decades, the number of people expected to live in cities will grow to 75%, while population growth over the 25 years will be concentrated in cities and towns [4,5]. Poor environmental quality and ecological efficiency, together with a scarce infrastructure development and traffic congestion, negatively affect the economic competitiveness, livability, and attractiveness of cities [6,7]

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Conclusion