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

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.