Rui Cunha Marques ^†

Duarte Silva ^‡

^† Centro de Sistemas Urbanos e Regionais

Instituto Superior Técnico

Universidade Técnica de Lisboa

rcmar@civil.ist.utl.pt

^‡ Rave

dnsilva@rave.pt

 Statistical inference of efficiency estimators obtained with the DEA nonparametric frontier technique. A Bootstrap methodology

Abstract

The efficiency measurement of decision making units is a key-task in contemporary societies. Despite the existence of several methodologies with this aim none of them is clearly superior. One of the most used is the non-parametric technique of data envelopment analysis (DEA). The DEA method has many advantages, therefore, being very popular and widely adopted. However, it doesn’t allow for the results statistical inference, which can constrain its use. This document provides some insights for that debate, discussing and applying the DEA technique to 70 water services in Portugal. Later, a re-sampling (bootstrap) methodology is applied to the results attained by DEA, enabling its statistical inference. The quality of the values obtained by the bootstrap depends much on the average efficiency level and on its dispersion. That is, if the average inefficiency gap and its dispersion are considerable, the results will be far from the ones wished. Nevertheless, under the opposite circumstances, the results are interesting and satisfactory, surpassing the traditional drawbacks pointed at DEA. 

Keywords: Efficiency, DEA, Statistical Inference, Bootstrap, Water Services

Resumo

A medição de eficiência de unidades organizatórias ou unidades de decisão constitui uma tarefa-chave nas sociedades contemporâneas. Para a sua prossecução existem várias metodologias disponíveis embora nenhuma seja claramente superior. Um dos métodos mais conhecidos, e aqui analisado, consiste na técnica não paramétrica data envelopment analysis (DEA). Esta técnica possui diversas vantagens, sendo, portanto muito popular e largamente adoptada. Todavia, a DEA não permite a inferência estatística dos resultados obtidos, o que condiciona o seu uso empírico. Este documento fornece alguns contributos para esse debate, discutindo e aplicando a técnica DEA a 70 serviços de água em Portugal. Posteriormente, é empregue uma metodologia de bootstrap (reamostragem) aos estimadores de eficiência obtidos com a DEA, permitindo a sua inferência estatística. A qualidade dos resultados alcançados com o bootstrap depende muito do nível de eficiência médio e da sua dispersão. Isto é, quando a ineficiência média é considerável, tal como a sua dispersão, os resultados estão longe do desejável. Porém, quando o valor da ineficiência é reduzido e a sua amplitude é baixa os resultados são satisfatórios e bem interessantes, ultrapassando alguns dos problemas tradicionais apontados à DEA.

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