Using Data Envelopment Analysis to Construct Human Development Index

Using Data Envelopment Analysis to Construct Human Development Index

Paulo Nocera Alves Junior (University of São Paulo (USP), Brazil), Enzo Barberio Mariano (São Paulo State University (UNESP), Brazil) and Daisy Aparecida do Nascimento Rebelatto (University of São Paulo (USP), Brazil)
DOI: 10.4018/978-1-5225-0714-7.ch013
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Abstract

This chapter addresses problems related to methodological issues, such as data normalization, weighting schemes, and aggregation methods, encountered in the construction of composite indicators to measure socio-economic development and quality of life. It also addresses the use of several Data Envelopment Analysis (DEA) models to solve these problems. The models are discussed and applied in constructing a Human Development Index (HDI), derived from the most recent raw and normalized data, using arithmetic and geometric means to aggregate the indices. Issues related to data normalization and weighting schemes are emphasized. Kendall Correlation was applied to analyze the relationship between ranks obtained by DEA models and HDI. Recommendations regarding the advantages and disadvantages of using DEA models to construct HDI are offered.
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Data Envelopment Analysis And Composite Indicators

The first data envelopment analysis model was created by Charnes, Cooper, and Rhodes (1978). The CCR model is a nonparametric mathematical programming method used to measure the relative efficiency of decision-making units (DMUs) in a system with multiple inputs and outputs. The original was an input-oriented fractional programming model formulated as follows:

s.t.:
where is the amount of the ith output of the analyzed DMU; , the amount of its jth input; is the amount of the ith output of the kth DMU; , the amount of its jth input; is the weight of the ith output; , the weight of the jth input; m is the number of analyzed outputs; n, the number of analyzed inputs; and z, the number of analyzed DMUs.

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