The Data Envelopment Analysis and Equal Weights/Minimax Methods of Composite Social Indicator Construction: a Methodological Study of Data Sensitivity and Robustness

In the construction of composite or summary social indicators/indices, a recurrent methodological issue pertains to how to weight each of the quality-of-life/well-being components of the indices. Two methods of composite index construction that have been widely applied empirically in recent decades are Data Envelopment Analysis (DEA), which is based on an optimization principle, and the equal weights/minimax (EW/MM) method, which has been shown to have minimax statistical properties in the sense that it minimizes maximum possible disagreements among individuals on weights. This paper applies both of these methods to two empirical datasets of social indicators: 1) data on 25 well-being indicators used in the construction of state-level Child and Youth Well-being Indices for each of the 50 U.S. states, and 2) data on indicators of life expectancy, educational attainment, and income used in the construction of the United Nations Human Development Programme’s Human Development Index (HDI) for 188 countries. In these empirical contexts, we study issues of measurement sensitivity of the EW/MM and DEA methods to the numbers of indictors used in the construction of the composite indices and corresponding issues of robustness. We find that the DEA method is more sensitive to the numbers of component indicators than the EW/MM method. In addition, the composite indicators formed by the EW/MM and DEA methods become more similar as the numbers of indicators in the composites decreases. We also apply Chance-Constrained DEA method to reclassify countries in the HDI dataset by levels of human development. The resulting human development groupings of the DEA composite indices have a large overlap with those of the HDI in the Human Development Reports, which are based on fixed cut-off points derived from the quartiles of distributions of the HDI component indicators.