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

Author

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  • Chao Shi

    (University of Adelaide)

  • Kenneth C. Land

    (Duke University)

Abstract

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.

Suggested Citation

  • Chao Shi & Kenneth C. Land, 2021. "The Data Envelopment Analysis and Equal Weights/Minimax Methods of Composite Social Indicator Construction: a Methodological Study of Data Sensitivity and Robustness," Applied Research in Quality of Life, Springer;International Society for Quality-of-Life Studies, vol. 16(4), pages 1689-1716, August.
    • Handle: RePEc:spr:ariqol:v:16:y:2021:i:4:d:10.1007_s11482-020-09841-2
    DOI: 10.1007/s11482-020-09841-2
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    1. Paolo Paruolo & Michaela Saisana & Andrea Saltelli, 2013. "Ratings and rankings: voodoo or science?," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(3), pages 609-634, June.
    2. Kenneth Land & Vicki Lamb & Hui Zheng, 2011. "How are the Kids Doing? How do We Know?," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 100(3), pages 463-477, February.
    3. Hashimoto, Akihiro & Ishikawa, Hitoshi, 1993. "Using DEA to evaluate the state of society as measured by multiple social indicators," Socio-Economic Planning Sciences, Elsevier, vol. 27(4), pages 257-268, December.
    4. Marco Marozzi, 2016. "Construction, Robustness Assessment and Application of an Index of Perceived Level of Socio-Economic Threat from Immigrants: A Study of 47 European Countries and Regions," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 128(1), pages 413-437, August.
    5. Floridi, Matteo & Pagni, Simone & Falorni, Simone & Luzzati, Tommaso, 2011. "An exercise in composite indicators construction: Assessing the sustainability of Italian regions," Ecological Economics, Elsevier, vol. 70(8), pages 1440-1447, June.
    6. Saltelli, Andrea & Ratto, Marco & Tarantola, Stefano & Campolongo, Francesca, 2006. "Sensitivity analysis practices: Strategies for model-based inference," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1109-1125.
    7. Sudhir Anand & Amartya Sen, 2000. "The Income Component of the Human Development Index," Journal of Human Development and Capabilities, Taylor & Francis Journals, vol. 1(1), pages 83-106.
    8. Marco Marozzi, 2014. "Construction, dimension reduction and uncertainty analysis of an index of trust in public institutions," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(2), pages 939-953, March.
    9. Sudhir Anand and Amartya Sen, 2000. "The Income Component of Human Development Index," Human Development Occasional Papers (1992-2007) HDOCPA-2000-01, Human Development Report Office (HDRO), United Nations Development Programme (UNDP).
    10. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    11. John Ruggiero, 2005. "Impact Assessment Of Input Omission On Dea," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 4(03), pages 359-368.
    12. L Cherchye & W Moesen & N Rogge & T Van Puyenbroeck & M Saisana & A Saltelli & R Liska & S Tarantola, 2008. "Creating composite indicators with DEA and robustness analysis: the case of the Technology Achievement Index," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(2), pages 239-251, February.
    13. Kenneth Land & Vicki Lamb & Sarah Mustillo, 2001. "Child and Youth Well-Being in the United States, 1975–1998: Some Findings from a New Index," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 56(3), pages 241-318, December.
    14. Filippetti, Andrea & Peyrache, Antonio, 2011. "The Patterns of Technological Capabilities of Countries: A Dual Approach using Composite Indicators and Data Envelopment Analysis," World Development, Elsevier, vol. 39(7), pages 1108-1121, July.
    15. Matthias Staessens & Pieter Jan Kerstens & Johan Bruneel & Laurens Cherchye, 2019. "Data Envelopment Analysis and Social Enterprises: Analysing Performance, Strategic Orientation and Mission Drift," Journal of Business Ethics, Springer, vol. 159(2), pages 325-341, October.
    16. Kenneth C. Land & Alex C. Michalos, 2018. "Fifty Years After the Social Indicators Movement: Has the Promise Been Fulfilled?," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 135(3), pages 835-868, February.
    17. K-N Lau & P-Y Lam, 2002. "Economic freedom ranking of 161 countries in year 2000: a minimum disagreement approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(6), pages 664-671, June.
    18. A. Charnes & W. W. Cooper, 1963. "Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints," Operations Research, INFORMS, vol. 11(1), pages 18-39, February.
    19. A. Charnes & W. W. Cooper, 1959. "Chance-Constrained Programming," Management Science, INFORMS, vol. 6(1), pages 73-79, October.
    20. Färe, Rolf & Karagiannis, Giannis & Hasannasab, Maryam & Margaritis, Dimitris, 2019. "A benefit-of-the-doubt model with reverse indicators," European Journal of Operational Research, Elsevier, vol. 278(2), pages 394-400.
    21. Marco Marozzi, 2015. "Measuring Trust in European Public Institutions," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 123(3), pages 879-895, September.
    22. Badea, Anca Costescu & Rocco S., Claudio M. & Tarantola, Stefano & Bolado, Ricardo, 2011. "Composite indicators for security of energy supply using ordered weighted averaging," Reliability Engineering and System Safety, Elsevier, vol. 96(6), pages 651-662.
    23. Despotis, D.K., 2005. "Measuring human development via data envelopment analysis: the case of Asia and the Pacific," Omega, Elsevier, vol. 33(5), pages 385-390, October.
    24. M. Saisana & A. Saltelli & S. Tarantola, 2005. "Uncertainty and sensitivity analysis techniques as tools for the quality assessment of composite indicators," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(2), pages 307-323, March.
    25. Zhou, P. & Ang, B.W. & Poh, K.L., 2007. "A mathematical programming approach to constructing composite indicators," Ecological Economics, Elsevier, vol. 62(2), pages 291-297, April.
    26. Saisana, Michaela & d'Hombres, Béatrice & Saltelli, Andrea, 2011. "Rickety numbers: Volatility of university rankings and policy implications," Research Policy, Elsevier, vol. 40(1), pages 165-177, February.
    27. Frederik Booysen, 2002. "An Overview and Evaluation of Composite Indices of Development," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 59(2), pages 115-151, August.
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