Abstract
This paper builds on the extensive literature of the benefit-of-the-doubt (BoD) methodology to set weights for composite indicators (CIs). The proposed methodology, meta-goal programming benefit of the doubt (MGP-BoD), proved to overcome some of the BoD shortcomings and enhance its performance. MGP-BoD belongs to the family of common-weights BoD models. It comprises of two sets of goals and two meta-goals. Among other merits, results prove two additional benefits of the MGP-BoD over older BoD. First, it enhances BoD discriminating power by eliminating all ties in CI values and, hence, country ranks. This high discriminating power is achieved in only one totally endogenous step. Second, MGP-BoD weights add up to one. This makes weights more insightful, interpretable, comparable to weights from other weighting systems, and easier to interpret compared to BoD. These additional merits favor MGP-BoD over previous weighting methods. In the meantime, the proposed method preserves a significantly high correlation with previous methods results as shown a set of Pearson and Spearman correlation tests to compare it to various previous methodologies. To validate the proposed methodology, it has been thoroughly tested using sensitivity and classification analyses. All tests are found highly significant. Nevertheless, the method has its own limitations that suggest future research points. Finally, the paper offers a new human development indicator (HDI) using 2012 data using MGP-BoD. The proposed HDI offers an alternative to the currently used equal-weights HDI that offers distinguishable country ranks and more policy-guiding weights. The highest weights are assigned to education variables.
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Notes
A sub-indicator will be the generic name used for every column of data entered in the composition of a CI using the BoD method. It can either be a variable or a sub-index created from a group of variables.
For the different forms of MGP, please refer to Uría et al. (2002). Each of the forms serves a different purpose. MGP is originally created to improve the model's results by offering the flexibility to add constraints on the deviations of each goal in the GP if required. In this research, we focused on using it to explicitly know the achievability of each of our two equal-priority goals separately, which would have been merged under the value of the achievement function if only the original GP had been used. This feature of MGP increases in importance as the number of goals increases.
Pearson and Spearman Coefficients range between 0.732 and 0.995; and 0.739 and 0.994, respectively, with p value 0.000 for all the correlation coefficients.
Group 1 was correctly classified by 85.1 %, Group 2 by 93.6 %, Group 3 by 83.0 %, and Group 4 by 93.5 %.
A technical note for the computation of ranking ties is that the ranks for ties in HDI values are registered as the average rank of values that was used in Spearman Rank Correlation Coefficient's calculations.
Weights and country rankings were calculated by the MGP-BoD method separately on 11 country groups of 2012, in addition to the full country list of 187 countries as follows. Geographically, country groups included the African Union, European Union, Arab League, OECD, Latin America and the Caribbean, South Asia, Middle East and North Africa. Moreover, the four groups of country income levels were also tested. i.e. High-, Upper Middle-, Lower Middle-, and Low-Income countries.
For example, different country groups have different means (as proven by ANOVA tests on the various groups) and variances of variables.
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Acknowledgments
The authors would like to extend their thanks to the anonymous reviewers for their constructive remarks for improving the manuscript and clarifying its ideas. Thanks are also due to Dr. Mohamed Ossman, Dr. Hesham Abdel Meguid, and Dr. Mahmoud Rashwan for their helpful technical advice.
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Sayed, H., Hamed, R., Ramadan, M.AG. et al. Using Meta-goal Programming for a New Human Development Indicator with Distinguishable Country Ranks. Soc Indic Res 123, 1–27 (2015). https://doi.org/10.1007/s11205-014-0723-6
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DOI: https://doi.org/10.1007/s11205-014-0723-6