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Measuring human development by means of composite indicators: open issues and new methodological tools

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Abstract

Over the years, the Human Development Index has become a reference measure of quality of life and well-being. Its growing importance has been accompanied by a lively debate in the literature concerning the pros and cons of this index. Many works have attempted to provide solutions to Human Development Index related problems. In this paper, we will focus on some of these problems, which are typical not only for the measurement of human development, but for the construction of composite indicators. We will try to provide an answer by proposing two new methodological tools, the \(Min-BoD\) interval of synthesis and the mid aggregation point, which present interesting potentialities to be used in empirical analyses and for policy evaluations, not only in the human development measurement. The proposed tool have been applied to the Human Development Index data collected for 189 countries in 2019.

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Data availability

The data used for the analysis conducted in this paper are available and freely accessible at the following link: https://hdr.undp.org/en/data.

Notes

  1. In particular, some authors focused on the lack of concern for distributive issues (Anand and Sen 2000b), emphasising the need to identify methods capable to incorporate distributional inequalities of income, education, and longevity (Hicks 1997; Foster et al. 2005). In order to try to overcome this limitation, in 2010 UNDP introduced the Inequality-adjusted Human Development Index—IHDI, a measure that accounts for inequality in the society, following the preliminary analyses made by Alkire and Foster (2010), and that is obtained by combining the estimate of the basic HDI to the Atkinson measure of inequality (Atkinson 1970).

  2. Three of the four indicators were revised: GDP per capita was replaced by GNI per capita (both valued in PPP US), literacy and gross enrolments were replaced by mean years of schooling and expected years of schooling.

  3. We need to clarify that, as shown in different studies (see, for instance, Bollen (2007), Bollen and Diamantopoulos (2017)), the choice of the measurement model only depends on the nature of the latent variable, the appropriateness to the phenomenon to be measured and the direction of relationships between constructs and measures. It is not a personal choice of the researcher.

  4. Until 1993, the normalisation method used was a Min–Max, with minimum and maximum values for all three components based on variable criteria, like the actual minimum and maximum in the current year, or an average threshold value, as with income (Stanton 2007). This choice was strongly criticised in the literature (Kelley 1991; McGillivray 1991; McGillivray and White 1993; Doessel and Gounder 1994; Paul 1996), mainly because it did not allow any temporal comparability.

  5. Until 2010, the HDI was calculated as an unweighted arithmetic mean of the normalised elementary indicators. This choice has been strongly criticised in the literature (Desai 1991; Palazzi and Lauri 1998; Sagar and Najam 1998), because it implied perfect substitutability allowing that a deficit in one dimension could be compensated by a surplus in another.

  6. The more variable the distribution, the smaller the geometric mean with respect to the arithmetic mean. Consequently, if two units have the same arithmetic mean in the elementary indicators, the unit with higher variability will have a geometric mean smaller than that of the unit with lower variability.

  7. For instance, a dashboard allows to avoid an arbitrary choice of the functional form and the weighting scheme and to observe a phenomenon from multiple points of view, However, it does not allow a simple and direct understanding of the phenomenon under consideration (Saisana and Tarantola 2002; OECD 2008).

  8. In most cases, the indicator systems are in the form of three-way data time arrays. These data structures are characterized by a greater complexity of information, consisting in the fact that multivariate data are observed at different times (D’Urso 2000). The statistical tools presented in this paper are applied to multi-indicator systems in a specific year, i.e. a specific slice of a three-way time data array. Application to temporal data will be the subject of a future work.

  9. The direction of the relation between the indicator and the phenomenon defines polarity; this, it depends on the type of composite. Some indicators can present positive polarity (i.e. they have the same direction of the phenomenon), others negative polarity (i.e. they are negatively related with the phenomenon).

  10. It applies if indicator has positive polarity, otherwise we compute the complement to respect to 1 to Eq. 1.

  11. For example, since the weights are specific for each unit, cross-unit comparisons are not possible and the values of the scoreboard depend on the benchmark performance. Moreover, another drawback is the multiplicity of equilibria. Hiding a problem of multiple equilibria makes the weights not uniquely determined (even if the composite indicator is unique). The optimisation process could lead to many 0-weights if no restrictions are imposed on the weights. For a detailed analysis, please see Vidoli and Mazziotta (2013).

  12. http://hdr.undp.org/en/content/download-data.

  13. For detailed information, please see: http://hdr.undp.org/sites/default/files/hdr2019_technical_notes.pdf.

  14. When a variable exceeds the upper bound of its dimension, the value is truncated at the upper bound so that the range of normalised indicators is always between 0 and 1 and none of the dimensional sub-indices exceeded 1.

  15. In this application, we consider only 3 dimensions and 4 indicators. It should be made clear that the methods presented are applicable for any indicator system regardless of the number of dimensions and indicators.

  16. As specified in Scrucca et al. (2016), in the multivariate setting, the volume, shape, and orientation of the covariances can be constrained to be equal (E) or variable (V) across groups. Thus, 14 possible models with different geometric characteristics can be specified.

  17. We have chosen these four nations because of their similarity and because they are often used as comparisons with each other.

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Authors and Affiliations

  1. Department of Social Sciences and Economics, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185, Rome, Italy

    Leonardo Salvatore Alaimo

  2. Department of Statistics, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185, Rome, Italy

    Emiliano Seri

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  1. Leonardo Salvatore Alaimo
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Although this paper should be considered the result of the common work of the two authors, Leonardo Salvatore Alaimo has mainly written Sections 3, and 4; Emiliano Seri has mainly written Section 1, all authors have written Section 2, 5 and 6.

Leonardo Salvatore Alaimo: Conceptualization, Supervision, Writing - Original Draft, Software - Resources, Methodology, Formal analysis, Visualization, Writing - review and editing.

Emiliano Seri: Conceptualization, Writing - Original Draft, Data curation, Software - Resources, Methodology, Formal analysis.

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Appendix A

Appendix A

See Figures 5, 6, 7, 8, 9 and 10 and Tables 5, 6 and 7.

Table 5 Basic indicators of HDI: summary statistics
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Table 6 GMMs selection: number of components; models with different parameters; BIC values
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Table 7 Comparison of aggregation methods on HDI data: country code (CC); county; Human Development Index (HDI); arithmetic mean (AM); quadratic mean (QM); cubic mean (CM); maximum (Max); minimum (Min); benefit of the doubt (BoD); mid aggregation point (map); cluster (Clus). World countries; year 2019
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Fig. 5
figure 5

Countries of cluster 1-A according to dimensional indices of HDI:—\(BoD-Min\) interval of synthesis; \({\bullet }\) mid aggregation point—map; \(\times \) minimum; \(\bigstar \) geometric mean (HDI of UNDP); \(\blacktriangle \) arithmetic mean; \(\blacklozenge \) quadratic mean; \(\blacksquare \) cubic mean; \(*\) maximum. Year 2019

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Fig. 6
figure 6

Countries of cluster 1-B according to dimensional indices of HDI:—\(BoD-Min\) interval of synthesis; \({\bullet }\) mid aggregation point—map; \(\times \) minimum; \(\bigstar \) geometric mean (HDI of UNDP); \(\blacktriangle \) arithmetic mean; \(\blacklozenge \) quadratic mean; \(\blacksquare \) cubic mean; \(*\) maximum. Year 2019

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Fig. 7
figure 7

Countries of cluster 2-A according to dimensional indices of HDI:—\(BoD-Min\) interval of synthesis; \({\bullet }\) mid aggregation point—map; \(\times \) minimum; \(\bigstar \) geometric mean (HDI of UNDP); \(\blacktriangle \) arithmetic mean; \(\blacklozenge \) quadratic mean; \(\blacksquare \) cubic mean; \(*\) maximum. Year 2019

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Fig. 8
figure 8

Countries of cluster 2-B according to dimensional indices of HDI:—\(BoD-Min\) interval of synthesis; \({\bullet }\) mid aggregation point—map; \(\times \) minimum; \(\bigstar \) geometric mean (HDI of UNDP); \(\blacktriangle \) arithmetic mean; \(\blacklozenge \) quadratic mean; \(\blacksquare \) cubic mean; \(*\) maximum. Year 2019

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Fig. 9
figure 9

Countries of cluster 2-C according to dimensional indices of HDI:—\(BoD-Min\) interval of synthesis; \({\bullet }\) mid aggregation point—map; \(\times \) minimum; \(\bigstar \) geometric mean (HDI of UNDP); \(\blacktriangle \) arithmetic mean; \(\blacklozenge \) quadratic mean; \(\blacksquare \) cubic mean; \(*\) maximum. Year 2019

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Fig. 10
figure 10

Countries of cluster 3 according to dimensional indices of HDI:—\(BoD-Min\) interval of synthesis; \({\bullet }\) mid aggregation point—map; \(\times \) minimum; \(\bigstar \) geometric mean (HDI of UNDP); \(\blacktriangle \) arithmetic mean; \(\blacklozenge \) quadratic mean; \(\blacksquare \) cubic mean; \(*\) maximum. Year 2019

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Alaimo, L.S., Seri, E. Measuring human development by means of composite indicators: open issues and new methodological tools. Qual Quant (2023). https://doi.org/10.1007/s11135-022-01597-1

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