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Social Indicators Research

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03-01-2021 | Original Research

A VEA Benefit-of-the-Doubt Model for the HDI

Authors: Panagiotis Ravanos, Giannis Karagiannis

Published in: Social Indicators Research | Issue 1/2021

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Abstract

The Benefit-of-the-Doubt (BoD) model for constructing composite indicators does not account for prior judgments concerning the relative importance of individual indicators. In this paper we combine the BoD model with Value Efficiency Analysis to propose a new formulation that incorporates external preferences and value judgments by means of a “model” decision-making unit which serves as the benchmark for all other units. We explore the potential of the proposed model by using it to re-estimate the United Nations Human Development Index.

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For example, consider two countries A and B being evaluated on the basis of two indicators, namely ${I}_{1}$ (patents) and ${I}_{2}$ (research grants, in thousand $). If country A outperforms B in terms of patents but is outperformed by B in terms of research grants, the BoD model will base the composite indicator of country A only on the patents indicator and assign a zero weight on the research grants indicator, while the reverse will occur for country B. Comparing the performance of the two countries using these composite indices would be deemed inappropriate.

The benefit-of-the-doubt weighting might also be criticized for dismissing one of the three basic requirements in social choice theory in response to Arrow’s theorem, namely anonymity or the assignment of equal weights to all indicators. Nevertheless, OECD (2008, p. 105) argue that anonymity is not an essential requirement in the construction of a composite indicator, as equal weighting is usually only one of the possible weighting schemes.

For a comprehensive treatment of VEA see Joro and Korhonen (2015)

We should emphasize that the paper’s aim is to provide an alternative approach to that of weight restrictions in incorporating DM preferences to the conventional BoD model, rather than an approach that performs better in restricting the flexibility of weights in conventional BoD, compared to weight restrictions.

The BoD is one of the four approaches proposed by OECD (2008) for constructing composite indicators. However, CI construction is a constantly expanding research field, in which several new methodological advancements exist. Some of these contributions are related to the BoD model, others make use of multicriteria decision-making approaches, such as goal-programming and non-compensatory approaches, while there are also mixed or hybrid approaches combining different methodologies to construct a composite indicator. A review of these approaches is a task out of the scope of the present paper, and the interested reader is referred to Greco et al. (2019) and El Gibari et al. (2019) for recent reviews.

We emphasize that such subjectivity is also inherent in several stages of the composite indicator construction process, such as the selection of the relevant indicators to be included in the composite and the normalization scheme. It is frequently present in the selection of weight bounds in weight-restricted BoD as well. Thus, malevolent DMs can also select weight bounds that will curb the BoD efficiency frontier, resulting in an evaluation process that favors certain DMUs.

Some MPS selection alternatives might prove to be as time-consuming as the process of selecting weight restrictions bounds. Nevertheless, as Korhonen et al. (2002) ague, DMs are more keen on simply pointing at a DMU rather that engaging in the task of selecting weight bounds, meaning that the concept of the MPS is generally easier to understand and to select, compared to absolute or relative weight bounds.

The use of AHP for MPS selection has been proposed in Korhonen et al. (2002).

We thank an anonymous referee for suggesting this alternative, which is inspired from the multicriteria TOPSIS (Technique for Ordered Similarity to Ideal Solution, see Huang and Yoon 1981) technique. TOPSIS also involves an Anti-Ideal DMU, namely one utilizing the minimum observed indicator values across DMUs, but such a benchmark choice is not suggested as an MPS as it would be more likely to represent the least rather that the most preferred solution.

For a recent review of the underpinnings and development of the HDI see Hirai (2017).

There is a long discussion in the literature about the logarithmic transformation of the income variable; see Kelley (1991), Chakravarty (2011), Ravallion (2012), and Herrero et al. (2012).

Prior to 1994, the goalposts were set by the sample minimum and maximum values.

For comparative results regarding the first three of these normalizations for the HDI see Karagiannis and Karagiannis (2020).

Sagar and Najam (1998), Prados de la Escosura (2010), Herrero et al. (2010), and Zhou et al. (2010) have also used geometric aggregation while Noorbakhsh (1998a; b) used the L₂ distance of each country from an ideal country that has the sample maximum value of indicators, Luque et al. (2016) and Krishnakumar (2018) set the HDI equal to the minimum of the three indicators (a scheme that allows for no substitutability), and Noorbakhsh (1998a) used the Borda’s aggregation rule.

Tofallis (2013) used a multiplicative BoD model that satisfies both unit and scale invariance but which, according to van Puyenbroeck and Rogge (2017), can be no longer considered as a geometric weighted average of indicators, as it violates the linear homogeneity property.

The procedure is repeated in Lind (2019) using world data for the years 1990–2017. The findings differentiate from the 2010 study in that the weight of income is now the lowest.

In this variant of the BoD model, ${\sum }_{j=1}^{J}{u}_{j}^{k}=1$ in addition to other restrictions in (1).

The artificial country with all indicators set at 0.5 is a multiple of the “Ideal DMU” country, for which all indicator values are equal to one. Hence, the radial projection of the Ideal DMU on the efficient frontier and by extension, its DEA-efficient peers, coincide with those of the artificial country (i.e. Norway and Australia). Thus, the use of an “Ideal DMU” country as the MPS will produce the same results with our second and third proposed alternatives.

Notice that, as Karagiannis (2017) has shown, the average accurately reflects the aggregate in the case of the BoD and thus, the numbers in the following Tables and Figures can be seen as aggregate values.

In terms of Fig. 1, we may think of Hong-Kong as being DMU A, for which the preferred range of mixes (between the I₂ axis and OB) is very wide and unbalanced. On the other hand, we may think of Singapore and Australia as being DMUs B and D respectively, the preferred mix ranges of which are slightly less wide but relatively more balanced compared to that of DMU A.

In terms of Fig. 1, we may think of Norway as being DMU C that displays the most balanced performance but has a relatively narrow preferred mix range, potentially serving as a peer for a few number of inefficient DMUs and of Qatar as being DMU F whose mix favors extremely indicator 2.

With reasonable pairs and triads, we mean pairs or triads of countries that share at least one common facet of the BoD-efficient frontier.

The former choice is also supported by empirical findings indicating that using the average of the two variables results in substantial information loss (Canning et al., 2013).

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Title: A VEA Benefit-of-the-Doubt Model for the HDI
Authors: Panagiotis Ravanos
Giannis Karagiannis
Publication date: 03-01-2021
Publisher: Springer Netherlands
Published in: Social Indicators Research / Issue 1/2021
Print ISSN: 0303-8300
Electronic ISSN: 1573-0921
DOI: https://doi.org/10.1007/s11205-020-02589-0

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