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On a Generalized Non-compensatory Composite Index for Measuring Socio-economic Phenomena

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Abstract

Composite indices for measuring multidimensional phenomena have become very popular in a variety of economic, social and policy domains. The literature offers a wide range of aggregation methods, all with their pros and cons. The most used are additive methods, but they imply requirements and properties which are often not desirable or difficult to meet. For example, they assume a full substitutability among the components of the index: a deficit in one dimension can be compensated by a surplus in another. In this paper, we consider a non-compensatory composite index for spatial comparisons and its variant for spatio-temporal comparisons. A study of the aggregation function is, for the first time, presented and its main properties are formally defined. As an example of application, a set of individual indicators of well-being for OECD countries is considered and a comparison between the two approaches is provided, in order to show what they offer and how they work.

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Notes

  1. Note that compensability/non-compensability does not imply dependence/independence and vice versa. For example, “Hospital beds (per 1000 people)” and “Hospital doctors (per 1000 people)” are two dependent (positively correlated) indicators but they are non-substitutable, because a deficit in beds cannot be compensated by a surplus in doctors and vice-versa. “Average water use (per person)” and “Bottled water consumption (per capita)” may be linearly independent (incorrelated) indicators, but they are substitutable.

  2. A measurement model describes the relationship between a concept and its measures (indicators).

  3. Although the reflective model dominates the psychological and management sciences, the formative model is common in economics and sociology (Coltman et al. 2008).

  4. To overcome the assumption of complete substitutability among the indicators, some authors propose multiplicative aggregation methods, such as the geometric mean (OECD 2008; Zhou et al. 2010). However, it can be used only for sets of positive values which are interpreted according to their product and not their sum. Besides, the value of the geometric mean is ‘biased’ low. Thus it may be useful for measuring phenomena like development (e.g., the HDI), but not like poverty.

  5. Variability effect may be minimized by normalizing individual indicators with a method that brings them to have equal or similar variances.

  6. Note that individual indicators are converted to a common scale with a mean of 100 and standard deviation of 10. So, the transformed values will fall approximately in the range (70; 130). The z scores are adjusted to avoid negative values and obtain more visually manageable scores (Booysen 2002).

  7. They refer to column values of the matrix X.

  8. They refer to row values of the matrix Z.

  9. It is a generalized form since it includes ‘two indices in one’.

  10. Note that a change on z ij for the unit i implies a change on z hj for the unit h (h ≠ i), so that the mean and standard deviation of the standardized indicator j are 100 and 10, respectively. On the contrary, a change on r ij for the unit i does not affect the value of r hj for the unit h (h ≠ i).

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Acknowledgments

The paper is the result of the common work of the authors: in particular M. Mazziotta has written Sects. 1, 3.1, 3.2, 5 and A. Pareto has written Sects. 2, 3.3, 3.4 and 4.

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  1. Italian National Institute of Statistics, Viale Oceano Pacifico 171, 00144, Rome, Italy

    Matteo Mazziotta & Adriano Pareto

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  1. Matteo Mazziotta
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  2. Adriano Pareto
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Correspondence to Adriano Pareto.

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Mazziotta, M., Pareto, A. On a Generalized Non-compensatory Composite Index for Measuring Socio-economic Phenomena. Soc Indic Res 127, 983–1003 (2016). https://doi.org/10.1007/s11205-015-0998-2

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