“Mirror, mirror, on the wall, who in this land is fairest of all?”—Distributional sensitivity in the measurement of socioeconomic inequality of health

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Abstract

This paper explores four alternative indices for measuring health inequalities in a way that takes into account attitudes towards inequality. First, we revisit the extended concentration index which has been proposed to make it possible to introduce changes into the distributional value judgements implicit in the standard concentration index. Next, we suggest an alternative index based on a different weighting scheme. In contrast to the extended concentration index, this new index has the ‘symmetry’ property. We also show how these indices can be generalized so that they satisfy the ‘mirror’ property, which may be seen as a desirable property when dealing with bounded variables. We compare the different indices empirically for under-five mortality rates and the number of antenatal visits in developing countries.

Introduction

Pereira (1998) and more recently Wagstaff (2002) have proposed to extend the concentration index by including a distributional judgement parameter. The extension is seen as a device which makes it possible to incorporate attitudes towards inequality into the calculation of the index of socioeconomic inequality of health. It builds on suggestions of Kakwani (1980) developed by Yitzhaki (1983), who shows how a similar extension of the Gini coefficient allows the expression of distributional judgements in the context of income inequality measurement.

The extended concentration index can be applied to a broad range of health and health care variables. Following Pereira (1998) and Wagstaff (2002), who have used the index to calculate the degree of socioeconomic inequality in child mortality in developed as well as developing countries, there are now a growing number of empirical studies which have applied the index to various health variables. Examples include health limitations within eight European countries across time (Hernández-Quevedo et al., 2006), child malnutrition in Nigeria (Uthman, 2009), immunization ratios in developing countries (Gaudin and Yazbeck, 2006, Meheus and van Doorslaer, 2008), and child mortality and child malnutrition in India (Arokiasamy and Pradhan, 2011).

In line with recent research on health inequality measurement, we make a clear distinction between bounded and unbounded variables, and hence treat them separately. The main reason for this different treatment is that bounded variables, in contrast to unbounded variables, can be looked at from two points of view: the positive side, where the focus is on ‘good health’ (e.g. the proportion of children without malnutrition), and the negative side, where the emphasis is on ‘ill health’ (e.g. the proportion of children with malnutrition).

In this paper we first of all explore whether the extended concentration index is an appropriate tool to take into account attitudes to inequality when measuring the socioeconomic inequality of health. This form of inequality measurement tries to answer the question: “To what extent are there inequalities in health that are systematically related to socioeconomic status?” (Wagstaff et al., 1991: 546). Our initial focus is on understanding the precise way the extended concentration index incorporates distributional sensitivity when it is applied to unbounded health variables (Section 3). Next, we identify a property which the index does not have, and suggest an alternative index – the symmetric index – based upon a different distributional weighting scheme (Section 4). We then move to bounded variables, and generalize both the extended concentration index and the symmetric index (Section 5). An empirical study serves to illustrate the differences between the indices (Section 6).We also include an appendix specifying how we deal with small-sample bias, ties in the ranking variable, and differences in (ex-post) sampling probabilities when doing empirical work using finite samples.

Section snippets

Preliminaries

In the first part of this paper we consider unbounded ratio-scale health variables. These are variables which have no natural upper bound and vary between 0 and +∞; health expenditure is an example. In section 5 we will turn our attention to bounded variables, which occur very frequently in the domain of health.

Suppose the population N consists of n individuals, where n is a finite, positive natural number. Let N = {1,2,…,n}, and assume that individuals are ranked according to their socioeconomic

The extended concentration index

Following suggestions by Kakwani (1980) and Yitzhaki (1983), both Pereira (1998) and Wagstaff (2002) have introduced the following extended concentration index:C(h,ν)=1νnμhi=1n(1Ri)ν1hiwhere ν1 is a distributional sensitivity parameter. Expression (3) can be formulated in many equivalent ways. Using the definitions of the previous section, (3) can be transformed into a weighted sum of health shares:C(h,ν)=1μhi=1n1ν(1Ri)ν1nhi

Since p corresponds to Ri, the continuous counterpart of (4)

Univariate vs. bivariate inequality

The extended concentration index has been obtained by applying a concept used for the measurement of the inequality of income – the extended Gini coefficient – to the measurement of the socioeconomic inequality of health. Basically, a one-dimensional construction is transplanted into a two-dimensional context. It cannot be taken for granted, however, that anything which works well in a univariate environment is automatically suited for a bivariate world.

Here we propose a simple test to check

Bounded variables

While the extended and symmetric concentration indices can be applied to unbounded variables, our focus now shifts to the case of bounded health variables, i.e. health variables which can be looked at from two points of view: the positive side, where the focus is on ‘good health’ (e.g. the proportion of children without malnutrition), and the negative side, where the emphasis is on ‘ill health’ (e.g. the proportion of children with malnutrition). For any good health variable which has a finite

The data

In this section we will illustrate some of the measurement issues concerning each of the four previously discussed inequality measures using real data. All calculations8 are based on data collected from the Demographic and Health Surveys (DHS) which involve a range of measures regarding health (and ill health) and use of types of health care collected over 40 developing countries. The DHS has

Conclusions

In this paper we have explored various ways to incorporate attitudes towards inequality into the measurement of socioeconomic health inequalities. We started by revisiting the extended concentration index that was proposed by Pereira (1998) and Wagstaff (2002). Its asymmetric weighting scheme is based on the idea – borrowed from the income inequality literature – that we should give relatively higher (absolute) weights to the poor than to the rich. But this comes at a price: the index can in

Acknowledgments

Tom Van Ourti is supported by the NETSPAR project ‘Income, health and work across the life cycle II’, and acknowledges support by the National Institute on Ageing, under grant R01AG037398-01. We have benefited from the comments and suggestions of two anonymous referees, Ramses Abul Naga, Paul Allanson, Clément de Chaisemartin, Gustav Kjellsson, Andreas Knabe, Ann Lecluyse, Dennis Petrie, and participants of seminars at Erasmus University Rotterdam, University of Antwerp, Lund University, the

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