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World Development Vol. 35, No. 7, pp. 1259–1276, 2007 Ó 2007 Elsevier Ltd. All rights reserved 0305-750X/$ - see front matter www.elsevier.com/locate/worlddev doi:10.1016/j.worlddev.2006.10.011 Multidimensional Measures of Well-Being: Standard of Living and Quality of Life Across Countries VALÉRIE BÉRENGER Université de Nice-Sophia Antipolis, CEMAFI (Centre d’Etudes en Macroéconomie et Finance Internationale), Nice, France and AUDREY VERDIER-CHOUCHANE * African Development Bank, Tunis, Tunisia Summary. — Using Sen’s capability approach, we propose to measure two components of wellbeing—standard of living and quality of life. Unlike the UNDP Human Development Index, the two indices do not mix measures of resource availability and of functioning and capability. The empirical results for 170 countries are based on two multidimensional analyses, the Totally Fuzzy Analysis and the Factorial Analysis of Correspondences. The paper also compares our results with the HDI and GDP per capita. It focuses on Africa, presents policy implications, and discusses aggregation and redundancy in multidimensional indices. Ó 2007 Elsevier Ltd. All rights reserved. Key words — Africa, totally fuzzy analysis, factorial analysis of correspondences, multidimensional indices, Sen’s capability approach 1. INTRODUCTION International organizations now recognize that human development goes beyond economic growth and is a multidimensional phenomenon covering all aspects of well-being. This partly dates from Sen’s work on social justice and inequalities (Sen, 1985, 1992), which inspired a new concept of development. Sen’s capability approach contributed to the design of the UNDP Human Development Index (HDI) in 1990, which was intended as a more comprehensive indicator than per capita income for comparing the well-being of countries. However, the HDI’s critics 1 say its indicators are too few and too arbitrarily chosen and that its definition is still inadequate and does not allow the capability approach to work. This article defines two composite indices— SL (Standard of Living) and QL (Quality of Life)—across 170 countries, supporting Sen’s capability approach. Focusing on 52 African countries, we adopt and compare two recent methodologies, Totally Fuzzy Analysis (TFA) and Factorial Analysis of Correspondences (FAC), to analyze the usefulness of these indices. Our broader well-being indices are compared with the HDI and GDP per capita to * Dr. Valérie Bérenger is from the CEMAFI (Centre d’Etudes en Macroéconomie et Finance Internationale), Université de Nice-Sophia Antipolis, and Dr. Audrey Verdier-Chouchane is from the Development Research Department, African Development Bank. We thank Bernhard Gunter and four anonymous reviewers for their very helpful comments and valuable inputs as well as Louis Kasekende, Temitope Waheed Oshikoya, and Désiré Vencatachellum for their significant contributions to this work. Greg Chamberlain and Diane Brothwell provided excellent assistance in editing the manuscript. Financial support from the African Development Bank is gratefully acknowledged. We retain responsibility for any remaining errors. Final revision accepted: October 2, 2006. 1259 1260 WORLD DEVELOPMENT examine the cogency of the HDI and the redundancy issues. Section 2 here deals with the concepts and justification for the two indices (SL and QL), while Section 3 presents the two methodologies and the obtained results in Africa. Policy recommendations and discussion are presented in Section 4. Section 5 presents our conclusions. 2. CONCEPTS FOR STANDARD OF LIVING AND QUALITY OF LIFE GDP per capita is the most commonly used indicator to compare wealth among countries 2 and is a measure of well-being and development exclusively based on material wealth. However, insufficient income is merely one dimension of under-development, so development cannot be understood by only taking into account economic performance. Attempts were made in the 1970s to construct socio-economic indicators as an alternative to GDP per capita, which was criticized as capturing neither distributional aspects nor social and human welfare dimensions (Desai, 1991). The standard human development concept dates from the 1990 Human Development Report (UNDP, 1990). It drew on Sen’s work and led to growing acknowledgement of the multidimensional nature of development and to different strategies for moving from promotion of growth to promotion of well-being. It also highlighted the need to construct alternative composite indices, including non-monetary indicators, to assess the achieved development levels. The HDI was launched in 1990 to represent the broad ideas included in the human development concept. 3 So the capability approach has helped enlarge the concept of human development. International organizations such as the World Bank (2006) have adopted notions of ‘‘quality of growth’’ and ‘‘pro-poor growth’’ that reflect greater concern about non-monetary dimensions of well-being. (a) Sen’s capability approach and the need for going beyond the HDI Sen’s capability approach (1985) proposes a normative framework to evaluate individual well-being, social relationships and changes in society. 4 Its main components are the ‘‘commodities’’ or resources, the ‘‘functionings’’ and the ‘‘capabilities.’’ The ‘‘commodities’’ are all goods and services, not just merchandise. They can include transfers in kind and make possible the ‘‘functionings,’’ which take into account achievements of individuals— what they ‘‘are’’ and what they ‘‘make’’ with their resources—and reflects life-style. The concept of ‘‘capabilities’’ is related to ‘‘functionings’’ but also includes notions of opportunity and freedom—the range of opportunities a person has and can choose from. ‘‘Capabilities’’ are various combinations of functionings (beings and doings) that the person can achieve. ‘‘Capability is, thus, a set of vectors of functionings, reflecting the person’s freedom to lead one type of life or another (. . .) to choose from possible livings’’ (Sen, 1992, p. 40). A functioning is an achievement, while capability is about the ability to produce it. Functionings are thus more directly related to living conditions, while capability is a concept of freedom, in a positive sense. According to Sen’s definition, the UNDP (1997) defines human development as increasing people’s choices by expanding their human capabilities and opportunities. Under-development is thus not a deprivation of basic needs, but is a deprivation of basic capabilities or freedoms that would allow an individual to have the kind of life he/she wants. 5 Sen’s (1999) approach is qualitative and multidimensional. He puts human beings at the center of the development concept. The aim of development is to enhance human capabilities so as to lead full, productive and satisfying lives. A higher income is necessary but not sufficient and thus calls for wider measures of well-being. The HDI was supposed to use Sen’s approach to make international comparisons. It has been improved, in particular, for GDP calculation and extremes fixing. 6 It has also led to other indices such as the Human Poverty Index (HPI) which assesses human development not on average national achievement but on how many people live in deprivation. Several heterodox World Bank studies consider indicators of inequality for analysis of true development. But Easterly (2002), who examines inequality as a barrier to prosperity and growth, and Pritchett, Suryahadi, and Sumarto (2000), who look at vulnerability to poverty, use household data. After GDP per capita, the HDI is the most discussed measure of well-being. The literature seems to take two approaches that are not inevitably exclusive of each other. In the first, the main criticism of the HDI relates to its very narrow definition of human MULTIDIMENSIONAL MEASURES OF WELL-BEING well-being. New indices, sometimes excluding the income component, have been proposed without having content necessarily justified or based on an explicit theoretical approach of well-being. The Physical Quality of Life Index (PQLI) developed by Morris (1979) takes into account life expectancy, infant mortality, and literacy. The Quality of Life Index of Dasgupta and Weale (1992) adds civil liberties and political rights to the HDI. The Index of Economic Well-Being proposed by Osberg and Sharpe (1998) is similar, though it also takes into account economic aspects of well-being neglected by GDP per capita (such as production stocks, unequal income distribution and uncertainty about future income). Rahman, Mittelhammer, and Wandschneider (2003) propose a composite index of well-being based on eight social dimensions, each including indicators for social relationships, emotions, health, work, material well-being, civil, and political liberties, personal security, and environment quality. The index is applied to 43 countries using the Borda rule 7 and the principal components analysis method. Several other studies (Ivanova et al., 1999; Ogwang & Abdou, 2003; Qizilbash, 2004) point out the difficulties and risks of creating indices, in view of the multidimensional aspects of wellbeing, the redundancy of variables and the measurement sensitivity to any weighting system. McGillivray (1991) and McGillivray and White (1993) highlight the redundancy between the HDI and its components and say the HDI is ‘‘yet another redundant index’’ and that its significantly high correlation with GDP per capita demolishes the argument that it would produce different rankings of countries. To overcome this drawback, McGillivray (2005) has recently applied principal components analysis and regression estimates to the HDI components to extract an aggregate measure of non-economic aspects of human well-being. Cahill (2005) analyses the implications of such correlations for the choice of weighting. The main conclusion is that high correlations between HDI components would produce a composite index insensitive to the weighting. In the second approach, the HDI’s reductionist nature is also criticized but bigger questions are raised, such as the relationship between the capability approach and the concept of human development (Gasper, 2002), or broader ones, about the content and empirical measurement of ‘‘capabilities.’’ Most studies supporting the capability approach use disaggregated data from household surveys 8 and very few use 1261 aggregated data to allow international comparisons as our indices permit. Slottje (1991) uses 20 indicators to build a composite index of well-being for 126 countries. Baliamoune (2003) explicitly uses Sen’s capability approach and proposes classifying countries according to new indicators close to the concept of freedom conveyed by ‘‘capability.’’ (b) Alternative applications of the capability approach Studies using Sen’s approach have flaws. They do not measure ‘‘capability.’’ With limited data available, usually only ‘‘functionings’’ carried out are used as a proxy of ‘‘capabilities.’’ These attempts are also sometimes far from the conceptual framework they are supposed to be linked to because the composite indices rely on a combination of indicators that are different by nature, some corresponding to ‘‘capabilities’’ (civil liberties and political rights), others to ‘‘functionings’’ (literacy) and others still to resources or assets (such as the number of telephones per capita). Well-being, standard of living and quality of life are generally not differentiated in these studies and they apply different concepts and realities, raising two questions—which and how many indicators to use to move towards the concept of human development, and the matter of new and more complete indices to make the distinction between the various concepts of Sen’s approach. Sen gives no list of ‘‘capabilities’’ to take into account for constructing well-being indices and allows multiple proposals (Alkire, 2002). The three HDI components could be justified conceptually as being universal, basic to life and measurable but they raise the non-inclusion of other dimensions. For example, Dasgupta (1990, 1992) criticizes the HDI for neglecting human rights. The choice of indicators suggests that if ‘‘capabilities’’ were carried out in these three basic dimensions, it would be done in the other dimensions of human development. With the capability approach, while the education and life expectancy indicators refer to ‘‘functionings,’’ the income per capita component seems to be a ‘‘commodity.’’ As the human development concept has emerged from the GDP limitations, it seems inappropriate to include an income component in an index of well-being. As Anand and Sen (2000) themselves argue, income can be an indirect indicator of some capabilities. However, 1262 WORLD DEVELOPMENT well-being is not determined by possession of resources but by their transformation into ‘‘functionings’’ which depends on personal, social and environmental factors. GDP per capita is necessary but not sufficient for human development as shown by countries where high and growing GDP per capita has not led to enrichment of human lives (Sen, 1999). The income component affects the purity of the HDI as a capability-based measure. First, the level of GDP per capita is a poor indicator of the means of a group of people and its usefulness for the expansion of social services and infrastructure development is not clear (Anand & Ravallion, 1993; Anand & Sen, 2000; Sen, 1981, 1999). Means indicators that are determinants of well-being and part of the standard of living index are needed. Second, GDP per capita is a bad proxy of freedoms and quality of life. Like our indices, the PQLI and the Capability Poverty Measure (CPM), used in the 1996 Human Development Report (UNDP, 1996) and replaced the following year by the HPI (with a variant for developing and industrialized countries), are examples of non-income measures. The HPI replaces the income component by several means indicators, while the CPM focuses on human capabilities, functionings and outcomes. Unlike the HDI, these indices are headcount proxies measuring the percentage of people in each country who lack basic human capabilities. (c) Justification of Standard of Living and Quality of Life Indices Standard of Living (SL) and Quality of Life (QL) are not new indices of well-being, but past indices differ from ours in that they capture different dimensions of well-being, use different methods of aggregating and have different theoretical foundations. To take other aspects of development into account, while distinguishing between the concepts, we define the composite indices of SL and QL as based on ‘‘commodities’’ on the one hand and the ‘‘functionings’’ and ‘‘capabilities’’ on the other. SL corresponds to the quantity of goods and services and to the services the GDP produces. It includes several means indicators that correspond to ‘‘commodities’’ that could be called inputs. QL includes (unlike SL) more intangible or qualitative aspects such as quality of education, extent of child labor and quality of the environment. It is a combi- nation of ‘‘functionings’’ and/or ‘‘capabilities’’ indicators within the meaning of freedoms. They are result indicators that refer to output within a transformation system of ‘‘commodities,’’ as Sen suggests. SL involves nine indicators in three domains (education, health, and material well-being). Public expenditure as a percentage of GDP in education and health take into account the money allocated to these social services. The number of doctors/physicians is an indicator of health facilities. Access to safe water reflects public facilities available and a means to prevent illness and epidemics. The age dependency ratio and net primary school enrollment indicators are more difficult to justify as means indicators and have been chosen on the basis of data availability. The teacher/student ratio would have been a better means indicator but was not available for many countries. The age dependency ratio is the demographic pressure. It is a summary of ageing that includes both young and old in relation to the potentially active population, so is a rough indicator of education. QL focuses on measures of well-being or human outcomes that include explicit references to human freedoms. It tries to take into account the capability of participating in community life that was dropped from the HDI. The main indicators emphasize the ‘‘being and doings’’ of a population, their opportunities as well as their non-opportunities. Capability failure can stem from violation of personal rights or absence of positive freedoms (Sen, 1992). The QL composite index is a combination of nine indicators covering three domains: health, education, and environment in a broad sense. Education quality includes capabilities that education can provide. Adult literacy is accompanied by two other indicators measuring children’s and women’s capabilities. Child labor indicates denied opportunities to acquire human capabilities needed in productive and social life. Female labor captures the intensity of gender equality in productive activity. It may also depict to a lesser extent ‘‘outcomes’’ of education as capability of entering the labor market. Life expectancy is an indicator of capacity to live a long life, maternal mortality accounts for capacity to give birth in good health conditions and the percentage of underweight or stunted children accounts for the potential for being well nourished. Civil rights and political freedoms refer to the aim of development relating to the actual freedom enjoyed MULTIDIMENSIONAL MEASURES OF WELL-BEING by the population involved. Trade openness involves the capability to exchange goods with partners and contribute to better quality products. Carbon dioxide (CO2) is not directly related to air pollution but to resource depletion. However, all fuels produce CO2 when burned but sometimes also other pollutants (nitrogen oxides, gaseous hydrocarbons, and carbon monoxide). The more CO2 emissions, the more likely are other dangerous emissions and worse quality of air. The choice of indicators in Table 1 is justified by arguments above but is also limited by availability of data to compile SL and QL indices for at least as many countries as there is data for the HDI and GDP per capita (we have 170 countries). Division of indicators between SL and QL is not always easy to establish. The concept of ‘‘capability’’ is difficult to discern from country data because it is initially defined in reference to individuals and their 1263 relationships with other members of society. Several lists of ‘‘basic capabilities’’ are proposed in the literature (Alkire, 2002) to approach the concept of human development but their use in identifying indicators is mostly limited to the disaggregated household data. Several indicators can be interpreted at the same time as a ‘‘commodity,’’ a ‘‘functioning’’ or a ‘‘capability.’’ So it is hard to produce a division of indicators that is not contestable. 3. CONSTRUCTION OF WELL-BEING INDICES IN AFRICAN COUNTRIES (a) Methodologies used for analysis of Standard of Living and Quality of Life The construction of SL and QL indices and measuring the degree of deficiency or ‘‘deprivation’’ for each country in these domains Table 1. List of selected indicators Standard of living Standard of health Public health expenditure (% of GDP) Improved water source (% of population with access) Physicians (per 1,000 people) Standard of education Age dependency ratio (dependents to working-age population) Public spending on education, total (% of GDP) Net primary enrolment (%) Material well-being Vehicles (per 1,000 people) Roads paved (% of total roads) Television sets (per 1,000 people) Quality of life Quality of health Under-weight or under-height children under age five (%) Life expectancy at birth (years) Maternal mortality reported (per 100,000 live births) Quality of education Literacy rate, adult total (% of people aged 15 and above) Labor force, children 10–14 (% of age group) Labor force, female (% of total labor force) Quality of environment Openness (trade, % of GDP) CO2 emissions (metric tons per capita) Political rights and civil liberties (index)a Source: UNDP (2002) and World Bank (2002) data. a Indices of political rights and civil liberties are available on the House of Freedom website: www.freedomhouse.org/ ratings/index.htm. 1264 WORLD DEVELOPMENT requires a suitable methodology. Well-being is multidimensional so we shall use and compare the methodology from the fuzzy sets approach (Totally Fuzzy Analysis) and from the simple Factorial Analysis of Correspondences. 9 (i) Measuring Standard of Living and Quality of Life using the fuzzy sets approach As components of human well-being, Standard of Living and Quality of Life are multidimensional and vague concepts. The fuzzy sets theory, invented by Zadeh (1965) and developed by Dubois and Prade (1980), is a suitable mathematical tool to analyze phenomena that are hard to place in a set. Use of this methodology in economics is quite new. The best-known studies based on the fuzzy sets approach are multidimensional analyses of poverty. 10 However, these are mostly based on micro-level data from census and household surveys, rarely on macro-level data. To our best knowledge, Baliamoune (2003) has been the pioneer in the use of fuzzy-set theory to construct well-being measures at the macro-level. Compiling several human well-being indices, Baliamoune (2003) yields rankings for 48 countries measuring their achievements in education, life expectancy and political and civil rights. The non-linear membership function used to assess well-being across countries includes rules and goals and incorporates the idea of lower and upper limits. 11 Using the same methodology in 14 Pacific Asian countries, Baliamoune-Lutz and McGillivray (2006) provide a fuzzy representation of the HDI and its three components. Comparisons with non-fuzzy estimates suggest that fuzzy measures should be used more widely to assess well-being outcomes. Our composite indices using the fuzzy sets approach are constructed in two stages (see Appendix A). The first involves definition of the membership function of a given set associated with each country and indicator. The function can take several forms (Baliamoune, 2003; Lelli, 2001), but we consider the ‘‘Totally Fuzzy Analysis (TFA),’’ as defined by Cerioli and Zani (1990), in contrast to the ‘‘Totally Fuzzy and Relative’’ approach (TFR) of Cheli and Lemmi (1995). The value of the membership function will provide a country-specific deprivation degree relative to a given indicator, increasing linearly between zero and one. The second stage involves the different degrees of deprivation in each country, with each indicator aggregated to obtain composite SL and QL indices for each country. So under- development can be defined as an accumulation of ‘‘deprivations’’ or ‘‘shortfalls.’’ Conversely, the index value can be interpreted as an accumulation of ‘‘effective achievements.’’ The higher the SL (or the QL), the closer the value index is to zero or the closer the value is to one, the higher the degree of deprivation relative to the SL (or the QL). Application of fuzzy sets methodology to indicators yields country rankings according to the SL and QL indices. Due to the additionally decomposable nature of fuzzy indices, SL and QL can be broken down to obtain several sub-indices by domain (such as education and health). The breakdown provides key information about the level and structure of well-being and particularly about domains that contribute most to deprivation and under-development. It also offers information for policymakers designing structural socio-economic policies to eradicate the main causes of under-development. Identification of areas where structural intervention is necessary could lead to capability-building policies. At first glance, the TFA method cannot say which countries could receive aid to help build socio-economic structures in a given area, except by arbitrarily fixing a cut-off line. But a dichotomous approach can obtain a critical value from cumulative distribution of the deprivation index in terms of SL, QL and their components. This critical value is a threshold to estimate the number of countries with genuine deprivation in a particular domain (see Appendix A). TFA offers various means of capturing information from well-being indicators among countries. The most common criticism of this kind of method concerns choice of a weighting system. One way to test the robustness of rankings is to compare results obtained with TFA with those produced by FAC. (ii) Charts of SL and QL obtained by Factorial Analysis of Correspondences FAC is a descriptive method for qualitative data suggested by Benzécri et al. (1973) to study contingency tables (see Appendix B) and discover simple patterns in the relationships between variables. It provides orthogonal basis vectors of the data space by computing the eigenvalues of a matrix drawn from the data, reducing the dimensionality of the input data by extracting the most important features (the factors or principal components). These are sorted such that the first captures the maximum MULTIDIMENSIONAL MEASURES OF WELL-BEING variance of the data, and the others capture the decreasing amount of variance. With our well-being indices, where there are nine indicators (dimensions) for each country and 170 countries (dimensions) for each indicator, the two dimension-charts from FAC present the projections of all variables as close as possible from observation. This interprets the proximity between countries and indicators and also between both kinds of variables (see Appendix B). Each indicator has a contribution (weight) in definition of the main axis (axis 1) that we shall use further. We applied these two methods to 170 countries (see Appendix C) for the year 2000, using the indicators in Table 1. We now present the general results and then focus on the 52 African countries available (Sao Tome & Principe is missing due to lack of data). (b) Indices and sub-indices for Standard of Living and Quality of Life TFA enables us to calculate SL and QL as well as the various sub-indices for each of the 170 countries. Table 2 shows the statistical indicators of these indices and sub-indices. Determining the breaking value in relation to the international average score enables calculation of the percentage of countries by geographical region (Rest of the World and Africa) with a deficit in each domain (Table 3). Material well-being is the area, internationally, where deprivation is highest. The average score is highest in Africa, making it the world’s poorest region. It has high SL deprivation, with 96.2% of its 52 countries having an insufficient score. Where countries can be described as ‘‘rich’’ or ‘‘poor,’’ those in Africa would express deficiencies in each domain. All the average scores are higher than 1265 the breaking values, suggesting that Africa has handicaps in all SL dimensions. The continent has deficiencies in all considered QL domains, but the percentage of countries with a deficit is much smaller than for SL. Quality of education is the area in which the continent has most deficit countries (59.6%) and 57.7% have a quality of health less than the breaking value. 12 (c) Graphical analysis for African countries FAC was initially done at world level (170 countries). Charts have been created for the 52 African countries, so their coordinates for SL and QL indices are analyzed in comparison with data for 170 countries. The most representative SL indicators (Figure 1) on axis 1 are for access to safe water, education, and transport. These are the indicators whose contributions and square cosines are highest. On the left are countries with a low public education expenditure and a problem with the access to safe water. Almost all the African countries have negative coordinates and are behind the center of gravity, which would be the international ‘‘average.’’ On axis 2, material well-being (vehicles and TV) is more important in the top quadrant (especially for North African countries). The same analysis for QL shows that African countries were ranked primarily according to trade openness, life expectancy, and literacy. Again, the ‘‘richest’’ countries are in the top right quadrant. Contrary to SL, several countries have positive coordinates on axis 1, which shows that their quality of life is higher than the international average. This is so with North African countries, but also with some of the islands (Cape Verde, Mauritius, and the Seychelles). The other countries are rather close Table 2. Statistical indicators for SL and QL components at international level Average Standard deviation Median Breaking value Standard of Living Standard of health Standard of education Material well-being 0.421 0.380 0.365 0.622 0.186 0.208 0.180 0.262 0.397 0.349 0.307 0.668 0.431 0.427 0.374 0.527 Quality Quality Quality Quality 0.217 0.218 0.249 0.184 0.130 0.191 0.183 0.099 0.179 0.136 0.215 0.162 0.341 0.391 0.398 0.253 of Life of health of education of environment Source: Authors’ calculations based on UNDP (2002) and World Bank (2002) data. 1266 WORLD DEVELOPMENT Table 3. Average score and percentage of countries with deficits Rest of the world African countries Average score % Average score % Standard of Living Standard of health Standard of education Material well-being 0.343 0.305 0.287 0.533 50.8 22.0 16.1 47.5 0.599 0.549 0.540 0.826 96.2 75.0 80.8 94.2 Quality Quality Quality Quality 0.162 0.131 0.173 0.181 8.5 5.9 10.2 20.4 0.335 0.415 0.422 0.191 51.9 57.7 59.6 13.5 of Life of health of education of environment Source: Authors’ calculations based on UNDP (2002) and World Bank (2002) data. Standard of Living 2000 0.53 Sudan Gabon 0.33 Ghana Egypt Eq. Guinea TV Zambia Mauritania Zimbabwe Mauritius Tunisia 0.13 Morocco Nigeria Guinea -1.4 -1.2 -1 Somalia Eritrea ROADS Djibouti Niger -0.8 -0.6 Benin Burundi Senegal PHYSICIANS Seychelles 0 Algeria-0.4 WATER SCHOOLENROL Cote d'ivoire Cameroon Tanzania EDUCAT Madagascar Uganda AGEDEPBotswana Liberia Mali Ethiopia S. LeoneKenya Togo Cape Verde Mozambique Comoros CAR Angola Gambia Lesotho Malawi Congo Rwanda Botswana Guinea Bissau Chad DRC Namibia -0.2 Swaziland 0.2 0.4 -0.07 HEALTH -0.27 South Africa VEHICLES Libya -0.47 indicators African countries Figure 1. Standard of Living in African countries. to each other and form a fairly homogeneous group where life expectancy is weak and literacy is low (Figure 2). 4. DISCUSSION AND POLICY IMPLICATIONS (a) Aggregation in multidimensional indices and choice of weighting system Composite indices are usually constructed in several stages, including choice of variables, scaling, weighting, and aggregative procedure (for an overview, see Booysen, 2002), but the crucial problem is to assign suitable weights to the indicators. Information can be aggregated into a single measure in two main ways. One is by bringing into play the arbitrariness and beliefs of the researcher and may involve public and expert judgments. With the HDI, PQLI, and Borda rule, the most-used method is giving equal weights to the attributes of the composite index assuming they are equally important in capturing the several aspects of the concept. The other main way of aggregating MULTIDIMENSIONAL MEASURES OF WELL-BEING 1267 Quality of Life 2000 TRADE 0.39 Seychelles 0.29 0.19 Angola Mauritius Swaziland Ghana Liberia Namibia Djibouti Lesotho Eq. Guinea Gambia 0.09 Mauritania Congo Guinea Bissau Cote d'ivoire Togo Nigeria Guinea Botswana S. LeoneMozambique Eritrea Senegal Morocco MalawiMATERMORT Zimbabwe Mali Zambia Rwanda Somalia -0.01 Gabon Niger Benin -0.35 UNDERWEIGHT -0.85 Ethiopia 0.15 Kenya Comoros Burundi CAR DRCChad Cameroon Algeria Madagascar Burkina Faso CHILDLABOR Tanzania South Africa -0.11 Uganda Sudan Egypt Tunisia Cape Verde 0.65 1.15 LIBERTY Libya LITERACY FEMLABOR -0.21 LFEXPECIT -0.31 CO2 -0.41 indicators African countries Figure 2. Quality of Life in African countries. supports the objectivity of weighting schemes and uses multivariate techniques for determining the weights. Most common is the principal component analysis (Rahman et al., 2003; Ram, 1982; Slottje, 1991) in which the attributes are weighted with the degree of variance from the original set of variables explained by the first principal component. The choice of aggregation function is also crucial as it affects the compensability of additive aggregations. The derived indices can be either additive or functional, depending on the context of analysis. Morris (1979) says that if the aim is to measure relative performance of individual countries, the simplest technique is the additive aggregation method. Although methodologies can lead to rankings sensitivity according to a particular weighting scheme, the recent study of Cahill (2005) suggests this is not always the case. Well-being measures are clearly not robust to alternative methods of aggregation, but the use of fuzzy set theory and factorial analysis allows for less arbitrary assignment of weights to components of the indices. The two methods are complementary as they each use one way of aggregation. For TFA, weights are based on frequency of symptoms of under-development. The weight xj is an inverse function of the proportion of countries that are deprived relative to indicator j. It implicitly relies on the belief that the smaller is the proportion of countries scoring low on a specific indicator, the larger is the weight attributed to it in the aggregate set. For example, in the SL index, the biggest weight is attributed to safe water and a small weight to cars. So a high deprivation of cars would have less importance than low access to safe water in assessing the relative performance of countries according to SL. FAC, like principal component analysis, attributes a weight objectively to the components according to their percentage of variance in calculation of the first axis. To compare the two methods, we ranked countries in descending order of well-being. The two methods of analysis do not give exactly the same results. 13 These differences are mainly due to the weights given to the indicators (Table 4). So TFA gives the biggest weight to standard of education (more than 43%) in calculation of SL and to quality of health in QL (more than 35%). FAC gives the biggest weight to material well-being (more than 45%) and quality of health (more than 58%). 1268 WORLD DEVELOPMENT Table 4. Weights of indicators using different methods Standard of health Weights TFA Weights FAC 0.3526 0.2507 Standard of Material Total Quality of education well-being health 0.4486 0.2932 0.1988 0.4561 1.0 1.0 0.3540 0.5804 Quality of education Quality of environment Total 0.3279 0.2172 0.3181 0.2024 1.0 1.0 Source: Authors’ calculations based on UNDP (2002) and World Bank (2002) data. The weighting system significantly changes the results but more comprehensively, the matrix of the rank correlations (Appendix D) proves that differences in ranking are not significant and, on the contrary, with TFA and FAC methodologies, are statistically correlated. Another set of interesting results comes from the rank correlation between SL and QL determined by GDP per capita, and the HDI. The correlation coefficients of the two methods are systematically lower with GDP per capita than with the HDI, but remain generally high, meaning economic performance is strongly related to well-being in all its other dimensions. Also, a high correlation is found between rankings of countries according to GDP per capita and the HDI (R2 = 0.94), a result McGillivray (1991) explains by the high correlations between HDI components and GDP per capita. And the strong correlations between SL and QL indices with the HDI indicate that, despite the serious criticism of the HDI’s reductionist approach to human well-being, it reflects well the basic dimensions of human development. Our results are robust and reinforce each other since the country rankings according to TFA, FAC, HDI, and GDP per capita are not very different. This is not surprising, though detailed study of the rank variations reveals nuances in this simple idea. (b) Analysis of correlations and redundancies between indicators The correlations between SL, QL and their components (Appendix E) show quality of environment as the only indicator statistically correlated neither with SL and QL nor the other indicators. The main reason is the heterogeneity of the quality of environment components (trade openness, CO2 emissions and liberties, and freedoms). More generally, the indicators are statistically and significantly correlated with each other. According to Cahill (2005), this result might explain the high rank correlations between our indices using two different methods and weighting schemes. The matrix of correlations (Appendix F) also shows that GDP per capita is more strongly correlated with SL than with QL, which can be considered through a capability approach. The coefficients of correlation between our two indices and the HDI are also far higher than with GDP per capita, which shows that our indices are closer to the HDI than to GDP per capita. SL is most strongly correlated with standard of education and QL with quality of education, which confirms that ‘‘education’’ plays an important part in defining a country’s human development performance. Education should thus be one of the three mega-variables in the HDI. This supports the recent finding of McGillivray (2005) that adult literacy best captures the non-economic dimension of well-being. In contrast, Dasgupta and Weale (1992) and Rahman et al. (2003) find that health (such as life expectancy) is the closest measure of well-being. The ability to read and write is very important and allows a person to stand up for his/ her rights. Education also helps to overcome negative processes such as child labor or social barriers and to empower disadvantaged groups. An educated person may also survive better or longer and participate in political change. According to Sen, education expands the real freedoms that people value. For redundancy, we use McGillivray and White (1993) criteria for redundancy of 0.7 (level 2) and of 0.9 (level 1). Correlation coefficients (Appendix F) are thus mainly level 2 of redundancy. But the correlation between QL and the GDP per capita, at 95% level, indicates absence of redundancy (in terms of value). This striking result brings empirical support to the conceptual justification of QL. Indeed, the QL index measures ‘‘the end’’ rather than ‘‘the means,’’ as does the GDP per capita. Though they are conceptually distinct, the high redundancy between SL and QL was expected as the means and outcomes indicators can be seen as inputs and outputs of a production or welfare function. MULTIDIMENSIONAL MEASURES OF WELL-BEING (c) Policy recommendations for African countries One way of understanding well-being in Africa is to look at the rank changes in countries in the SL and QL indices, GDP per capita and the HDI. GDP per capita has very many outlier cases in both directions: low wealth but fairly high well-being and high wealth but low wellbeing (Appendix G). So a country can be much better or much worse ranked, according to the index applied. The very large rank variations then give an indication of the deficiencies of some indices. For example, it is preferable to use SL rather than QL to rank North African countries (Egypt, Libya, Algeria, and Tunisia). The rank is higher according to GDP per capita for Equatorial Guinea, Gabon, Namibia, Botswana, and South Africa, suggesting that these countries are richer than they are developed. QL is more important than other measures in Ghana, Tanzania, and Zambia. According to Sen’s capability approach, we could say whether standards of health and education are associated with good functionings (or quality) in each sector. In health, we could check whether public expenditure, access to water and the number of doctors allow mothers and children to live in healthy conditions and the population to have high life expectancy at birth (as in Algeria, Egypt, Mauritius, Morocco, the Seychelles, Swaziland, and Tunisia). In education, the same would indicate whether public spending, school enrollment and the number of ‘‘dependents’’ allows females and children to work in good conditions and adults to be literate (as in Algeria, Botswana Cape Verde, Congo, Gabon, Lesotho, Libya, Mauritius, Namibia, the Seychelles, South Africa, Swaziland, Tunisia, and Zimbabwe). In other countries, either small resources (a low standard) or weak functionings (a low quality) prevent the two sectors from being efficient. These results could be used to make better and more efficient public expenditure allocation to sectors. African countries should increase their investment in human capital and infrastructure to improve health, education, and material well-being. To enable efficient transformation of resources into capabilities, Africa has to give high priority to improving governance, maintaining peace and security and increasing democratization and human rights. Sen argues that development is freedom, so a variety of institutions (such as NGOs, media and international and local communities) con- 1269 tribute to development through enhancing individual freedoms. They are extremely important agents of Africa’s future development. 5. CONCLUSION The two methods of well-being measurement, TFA and FAC, take into account several dimensions of well-being (such as liberties, child labor, or the number of vehicles) and enable two indices to be constructed according to Sen’s capability approach. Unlike the HDI, the two indices do not mix measures of resource availability and of functioning and capability. The results for SL and QL show that African countries have substantial deficiencies in many areas, except perhaps quality of environment, and highlight the importance of education as a key variable in a country’s multidimensional development. We also compare monetary performances with the HDI and the SL and QL indices. Although most components might be dependent on income, SL and QL completely exclude any monetary indicator. Low correlation between QL and GDP per capita gives empirical support to the conceptual distinction. Detailed analysis of indices and sub-indices also makes it possible to distinguish between ‘‘lack of resources’’ and ‘‘weak functioning’’ by domain. The weighting systems substantially change the rankings, but the two methods are complementary as they each use a different way of aggregation. For TFA, weights are based on allegation. For FAC, weights are objectively calculated. However, by considering the rank correlations, the differences between the two methods are not significant. Though the HDI seems restrictive, it does in fact take the essential indicators into account, since it establishes country rankings very close to those of our two indices. But due to their diversity and originality, the SL and QL indices cover a much greater area than the HDI. They can be disaggregated and information can be better used to establish social and economic policies to fight structural under-development. They are based on Sen’s capability approach, allow assessment of two measurements of human well-being and create a clear framework for evaluating development policies and processes. Sen (1999) argues that development occurs when people are able to achieve what makes their life valuable. Good governance, democratization and respect for human rights are key issues in Africa’s development. 1270 WORLD DEVELOPMENT NOTES 1. Ivanova, Arcelus, and Srinivasan (1999), Kelley (1991), McGillivray (1991) and Srinivasan (1994) have criticized the HDI. 2. Even though GDP per capita is a flow concept, it is generally used as a measure of a stock concept. 3. The HDI is the unweighted average of three subindices of basic well-being: life expectancy at birth, educational attainment and GDP per capita expressed in real terms and purchasing power parity. Each indicator is normalized, so it takes values between zero and one. Scaling makes it possible to compare countries’ relative performances in each dimension. The HDI does not measure absolute but relative levels of human development by ranking countries. 4. His approach has not only been used in development economics, but also in other analyses such as political philosophy, social policy, and welfare economics. 5. The distinction refers to the concept of ‘‘basic needs’’ proposed by the International Labour Organisation in the 1970s and by Hicks and Streeten (1979) and defined as physical necessities (food, shelter, and public goods). The concept was then reintroduced by the World Bank (2001), but it is currently very close to the concept of ‘‘basic capabilities.’’ 6. Jahan (2002) presents the refinements in the HDI methodology over time. 7. The method has been used by Dasgupta and Weale (1992) as an implicit criticism of the cardinal information base that underlies the HDI. Relying exclusively on ordinal information, the Borda method simply involves assigning a rank order score to each component index and adding up the rank order scores to obtain the Borda score. 8. See Schokkaert and van Ootegem (1990), Brandolini and d’Alessio (1998), Chiappero Martinetti (2000), Lelli (2001), and Qizilbash (2002). 9. These two methods were used in the context of individual data by Lelli (2001). 10. 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(1991). Policy undertakings by the seven ‘‘summit’’ countries: ascertaining the degree of compliance. 1272 WORLD DEVELOPMENT Carnegie-Rochester Conference Series on Public Policy, 35, 267–307. World Bank (2001). World Development Report 2000/01 – Attacking Poverty. New York: Oxford University Press. World Bank (2002). World Development Indicators. Washington, DC. World Bank (2006). World Development Report—Equity and development. New York: Oxford University Press. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–343. Second step: weighted indices of SL and QL Following Cerioli and Zani (1990), composite indices are defined by taking the weighted arithmetical mean of the membership functions according (respectively) to the component M and M 0 indicators: M X xj lj ðiÞ; lSL ðiÞ ¼ j¼1 lQL ðiÞ ¼ M0 X x0j l0j ðiÞ j0 ¼1 APPENDIX A. TOTALLY FUZZY ANALYSIS First step: degree of deprivation for each indicator Assume i 2 [1, N] countries, j 2 [1, M] indicators of Standard of Living (SL) and j 0 2 [1, M 0 ] indicators of Quality of Life (QL). Consider Xj = {xj/j = 1, . . . , M} and X j0 ¼ fxj0 =j ¼ 1; . . . ; M 0 g vectors of components respectively of SL and QL. Variables xij and xij0 are the values taken by indicators j and j 0 for the ith country. When ranking values of j and j 0 by increasing order (the lower the value of a given indicator, the higher the deprivation), functions lj(i) and lj0 ðiÞ are defined as: 8 > 1 if xij 6 xmin j ; > > < xmax xi j j min lj ðiÞ ¼ xmax xmin if xj < xij < xmax ; j > j j > > :0 if xij P xmax j with xmin ¼ Mini ðxij Þ and xmax ¼ Maxi ðxij Þ. j j Functions lj(i) and lj0 ðiÞ provide the deprivation degrees of the ith country relative to indicators j and j 0 . Inversely, if indicators are rearranged by decreasing value (which is the case for CO2 emission), functions lj(i) and lj0 ðiÞ are then defined as: 8 ; 1 if xij P xmax > j > > < xij xmin < xij < xmax ; lj ðiÞ ¼ xmax xj min if xmin j j j j > > > :0 if xij 6 xmin j : These functions are increasing linearly between zero and one according to the degree of deprivation. P 0 with xj P 0 and M j¼1 xj ¼ 1, where xj and xj are the weights attributed, respectively, to indicators j and j 0 . Chiappero Martinetti (1996) says the function must have a value between maximum and minimum and must allow interaction between the indicators. The weights are defined as N ln l1j 1 X with l j ¼ l ðiÞ: xj ¼ P M 1 N i¼1 j j¼1 ln l j The weight xj is an inverse function of the mean deprivation level relative to the indicator j. The logarithmic curve function introduced into the weighting system shows that well-being does not vary in a linear way. Third step: definition of a critical value The critical value (or breaking value) ljcrit associated to indicator j can be defined as: j F ðlj critÞ ¼ 1 l with F the cumulative distribution function and j the average value of indicator j which indil cates, dichotomously, the proportion of under-developed countries according to j. APPENDIX B. FACTORIAL ANALYSIS OF CORRESPONDENCES Data are presented in a NIJ table in which the rows (countries) are numbered by i = 1, . . . , p and the columns (indicators) by j = 1, . . . , q. Alternatively, the PIJ table, whose general term is pij = nij/n, provides the two marginal distributions: pi = ni/n and pj = nj/n as well as the conditional distributions in rows and columns, called ‘‘row’’ profile and ‘‘column’’ profiles, respectively: pij ¼ pij =pi and pji ¼ pij =pj . MULTIDIMENSIONAL MEASURES OF WELL-BEING First step: calculation of distances To measure the distance between two profiles, we compare the same rank terms (e.g., p1j and p2j ). The v2 distance between the row pro0 files is d(i, P i ) whose square is given by d 2 ði; i0 Þ ¼ qj¼1 ðpij pi0j Þ2 =pj . The v2 distance between the column profiles is similarly defined: p X 0 ðpji pji Þ2 =pi : d 2 ðj; j0 Þ ¼ i¼1 Second step: calculation of principal axes FAC provides orthogonal basis vectors— principal axes—preserving the distances and calculated according to the least squared method. The origin of the axes (0, 0) shows the marginal distribution, the center of gravity or the ‘‘average country’’. The duality principle makes it possible to show the two ‘‘profiles’’ on the same chart, interpret proximity between a row and a column profiles and thus explain the connection between two variables. The FAC duality princi- 1273 ple is essential but a difficult property whose interpretation is delicate. For details, see Casin (1999) and Foucart (1997). Third step: interpretation parameters The clouds of points N(I) and N(J) on the principal axes correspond to projections as close as possible from observation. Two values for interpretations are calculated: the contribution (with variance taken as the indicator) and the quality of representation (with squared cosine taken as the indicator). Contributions are used to measure the influence (weight) of a point (e.g., of a country i) in defining a principal axis. The sum of the contributions for each axis equals one. The proximity between projections does not always reflect the proximity between the profiles. Some points can be badly shown or moved away from the profiles they represent. Angle h measures the proximity between the point in space and its projection on the plan. So a weak angle indicates good proximity (the square cosine is close to one) and an angle close to 90° (the square cosine is close to zero) indicates a bad one. APPENDIX C. LIST OF COUNTRIES Afghanistan Albania Algeria Angola Argentina Armenia Australia Austria Azerbaijan Bahamas, The Bahrain Bangladesh Barbados Belarus Belgium Belize Benin Bhutan Bolivia Bosnia and Herzegovina Botswana Brazil Brunei Bulgaria Burkina Faso Burundi Cambodia Cameroon Canada Cape Verde Central African Republic Chad Chile China Colombia Comoros Congo, Dem. Rep. Congo, Rep. Costa Rica Cote d’Ivoire Croatia Cuba Cyprus Czech Republic Denmark Djibouti Dominican Republic Ecuador Egypt, Arab Rep. El Salvador Equatorial Guinea Eritrea Estonia Ethiopia Fiji Finland France Gabon Gambia, The Georgia Germany Ghana Greece Guatemala Guinea Guinea-Bissau Guyana Haiti Honduras Hong Kong, China Hungary Iceland India Indonesia Iran, Islamic Rep. (continued on next page) 1274 WORLD DEVELOPMENT APPENDIX C—continued Iraq Ireland Israel Italy Jamaica Japan Jordan Kazakhstan Kenya Korea, Rep. Kuwait Kyrgyz Republic Lao PDR Latvia Lebanon Lesotho Liberia Libya Lithuania Luxembourg Macedonia, FYR Madagascar Malawi Malaysia Maldives Mali Malta Mauritania Mauritius Mexico Moldova Mongolia Morocco Mozambique Myanmar Namibia Nepal Netherlands New Zealand Nicaragua Niger Nigeria Norway Oman Pakistan Panama Papua New Guinea Paraguay Peru Philippines Poland Portugal Qatar Romania Russian Federation Rwanda Samoa Saudi Arabia Senegal Seychelles Sierra Leone Singapore Slovak Republic Slovenia Somalia South Africa Spain Sri Lanka Sudan Suriname Swaziland Sweden Switzerland Syrian Arab Republic Tajikistan Tanzania Thailand Togo Trinidad and Tobago Tunisia Turkey Turkmenistan Uganda Ukraine United Arab Emirates United Kingdom United States Uruguay Uzbekistan Vanuatu Venezuela, RB Vietnam Yemen, Rep. Zambia Zimbabwe APPENDIX D. RANK CORRELATIONS SL (fuzzy) QL (fuzzy) SL (FAC) QL (FAC) GDP per capita HDI SL (fuzzy) 1 QL (fuzzy) 0.82894 (<0.0001) 1 SL(FAC) 0.832065 (<0.0001) 0.71765 (<0.0001) 1 QL (FAC) 0.8960 (<0.0001) 0.75068 (<0.0001) 0.843957 (<0.0001) 1 GDP per capita 0.83276 (<0.0001) 0.68621 (<0.0001) 0.867768 (<0.0001) 0.864837 (<0.0001) 1 HDI 0.91287 (<0.0001) 0.79406 (<0.0001) 0.887808 (<0.0001) 0.926069 (<0.0001) 0.94121 (<0.0001) 1 MULTIDIMENSIONAL MEASURES OF WELL-BEING 1275 APPENDIX E. CORRELATIONS OF INDICES AND SUB-INDICES Standard Standard Material of of Well-being Health Education Quality of Health Standard of Health 1 Standard Education 0.72889 (<0.0001) Material well-being 0.74575 0.66131 (<0.0001) (<0.0001) 1 Quality Health 0.78611 0.80929 (<0.0001) (<0.0001) 0.73164 (<0.0001) Quality Education 0.71107 0.82384 (<0.0001) (<0.0001) 0.68980 0.79712 (<0.0001) (<0.0001) Quality of Environment Quality Quality Standard Quality of of of of Education Environment Living Life 1 0.16860 (0.028) 0.03223 (0.6765) 0.14462 (0.0599) 1 0.09053 (0.2403) 1 0.21796 (0.0043) 1 Standard of Living 0.85466 0.89685 (<0.0001) (<0.0001) 0.88348 0.86252 0.86198 (<0.0001) (<0.0001) (<0.0001) 0.10992 (0.1536) 1 Quality of Life 0.71498 0.77968 (<0.0001) (<0.0001) 0.61419 0.79214 0.93196 (<0.0001) (<0.0001) (<0.0001) 0.50722 (0.0001) 0.81180 (<0.0001) 1 APPENDIX F. CORRELATIONS WITH GDP PER CAPITA AND HDI Standard of Living Standard of Living Quality of Life GDP per capita HDI 1 Quality of Life 0.8096 (<0.0001) 1 GDP per capita 0.71151 (<0.0001) 0.50248 (<0.0001) 1 HDI 0.92149 (<0.0001) 0.80397 (<0.0001) 0.75804 (<0.0001) 1 Calculations based on 166 countries. GDP per capita is in current dollars based on purchasing power parity, identical to the one UNDP uses for calculating the HDI. The negative correlation coefficients are because high levels of SL and QL indices correspond to values close to zero, contrary to GDP per capita and the HDI. APPENDIX G. RANK VARIATIONS ACCORDING TO VARIOUS INDICES IN AFRICA Rank variations According to: % of displaced African countries Most important declines Between SL and QL QL 32.7% Between SL and GDP GDP 42.9% Between QL and GDP GDP 32.7% Egypt (56) Libya (36) Algeria (31) Tunisia (23) Comoros (21) Rwanda (21) Egypt (36) Congo Rep. (25) Zambia (22) Comoros (21) Rwanda (18) Zambia (48) Tanzania (42) Malawi (42) Congo Rep (42) Ghana (41) Madagascar (32) (continued on next page) 1276 WORLD DEVELOPMENT APPENDIX G—continued Rank variations According to: % of displaced African countries Between SL and QL QL 32.7% Between SL and GDP GDP 42.9% Between QL and GDP GDP 32.7% Ghana (57) Djibouti (49) Liberia (44) Tanzania (37) Nigeria (29) Equ. Guinea (107) Gabon (54) Namibia (53) Botswana (46) South Africa (38) Equ. Guinea (113) South Africa (52) Libya (50) Botswana (46) Gabon (46) Namibia (43) Greatest improvements Rank variations According to: % of displaced African countries Most important declines Greatest improvements Between GDP and HDI HDI 64.0% Between SL and HDI HDI 57.1% Between QL and HDI Equ. Guinea (70) South Africa (55) Botswana (55) Namibia (50) Gabon (41) Swaziland (37) Egypt (52) Zimbabwe (43) Algeria (34) Botswana (27) Malawi (25) Congo Rep. (19) Zambia (32) Djibouti (29) Ghana (28) Benin. (27) Cape Verde (22) Congo Rep. (25) Madagascar (14) Tanzania (14) Malawi (10) Comoros (9) Equ. Guinea (37) Libya (32) Ghana (15) Gabon (14) Madagascar (14) Libya (50) Equ. Guinea (43) Seychelles (17) Rwanda (15) Eritrea (14) HDI 65.3%