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Journal of the Operational Research Society (2005) 56, 969–980

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A reassessment of the human development index via data envelopment analysis DK Despotis* University of Piraeus, Greece To consider different aspects of life when measuring human development, the United Nations Development Program introduced the Human Development Index (HDI). The HDI is a composite index of socioeconomic indicators that reflect three major dimensions of human development: longevity, knowledge and standard of living. In this paper, the assessment of the HDI is reconsidered in the light of data envelopment analysis (DEA). Instead of a simple rank of the countries, human development is benchmarked on the basis of empirical observations of best practice countries. First, on the same line as HDI, we develop a DEA-like model to assess the relative performance of the countries in human development. Then we extend our calculations with a post-DEA model to derive global estimates of a new development index by using common weights for the socioeconomic indicators. Finally, we introduce the transformation paradigm in the assessment of human development. We develop a DEA model to estimate the relative efficiency of the countries in converting income to knowledge and life opportunities. Journal of the Operational Research Society (2005) 56, 969–980. doi:10.1057/palgrave.jors.2601927 Published online 22 December 2004 Keywords: human development index; data envelopment analysis; development

Introduction In the early development literature, income per capita was traditionally used for measuring human development in a country. Although the critique on the use of only the GDP per capita as a proxy of development is dated back to the 1950s, in the past 2 decades it has been fully recognized that pure economic indicators cannot sufficiently capture the multidimensionality of human development.1,2 In this line of thinking, in 1990 the United Nations Development Program introduced the Human Development Index (HDI), which ever since has been published annually in the Human Development Report3 (HDR). HDR is one of the major contributions that reoriented the debate on the measurement of development beyond the traditional economic perspective towards a broader scheme that incorporates different aspects of life into measures of human development. The HDI is a composite index of specific socio-economic indicators that reflect three major dimensions of human development: longevity, knowledge and standard of living. Since its establishment, the HDI has met considerable criticism for various attributes such as the way its component indices are derived by the raw data4 and the additivity of the aggregation method.5 Neumayer6 provides a comprehensive overview of the literature on alternative *Correspondence: DK Despotis, University of Piraeus, Department of Informatics, Decision Support Systems Laboratory, 80 Karaoli & Dimitriou Street, 18534 Piraeus, Greece. E-mail: [email protected]

computational methods for calculating the HDI. Another critical issue in calculating the HDI is the fact that equal weights are given to its component indices. Although this assumption has been supported in the HDRs, it has met also considerable criticism in the literature.7,8 A recent development on this issue is Mahlberg and Obersteiner’s9 proposal to use the data envelopment analysis (DEA) approach for computing the HDI. They base their proposal on two basic arguments: (a) human development of a country should be benchmarked against best practice countries and (b) the weights of the component indices should be directly derived by the data themselves. DEA10–12 is the leading technique for measuring the relative efficiency of decision-making units on the basis of multiple inputs and outputs. The efficiency of a unit is defined as the weighted sum of its outputs divided by a weighted sum of its inputs and it is measured on a bounded ratio scale. The weights for inputs and outputs are estimated by a linear program in the best advantage for each unit so as to maximize its relative efficiency. Basically, DEA provides a categorical classification of the units into efficient and inefficient ones by assuming either constant10 or variable11 returns to scale for the inputs and outputs. DEA is currently used in various fields to measure the performance of diverse entities, considered as decision-making units. Recent works include, among others, the programming approach to the construction of a child quality of life (CQL) index across developing countries,13 the investigation of the role of knowledge management in the performance of

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intersectoral R&D projects,14 the measurement of educational performance,15 the consideration of service quality factors in measuring bank performance,16 the investigation of the effect of gender on the compensation for senior executives,17 the measurement of productivity growth of IT industries in countries of the OECD18 and the assessment of development in Asia and The Pacific.19 In this paper, the assessment of the HDI is reconsidered in the light of data envelopment analysis. Instead of a simple rank of the countries according to the HDI, human development is benchmarked on the basis of empirical observations of best practice countries. The paper is organized as follows: In the next, section we outline the calculation method for deriving the HDI in its latest form. Next, we revisit Mahlberg and Obersteiner’s formulations and, on the same line as HDI, we develop a simplified indexmaximizing model to assess the relative performance of the countries in terms of human development. Then we extend our formulation with a post-DEA model to derive global estimates of a new development index, comparable with the HDI, by using optimal common weights for the socioeconomic indicators. Further, we introduce the transformation paradigm in the assessment of human development. We consider income as an instrument for human development rather than an end in itself. With this line of thinking, we develop a DEA model to estimate the relative efficiency of the countries in converting income to knowledge and life opportunities. The paper ends with some concluding remarks.

The human development index The HDI is a composite index calculated on the basis of three socioeconomic indicators that reflect three major dimensions of human development: longevity, educational attainment and standard of living. Longevity is measured by life expectancy at birth (ie the average number of years a person is expected to live from the time of his/her birth). Educational attainment is measured by a weighted average of the adult literacy rate and the combined — primary, secondary and tertiary — gross educational enrolment ratios. An adjusted GDP per capita, converted into US dollars on the basis of the purchasing power parity exchange rate (PPP USD), is used as a measure of a decent standard of living. For the components of the HDI, except of the GDP per capita, individual indices are calculated according to the general linear transformation: 0

index ¼

country s actual value  fixed minimum value fixed maximum value  fixed minimum value

The fixed minimum and maximum values are set as shown in Table 1. To construct the income index, the following non-linear transformation is applied on GDP per capita, taking into

Table 1

Fixed minimum and maximum values of the indicators

Life expectancy at birth (LEB) Adult literacy rate (ALR) Combined gross enrolment ratio (GER) GDP per capita (GDP)

Minimum value

Maximum value

25 years 0% 0%

85 years 100% 100%

USD 100

USD 40000

account diminishing returns of higher incomes (utility adjustment): income index ¼ logðcountry0 s actual GDP per capitaÞ  logðfixed minimum valueÞ logðfixed maximum valueÞ  logðfixed minimum valueÞ

The argument for the above utility adjustment in the income index is that achieving a decent standard of living does not require unlimited income.3 The way the HDI is derived by its components is illustrated in Figure 1. For the complete data and the indices for 174 countries, one can refer to the HDR 2000.3 The relative position of the countries in the HDI ranking can be attributed to two main reasons: one is structural and is related to the data themselves, the other is linked with the particular weighting scheme (equal weights) used in the HDI. As shown in Figure 2, for example, the upper group of the four countries (Oman, Lebanon, Jamaica and Azerbaijan) is structurally superior to the lower group (Mozambique, Burkina Faso, Sierra Leone and Niger) since every country in the first group dominates every country in the second group on all the component indices. Whatever the weights are for composing the HDI from its component indices, the countries of the first group will always be ranked at a higher position than the countries of the second group. Within the two groups, however, the rank of the countries depends strongly on the weights assumed in the HDI and could be reversed if another weighting scheme is selected.

A DEA-like approach to the HDI As discussed in the previous section, a critical issue in estimating the HDI is the fact that equal weights are assumed for its three component indices. Facing this issue, Mahlberg and Obersteiner9 introduced the idea of using the DEA approach to assess the relative performance of the countries in terms of human development, as this notion is defined and on the basis of the data given in the Human Development Report of 1998. In line with HDI, in which the

DK Despotis—A reassessment of the HDI 971

Dimensions of human development

Longevity

Indicators and data available

Component indices Life expectancy index

Life expectancy at birth (LEB)

LEI =

Adult literacy rate (ALR) Educational attainment

Standard of living

GDPI =

log (GDP) − log (100) log (40,000) − log (100)

Composition of the HDI.

1.0 Oman Lebanon Jamaica Azerbaijan Mozambique Burkina Faso

value of the composite index for each one of the countries. Then we extend our calculations through a goal-programming model to derive a new measure of human development. The estimation of this new development measure is made under the same assumptions as the original HDI, except that of the equal weights given to the three major component indices LEI, EDI and GDPI.

Sierra Leone

0.2

An index-maximizing model

Niger

0.0

LEI + EDI + GDPI 3

Adjusted GDP index

Figure 1

0.4

HDI =

2 ALR 1 GER EDI = + 3 100 3 100

GDP per capita (PPP USD)

0.6

LEB − 25 85 − 25

Educational attainment index

Combined gross enrolment ratio (GER)

0.8

Human development index (HDI)

LEI

Figure 2

EDI

GDPI

Countries of high and low HDI.

component indices are all considered to contribute positively to the HDI, the authors suggest an output-oriented DEA model by assuming constant returns-to-scale. In their model, all the individual indicators are considered as outputs and a dummy input (equal to one) is assumed for all the countries. Moreover, the weights are constrained to sum to unity. They observe that many countries achieve their DEA score by assigning extreme weights to the indicators (weight of 1 to one of the indicators and zero weights to the others). To avoid that, they introduce arbitrary bounds on the weight ratios to constrain the flexibility of the model in selecting the weights. Then they invert the DEA scores to make them comparable to the HDI. In the rest of this section, first we revisit Mahlberg and Obersteiner’s basic formulation to present a simplified indexmaximizing LP model, which we use to estimate an ideal

Let C be the set of the 174 countries of the study, jAC stand for any country in C and j0 stand for the evaluated country. Let also wLEI, wEDI and wGDPI be the unknown weights of the three indices LEI, EDI and GDPI, respectively. The linear model (1) below estimates the weights wLEI, wEDI and wGDPI that maximize the weighted sum of the three components of the HDI, for the evaluated country j0, and it is solved for one country at a time. The weighted sum of the component indices is constrained to be less or equal to one for all the countries. The infinitesimal e is introduced to assure that none of the weights will take a zero value. max hj0 ¼ wLEI LEIj0 þ wEDI EDIj0 þ wGDPI GDPIj0 s:t: wLEI LEIj þ wEDI EDIj þ wGDPI GDPIj p1; j 2 C

ð1Þ

wLEI ; wEDI ; wGDPI Xe Straightforwardly, model (1) is equivalent to an inputoriented, constant returns-to-scale DEA model with three outputs (LEI, EDI and GDPI) and one dummy input of 1

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for all the countries (similarly to the Mahlberg and Obersteiner’s formulation). Let hoj be the optimal value of the objective function when the model (1) is solved for country j. In accordance with the HDI, the values hoj (jAC) are bounded in the interval [0,1]. Countries that achieve a score of hoj ¼ 1 are in correspondence to the so-called ‘efficient units’ in the DEA terminology. Respectively, if the score is hoj o1, the country j might be considered as ‘inefficient’. However, ‘efficiency’ has no substantial meaning in this case, as no input dimension is considered in the above formulation and, thus, no kind of transformation of inputs to outputs is assumed. As hoj is based on positive outcomes in the maximization sense, countries that are dominated in all aspects by at least one other country are evidently classified as ‘inefficient’. Unlike the HDI, the above DEA-like approach to the assessment of human development is a relative measure. Each country is compared with ‘best practice’ countries when it assesses its composite performance on the human development indicators. The weights that each country selects during the optimization process to aggregate the individual indicators are in favour of that country. Thereby, countries that achieve a low-valued hoj in model (1) undoubtedly show a poor performance on human development, regardless of the weighting scheme used for aggregating the development indicators. The results obtained from the analysis are given in the Appendix. Due to space limitations, only some of the countries are displayed. The results of the complete set of countries are available on request. Out of the 174 countries, 11 achieve the highest possible DEA score of 1 (column 3). Of them 10 are among the 11 top-ranked countries according to the HDI. The 11th country with a score of 1 is Luxembourg, which is stepped up from the 17th HDI rank. This is not surprising as Luxembourg has the highest GDP per capita in the world, with a difference of 3900 USD from the second higher GDP per capita, that of the United States. Table 2 shows the frequencies with which the

‘efficient’ countries appear in the reference sets of the rest of the countries. In that particular view, Canada, the HDIrank-one country, justifies its position in the HDI ranking as it is used as reference for almost 65% of the ‘inefficient’ countries. One can use the above frequencies to discriminate and rank the 11 efficient countries and then rank the rest of the countries according to their DEA scores. The ranking, however, obtained in this manner is not directly comparable to the HDI ranking for one main reason: the HDI scores are obtained by assuming fixed weights (in fact equal weights) for the component indicators across all the countries, while each country selects its own weights to estimate its ideal score.

A fair assessment of the HDI based on common weights The DEA approach is meaningful in identifying the ‘inefficient’ countries. The DEA scores, however, cannot be used to rank the countries in terms of human development, given that the scores are not based on common weights. What we need therefore is a common set of weights for the three component indicators, fairly assessed across all the countries, in order to obtain global and, to some extent, incontestable scores, substitutes of the HDI. We proceed for this purpose to the estimation of common weights in a manner that the resulting efficiency scores (global scores) are as close as possible to the ideal scores. To discriminate further among the 11 countries that achieve a DEA score of 1, we deal only with ‘globally efficient’ countries. These are the countries that maintain their 100% efficiency score (ie hoj ¼ 1) under a common weighting structure. We suggest for this purpose the following model with parameter t (c.f. Despotis20 for more details): min

t

174 1 X dj þ ð1  tÞz 174 j¼1

s:t: wLEI LEIj þ wEDI EDIj þ wGDPI GDPIj þ dj ¼ hoj ; j 2 C Table 2

Number of times each efficient country is used as a reference

Country

Frequency

Canada Japan Australia Sweden Belgium United Kingdom Finland Luxembourg Norway United States Iceland

105 85 70 70 70 70 70 16 7 6 4

dj  zp0; j 2 C wLEI ; wEDI ; wGDPI Xe zX0; dj X0; j 2 C

ð2Þ

In the above model (2), two different norms are used to measure the distance between the given DEA scores and the global scores, which are to be estimated. The first term of the objective function, when considered solely for t ¼ 1, represents the mean deviation (the L1 norm) between the DEA scores and the adjusted global efficiency scores for all the countries. In this case, model (2) works as a non preemptive goal-programming model. The second term, when

DK Despotis—A reassessment of the HDI 973

considered solely for t ¼ 0, represents, through the nonnegative variable z, the maximal deviation (the LN norm) between the above efficiency scores and model (2) is reduced to a minmax goal-programming model. Varying the parameter t between these two extreme values, we provide the model with the flexibility to ‘compromise’ between the two norms and to explore different sets of common weights (and consequently different global efficiency patterns), beyond the extreme ones that minimize the maximal and the mean deviation, respectively. Once the different global efficiency patterns have been estimated, we can rank the DEA-efficient countries by the factor qj þ hj, where qj is the number of times a country j, with hoj ¼ 1, maintains its score under global assessments and  hj is its average global efficiency score. The results obtained by applying model (2) are given in the Appendix: columns 4– 6 provide the three different global efficiency patterns (GLE) obtained by three different sets of common weights, valid for distinct ranges of the parameter t equal in number. Next is the column with the average global efficiency scores (AVGLE) and then the column with the prioritization factor, which is used to rank the 11 DEA-efficient countries. Column 9 shows the differences between the HDI and the proposed GLE ranks. The two rankings are highly correlated (Kendall’s tau ¼ 0.881). Comparison of the HDI and the GLE rankings with the rankings induced on the countries by the component indices LEI, EDI and GDPI shows that the original HDI is mostly correlated with the income index GDPI (Kendall’s tau ¼ 0.806), while the GLE rank is mostly in accordance to the life expectancy index LEI (Kendall’s tau ¼ 0.840). The highest rank difference is (37), which causes the demotion of Qatar from the 42nd position (HDI) to the 79th position (AGLE). Table 3 lists the countries with the highest rank differences.

As shown in Figure 3, the rank differentials for the majority of the countries (69%) lie in the interval [7,7].

The transformation paradigm in assessing human development When assessing human development with the HDI, longevity, education and income are seen rather as goods in themselves than as means to other ends. Such a treatment is reasonable because these three variables, as they are used for the assessment of the HDI, express essential elements of

Countries with the highest rank differences (absolute difference X 20)

Table 3 Country

Fiji Oman Tajikistan Kuwait United Arab Emirates Botswana Russian Federation Cuba Brazil Saudi Arabia Seychelles Georgia Albania Saint Kitts and Nevis Azerbaijan Jamaica Sri Lanka Armenia Qatar

HDI rank

Rank difference

66 86 110 36 45 122 62 56 74 75 53 70 94 47 90 83 84 93 42

20 21 21 22 22 22 23 24 24 24 25 25 26 27 27 28 28 33 37

50 47

No. of Countries

40 39 34 30

20

10

10

9 7

6

5

6 3

4

13 - 18

23 - 28

0 -38 - -33

-28 - -23

-33 - -28

-18 - -13

-23 - -18

-8 - -3

-13 - -8

3-8 -3 - 3

8 - 13

18 - 23

33 - 38

28 - 33

Rank differential

Figure 3

Distribution of rank differential between the HDI and the AVGLE scores.

974 Journal of the Operational Research Society Vol. 56, No. 8

social prosperity. As far as it concerns the income, the utility adjusted GDP index places emphasis on the basic income needed to acquire essential goods and services such as food, clothes and shelter. This justifies to some extent the fact that income is also seen in the HDI as a good in its self. As mentioned in the Human Development Report3 of 2000, however, the link between economic prosperity and human development is neither automatic nor obvious. Indeed, there are countries, such as India and Armenia, with similar incomes that show considerable differentiation in the other two dimensions of human development: educational attainment and life expectancy (the figures for GDP per capita, life expectancy and educational attainment are, respectively, 2077, 62.9 and 55.13 for India and 2072, 70.7 and 89.47 for Armenia). At the same time, there are countries (Brazil and Uzbekistan, for example) that achieve similar levels of education and life expectancy, although they start from different incomes (the corresponding figures are 6625, 67.1 and 84.33 for Brazil and 2053, 67.8 and 84.33 for Uzbekistan). This observation suggests that the countries convert income to human development less or more effectively. The capability of the countries to convert economic prosperity into better lives for their people could be modelled and assessed if income is viewed as a means to improve the potential of people, beyond the achievement of a decent standard of living. As mentioned in Raab et al,13 increasing incomes correlate positively with the direct provision of public services. Higher average incomes are linked directly to the financing of public services, including education and health services. This is the transformation approach to human development that, in the HDI context, puts income in the input side and educational attainment and life expectancy in the output side. Unlike the HDI, where income is discounted to reflect only the ‘basic-commodities’ dimension, we use the real GDP per capita in our input– output paradigm to reflect the development of peoples’ abilities to access the resources needed to acquire knowledge as well as to develop life opportunities through access to enhanced health services.3 In the context given above, we suggest the following variable returns-to-scale DEA model (3) to assess the relative

Table 4 High income countries

Mean Stand. Dev. Variance Minimum Maximum

performance of the countries, letting both technical and scale efficiencies be accounted. max s:t:

ej0 ¼ wLEI LEIj0 þ wEDI EDIj0  u0

wGDPI GDPIj0 ¼ 1 wLEI LEIj þ wEDI EDIj  wGDPI GDPIj  u0 p0; j 2 C ð3Þ

wLEI ; wEDI ; wGDPI Xe; u0 free in sign

Recall here that in model (3), C denotes the set of the countries studied; jAC stands for any country in C and j0 stands for the evaluated country. The unknown weights of the indices LEI, EDI and GDPI are denoted by wLEI, wEDI and wGDPI respectively. Let eoj be the optimal value of the objective function when the model (3) is solved for country j. The countries that achieve a score eoj ¼ 1 are efficient. Efficiency assessments are carried out first within the whole set of countries (universal model) and then separately in three country groups. The groups are formed on the basis of World Bank classification of countries in income aggregates (high, middle and low GNP3). The statistics of the three groups are given in Table 4. The DEA scores obtained with model (3) by performing universal as well as intra-groups assessments are given in the Appendix, in columns 11–13. Of the 174 countries, 97 rank higher on the HDI than on GDP per capita. The almost empirical statement, provided in the HDR, that these countries have converted income into human development effectively, receive an almost causal interpretation in our transformation approach. All universally efficient countries belong in the above group of the 97 countries. The group’s average efficiency is 0.688, with standard deviation of 0.226 and median 0.667. This group clearly differentiates from the group of 72 countries that rank lower on HDI than on GDP per capita. The latter group’s average efficiency is 0.344, with a standard deviation 0.160 and median 0.311. The transformation approach introduced in this section provides the instrument to unfold development issues that cannot be seen with the original HDI. Take, for example, Italy and New Zealand. They are two of the most developed countries in the world (both within OECD) that are not discriminated by the HDI (both achieve the same score over

Statistics of income aggregates Middle income countries

Low income countries

GDP

LEI

EDI

GDP

LEI

EDI

GDP

LEI

EDI

0.526 0.111 0.012 0.347 0.837

0.870 0.027 0.001 0.782 0.917

0.924 0.072 0.005 0.731 0.993

0.143 0.071 0.005 0.029 0.335

0.733 0.105 0.011 0.353 0.858

0.811 0.110 0.012 0.481 0.950

0.032 0.016 0.000 0.009 0.075

0.497 0.160 0.025 0.215 0.782

0.554 0.192 0.036 0.148 0.900

DK Despotis—A reassessment of the HDI 975

the HDI). Contrarily to Italy, however, New Zealand proved to be efficient in translating income to social development and this finding is clearly supported by the figures themselves (see Table 5). The AVGLE scores achieved by the indexmaximizing model also confirm this differentiation of the two countries. Another characteristic example is that of the Philippines and Ukraine. Both are countries with low income that achieve the same HDI value. However, only Ukraine is proved to be efficient, both universally as well as within the group of low-income countries. Moreover, Ukraine is one of the reference countries of Philippines, when efficiency is assessed universally. It is the nature of the transformation approach that allows for a better discrimination among the countries, which then might be seen as an origin for further investigation of development issues by which the differentiations are eventually prompted.

High-income countries Canada, Sweden, Japan, United Kingdom, New Zealand, Spain, Greece and Slovenia are the eight out of the 34 highincome countries that are proved to be efficient in transforming economic prosperity into social development, when evaluated within the group. All of them but Slovenia remain efficient under universal assessments also. Another seven countries (Australia, Iceland, Belgium, Finland, Switzerland, Italy and Hong Kong, China) maintain their efficiency score when moving from group to universal assessments. These countries maintain also their reference sets (the countries against which they are benchmarked) in both types of efficiency assessments, as their reference countries are within the group (see Table 6). This suggests that the relative performance of 14 high-income countries (all mentioned above but Slovenia) is not affected by the grouping in income aggregates. The rest of the countries of the group show a decrement in their relative performance score when evaluated universally, with the decrement varying from 0.11% (Norway) to 84.08% (Qatar). Additionally, one might notice that the extra-group country that is most frequently used as a benchmark for the inefficient

Table 5

high-income countries, when efficiency is assessed universally, is Cuba. The country that draws the attention again is Luxembourg. Luxembourg is the HDI-rank 17 country that is raised to the 11th position by the index-maximizing model and GLE assessment presented in the previous section. This can be justified by the GDP per capita of this country, which is the highest in the world. However, this advantage of Luxembourg turns into its disadvantage, when assessing its efficiency according to the input-output paradigm. Indeed, Luxembourg has the lowest efficiency score (0.414) in the group of high-income countries and loses 42.04% of it when its performance is assessed universally.

Low-income countries Azerbaijan, Armenia, Tajikistan, Solomon Islands, Yemen, Tanzania, Malawi and Sierra Leone are efficient with respect to both universal and intra-group assessments. All the inefficient countries, except Turkmenistan, attain the same DEA score and have exactly the same reference countries, all within the group, in both types of assessments (see Table 7). This suggests that the low-income countries form a solid group of countries whose relative performance in converting income to human development is not affected by their income classification.

Middle-income countries Barbados (1), Rep. of Korea (3), Poland (4), Estonia (6), Costa Rica (0), Dominica (1), Cuba (10), Georgia (18), Ukraine (14), Jamaica (3), Sri Lanka (18), Albania (21), South Africa (12), Uzbekistan (48) and Djibouti (13) are the 15 out of the 81 countries of the group — followed by their frequency in appearing in reference sets — that have proved to be efficient in intra-group assessments. However, only five of them — Estonia (5), Cuba (31), Georgia (14), Ukraine (13) and Jamaica (21) — maintain their efficiency when they are evaluated universally.

Couples of countries with the same HDI value but with different efficiency scores

Life expectancy at birth

Adult literacy rate

Combined primary, secondary and tertiary gross enrolment ratio

GDP per capita

Italy New Zealand

78.3 77.1

98.3 99.0

83 96

Philippines Ukraine

68.6 69.1

94.8 99.0

Indonesia Viet Nam

65.6 67.8

85.7 92.9

Country

HDI

VRS DEA scrores (Universal model)

VRS DEA scores (intra-roup)

AVGLE

20585 17288

0.903 0.903

0.742 1.000

0.742 1.000

0.968 0.972

83 78

3555 3194

0.744 0.744

0.666 1.000

0.843 1.000

0.847 0.857

65 63

2651 1689

0.671 0.671

0.342 0.631

0.342 0.631

0.766 0.807

976 Journal of the Operational Research Society Vol. 56, No. 8

Table 6

Reference sets in universal (U) and group (C) assessments for the high-income countries United New Extra-group Canada Sweden Japan Kingdom Zealand Spain Greece Slovenia reference countries

Norway United States Australia Iceland Belgium Netherlands Finland France Switzerland Germany Denmark Austria Luxembourg Ireland Italy Cyprus Israel Singapore Hong Kong, China (SAR) Malta Portugal Slovenia Brunei Darussalam Bahamas Kuwait Qatar

U/C U/C U/C

U/C U/C

C C

Cuba Cuba, Georgia

U/C U/C

U/C U/C U/C U/C

U/C U/C

C C

U/C U

U U/C U

U

U/C U/C

U/C

United Arab Emirates

Unlike the low-income and, to some extent, the highincome groups, the middle-income countries show a considerable variation in their efficiency performance when moving from intra-group to universal assessments. This variation is extended to the composition of the reference sets as well: Belarus and the Russian Federation are the only countries of the group with a pure intra-group reference set (actually the same set, consisting of Estonia and Ukraine). All the other inefficient countries of the group, when evaluated universally, are linked with at least one reference country outside the group, from both the high-income and the low-income groups. More than half of the inefficient countries (51.3%) are linked with pure extra-group reference sets, all consisting of low-income countries, namely, Azerbaijan, Armenia, Tajikistan, Solomon Islands, Yemen, Tanzania and Malawi. The high-income countries that are used as benchmarks by the middle-income countries are Sweden, New Zealand, Spain and Greece.

Concluding remarks The human development index is revisited in the light of data envelopment analysis. A new measure of human

U U

Estonia U/C U/C C C C C U/C U

Cuba U/C C C U/C U/C U/C U/C U/C U/C U/C C C C U/C C C

C

Cuba Estonia, Ukraine Cuba Cuba Cuba, Georgia Cuba Cuba Cuba

C

Cuba Cuba, Georgia Cuba, Georgia Cuba, Jamaica Cuba, Jamaica, Armenia Cuba Jamaica, Armenia, Solomon Islands Jamaica

development is proposed that is obtained with a two-phase process. All the assumptions underlying the HDI are kept except that of the equal-weights scheme for the three major indicators. First, an ideal value of the composite human development index is estimated for each country by a DEAlike index-maximizing model. Then in a second stage, a goalprogramming model is solved to obtain global estimates of human development, based on optimal common weights for the component indicators. The new measure of human development is comparable and highly correlated with the HDI. The superiority of the new measure, however, is based on the fact that the weights assumed for the component indicators, as a result of an optimization process, are less arbitrary and contestable. The transformation paradigm is also introduced in this paper to assess the relative efficiency of the countries in translating income to social prosperity. The real GDP per capita is used in this case as input in a variable returns-toscale DEA model with educational attainment and life expectancy as outputs. The impact of the utility adjustment of the income on the efficiency performance of the countries has also been examined. Performing intra-group efficiency assessments with the utility adjusted GDP per capita as input showed

DK Despotis—A reassessment of the HDI 977

Table 7

Reference sets in universal (U) and group (C) assessments for the low-income countries Azerbaijan Armenia Tajikistan Solomon Yemen Tanzania, Malawi Sierra Extra-group Islands U. Rep. Of Leone reference countries

Kyrgyzstan China Turkmenistan C Moldova, Rep. of U/C Vietnam Indonesia Honduras Nicaragua Mongolia Myanmar Lesotho India Ghana Zimbabwe Sa˜o Tome´ and Principe Cameroon Pakistan Cambodia Comoros Kenya Congo Lao People’s Dem. Rep. Madagascar Bhutan Sudan Nepal Togo Bangladesh Mauritania Haiti Nigeria Congo, Dem. Rep. Of the Zambia Coˆte d’Ivoire Senegal Benin Uganda Eritrea Angola Gambia Guinea Rwanda Mali Central African Republic Chad Mozambique Guinea-Bissau Burundi Ethiopia Burkina Faso Niger

U/C U/C U/C

U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C

U/C U/C Ukraine U/C U/C U/C U/C

U/C U/C

U/C

U/C U/C U/C U/C

U/C U/C U/C

U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C

U/C U/C U/C U/C

U/C U/C

U/C U/C U/C U/C U/C U/C U/C U/C U/C

U/C

that there is a constant improvement of the efficiency scores across all the high- and low-income inefficient countries (see Figure 4a and c) and no change in the composition of the set of efficient countries. The situation is a little bit different in the group of middle-income countries (see Figure 4b). The irregularity observed in the set of the efficient countries

U/C

U/C U/C U/C U/C

U/C

U/C

U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C

U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C U/C

is caused by Poland, Dominica and South Africa, which become inefficient when the adjusted GDP is taken as input. The income aggregates might be also used to perform, for example, regional assessments of efficiency performance but it is beyond the scope of this paper.

978 Journal of the Operational Research Society Vol. 56, No. 8

Efficiency scores -intra group assessments

a

1.2 1.0 0.8 0.6 0.4

Efficiency scores-intra group assessments

real GDP

0.2 0.0

b

adjusted GDP

High-income countries

1.2 1.0

adjusted GDP

0.8 0.6 0.4 real GDP 0.2 0.0 Middle-income countries

Efficiency scores-intra group assessments

c

1.2 1.0

adjusted GDP

0.8 0.6 0.4 0.2 0.0

real GDP Low-income countries

Figure 4 Differentiation in efficiencies between adjusted and real GDP. (a) High-income countries, (b) middle-income countries and (c) low-income countries.

4 Noorbakhsh F (1998). A modified Human Development Index. World Dev 26: 517–528. 5 Sagar AD and Najam A (1998). The human development index: a critical review. Ecol Econ 25: 249–264. 6 Neumayer E (2001). The human development index — a constructive proposal. Ecol Econ 39: 101–114. 7 Desai M (1991). Human development: concepts and measurement. Eur Econ Rev 35: 350–357. 8 Kelly AC (1991). The human development index: ‘handle with care’. Population Dev Rev 17: 315–324. 9 Mahlberg B and Obersteiner M (2001). Remeasuring the HDI by data envelopment analysis. International Institute for Applied Systems Analysis (IIASA), Interim Report IR-01-069, Laxemburg, Austria. 10 Charnes A, Cooper WW and Rhodes E (1978). Measuring the efficiency of decision making units. Eur J Opl Res 2: 429–444. 11 Banker RD, Charnes A and Cooper WW (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Mngt Sci 30: 1078–1092. 12 Cooper WW, Seiford LM and Tone K (1999). Data Envelopment Analysis. Kluwer Academic Publishers: Boston. 13 Raab R, Kotamraju P and Haag S (2000). Efficient provision of child quality of life in less developed countries: conventional development indexes versus a programming approach to development indexes. Socio-Econ Plann Sci 34: 51–67. 14 Revilla E, Sarkis J and Modrego A (2003). Evaluating performance of public–private research collaborations: a DEA analysis. J Opl Res Soc 54: 165–174. 15 Mayston DJ (2003). Measuring and managing educational performance. J Opl Res Soc 54: 679–691. 16 Mukherjee A, Nath P and Pal M (2003). Resource, service quality and performance triad: a framework for measuring efficiency of banking services. J Opl Res Soc 54: 723–735. 17 Bowlin WF, Renner CJ and Rives JM (2003). A DEA study of gender equity in executive compensation. J Opl Res Soc 54: 751–757. 18 Shao BBM and Shu WS (2004). Productivity breakdown of the information and computing technology industries across countries. J Opl Res Soc 55: 23–33. 19 Despotis DK (2004). Measuring human development via data envelopment analysis: The case of Asia and The Pacific. Omega. Int J Mngt Sci (in press). 20 Despotis DK (2002). Improving the discriminating power of DEA: focus on globally efficient units. J Opl Res Soc 53: 314–323.

Received June 2003; accepted October 2004 after two revisions

References 1 Hicks N and Streeten P (1979). Indicators of development: the search for a basic needs yardstic. World Dev 7: 567–580. 2 Streeten P et al. (1981). First Things First: Meeting Basic Needs in Developing Countries. Oxford University Press: New York. 3 UNDP (2000). Human Development Report 2000. United Nations Development Program, Oxford University Press: New York.

Appendix Results obtained by the index-maximizing model and the transformation approach: top 20 countries in the HDI rank plus the intra-group efficient countries

HDI rank

Country (2)

1 2 3 4 5 6 7 8 9 10

Canada Norway United States Australia Iceland Sweden Belgium Netherlands Japan United Kingdom Finland France Switzerland Germany Denmark Austria Luxembourg Ireland Italy New Zealand Spain Greece Slovenia Barbados

11 12 13 14 15 16 17 18 19 20 21 25 29 30

Group

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.997 1.000 1.000

1.000 0.988 0.971 0.994 0.978 0.997 0.987 0.990 0.976 0.987

1.000 0.986 0.963 0.989 0.990 0.995 0.976 0.984 0.999 0.976

1.000 0.986 0.963 0.989 0.991 0.994 0.975 0.984 1.000 0.975

1.000 0.987 0.966 0.991 0.986 0.995 0.979 0.986 0.992 0.979

4.000 0.987 0.966 0.991 0.986 0.995 0.979

0 3 7 0 1 3 0 4 7 2

HI HI HI HI HI HI HI HI HI HI

1.000 0.719 0.545 0.916 0.803 1.000 0.875 0.889 1.000 1.000

1.000 0.720 0.569 0.916 0.803 1.000 0.875 0.890 1.000 1.000

0.00 0.11 4.20 0.00 0.00 0.00 0.00 0.09 0.00 0.00

1.000 0.982 0.996 0.976 0.986 0.976 1.000 0.974 0.975 0.987 0.978 0.968 0.936 0.944

0.985 0.979 0.956 0.967 0.961 0.957 0.920 0.964 0.957 0.977 0.974 0.946 0.929 0.932

0.971 0.982 0.977 0.967 0.948 0.960 0.941 0.958 0.973 0.969 0.978 0.967 0.922 0.943

0.971 0.982 0.978 0.967 0.947 0.960 0.942 0.958 0.974 0.969 0.978 0.968 0.922 0.944

0.976 0.981 0.970 0.967 0.952 0.959 0.934 0.960 0.968 0.972 0.977 0.960 0.924 0.940

0.976

2 1 3 4 9 5 6 2 2 5 7 6 2 5

HI HI HI HI HI HI HI HI HI HI HI HI HI MI

0.975 0.812 0.654 0.673 0.614 0.561 0.240 0.683 0.742 1.000 1.000 1.000 0.605 0.679

0.975 0.813 0.654 0.723 0.687 0.661 0.414 0.756 0.742 1.000 1.000 1.000 1.000 1.000

0.00 0.09 0.00 6.92 10.63 15.03 42.04 9.62 0.00 0.00 0.00 0.00 39.52 32.13

1.992 0.979

0.934

DK Despotis—A reassessment of the HDI 979

(1)

DEA score

GLE_2 t ¼ 0.991-0.995 GLE_1 GLE_3 Prioritization t ¼ 0.0-0.990 wLEI ¼ 0.815 t ¼ 0.996-1.0 factor for HDI wLEI ¼ 0.433 wEDI ¼ 0.267 wLEI ¼ 0.834 DEA efficient rank–GLE wEDI ¼ 0.613 wGDPI ¼ 0.043 wEDI ¼ 0.250 rank wGDPI ¼ 0.032 wGDPI ¼ 0.002 AVGLE countries

Reduction of DEA score when going from group to VRS DEA VRS DEA universal scores scores efficiency (universal (intraassessment group) model) (%)

31 44 46 48 51 56 70 78 83 84 90 93 94 103 106 110 121 148 149 156 163 174

Country Korea, Rep. of Poland Estonia Costa Rica Dominica Cuba Georgia Ukraine Jamaica Sri Lanka Azerbaijan Armenia Albania South Africa Uzbekistan Tajikistan Solomon Islands Yemen Djibouti Tanzania, U. Rep. of Malawi Sierra Leone

DEA score

Group

0.956 0.930 0.953 0.931 0.927 0.927 0.906 0.926 0.909 0.878 0.906 0.901 0.871 0.887 0.849 0.896 0.853

0.926 0.911 0.898 0.894 0.904 0.910 0.898 0.883 0.842 0.856 0.878 0.879 0.828 0.744 0.826 0.853 0.686

0.900 0.894 0.850 0.924 0.926 0.927 0.891 0.845 0.888 0.877 0.853 0.860 0.861 0.618 0.806 0.815 0.788

0.899 0.894 0.848 0.925 0.927 0.927 0.890 0.843 0.890 0.878 0.852 0.859 0.862 0.612 0.805 0.813 0.793

0.908 0.900 0.866 0.914 0.919 0.921 0.893 0.857 0.873 0.870 0.861 0.866 0.850 0.658 0.813 0.827 0.756

7 2 15 13 18 24 25 13 28 28 27 33 26 18 12 21 8

MI MI MI MI MI MI MI MI MI MI LI LI MI MI MI LI LI

0.740 0.831 1.000 0.939 0.939 1.000 1.000 1.000 1.000 0.962 1.000 1.000 0.947 0.110 0.513 1.000 1.000

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

26.01 16.92 0.00 6.07 6.07 0.00 0.00 0.00 0.00 3.85 0.00 0.00 5.33 89.01 48.68 0.00 0.00

0.609 0.489 0.605

0.522 0.484 0.534

0.577 0.480 0.471

0.580 0.480 0.468

0.560 0.481 0.491

10 4 6

LI MI LI

1.000 0.382 1.000

1.000 1.000 1.000

0.00 61.80 0.00

0.642 0.289

0.496 0.269

0.367 0.252

0.361 0.251

0.408 0.257

3 0

LI LI

1.000 1.000

1.000 1.000

0.00 0.00

HI ¼ high income (GNP per capita of $9,361 or more); MI ¼ middle income (GNP per capita $761–$9,360); LI ¼ low income (GNP per capita $760 or less). Values for GNP per capita are for the year 1998.

980 Journal of the Operational Research Society Vol. 56, No. 8

HDI rank

GLE_2 GLE_1 GLE_3 t ¼ 0.991-0.995 Prioritization t ¼ 0.0-0.990 wLEI ¼ 0.815 t ¼ 0.996-1.0 factor for HDI wLEI ¼ 0.433 wEDI ¼ 0.267 wLEI ¼ 0.834 DEA efficient rank–GLE wEDI ¼ 0.613 wGDPI ¼ 0.043 wEDI ¼ 0.250 rank wGDPI ¼ 0.032 wGDPI ¼ 0.002 AVGLE countries

Reduction of DEA score when going from group to VRS DEA VRS DEA universal scores scores efficiency (universal (intraassessment group) model) (%)