Human Development Index: a non-compensatory assessment

HUMAN DEVELOPMENT INDEX: A NON-COMPENSATORY ASSESSMENT Sebastián Lozano Segura1 Ester Gutiérrez Moya2 INTRODUCTION In 1990, the United Nations Development Programme (UNDP) introduced the Human Development Index (HDI) as a summary measure of Human Development (HD) on three basic dimensions, namely longevity, knowledge and standard of living. An index is computed for each of these three dimensions and a simple average computed. Since its conception, the HDI has been the focus of a public debate. Apart from other criticism (e.g. Srinivasan 1994), some scholars have called it redundant in the sense that HDI is generally highly correlated with its component indexes (see e.g. McGillivray 1991, Srinivasan 1994 and Cahill 2005). Other researchers (e.g. Trabold-Nübler 1991, Lüchters and Menkhoff 1996) have shown so- 1PhD. in Industrial Engineering, University of Seville, Spain. Degree in Industrial Engineering from the University of Seville, Spain. Professor of Quantitative Methods in Management in the Department of Management at the University of Seville, Spain. E-mail: [email protected]. Address: Camino de los Descubrimientos s/n, 41092-Seville (Spain). 2PhD. in Economics, University of Seville, Spain. Master Science in Statistics, University of Seville, Spain. Degree in Business Management and Administration, University of Seville, Spain. Degree in Statistics, University of Seville, Spain. Associate professor in the Department of Management at University of Seville, Spain. E.mail: eg[email protected]. Address: Camino de los Descubrimientos s/n, 41092-Seville (Spain). This article was received on April 22, 2008 and his publication approved on April 17, 2009. 223 224 Cuadernos de Economía, 28(50), 2009 me undesirable consequences of the way some components are derived, thus leading UNDP to refine the HDI along the years to correct those flaws. Morse (2003) presents a summary of the evolution in the calculation of the HDI. It is not the aim of this paper to discuss the choice of capabilities included in the HDI. An important issue is that the aggregation of the component indices forces the specification of tradeoffs between the various HDI dimensions (Kelley 1991). The index allows attainments in any one of the three dimensions to be traded off against another (Ravallion 1997). In fact, the equal weighting of the component indexes suggests a perfect substitution between them and therefore implicit trade-offs between the corresponding dimensions (Desai 1991). He suggests the use of a log additive formula as a way of restricting substitutability. Along the same lines, Sagar and Najam (1998) propose a Reformed HDI that, instead of averaging the component indexes, multiplies them so that a high value of the HDI would require high values of the three component indexes simultaneously. However, as recognized in Hopkins (1991) there is no a priori rationale that allows one to add life expectancy to literacy. Most researchers ha- ve however maintained the additivity of the component indices, including those such as the Modified HDI (Noorbakhsh 1998a) and the Rescaled New HDI (Mazumdar 2003) that use Euclidean vector distance. Not all approaches, however, have maintained the equal weighting of the components. Thus, Noorbakhsh (1998b) use weights derived from the data using Principal Component Analysis, while the Data Envelopment Analysis approach in Despotis (2005a, 2005b) and more recently Lozano and Gutiérrez (2008) determine different weights for each country so that it appears under the best possible light. In this paper, we propose an explicit Non-Compensatory (NC) criterion that is based on the assumption that the achievements in one dimension cannot compensate an underachievement in another. In this way the simplicity of HDI of providing a single figure from a reduced number of component indicators is maintained. However, “the task of specification must relate to the underlying motivation of the exercise as well as dealing with the social values involved” (Sen 1989). Thus, the philosophical principle emphasized in NCHDI is that of the inalienability of the inherent rights to human development in all its different dimensions. This concept is especially important since the measures of deprivation considered in HDI correspond to basic human needs that can foreclose many other capabilities. On the one hand, averaging, in a weighted or unweighted way, implies an implicit con- Human Development Index Sebastián Lozano y Ester Gutiérrez 225 doning of part of these deprivations, most importantly, those that are most acute. On the other hand, the non-compensatory principle is consistent with the non-commensurability of the diverse aspects of development. On these ethical and practical grounds is based our proposal for a non-compensatory assessment of the HDI. Note that we are not rejecting the possibility or convenience of devising a composite, aggregate measure of human development. Our objections are against the usual ways of carrying out such aggregation. The structure of this paper is the following. In section 2, after detailing the calculation of HDI, the NCHDI is introduced and discussed. Section 3 presents the results of the NCHDI vis-à-vis HDI for the data of the last five years. The last section summarizes and concludes. NON-COMPENSATORY HDI The three component indexes of the HDI (life expectancy index, education index and GDP per capita index) are computed based on four indicators: Life Expectancy at Birth (LEB) indicator, ranging from 25 to 85 years Adult Literacy Rate (ALR), ranging from 0 to 100 Combined primary, secondary and tertiary Gross Enrolment Ratio (GER), ranging from 0 to 100 Logarithm of the Gross Domestic Product (LGDP) per capita in US Dollars purchasing power parity, ranging from log(USD100) to log(USD40000) The corresponding Life Expectancy Index (XLE) is computed as: XLE =LEB −25 85 −25 The Adult Literacy Index (XAL), computed as: XAL =ALR −0 100 −0 is combined (with respective weights 2/3and 1/3) with the corresponding Gross Enrolment Index (XGE): XGE =GER −0 100 −0 giving the Education Index (XE): XE =2 3·XAL +1 3·XGE 226 Cuadernos de Economía, 28(50), 2009 Finally, the GDP per capita Index (XGDP): XGDP =LGDP −log(100) log(40000) −log(100) allows the HDI to be computed as the simple average of the three component indices: HDI =1 3·XLE +1 3·XE +1 3·XGDP The NC approach we propose does not allow for any trade off (neither explicit nor implicit) between the different HDI dimensions. All of them are considered basic and inalienable. Neither adding nor multiplying the component indices nor any similar way of introducing compensatory effects between them is considered admissible. A suitable NCHDI index may be computed as the minimum of the component indices, i.e. NCHDI = m´ın{XLE, XE, XGDP } This index corresponds to one minus the Tchebycheff distance between the vector of component indices and the Ideal Point (1,1,1). This Ideal Point represents attaining the maximum values of the goalposts of the different HDI dimensions. The distance to such a reference point may represent a measure of the lack of attainment of these goals. But instead of using rectangular distance (a.k.a. l1metric) as HDI does, or Euclidean distance (a.k.a. l2metric) as the Modified HDI or Rescaled New HDI do, we propose using Tchebycheff distance (a.k.a. l∞metric) which does not require additivity and is NC. The Tchebycheff distance between two vectors is equal to the maximum of the absolute value of the component-wise difference between both vectors. Thus, NCHDI = 1 − |(1,1,1) −(XLE, XE, XGDP )|∞ = 1 −m´ax{1−XLE, 1−XE, 1−XGDP} = 1 −(1 −m´ın{XLE, XE, XGDP}) = m´ın{XLE, XE, XGDP} This minimum criterion is used in Multiple Attribute Decision Making (e.g. Yoon and Hwang 1995, p. 28) and reflects a pessimistic evaluation approach that scores an alternative according to its worst performance among the different criteria. Similarly, NCHDI scores each country according to its lowest level of goal achievement. This way of assessing the HDI sends a clear signal to each country about where its priority should be. It also makes explicit that none of the HDI dimensions (a long and healthy life, knowledge and a decent standard of living) may be left behind. All of them are considered equally important and desirable. For those countries that have unbalanced component indices, the NCHDI provides an Human Development Index Sebastián Lozano y Ester Gutiérrez 227 incentive to improve the lagging dimension. We consider this ability of NCHDI to identify the most largely unmet needs rather useful. In addition, NCHDI’s maximin structure is analogous, mutis mutandis, to the difference principle in Rawls’ Theory of Justice (Rawls 1971). Thus, the improvements in some dimensions of the HDI are not worth much if they are not accompanied by parallel improvements in the worst off dimensions. In other words, according to NCHDI, improving the most neglected dimension of human development has a higher priority than improving those better off. In this sense, it can be said that NCHDI implicitly establishes priorities but in a dynamic, non-parametric and socially just way. It is trivial to prove the following two properties: a. NCHDI ≤HDI b. NCHDI =HDI if and only if XLE =XE =XGDP = NCHDI =HDI Three additional considerations are in order. First, that the NC criterion has a clear drawback, which is that not all improvements in the component indices translate into improvements in the NC-HDI, i.e. it can happen that a country may improve one component while its NC-HDI may not improve. This happens whenever the lowest component index does not improve. Although this lack of monotonicity is an undesirable feature, it is unavoidable and intrinsic to its NC character. The second remark is that NCHDI selects one of three component indices, discarding the other two. This is not equivalent to the approaches (such as Ogwang 1994, Ogwang and Abdou 2003) that propose to use just one of the component indices to compute the HDI. The difference lies in that which of the three components is selected is not fixed but can change from one country to another. Finally, the same as the HDI, the proposed NCHDI can be used not only at the national level but also at the regional or local level, thus helping to detect the specific and more urgent problems in each geographical area. ANALYSIS AND DISCUSSION OF RESULTS The proposed NCHDI has been computed for the HDI 2000 through HDI 2004 contained in the Human Development Reports (HDR) of the latest five years (i.e. HDR 2002 through HDR 2006 respectively). Table 1 shows the Pearson’s correlation coefficient between NCHDI and HDI for the five years. It can be seen that there is a significantly strong but not 228 Cuadernos de Economía, 28(50), 2009 perfect linear relationship between both indices. This can also be seen in Figure 1, which shows a scatter plot of HDI versus NCHDI for year 2004. The graphs for the other four years are similar and are not shown to save space. Note that, as expected, all points fall below the diagonal, which corresponds to NCHDI=HDI. The closer a point is to the diagonal, the more balanced are the corresponding HDI component indices and, on the contrary, the farther from the diagonal, the more unbalanced the HDI component indices. Figure 2 shows, for year 2004, the distribution of the difference between the maximum and the minimum HDI components as well as that of the difference between the average component index (i.e. the HDI) and the minimum component index (i.e. the NCHDI). Note that the imbalance in the HDI component indices can be important in some cases and that such imbalance is generally reflected in a larger HDINCHDI difference. TABLE 1. PEARSON’S CORRELATION COEFFICIENT BETWEEN HDI ANDNCHDI. ALL CORRELATIONS SIGNIFICANT AT THE 0.01 LEVEL (TWO-TAILED) 2004 2003 2002 2001 2000 rt0.950 0.948 0.953 0.934 0.954 Source: HDR 2006, 2005, 2004, 2003, 2002. FIGURE 1. SCATTER PLOT SHOWING NCHDI 2004 VERSUS HDI 2004 Source: HDR 2006. NCHDI highlights the need to improve in those HDI dimensions that fare worst for each country. HDI, on the contrary, can mask underperformance of a certain dimension with a good performance in another, thus Human Development Index Sebastián Lozano y Ester Gutiérrez 229 in a certain sense hiding or de-emphasizing the problem. Take the case of Botswana, for example. In 2004, its HDI has been a low but seemingly “reasonable” value 0.570 that makes it in position 131 out of 177 in the HDI ranking. This relatively high HDI is the average of two high components XE = 0.777 and XGDP = 0.768 and a worrisomely low value XLE = 0.165. The latter is the one that NCHDI takes and corresponds to next to last position in NCHDI ranking. Our claim is that the relatively high GDP per capita and enrollment and literacy rates of Botswana cannot compensate its dramatic 34.9 years of Life Expectancy at Birth. This is why we believe that the proposed NCHDI is more valid the HDI, i.e. because it gives a clearer picture of the real situation of Human Development. FIGURE 2. DISTRIBUTION OF THE DIFFERENCES BETWEEN HDI COMPONENTS FOR YEAR 2004. Source: HDR 2006. Since, as Booysen (2002) argues, composite indices such as the HDI have an ordinal nature (insofar as the magnitude of the differences between the index values for two countries cannot be interpreted meaningfully), we have carried out the non-parametric Mann-Whitney rank sum test to see if the rankings derived from HDI and NCHDI belong to the same distribution. Table 2 shows the corresponding Ustatistic and p-value for each of the five years. Since in all cases the statistic is significant at 0.01 level, the null hypothesis that the ranking given by HDI and NCHDI are similar is rejected, i.e. the NCHDI leads to a different ranking from that of the HDI. Whether the NCHDI ranking is more or less valid than that of HDI depends on whether the NC criterion is adopted or not. 230 Cuadernos de Economía, 28(50), 2009 TABLE 2. MANN WHITNEY’S U TEST BETWEEN HDI AND NCHDI. IN ALL FICE YEARS THE STATISTIC IS SIGNIFICANT AT THE 0.01 LEVEL 2004 2003 2002 2001 2000 U 11663 11548.5 11442.5 11146.5 11108.5 p-value 0.000 0.000 0.000 0.000 0.000 Source: HDR 2006, 2005, 2004, 2003, 2002. Figure 3 shows, for the year 2004, the histogram showing the distribution of the rank difference between and NCHDI. Its apparent normality (with zero mean and a standard deviation of 12.9) is confirmed, at a 0.01 significance level, by a Kolmogorov-Smirnov-Lilliefors normality test. The same normality behavior happens (with similar means and standard deviations) for the other four years. FIGURE 3. DISTRIBUTION OF RANK DIFFERENCES BETWEEN HDI AND NCHDI FOR YEAR 2004 Source: HDR 2006. Figure 4 plots HDI and NCHDI versus Cumulative Global Population for year 2004. The HDI graph results from ordering the countries in decreasing order of HDI and accumulating their population in that order. The same is done for the NCHDI graph. Note that, since , the NCHDI graph is always below that of HDI and this implies that NCHDI presents a bleaker picture of global HD than the more optimistic HDI. Think that the horizontal line HDI =NCHDI = 1 corresponds to the Ideal Point given by the UNDP goalposts. Therefore, the lower the graph, the clearer Human Development Index Sebastián Lozano y Ester Gutiérrez 231 is the work that has still to be done to bring the HD of the world population up to those goalposts. FIGURE 4. HDI AND NCHDI VERSUS CUMULATIVE GLOBAL POPULATION FOR YEAR 2004 Source: HDR 2006. Table 3 shows how many times each of the three HDI component indices gives the minimum that determines the value of the NCHDI. Note that the XGDP component has lagged behind in more than 50 % of the cases, XLE in more than 35 % of the cases and XE in only 10 % of the cases. This seems to indicate that half of the countries should concentrate on improving the economic well being of their citizens, another significant number of countries should concentrate in improving their health and life expectancy and only a minority should worry most about the educational level of the population. Although the distribution was fairly stable for four years it seems that in year 2004 there was an increase in the number of countries with minimum value of XLE at the expense of component XGDP . This seems to imply that for some countries the XGDP improved enough to stop being lower than XLEB. This type of reasoning, however, must be made with caution since if the difference between the HDI component indices of a country is small then a small differential improvement may be enough for changing the component that is the minimum. It may also happen that both components decrease but one decreases less than the other by an amount enough to stop being the minimum. Therefore, the changes in the HDI component indices must be analyzed on a case-by- case basis. What NCHDI does, with respect to HDI, is to increase the visibility and individual importance of the component indices, a visibility and an importance that are highly diminished after the additive aggregation process performed by the HDI.