Estelar 2.2 COMPONENT-WISE REVIEW COMPONENT OF LONGEVITY COMPONENT OF EDUCATIONAL ATTAINMENT COMPONENT OF INCOME

CHAPTER-II THE EVOLUTION OF HUMAN DEVELOPMENT INDEX 2.1 AN OVERVIEW OF HDR-METHODOLOGY 2.1.1 PERIOD FROM 1990 TILL 1993- A NASCENT PHASE 2.1.2 HDR 1994- A STEPPING STONE FOR CURRENT METHODOLOGY 2.1.3 CRUCIAL SIGNIFICANCE FOR HDR 1995 2.1.4 PHASE OF STABILIZED METHODOLOGY IN HDRs: DURING 1995 TO 1998 2.1.5 METHODOLOGY IN HDR FROM 1999- A CIRCUMLOCUTORY APPROACH 2.2 COMPONENT-WISE REVIEW 2.2.1 COMPONENT OF LONGEVITY 2.2.2 COMPONENT OF EDUCATIONAL ATTAINMENT 2.2.3 COMPONENT OF INCOME

17 CHAPTER-II THE EVOLUTION OF HUMAN DEVELOPMENT INDEX 2.1 AN OVERVIEW OF HDR- METHODOLOGY While aiming at the human-centered development through widening of the people s options to lead a long and healthy life, to be knowledgeable, and to maintain a descent standard of living, it needs to be appreciated that there is no automatic link between the level of per capita GDP in a country and the level of its human development. In the wake of limitations of income alone as a comprehensive yardstick for measurement of human development, people therefore, started looking beyond figures of growth rate in GDP and emergence of composite indices of well-beings and standard of living index began to appear initially as Physical Quality of Life Index (PQLI) and Basic Needs Approach etc. before advent of the concept of Human Development Index (HDI) in early Nineties. Co-terminus with the growth rate in GDP, the quality of life thus also began to be regarded as an important aspect of human development. Keeping in view longevity, education and income as the most important capabilities affecting wellbeing of the people at large, the UNDP in its HDRs accordingly dogmatized adoption of life expectancy, educational attainment and real GDP per capita income in PPP$ for the purpose of framing the HDI as the simple (unweighted) average of the values of measurement indicators for life expectancy at birth, educational attainment and the adjusted GDP per capita.

18 The HDI assumes vast significance by virtue of its coverage of important disciplines of people s quality of life rather than only material well-being. One may easily measure and compare spatial and time-series progress in human development amongst different countries. The HDI commands adequate popularity due to its transparency, being simple to construct and easy to comprehend. Nevertheless, it remained under variety of conceptual and rudimentary criticisms especially during first decade of its existence. The meaning and usefulness of HDI, according to Allen C. Kelley (1991), can be assessed on two grounds, viz. the extent to which it is based on an appropriate conceptual framework and is properly measured and the extent to which it provides new or modified insights into development. Pal and Pant (1993) critically assessed the methodology in HDR. McGillivray and White (1993) proposed improvements in the HDI in terms of its weighting system, composition and comparability. Michael Hopkins (1991) had examined the issues associated with the HDI from operational point of view. Meghnad Desai (1991) argued that the equal weighting system for all the three components of the HDI was not strictly true since the income variable happened to be truncated and then concavified. The problem of implicit weights concealed by the explicit equal weights has drawn adequate attention of the researcher all over the globe. Various possible options have been tried out in the literature- for instance establishing weights by: a social welfare function, a priori assumptions, taking Geometric Mean of the measures of deprivation indicators rather than Arithmetic Mean, regression coefficients besides Principal Components Analysis (PCA) using the variance of linear combinations of the components to determine potential weights and BORDA method ranks in which the ranks for the three components of the HDI are

19 added together, with new sums of the ranks then becoming the composite index s values and re-ranking of the countries done thereafter in descending order according to this composite index. Biswas and Caliendo (2001) also using the PCA method arrived at nearly equal weights for the three components Life Expectancy Index (34 percent), Education Index (34 percent) and GDP Index (32 percent). Earlier, Noorkbakhsh (1998) compared several different methods of arriving at a composite index using the HDI data, including the arithmetic mean, PCA and BORDA methods and found that the ranks for all methods are very similar. Since the changed approaches for construction of HDI don t cause significant differences in the ranking pattern of the countries, with the values of Spearman Rank Correlation Coefficients also turning out to be very high, it provides ample justification for approach of UNDP s methodology experts in considering un-weighted simple average of the constituent-indicators for framing the HDI. Stimulating criticisms and debates for improvements of the HDI were attempted from all over the world. One may refer to the details of work by Dasgupta et.als (1992), Chowdhury (1991), Bhanoji Rao (1991), Paul Streeten (1993), Tilak (1992), Srinivasan (1994), McGillivray (1991), Srinivasan and Verma (1993), Sagar and Najam (1998) and Mukherjee (1993). The overall methodology for computation of the HDI has undergone a drastic change over the period of Nineties. While longevity has throughout been measured by life expectancy at birth as the sole unadjusted indicator, the methodology for arriving at the HDI has seen several modifications in respect of the other two components of educational attainment and income ever since the first HDR in 1990 was brought out. Bhatnagar (2001-a) has comprehensively reviewed the methodology followed in the Human Development Reports of UNDP from inception

20 particularly with reference to the treatment given to the income component in computation of the Human Development Index for various countries. Let us consider four variables defined as follows: X 1 = Life expectancy at birth X 2 = Adult literacy rate X 3 = Percentage of combined gross enrolment ratios X 4u = Unadjusted Real GDP per capita (PPP$) X 4 = Adjusted or Discounted Real GDP per capita (PPP$) Let X ij denote the value of i th variable (i =1, 2, 3, 4) as delineated above in respect of the j th country belonging to the UNDP s HDR under consideration. Further, let us further denote by Max X ij and Min X ij the fixed maximum and minimum values corresponding to the variable X i (i=1, 2, 3, 4). Two sets of indicators viz., deprivation indicator and measurement indicator for the three different components viz., longevity, educational attainment and income have been referred to in the Literature relating to methodological aspects in the computation of the HDI. The computation of the HDI in various HDRs from 1990 to 1993 dwelled on the concept of deprivation indicator which in the case of i th variable for the j th country was defined as D ij = (Max X ij - X ij )/ (Max X ij -Min X ij ). Latter HDRs shifted the concept from deprivation indicator to another nomenclature namely, the measurement indicator which corresponding to the i th variable for the j th country has been defined as I ij = (X ij -Min X ij )/ (Max X ij -Min X ij ). Evidently, these two indicators are related to each other, being complementary to each other. Let I ej represent the value of a synthetic indicator for the j th country obtained by pooling the measure indicators corresponding to the adult literacy rate and the combined gross enrolment ratios through the algebraic

21 relation I ej = [{2(I 2j )+1(I 3j )}/3]; implying inter-alia that the aspect of knowledge in the HDI is presently measured as a synthetic combination of the adult literacy rate with the combined enrolment primary, secondary and tertiary ratios by taking their respective indices together after assigning them weights of two-third and one-third respectively. This synthetic combination is called educational attainment indicator. In the initial phase, more precisely from 1991 to 1994, the index of mean years of schooling was considered instead of the index of combined gross enrolment ratios, although the weighting system was the same i.e., the index of adult literacy rate in 2/3 rd proportion was combined with 1/3 rd proportion of mean years of schooling for arriving at the educational attainment indicator. As regards the income component, the HDR 1990 while working on the premise of diminishing returns of income for human development adopted logarithmic values of income level as the adjusted values for real GDP per capita in the construction of the HDI, giving zero weights to the incomes above the poverty line set out. The utility function of income variable in HDR 1990 was adopted as W (y)=logy, for 0<y y * and W(y)=logy *, for y y *, where y * denotes the threshold income level. Beyond the threshold income level, the phenomenon of diminishing marginal returns of income gets impeded. In HDR 1991, the UNDP deviated from its earlier approach and coined a fresh multi-step utility function with Atkinson s formulation as the radix. The well-known Atkinson's formulation (1970) widely used in Economic literature on Inequality is as follows: (2.1) W (y)=y (1- ) /(1- ) 0 <1

22 The HDR 1991 termed W (y) as the utility or well-being derived from the income level "y" with " " as the parameter measuring the extent of diminishing returns. Consider the full range of income segmented into smaller ranges as (0 to y * ), (y * to 2y * ), (2y * to 3y * ) and so on, with (n+1) th range represented as ny * to (n+1)y *, where y * stands for threshold income level. By using equation (2.1), the Atkinson based multi-step utility function was for the first time introduced in the HDR 1991 as follows (2.2A) W(y)=y, for 0<y y * (2.2B) W(y)=y * +2(y-y * ) 1/2, for y * <y 2y * (2.2C) W(y)=y * +2(y * ) 1/2 +3(y-2y * ) 1/3, for 2y * <y 3y * (2.2D) W(y)=y * +2(y * ) 1/2 +3(y * ) 1/3 +4(y-3y * ) 1/4, for 3y * <y 4y * (2.2E) W(y)=y * +2(y * ) 1/2 +3(y * ) 1/3 +4(y * ) 1/4 +5(y-4y * ) 1/5, for 4y * <y 5y * (2.2F) W(y)=y * +2(y * ) 1/2 +3(y * ) 1/3 +4(y * ) 1/4 +.+n{y-(n-1)y * } 1/n, for (n-1)y * <y ny * (2.2G) W(y)=y * +2(y * ) 1/2 +3(y * ) 1/3 +4(y * ) 1/4 +.+(n+1)(y-ny * ) 1/(n+1), for ny * <y (n+1)y * y * was christened as the threshold income level. In order to discount or adjust all those levels of the income which were more than the threshold income level, the above formulation for utility of income remained in use from 1991 to 1998 with minor modifications in the maximum and minimum values of threshold income on a worldwide basis. We have taken a closer look at Atkinson based formulation of multi-step utility function, which had been adopted by the UNDP in all its HDRs from 1991 to 1998 with a view

23 to discount or adjust the real GDP per capita incomes, which exceeded the threshold level. The HDR 1991 proceeded with the poverty line set at 4829 (PPP$). In the HDRs for 1992 and 1993 also the same level of poverty line income was utilized. In the HDRs for 1994 and 1995, the world average income of 5120 (PPP$) in 1992 was adopted as the threshold level. In the HDR 1996 the threshold level was taken as 5711(PPP$) which happened to be the world's average income in 1993. Again, in the HDR 1997 the world's average income (in 1994) of 5835 (PPP$) was treated as threshold level. In the HDR of 1998, the threshold income level had been taken as 5990 (PPP$), which was the 1995 s world average income. Let us re-designate for the sake of more comprehension the indicator corresponding to the life expectancy at birth as I Lj and that corresponding to adjusted income as I AIj for the j th country. Clearly, I 1j =I Lj and I 4j = I AIj. The HDI for any j th country in the HDR would be obtained as the simple average of I Lj, I ej and I AIj. The measurement indicator I AIj for any j th country used to be then worked out by appropriately using Atkinson based multi-step utility function (2.2A) to (2.2G) by first computing: (a) Max X 4j and Min X 4j as the adjusted values corresponding to (b) the overall Maximum and Minimum values for real GDP per capita as adopted by the UNDP in HDR; X 4j as the adjusted value corresponding to the real GDP per capita level for the j th country. According to Equation (2.2A), there would be no need to consider any adjustment or discounting in the values of real per capita GDP if they were below the threshold income level. However, discounting was carried out for those values of real GDP per capita which were higher than the threshold

24 income level by using the equations (2.2B) to (2.2G) depending upon the range segment within which they fell. The overall Minimum level for real GDP per capita being always less than the threshold income level, Min X 4j was obtained without any adjustment or discounting. The computed values of X 4j, Max X 4j and Min X 4j were used in the basic definition of indicator to obtain I AIj for the j th country. The evolution of UNDP methodology in HDR for the sake of computing HDI has passed through several milestones, which can be identified with the four major phases, namely, (i) Period during 1990 to 1993, (ii) Year 1994, (iii) Period during 1995 to 1998 and (iv) 1999 & onwards. Bhatnagar (2001-b) has demonstrated an analytical comparison amongst the approaches for computations of the HDI in various HDRs belonging to the different phases, while drawing a particular reference to India. 2.1.1 PERIOD FROM 1990 TILL 1993 - A NASCENT PHASE As the first report in the series brought out by the UNDP, the HDR 1990 resorted first to the computation of deprivation indicators for all the three components of longevity, educational attainment and income and defined HDI for any country as the magnitude of difference of the average deprivation index of all the components for any country from unity. While the deprivation index for the component of educational attainment was measured solely on the basis of adult literacy rate, the HDR 1990 had used life expectancy at birth for computing the deprivation index for the component of longevity. The logarithmic value of real GDP per capita was used in the HDR 1990 for computing the adjusted value in order to work out

25 the deprivation index in respect of the component of income, although with no diminishing returns on income. The maximum and minimum values for the components involved in the computation of HDI for various countries in the HDR 1990 depended on their extreme performance levels rather than on normative fixed values. The maximum and minimum values adopted by UNDP in the HDR 1990 were 78.4 years and 41.8 years respectively for the component of life expectancy at birth. The corresponding maximum and minimum values in the HDR 1990 were taken as 100% and 0% respectively for the component of adult literacy rate. We can observe the methodology of HDR 1990 through illustrative computation for any single country say India. TABLE 2.1 Computation of HDI for India in HDR 1990 Slno Description Data 1 India s life expectancy at birth 59 years 2 Maximum of all countries life expectancy at birth 78.4 years 3 Minimum of all countries life expectancy at birth 41.8 years 4 Deprivation index for life expectancy at birth for India ={(78.4-59)/(78.4-41.8)} 0.53 5 India's literacy rate 43% 6 Maximum of all countries' literacy rate 100% 7 Minimum of all countries' literacy rate 12.3% 8 Deprivation index for adult literacy rate in India 0.650 = {(100-43)/(100-12.3)} 9 India's real GDP per capita (as logarithmic value) =log 10 (1053) 3.02 10 Maximum log value of all countries' real GDP per capita 3.68

26 11 Minimum log value of all countries' real GDP per capita 2.34 12 Deprivation index for GDP per capita for India 0.493 = {(3.68-3.02)/(3.68-2.34)} 13 Average deprivation index for India ={(0.493+0.650+0.53)/3} 0.558 14 HDI for India in the HDR 1990 =(1-0.558) 0.442 In the HDR 1991, the maximum and minimum values in respect of life expectancy at birth were slightly changed from HDR 1990. The HDR 1991 for the first time introduced a concept of diminishing returns of income by defining a multi-step utility function based on Atkinson s formulation in lieu of logarithmic function of real GDP per capita. The maximum and minimum values of the real GDP per capita after applying adjustments through the utility function were accordingly worked out for the best and the worst performing countries, based on their observed past actual performance. An additional dimension of mean years of schooling was also introduced in the HDR 1991 to be considered along with adult literacy for the first time. The maximum and minimum values for the various variables involved in the HDR 1991 were as follows: TABLE 2.2 Maximum and Minimum values adopted by the HDR 1991 Slno Description Data 1 Maximum value of all countries life expectancy at birth 78.6 years 2 Minimum value of all countries life expectancy at birth 42 years 3 Maximum value for educational attainment 70.1 4 Minimum value for educational attainment 9.1 5 Maximum value for adjusted real GDP per capita 5070 PPP$ 6 Minimum value for adjusted real GDP per capita 350 PPP$

27 The HDI methodology adopted in HDR 1991 can be observed through the illustrated computation for India. TABLE 2.3 Computation of HDI for India in HDR 1991 Slno Description Data 1 India s life expectancy at birth 59.1 years 2 Deprivation index for life expectancy at birth for India 0.533 ={(78.6-59.1)/(78.6-42)} 3 India's literacy rate 44.1% 4 India s mean years of schooling 2.2 years 5 India s educational attainment == [{2(44.1)+2.2}/3] 6 Deprivation index for educational attainment in India = {(70.1-30.1)/(70.1-9.1)} 30.1 0.655 7 India's real GDP per capita 870 PPP$ 8 Deprivation index for GDP per capita for India 0.889 = {(5070-870)/(5070-350)} 9 Average deprivation index for India ={(0.533+0.655+0.889)/3} 0.692 10 HDI for India in the HDR 1991 0.308 For the country whose national performance level has been taken as maximum or minimum value for any component of the HDI, the value of corresponding deprivation indicator for that country would turn out to be zero while rest of the two deprivation indicators would continue to be computed as usual. We observe this part of the methodology adopted in HDR 1991 through an example of the computation of the HDI for Japan.

28 TABLE 2.4 Computation of HDI for Japan in HDR 1991 Slno Description Data 1 Japan s life expectancy at birth 78.6 years 2 Deprivation index for life expectancy at birth for Japan 0 ={(78.6-78.6)/(78.6-42)} 3 Japan's literacy rate 99% 4 Japan s mean years of schooling 10.4 years 5 Japan s educational attainment 69.466 = [{2(99)+10.4}/3] 6 Deprivation index for educational attainment in Japan 0.010 = {(70.1-69.466)/(70.1-9.1)} 7 Japan's real GDP per capita 5016 PPP$ 8 Deprivation index for GDP per capita for Japan 0.011 = {(5070-5016)/(5070-350)} 9 Average deprivation index for India =(0+0.010+0.011)/3} 0.007 10 HDI for Japan in the HDR 1991 0.993 The maximum and minimum values in the HDR 1992 for life expectancy at birth, adult literacy rate and mean years of schooling continued to be taken as the actually observed maximum and minimum values for these variables amongst the countries corresponding to their performance during earlier time period. The HDR 1992 decided to adopt the maximum and minimum values in respect of real GDP per capita on the basis of 1989's data. The Atkinson based multi-step formulation of utility function was utilized similar to HDR 1991 for discounting the levels of real GDP per capita which were above the threshold income level. The HDR 1992 used the data pertaining to 1990 for arriving at the corresponding maximum and minimum values in respect of life expectancy at birth, adult literacy rate and mean years of schooling.

29 The maximum and minimum values for the various variables involved in the HDR 1992 were as follows: TABLE 2.5 Maximum and Minimum values adopted by the HDR 1992 Slno Description Data 1 Maximum value of all countries life expectancy at birth 78.6 years 2 Minimum value of all countries life expectancy at birth 42 years 3 Maximum value of all countries adult literacy rate 99% 4 Minimum value of all countries adult literacy rate 18.2% 5 Maximum value of all countries mean years of schooling 12.3 years 6 Minimum value of all countries mean years of schooling 0.1 years 7 Maximum value for educational attainment 3.0 8 Minimum value for educational attainment 0 9 Maximum value for adjusted real GDP per capita 5079 PPP$ 10 Minimum value for adjusted real GDP per capita 380 PPP$ Taking illustrative case of computing the HDI for India, the methodology adopted in HDR 1992 can be observed as follows. TABLE 2.6 Computation of HDI for India in HDR 1992 Slno Description Data 1 India s life expectancy at birth 59.1 years 2 Deprivation index for life expectancy at birth for India 0.533 ={(78.6-59.1)/(78.6-42)} 3 India's literacy rate 48.2% 4 Deprivation index for adult literacy rate for India 0.629 ={(99-48.2)/(99-18.2)} 5 Measurement index for adult literacy rate for India =(1-0.629) 0.371

30 6 India s mean years of schooling 2.4 years 7 Deprivation index for mean years of schooling for India 0.811 ={(12.3-2.4)/(12.3-0.1)} 8 Measurement index for mean years of schooling for India 0.189 =(1-0.811) 9 India s educational attainment index 0.931 == [{2(0.371)+(0.189)}/3] 10 Deprivation index for educational attainment in India 0.690 = {(3.0-0.931)/(3.0-0} 11 India's real GDP per capita 910 PPP$ 12 Deprivation index for GDP per capita for India 0.887 = {(5079-910)/(5079-380)} 13 Average deprivation index for India ={(0.533+0.690+0.887)/3} 0.703 14 HDI for India in the HDR 1992 =(1-0.703) 0.297 In HDR 1992, Canada was the topper in the tally of countries arranged in the descending order of their HDI values. Similar to the HDR 1991, for the country whose national performance level had been taken as maximum or minimum value for any component of the HDI, the value of corresponding deprivation indicator turned out to be zero while rest of the two deprivation indicators for it were computed as usual. We observe this aspect again with the illustrative computation of the HDI for Canada. TABLE 2.7 Computation of HDI for Canada in HDR 1992 Slno Description Data 1 Canada s life expectancy at birth 77 years 2 Deprivation index for life expectancy at birth for Canada 0.044 ={(78.6-77)/(78.6-42)} 3 Canada's literacy rate 99% 4 Deprivation index for adult literacy rate for Canada ={(99-99)/(99-18.2)} 0

31 5 Measurement index for adult literacy rate for Canada 1 6 Canada s mean years of schooling 12.1 years 7 Deprivation index for mean years of schooling for India 0.016 ={(12.3-12.1)/(12.3-0.1)} 8 Measurement index for mean years of schooling for Canada 0.984 =(1-0.016) 9 Canada s educational attainment index 2.984 == [{2(1)+(0.984)}/3] 10 Deprivation index for educational attainment in Canada 0.005 = {(3.0-2.984)/(3.0-0} 11 Canada's real GDP per capita 17616PPP$ 12 Canada s adjusted real GDP per capita 5051 PPP$ 13 Deprivation index for GDP per capita for Canada 0.006 = {(5079-5051)/(5079-380)} 14 Average deprivation index for Canada ={(0.044+0.005+0.006)/3} 0.018 15 HDI for Canada in the HDR 1992 =(1-0.018) 0.982 The measurement of educational attainment in HDR 1993 was based on adult literacy rate and mean years of schooling after assigning a weight of two-thirds to the index of adult literacy rate and a weight of one-third to the index of mean years of schooling. The maximum value for educational attainment index in respect of all countries was taken as 3.00 and the minimum value was zero itself on the basis of performance of various countries. The deprivation index in respect of educational attainment corresponding to any country in HDR 1993 was defined as the ratio of difference of the computed value of educational attainment for the country from 3 to the difference between the maximum and minimum fixed values for educational attainment. If for any country (say j), the computed value of educational attainment was X Ej, the deprivation index in respect of educational attainment for the j th country would be

32 (2.3) D Ej = (3-X Ej )/3 where X Ej for the j th country was computed as (2.4) X Ej = {2(index of adult literacy rate)+1(index of mean years of schooling)} The maximum and minimum values for the various variables involved in the HDR 1993 were as follows. TABLE 2.8 Maximum and Minimum values adopted by the HDR 1993 Slno Description Data 1 Maximum value of all countries life expectancy at birth 78.6 years 2 Minimum value of all countries life expectancy at birth 42 years 3 Maximum value of all countries adult literacy rate 99% 4 Minimum value of all countries adult literacy rate 18.2% 5 Maximum value of all countries mean years of schooling 12.3 years 6 Minimum value of all countries mean years of schooling 0.1 years 7 Maximum value for educational attainment 3.0 8 Minimum value for educational attainment 0 9 Maximum value for adjusted real GDP per capita 5075 PPP$ 10 Minimum value for adjusted real GDP per capita 367 PPP$ Evidently, the maximum and minimum values in the HDR 1993 were identical to those of HDR 1992 except for the component of adjusted income, which differed both in terms of the maximum and minimum values.

33 The index of adult literacy rate for any j th country covered in the HDR 1993 would be first computed by taking difference of observed value of adult literacy rate from 99 and then dividing this difference by the difference between 99 and 18.2. Similarly the index of mean years of schooling for the same country would be next computed by taking difference of the observed value of the mean years of schooling from 12.3 and then dividing this difference by the difference between 12.3 and 0.1. Substituting the values of indices of the adult literacy rate and the mean years of schooling thus obtained the value of X Ej and D Ej were computed from equation (2.4) and (2.3) respectively. The deprivation index for the life expectancy at birth for the j th country in HDR 1993 was calculated as (2.5) D Lj =(78.6-X Lj )/(78.6-42) X Lj in above relation stands for the observed value of life expectancy at birth for the j th country. In order to compute the deprivation index for the income variable, the threshold income level in the HDR 1993 was taken as 4829 (PPP$). Any value of real GDP per capita for a country higher than the threshold level was discounted using Atkinson based formulation of multi-step utility function as delineated at (2.2A) to (2.2G), in order to obtain the adjusted value for real GDP per capita. The deprivation index for real GDP per capita in HDR 1993 was computed as (2.6) D AIj = (5075-X AIj )/(5075-367)

34 X AIj in Equation (2.6) stands for observed adjusted value for real GDP per capita for the j th country. The average deprivation index for the j th country was then obtained as (2.7) D j = {D Ej + D Lj + D AIj }/3 computed as The value of HDI for the j th country in HDR 1993 was finally (2.8) (HDI) j =(1-D j ) In HDR 1993, India s real GDP per capita was less than the threshold income while Japan had topped the list of countries in accordance with magnitude of the HDI values. We, therefore, observe the computational steps for HDI in the HDR 1993 with the help of illustrative example firstly for India as follows. TABLE 2.9 Computation of HDI for India in HDR 1993 Slno Description Data 1 India s life expectancy at birth 59.1 years 2 Deprivation index for life expectancy at birth for India 0.533 ={(78.6-59.1)/(78.6-42)} 3 India's literacy rate 48.2% 4 Deprivation index for adult literacy rate for India 0.629 ={(99-48.2)/(99-18.2)} 5 Measurement index for adult literacy rate for India 0.371 =(1-0.629) 6 India s mean years of schooling 2.4 years

35 7 Deprivation index for mean years of schooling for India 0.811 ={(12.3-2.4)/(12.3-0.1)} 8 Measurement index for mean years of schooling for India (1-0.811) 0.189 9 India s educational attainment index 0.931 == [{2(0.371)+(0.189)}/3] 10 Deprivation index for educational attainment in India 0.690 = {(3.0-0.931)/(3.0-0} 11 India's real GDP per capita 1072 PPP$ 12 Deprivation index for GDP per capita for India 0.85 = {(5075-1072)/(5075-367)} 13 Average deprivation index for India ={(0.533+0.690+0.85)/3} 0.691 14 HDI for India in the HDR 1992 =(1-0.691) 0.309 Nil value each for indices of deprivation for life expectancy at birth and adult literacy rate in respect of Japan would be obtained on account of the maximum values amongst all countries for both these variables emanating from Japan. We observe the computational steps for arriving at the HDI of Japan in the HDR 1993 as under. TABLE 2.10 Computation of HDI for Japan in HDR 1993 Slno Description Data 1 Japan s life expectancy at birth 78.6 years 2 Deprivation index for life expectancy at birth for Japan 0 ={(78.6-78.6)/(78.6-42)} 3 Japan's literacy rate 99% 4 Deprivation index for adult literacy rate for Japan 0 ={(99-99)/(99-18.2)} 5 Measurement index for adult literacy rate for Japan =(1-0) 1 6 Japan s mean years of schooling 12.1 years 7 Deprivation index for mean years of schooling for Japan ={(12.3-12.1)/(12.3-0.1)} 0.016

36 8 Measurement index for mean years of schooling for Japan 0.984 =(1-0.016) 9 Japan s educational attainment index= [{2(1)+(0.984)}/3] 2.984 10 Deprivation index for educational attainment in Japan 0.005 = {(3.0-2.984)/(3.0-0} 11 Japan s real GDP per capita 17616PPP$ 12 Japan's adjusted real GDP per capita 5049 PPP$ 13 Deprivation index for GDP per capita for Japan 0.006 = {(5075-5049)/(5075-367)} 14 Average deprivation index for Japan ={(0+0.005+0.006/3} 0.004 15 HDI for Japan in the HDR 1993 =(1-0.004) 0.996 A Bird s eye view of the methodology followed in the HDRs from 1990 to 1993 reveals commonality in the approach besides certain differing nodes. While HDR 1990 altogether lacked the fundamental concept of diminishing returns of income and accordingly had no built-in mechanism of discounting or adjusting the real GDP per capita income beyond any threshold level, a beginning was, however, made in HDR 1991 to provide for a multi-step formulation of Atkinson based utility function of real GDP per capita income, which was further continued also in HDR 1992 and HDR 1993 as a common approach. Another common feature in the methodological approach of the HDRs during 1990 to 1993 was that for each of these years there were no fixed normative values for maximum and minimum levels for various components involved in the computation of HDI for different countries and only their past actual extreme performance levels amongst all the countries covered under the HDR were regarded as the overall maximum and minimum values. Further, the HDRs of 1991, 1992 and 1993 utilized the same set of data on life expectancy at birth for arriving at the life expectancy deprivation indicator.

37 The maximum and fixed minimum values for the real GDP per capita in HDR 1993 were actually based on 1990 s data included in the Report. The approach in HDR 1992 was not much different from HDR 1993 except that the adjusted maximum and minimum values of real GDP per capita were taken as 5079 (PPP$) and 380 (PPP$) respectively in the HDR 1992 on the basis of 1989 data as differentiated from 5075 (PPP$) and 367 (PPP$) correspondingly in the HDR 1993. The same threshold income level of 4829 (PPP$) was adopted in both the HDRs for the purpose of computing the index of adjusted GDP per capita, after discounting the income levels above the threshold income level. The HDRs 1991 and 1992 too did differ on some counts. One of the major problems of the HDR 1991 arising due to conceptually incorrect combining of two different quantities namely, adult literacy rate (in percentage) with mean years of schooling (in number) was rectified by the UNDP in its subsequent HDR 1992. The weighted combination of adult literacy rate and mean years of schooling in the HDR 1991 was replaced with the weighted combination of the indices of adult literacy rate and the mean-years-of-schooling, both becoming unit free quantities in the HDR 1992 and thereby becoming amenable to algebraic operations. Thus during 1990 to 1993, the HDRs introduced the concept of diminishing returns of income, incorporated an additional dimension of mean years of schooling in the component of education and further modified weighted combination of adult literacy rate and mean years of schooling, treating them as indices to facilitate proper algebraic operation. These steady refinements clearly demonstrate that the beginning period was a nascent phase of methodology.

38 2.1.2 HDR 1994- A STEPPING STONE FOR CURRENT METHODOLOGY Commencing from 1991, HDR 1994 was the last Report which had used a weighted combination based on the mean years of schooling and the adult literacy rate for working out the educational attainment. Prior to the HDR 1994, the maximum and minimum values for these quantities were obtained as the actual extreme levels of past performance as observed for the countries. The HDR 1994 was a stepping stone because it was for the first time that fixed normative values were adopted for the maximum and minimum of life expectancy at birth, adult literacy rate, mean years of schooling and real GDP per capita for arriving at their respective indicators. The fixed maximum and minimum values adopted in HDR 1994 were as follows. TABLE 2.11 Fixed maximum & minimum values adopted in HDR 1994 Indicator Minimum Fixed Value Maximum Fixed Value 1. Life Expectancy at Birth 25 Years 85 Years 2. Adult Literacy Rate 0% 100% 3. Mean Years of Schooling 0 Year 15 Years 4. Real GDP per Capita 200 (PPP$) 40000 (PPP$) Corresponding to the maximum level of real GDP per capita at 40000 (PPP$), the discounted or adjusted value using the Atkinson based multistep utility function was worked out as 5385 (PPP$). However, the minimum value for real GDP per capita being less than the threshold income

39 level of 5120 PPP$ in HDR 1994, was not subjected to any discounting or adjustment. The indicators corresponding to the life expectancy at birth (say I Lj ), adult literacy rate (say I Aj ), mean years of schooling (say I Sj ) and adjusted real GDP per capita (say I AIj ) were calculated in the HDR 1994 as usual by defining each as the ratio of difference of the concerned variable from its normative fixed minimum value to the difference between its normative fixed maximum and minimum values. By pooling together indices of the adult literacy rate and the mean years of schooling in the proportion of 2/3 rd and 1/3 rd respectively, the measurement indicator for educational attainment was computed as I ej ={2(I Aj )+( I Sj )}/3. The value of HDI in the HDR 1994 for any j th country was computed as average of I Lj, I Ej and I AIj. We, first observe the computational methodology followed by the HDR 1994 in respect of the countries requiring no efforts of discounting of the real GDP per capita through an illustrative example of India, whose real GDP per capita was less than the threshold income level. TABLE 2.12 Computation of HDI for India in HDR 1994 Slno Description Data 1 India s life expectancy at birth 59.7 years 2 Indicator for life expectancy at birth for India 0.578 ={(59.7-25)/(85-25)} 3 India's literacy rate 49.8% 4 Indicator for adult literacy rate for India 0.498 ={(49.8-0)/(100-0)} 5 India s mean years of schooling 2.4 years 6 Indicator for mean years of schooling for India ={(2.4-0)/(15-0)} 0.16

40 7 India s educational attainment index 0.385 == [{2(0.498)+(0.16)}/3] 8 India's real GDP per capita 1150 PPP$ 9 Indicator for GDP per capita for India 0.183 = {(1150-200)/(5385-200)} 10 HDI for India ={(0.578+0.385+0.183)/3} 0.382 We, next look at the computational methodology in respect of the countries whose adjusted real GDP per capita turned out to be more than the threshold income level of 5120 PPP$ in HDR 1994, by taking an illustrative example of arriving at the HDI of Canada. TABLE 2.13 Computation of HDI for Canada in HDR 1994 Slno Description Data 1 Canada s life expectancy at birth 77.2 years 2 Indicator for life expectancy at birth for Canada 0.87 ={(77.2-25)/(85-25)} 3 Canada's literacy rate 99% 4 Indicator for adult literacy rate for Canada 0.99 ={(99-0)/(100-0)} 5 Canada s mean years of schooling 12.2 years 6 Indicator for mean years of schooling for Canada 0.813 ={(12.2-0)/(15-0)} 7 Canada s educational attainment index 0.931 == [{2(0.99)+(0.813)}/3] 8 Canada's real GDP per capita 19320PPP$ 9 Canada s Adjusted real GDP per capita 5347 PPP$ 10 Indicator for GDP per capita for Canada 0.993 = {(5347-200)/(5385-200)} 11 HDI for Canada ={(0.87+0.931+0.993)/3} 0.931

41 2.1.3 CRUCIAL SIGNIFICANCE FOR HDR 1995 The phase of refinement in the methodology for computation of the HDI picked up a few important changes with effect from HDR 1995, which included modifications in the components of educational attainment and the real GDP per capita income comprising HDI worked out in the HDR 1994. Prior to the HDR 1995, the indicator pertaining to educational attainment was calculated by combining the index of the mean years of schooling with the index of the adult literacy rate after associating 1/3 rd and 2/3 rd weights but from the HDR 1995, the component of mean years of schooling was replaced with a new component of combined primary, secondary and tertiary enrolment ratios. Further, the minimum (fixed) value of real GDP per capita income was reduced from 200 (PPP$) as used in the HDR 1994 to a level of 100 (PPP$) in the HDR 1995. In view of the above two significant changes, the HDR 1995 deserves a crucial significance in the process of development of UNDP s methodology for computation of the HDI, bridging the hiatus between the approach that existed in its HDR 1994 and what came up later as a change. 2.1.4 PHASE OF STABILIZED METHODOLOGY IN HDRs: DURING 1995 TO 1998 The overall methodology for computation of the HDI in the UNDP s HDR got stabilized during 1995 to 1998, utilizing the same four constituent components namely, the life expectancy at birth, the adult literacy, the combined gross enrolment ratios and the real GDP per capita. Their fixed minimum and maximum values, adopted by these HDRs, have also remained unchanged from 1995 to 1998. The fixed maximum and minimum values adopted in each HDR during 1995 to 1998 were as follows.

42 TABLE 2.14 Fixed maximum & minimum values adopted in HDRs during 1995 to 1998 Indicator Minimum Fixed Value Maximum Fixed Value 1. Life Expectancy at Birth 25 Years 85 Years 2. Adult Literacy Rate 0% 100% 3.Combined Gross Enrolment Ratios 0 Year 100% 4. Real GDP per Capita 100 (PPP$) 40000 (PPP$) As regards the component of income, the UNDP s methodology did not envisage any diminishing returns of income in terms of utility or welfare function for all values of real GDP per capita which were below the threshold income level y *. For subsequent ranges of income above y * there would exist the diminishing returns on income but the overall utility would rise slowly as the income level gradually increases. The methodology for computation of various indicators involved in the computation of the HDI remained the consistent during the period between 1995 to 1998 and the HDI was accordingly computed using the simple average of three measurement indicators of the life expectancy at birth, the educational attainment and the adjusted real GDP per capita, as usual. Adopting in the HDR 1995 the world s average income level of 5120 (PPP$) in 1992 as the threshold level y *, the values of the GDP per capita income levels above the threshold level in the HDR 1995 were discounted on the basis of Atkinson based formulation of utility function, by appropriately using equations (2.2A) to (2.2G).

43 The discounted value corresponding to fixed maximum income level of 40000 (PPP$) was obtained in the HDR 1995 by the following formula: (2.9) W(40000) = {(5120)+ 2x(5120) 1/2 + 3x(5120) 1/3 + 4x(5120) 1/4 + 5x(5120) 1/5 + 6x(5120) 1/6 + 7x(5120) 1/7 + 8x(40000-7x5120) 1/8 } = 5448 PPP$ Since fixed minimum value of 100 (PPP$) for the real GDP per capita was less than the value of y * (i.e., 5120 PPP$), there was no need to obtain the discounted value for it. One can accordingly write the following equations in the case of HDR 1995. (2.10A) (2.10B) Max X 4j = 5448 (PPP$) Min X 4j = 100 (PPP$) Thus, the indicator for adjusted real GDP per capita for any j th country (X 4j ) in the HDR 1995 was computed as (2.11) I AIj = (X 4j -100)/ (5448-100) No discounting of Real GDP per capita income was called for in respect of a country if it was less than the threshold income level of 5120 (PPP$) and in such a case the real GDP per capita was directly used for the computation of the relevant indicator of adjusted GDP per capita. In case the real GDP per capita income of any country happened to be more than the threshold income level, the Atkinson based multi-step utility

44 function was used to calculate the corresponding adjusted real GDP per capita and the same was subsequently used for obtaining the indicator of adjusted real GDP per capita. Let us consider below an illustrative case for the computation of India s HDI, in accordance with which India was placed under the category of Low Human Development in the HDR 1995 and in view of its real GDP per capita being less than the threshold income level, no adjusted real GDP per capita was required to be worked out for it. TABLE 2.15 Computation of HDI for India in HDR 1995 Slno Description Data 1 India s life expectancy at birth 60.4 years 2 Indicator for life expectancy at birth for India 0.59 ={(60.4-25)/(85-25)} 3 India's literacy rate 49.9% 4 Indicator for adult literacy rate for India 0.499 ={(49.9-0)/(100-0)} 5 India s combined gross enrolment ratios 55% 6 Indicator for combined gross enrolment ratios for India 0.55 ={(55-0)/(100-0)} 7 India s educational attainment index 0.516 == [{2(0.499)+(0.55)}/3] 8 India's real GDP per capita 1230 PPP$ 9 Indicator for GDP per capita for India 0.211 = {(1230-100)/(5448-100)} 10 HDI for India ={(0.59+0.516+0.211)/3} 0.439 For Canada, which was placed in the category of countries having High Human Development and topped the overall HDI ranking in the HDR 1995, the adjusted real GDP per capita was worked out using Atkinson

45 based multi-step utility function in view of its real GDP per capita income being higher than the threshold level. Since for Canada, the real GDP per capita fell between 20480 PPP$ and 25600 PPP$, hence Equation (2.2E) was applied to obtain its value of adjusted real GDP per capita through a mathematical expression namely, {5120+2x(5120) 1/2 +3x(5120) 1/3 + 4x(5120) 1/4 +5x(20520-4x5120) 1/5 } which was further simplified as 5359 (PPP$). Using the adjusted real GDP per capita value the corresponding indicator I AIj was computed using Equation (2.11). Various computational steps for arriving at the HDI for Canada can be seen as below. TABLE 2.16 Computation of HDI for Canada in HDR 1995 Slno Description Data 1 Canada s life expectancy at birth 77.4 years 2 Indicator for life expectancy at birth for Canada 0.873 ={(77.4-25)/(85-25)} 3 Canada's literacy rate 99% 4 Indicator for adult literacy rate for Canada 0.99 ={(99-0)/(100-0)} 5 Canada s combined gross enrolment ratios 100% 6 Indicator for combined gross enrolment ratios for India 1.00 ={(100-0)/(100-0)} 7 Canada s educational attainment index== [{2(0.99)+(1.00)}/3] 0.993 8 Canada's real GDP per capita 20520PPP$ 9 Indicator for GDP per capita for Canada 0.983 = {(5359-100)/(5448-100)} 10 HDI for Canada ={(0.873+0.993+0.983)/3} 0.950 There was no major change in the approach followed in HDR 1996 from the one followed in the HDR 1995 for the computation of HDI. These HDRs differed from each other only in terms of values taken for the

46 threshold income levels in both the Reports besides the data-set. As against the world s average income of 5120 (PPP$) of 1992 adopted as the threshold income level for the purpose of discounting the incomes above it in HDR 1995, the threshold income level in HDR 1996 was the world s average income of 5711 (PPP$) corresponding to the year 1993. By considering the threshold income level y * as 5711 (PPP$) in the HDR 1996, the maximum (unadjusted) real GDP per capita level of 40000 (PPP$) fell between 7y * and 8y *. While in the HDR 1995, the value of Max X 4j was obtained as 5448 (PPP$), its value was arrived at as 6040 (PPP$) in HDR 1996 as below. (2.12) MaxX 4j = W(40000)= {5711+ 2x(5711) 1/2 + 3x(5711) 1/3 + 4x(5711) 1/4 + 5x(5711) 1/5 + 6x(5711) 1/6 + 7x(5711) 1/7 + 8x(40000-7x5711) 1/8 } = 6040 (PPP$) The methodology followed by UNDP in its HDR 1996 can be observed first from the illustrative computation of the HDI for India in view of its status regarding the real GDP per capita income being below the threshold income level. TABLE 2.17 Computation of HDI for India in HDR 1996 Slno Description Data 1 India s life expectancy at birth 60.7 years 2 Indicator for life expectancy at birth for India ={(60.7-25)/(85-25)} 0.595 3 India's literacy rate 50.6% 4 Indicator for adult literacy rate for India ={(50.6-0)/(100-0)} 0.506

47 5 India s combined gross enrolment ratios 55% 6 Indicator for combined gross enrolment ratios for India 0.55 ={(55-0)/(100-0)} 7 India s educational attainment index== [{2(0.506)+(0.55)}/3] 0.521 8 India's real GDP per capita 1240 PPP$ 9 Indicator for GDP per capita for India= {(1240-100)/(6040-100)} 0.192 10 HDI for India ={(0.595+0.521+0.192)/3} 0.436 Since Canada s real GDP per capita income of 20950 (PPP) exceeded the threshold income level of 6040 (PPP$) in the HDR 1996, it was required to be adjusted using the Atkinson based multi-step utility function from Equation (2.2D) and obtained as {(5711) + 2x(5711) 1/2 + 3x(5711) 1/3 + 4x(20950 3x5711) 1/4 }, which finally simplified to 5947 (PPP$). The indicator of income component was obtained by using value of X 4j as 5947 (PPP$) in the following Equation. (2.13) I AIj = (X 4j -100)/ (6040-100) We observe the steps involved in computing Canada s HDI in the HDI 1996 as follows. TABLE 2.18 Computation of HDI for Canada in HDR 1996 Slno Description Data 1 Canada s life expectancy at birth 77.5 years 2 Indicator for life expectancy at birth for Canada 0.875 ={(77.5-25)/(85-25)} 3 Canada's literacy rate 99% 4 Indicator for adult literacy rate for Canada ={(99-0)/(100-0)} 0.99

48 5 Canada s combined gross enrolment ratios 100% 6 Indicator for combined gross enrolment ratios for India 1.00 ={(100-0)/(100-0)} 7 Canada s educational attainment index 0.993 == [{2(0.99)+(1.00)}/3] 8 Canada's real GDP per capita 20950PPP$ 9 Indicator for GDP per capita for Canada 0.984 = {(5947-100)/(6040-100)} 10 HDI for Canada ={(0.875+0.993+0.984)/3} 0.951 UNDP retained similar approach for computation of the HDI in its next HDR 1997 also except that the value of threshold level taken in the HDR 1997 was taken as 5835 (PPP$) as against the values of 5120 (PPP$) and 5711 (PPP$) in the earlier two HDRs. Since the fixed maximum real GDP per capita of 40000 (PPP$) lay between 6y * and 7y * in view of y * being 5835 (PPP$), the corresponding discounted/ adjusted value of the maximum income of 40000 (PPP$) in the HDR1997 was computed as 6154 (PPP$) from the following Atkinson based formula for the utility function: (2.14) W(40000)={(5835)+ 2x(5835) 1/2 + 3x(5835) 1/3 + 4x(5835) 1/4 + 5x(5835) 1/5 + 6x(5835) 1/6 +7x(40000-6x5835) 1/7 } The indicator of income component was obtained by using the following Equation. (2.15) I AIj = (X 4j -100)/ (6154-100) We again observe the computational step for arriving at the HDI in the HDR 1997 with the help of an illustrative case of India whose real GDP per

49 capita stood below the threshold income level of 5835 (PPP$) and involved no need for discounting or adjusting the income level in accordance with the principle of diminishing return of income. TABLE 2.19 Computation of HDI for India in HDR 1997 Slno Description Data 1 India s life expectancy at birth 61.3 years 2 Indicator for life expectancy at birth for India ={(61.3-25)/(85-25)} 0.605 3 India's literacy rate 51.2% 4 Indicator for adult literacy rate for India ={(51.2-0)/(100-0)} 0.512 5 India s combined gross enrolment ratios 56% 6 Indicator for combined gross enrolment ratios for India 0.56 ={(56-0)/(100-0)} 7 India s educational attainment index= [{2(0.512)+(0.56)}/3] 0.528 8 India's real GDP per capita 1348 PPP$ 9 Indicator for GDP per capita for India = {(1348-100)/(6154-100)} 0.206 10 HDI for India ={(0.605+0.528+0.206)/3} 0.446 Through another illustrative case of Canada, we again observe the computational steps for obtaining the HDI for the countries having real GDP per capita above the threshold income level. For Canada, the real GDP per capita fell between 17505 (PPP$) and 23340 (PPP$). Therefore, by using Equation (2.2D), its adjusted real GDP per capita was obtained as 6073 (PPP$) after simplifying the expression {(5835) + 2x(5835) 1/2 + 3x(5835) 1/3 + 4x(21451-3x5835) 1/4 }. For Canada, the values of indicator for income component in HDR 1997 was calculated by putting X 4j as 6073 (PPP$) in Equation (2.15).

50 As usual, the three indicators corresponding to life expectancy at birth, educational attainment and income components were used for computing the HDI for Canada as follows. TABLE 2.20 Computation of HDI for Canada in HDR 1997 Slno Description Data 1 Canada s life expectancy at birth 79 years 2 Indicator for life expectancy at birth for Canada ={(79-25)/(85-25)} 0.900 3 Canada's literacy rate 99% 4 Indicator for adult literacy rate for Canada ={(99-0)/(100-0)} 0.99 5 Canada s combined gross enrolment ratios 100% 6 Indicator for combined gross enrolment ratios for India 1.00 ={(100-0)/(100-0)} 7 Canada s educational attainment index= [{2(0.99)+(1.00)}/3] 0.993 8 Canada's real GDP per capita 21451PPP$ 9 Indicator for GDP per capita for Canada 0.987 = {(6073-100)/(6154-100)} 10 HDI for Canada ={(0.900+0.993+0.987)/3} 0.960 As regards the UNDP s methodology the computation of the HDI for different countries, there was hardly any change in HDR 1998 from earlier HDRs from 1995 till 1997. The method of computation of the life expectancy index, educational attainment index and the adjusted real GDP per capita index for the HDR 1998 was again the same as in the HDR 1997. The difference between the HDRs of 1997 and 1998 was mainly due to different values taken as the threshold income level in two Reports. The world s average income in the year 1995 i.e., 5990 (PPP$) was taken as the threshold income level y * in the HDR 1998.