1. Human Development Index: The Old, The New and The Elegant Srijit Mishra and Hippu Salk Kristle Nathan Seminar at National Institute of Public Finance and Policy, New Delhi 10 July 2013 1

2. Focus of the study NOT rationale behind choosing these 3 indicators NOT how the indicators are measured and scaled NOT how the indicators are normalized and weighed INVESTIGATES the appropriateness of the known two measures of HDI proposes an alternative technique Inverse of the Euclidean Distance from Ideal 2

3. HDI – the old (till 2009) Life Expectancy at birth 1.A long and healthy life 2.Knowledge 3.Ability to achieve decent standard living Adult literary rate (2/3)‏ Gross enrolment ratio (1/3)‏ 3 dimensions – h GDP per capita (PPP) e y 3 HDI LA = 1/3 (h) + 1/3 (e) + 1/3 (y) 0 ≤ h, e, y ≤ 1

4. Iso- HDI LA lines e h k j (1,1) (0,0) Iso-HDI lines – old HDI (perfect-substitutability)‏ 4

5. HDI – the new (from 2010) Life Expectancy at birth 1.A long and healthy life 2.Knowledge 3.Ability to achieve decent standard living 0 ≤ h, e, y ≤ 1 Mean years of schooling: adults (2/3)‏ Expected years of schooling: children (1/3)‏ 3 dimensions – h GNI per capita (PPP) e y 5 HDI GM = (h * e * y) 1/3

6. Iso- HDI GM lines k j (1,1) (0,0) e h Iso-HDI lines – new method 6

7. Displaced Ideal Zeleny (1974) better system should have less distance from “ideal”. dj‏dj‏ dk‏dk‏ j k e h ejej ekek hkhk hjhj HDI DI j > HDI DI k if and only if d j < d k HDI DI j = HDI DI k if and only if d j = d k HDI DI j d k I (1.0, 1.0)‏ Additive Inverse of distance = 7

8. HDI – the elegant (proposed) 1.A long and healthy life 2.Knowledge 3.Ability to achieve decent standard living 0 ≤ h, e, y ≤ 1 3 dimensions – h e y HDI DI = 1-(√((h 2 + e 2 + y 2 )/3)) 8

9. Iso- HDI DI lines k j (1,1) (0,0) e h Iso-HDI lines – elegant method 9

10. A measure of HDI should be greater (lower) if the index value in one dimension is greater (lower) with indices value remaining constant in all other dimension. LA, GM and DI satisfy I k Iso- HDI LA Iso- HDI GM e h 1 O For any random country k in Zone A h k ≥ h j, e k ≥ e j (h k =h j or e k =e j ) LA: HDI k > HDI j GM: HDI k > HDI j DI: HDI k > HDI j Zone B h k ≤ h j, e k ≤ e j (h k =h j or e k =e j ) LA: HDI k < HDI j DI: HDI k < HDI j Iso- HDI DI Axiom M: Monotonicity 10

11. Axiom A: Anonymity A measure of HDI should be indifferent to swapping of values across dimensions. LA, GM and DI satisfy Anonymity LA: h j + e j = h j’ + e j’ GM: h j * e j = h j’ + e j’ Note that this is a statistical property and does not invoke substitution between dimensions 11 DI: d j = d j’

12. A measure of HDI should have a minimum and a maximum i.e. HDI  (0,1) LA, GM and DI satisfy this; for GM the value will be zero if any dimension has no development e y h I e=1 y =1 h=1 O Axiom N: Normalization 12 HDI = 0: NO development ( h = 0, e = 0, y = 0 ) - “Origin” HDI = 1: COMPLETE development ( h = 1, e = 1, y = 1 ) – “Ideal”

13. Axiom U: Uniformity LA fails, GM and DI satisfy Illustration (1) Uniform to Non-Uniform j(0.5, 0.5)d j =√(0.50) GM =√(0.25) j’(0.6,0.4)d j’ = √(0.52) GM =√(0.24) Change in HDI: HDI LA j = HDI LA j’ HDI GM j > HDI GM j’ HDI DI j > HDI DI j’ Illustration (2) Non-Uniform to Uniform k(0.8, 0.4)d k =√0.80 GM =√(0.32) k’(0.6,0.6)d k’ =√0.72 GM =√(0.36) Change in HDI: HDI LA k = HDI LA k’ HDI GM k < HDI GM k’ HDI DI k < HDI DI k’ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.10.20.30.40.50.60.70.80.91 e O (0, 0) j j’ h k k’ Line of equality 13

14. I (1,1)‏ j k h e Movement is along the direction proportion to shortfall Ideal paths Iso-HDI lines Axiom S: Signalling DI satisfies LA and GM fail 14

15. Axiom H: Hiatus sensitivity e h Equal gap at higher attainment should be considered worse off DI satisfies LA and GM fail 15

16. M: Monotonicity A: Annonimity N: Normalization U: Uniformity S: Signalling H: Hiatus Sensitivity LA GM DI MANUSH Axioms 16

17. HDI rank: revisit with GM and DI LA ~ GM Top 54 countries did not change ranks Does not affect the Top Shift to GM was virtually no shift for high HD countries LA ~ GM ~ DI Does affect the Top COUNTRYHealth Index Educatio n Index Income Index Rank LA Rank GM Rank DI Rank Diff Range Ireland0.8900.9930.9945515-100.1035 Japan0.9540.9560.959883+50.0127 United States0.8810.9711.00012 21-90.1192 Italy0.9220.9580.94420 12+80.0367 Along expected lines Source: UNDP (2008) 17

18. HDI rank: revisit with GM and DI LA ~ GM Does it affect the Bottom? COUNTRYHealth Index Educatio n Index Income Index Rank LA Rank GM Rank DI Rank Diff Range Congo0.3460.560.328168169 0.2319 Ethiopia0.4460.380.39316916616830.0668 Chad0.4230.2960.444170 00.1478 Central African Republic0.3110.4230.418171 00.1119 Mozambique0.2960.4350.421172 00.1383 Mali0.4690.2820.39173 00.1868 Niger0.5130.2670.343174175 0.2460 Guinea-Bissau0.3470.4210.353175174 10.0734 Burkina Faso0.440.2550.417176 00.1847 Sierra Leone0.280.3810.348177 00.1014 DI too captures change in rank at the bottom The values of the indices influence the ranking, rather than aggregation technique Source: UNDP (2008) 18

19. HDI rank: revisit with GM and DI LA ~ GM Source: UNDP (2008) The difference was also captured by DI Countries where GM differed from LA most COUNTRYHealth Index Educatio n Index Income Index Rank LA Rank GM Rank DI Rank Diff Range Lesotho0.2930.7680.585138148 -100.4747 Swaziland0.2650.7300.647141151 -100.4645 Zimbabwe0.2650.7700.503151157 -60.5055 Papua New Guinea0.5320.5180.54114514013950.0234 Togo0.5470.5380.453152147 50.0940 19

20. Class of HDI M α =1-D αI ; D αI =(1/nΣ(1-x j ) α ) 1/α where (j=1,…,n) For α≥1, M α satisfies the axioms of –monotonicity, ∂M α /∂x j >0 for all j. –Anonymity, (xj,wj) swap values with (xi,wi), i≠j –normalization, M α  [0,1], and For α>12, M α satisfies the axioms of –uniformity (position penalty) and –signaling (path penalty) –hiatus sensitivity 20

21. References Anand, S and Sen, A (1994) Human Development Index: Methodology and Measurement, Human Development Report 1994. Mishra, Srijit and Nathan, Hippu Salk Kristle (2008) On A Class of Human Development Index Measures, WP-2008-020, Indira Gandhi Institute of Development Research, Mumbai. Nathan, Hippu Salk Kristle and Mishra, Srijit (2010), Progress in Human Development: Are we On the Right Path? International Journal of Economic Policy in Emerging Economies, Vol.3. No. 3, 199-221. Nathan, Hippu Salk Kristle, Mishra, Srijit and Reddy, B. Sudhakara (2008), An Alternative Measure of HDI, WP-2008-001, Indira Gandhi Institute of Development Research, Mumbai Nathan, Hippu Salk Kristle and Mishra, Srijit (forthcoming), Group Differential for attainment and failure indicators, Journal of International Development. UNDP (2008), Human Development Report 2007/08: Fighting Climate Change: Human Solidarity in a Divided World, Oxford University Press, New Delhi UNDP (2010), Human Development Report 2010: The Real Wealth of Nations; Pathways to Human Development, Oxford University Press, New Delhi 21