Human Development Index: The Old, The New and The Elegant

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

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

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

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

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

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

7. Displaced Ideal Zeleny (1974) better system should have less distance from “ideal”. I (1.0, 1.0)‏ = dj‏ hj Additive Inverse of distance j dk‏ h HDIDIj> HDIDIkif and only if dj < dk hk HDIDIj= HDIDIkif and only if dj = dk k HDIDIj< HDIDIkif and only if dj > dk ek ej e

8. 3 dimensions – A long and healthy life Knowledge Ability to achieve decent standard living h e y 0 ≤ h, e, y ≤ 1 HDIDI= 1-(√((h2 + e2 + y2)/3)) HDI – the elegant (proposed)

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

10. Axiom M: Monotonicity 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. For any random country k in Zone A hk ≥ hj , ek ≥ ej(hk=hj or ek=ej) LA: HDIk > HDIj GM: HDIk > HDIj DI: HDIk > HDIj Zone B hk ≤ hj , ek ≤ ej(hk=hj or ek=ej) LA: HDIk < HDIj LA: HDIk < HDIj DI: HDIk < HDIj Iso-HDIGM I Iso-HDIDI Iso-HDILA 1 h k LA, GM and DI satisfy O e

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

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

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

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

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

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

17. HDI rank:revisit with GM and DI LA ~ GM Does not affect the Top Top 54 countries did not change ranks Shift to GM was virtually no shift for high HD countries Along expected lines LA ~ GM ~ DI Does affect the Top Source: UNDP (2008)

18. HDI rank:revisit with GM and DI LA ~ GM Does it affect the Bottom? Source: UNDP (2008) DI too captures change in rank at the bottom The values of the indices influence the ranking, rather than aggregation technique

19. HDI rank:revisit with GM and DI LA ~ GM Countries where GM differed from LA most The difference was also captured by DI Source: UNDP (2008)

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

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