human development index: the old, the new and the elegant srijit mishra and hippu salk kristle...
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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
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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
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HDI – the old (till 2009)
Life Expectancy at birth1. 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
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HDILA = 1/3 (h) + 1/3 (e) + 1/3 (y) 0 ≤ h, e, y ≤ 1
Iso- HDILA lines
e
h
k
j
(1,1)
(0,0)
Iso-HDI lines – old HDI (perfect-substitutability)
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HDI – the new (from 2010)
Life Expectancy at birth1. 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
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HDIGM = (h * e * y)1/3
Iso- HDIGM lines
k
j
(1,1)
(0,0)
e
h
Iso-HDI lines – new method
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Displaced Ideal
Zeleny (1974)
better system should have less distance from “ideal”.
dj
dk
j
k
e
h
jd22 )1()1( jj he
ej ek
hk
hj
HDIDIj > HDIDI
k if and only if dj < dk
HDIDIj = HDIDI
k if and only if dj = dk
HDIDIj < HDIDI
k if and only if dj > dk
I (1.0, 1.0)
Additive Inverse of distance
=
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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
HDIDI = 1-(√((h2 + e2 + y2)/3))
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Iso- HDIDI lines
k
j
(1,1)
(0,0)
e
h
Iso-HDI lines – elegant method
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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-HDILA
Iso-HDIGM
e
h
1
O
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-HDIDI
Axiom M: Monotonicity
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Axiom A: Anonymity
A measure of HDI should be indifferent to swapping of values across dimensions.
LA, GM and DI satisfy Anonymity
LA: hj + ej = hj’ + ej’
GM: hj * ej = hj’ + ej’
Note that this is a statistical property and does not invoke substitution between dimensions
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DI: dj = dj’
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
hI
e=1
y =1
h=1
O
Axiom N: Normalization
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HDI = 0: NO development (h = 0, e = 0, y = 0) - “Origin”
HDI = 1: COMPLETE development (h = 1, e = 1, y = 1) – “Ideal”
Axiom U: Uniformity
LA fails, GM and DI satisfy
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 = HDILA
j’
HDIGMj > HDIGM
j’
HDIDIj > HDIDI
j’
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 = HDILA
k’
HDIGMk < HDIGM
k’
HDIDIk < HDIDI
k’
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
e
O (0, 0)
j
j’
h
k
k’Line of equality
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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
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Axiom H: Hiatus sensitivity
e
h Equal gap at higher
attainment should be
considered worse off
DI satisfies
LA and GM fail
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M: Monotonicity A: Annonimity N: Normalization U: Uniformity S: Signalling H: Hiatus Sensitivity
LAGM
DI
MANUSH Axioms
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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
COUNTRY Health Index
Education Index
Income Index
Rank LA
Rank GM
Rank DI
Rank Diff
Range
Ireland 0.890 0.993 0.994 5 5 15 -10 0.1035Japan 0.954 0.956 0.959 8 8 3 +5 0.0127United States 0.881 0.971 1.000 12 12 21 -9 0.1192Italy 0.922 0.958 0.944 20 20 12 +8 0.0367
Along expected lines
Source: UNDP (2008)
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HDI rank: revisit with GM and DI
LA ~ GM Does it affect the Bottom?
COUNTRY Health Index
Education Index
Income Index
Rank LA
Rank GM
Rank DI
Rank Diff
Range
Congo 0.346 0.56 0.328 168 169 169 -1 0.2319Ethiopia 0.446 0.38 0.393 169 166 168 3 0.0668Chad 0.423 0.296 0.444 170 170 170 0 0.1478Central African Republic 0.311 0.423 0.418 171 171 171 0 0.1119Mozambique 0.296 0.435 0.421 172 172 172 0 0.1383Mali 0.469 0.282 0.39 173 173 173 0 0.1868Niger 0.513 0.267 0.343 174 175 175 -1 0.2460Guinea-Bissau 0.347 0.421 0.353 175 174 174 1 0.0734Burkina Faso 0.44 0.255 0.417 176 176 176 0 0.1847Sierra Leone 0.28 0.381 0.348 177 177 177 0 0.1014
DI too captures change in rank at the bottom
The values of the indices influence the ranking, rather than aggregation technique
Source: UNDP (2008)
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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
COUNTRY Health Index
Education Index
Income Index
Rank LA
Rank GM
Rank DI
Rank Diff
Range
Lesotho 0.293 0.768 0.585 138 148 148 -10 0.4747Swaziland 0.265 0.730 0.647 141 151 151 -10 0.4645Zimbabwe 0.265 0.770 0.503 151 157 157 -6 0.5055Papua New Guinea 0.532 0.518 0.541 145 140 139 5 0.0234Togo 0.547 0.538 0.453 152 147 147 5 0.0940
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Class of HDI
• Mα =1-DαI ; • D αI=(1/nΣ(1-xj) α)1/α where (j=1,…,n)• For α≥1, Mα
satisfies 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
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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
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