Human Development index

1. Milorad Kovacevic
Human Development Report Office, UNDP
Workshop on Measuring Human Development,
June 14,2013
GIZ, Eschborn, Germany
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Human Development Index:
Challanges and a way forward
United Nations Development Programme
Human Development Report Office

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Human Development
A standard definition of human development (1990 HDR):
“[…] a process of enlarging people’s choices to live lives they
have reason to value… The most critical ones are to lead a long
and healthy life, to be knowledgeable and to enjoy a decent
standard of living.”
A broader definition (2010 HDR):
“Human development is the expansion of people’s freedoms to
live long, healthy and creative lives; to advance other goals they
have reason to value; and to engage actively in shaping
development equitably and sustainably on a shared planet”

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• Measuring is as more relevant than ever
• Quantifying and describing our changing world
• Finding ways of improving people’s well-being:
o Informed policy making and advocacy
• Human development is an evolving idea
• As the world changes – analytical tools change
• But there is a persistent importance of the chain:
Concepts Measurements Impacts

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Human Development Index
Emphasizes that outcomes for people and their capabilities
should be the ultimate criteria for assessing the progress of a
country, not economic growth alone.
Accounts for average achievements in
• life expectancy (proxy for leading a long and healthy life),
• education (proxy for being knowledgeable) and
• income per capita (proxy for command over resources to
have a decent standard of living).

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Human Development Index (Contd.)
A simple index (non-comprehensive) with the purpose of
- initiating discussions
- attracting attention to issues that prevent countries from
performing at a higher level
- international comparison and benchmarking
- temporal comparison

6. General criteria for a good HDI (Foster, 2013)
(I) Corresponds to strong policy and advocacy needs
• Understandable and easy to describe
- Understandable at a deeper level including goalposts and group-cutoffs
- Measuring absolute “size of HD” - independent from other countries
• Conforms to a notion of what is being measured
- Anchored in underlying variables
- Numbers mean something
(II) Concerns the intended purpose of the index
• It must fit the purpose for which it is being developed
- Complements GDP or/and GNI
- Compares HD achievements across countries
- Monitors progress across time for a given country
- Analytical utility (subgroups or dimensions)
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7. General criteria for a good HDI (contd.)
(III) Theoretically justified
• Technically solid
- Axioms to make sure that index’s properties conforms to purpose
- Theoretical framework (within human capabilities approach and/or
welfare economics)
(IV) Practicality
• Operationally viable and easily replicable
- Works with existing data for all the countries and all the years
- It can be updated in time
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8. How to anchor HDI values?
• Through normalized variables
- Necessary for comparability on the same scale.
- Only after rescaling they can be combined into a single scalar – a
composite index.
• Enable each dimension index to range between 0 and 1
𝐼𝑥 = 𝐼 𝑥, 𝑚𝑥, 𝑀𝑥 =
𝑥 − 𝑚𝑥
𝑀𝑥 − 𝑚𝑥
𝑥 − 𝑚𝑥 - net variable
𝑀𝑥 − 𝑚𝑥 - reference level (range)
• Cardinal interpretation:
- “Distance” travelled or
- Achievement in % of the reference level
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9. How to decide about goalposts (𝒎𝒙, 𝑴𝒙)?
• Purely data driven goalposts cause confusion
• Ought to have firm normative basis
• Different purpose of goalposts:
- Upper (aspiration level)
- may change periodically but infrequently, 5 – 10 years, normative targets
- In a constrained way (or proportionate)
- All past inconsistencies will then be caused by data revisions
- Lower (natural zeros) should stay fixed
• Properties of the index should not be compromised
- Equal implicit weights (by making the range of variation very similar)
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10. How to decide about demarcation cut-offs for categorizing
countries into different levels of HD?
• Fix absolute demarcation cut-offs for categorizing countries
- Choose relatively, then fix absolutely, or
- Look within variables for natural cut-offs
• Cut-offs are always arbitrary
- Like poverty lines, like middle class ranges
• But if fixed over time, countries can progress
- Consistent cut-offs can be maintained over time
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11. Changes in the HDI introduced in 2010
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Goal posts
Minima:
Fixed at “natural
zeros”
Maxima:
Observed
maxima
since 1980
Comments:
•A possible change of maxima every year;
•HDI level of Congo depends on LE of Japan,
education in USA and GNI of Qatar (!?)
Group cut-offs (relative)
Cut-offs:
Quartiles of HDI
distribution
Groups:
Quartile
groups of
equal size
Comments:
•Little movement mostly within the group
•To move to the higher quartile, another country has
to move to the lower
•Progress against other countries, rather than
against arbitrary numerical cut-offs
•Fuzzy incentives, less practical value for the country
HDI value and rank: change between two years
Due to:
• Real change in performance
• Data revision
• Change in goalposts (maxima)

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Logarithmic transformation of income
• Diminishing marginal utility of income
0
.00001
.00002
.00003
.00004
.00005
Density
0 20000 40000 60000 80000 100000
GNIpc
kernel = epanechnikov, bandwidth = 3.5e+03
GNIpc
0
.1
.2
.3
Density
4 6 8 10 12
lngni
kernel = epanechnikov, bandwidth = 0.3960
ln(GNIpc)
6
8
10
12
lngni
0 20000 40000 60000 80000
GNIpc
Log transformation

13. HDRO 13
Logarithmic transformation in other dimensions
• There are arguments for and against transforming the health and
education variables to account for diminishing returns.
• Health and education are not only of intrinsic value; they, like income,
are instrumental to other dimensions of human development not
included in the HDI.
• Their ability to be converted into other ends may likewise incur
diminishing returns.
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4
4.1
4.2
4.3
4.4
lle
50 60 70 80 90
le
Log(LE) vs. LE
0
.01
.02
.03
.04
.05
Density
40 50 60 70 80 90
le
kernel = epanechnikov, bandwidth = 2.7427
Life Expectancy
0
1
2
3
4
Density
3.8 4 4.2 4.4 4.6
lle
kernel = epanechnikov, bandwidth = 0.0388
Log(LE)

14. Alternative transformations for variables?
• Simplicity is always better
• By transforming variables it is harder to interpret change on the ground with
change in the index – it is a function of the normalized transformed
variables!
• No possibility for subgroup decomposition
• Chakravarty (2003) with all variables transformed by a common concave
function
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Aggregation: Geometric mean
𝐻𝐷𝐼Π = (𝐼𝐿𝐸)1/3[ 𝐼𝑀𝑌𝑆
1
2(𝐼𝐸𝑌𝑆)
1
2]1/3(𝐼ln(𝐺𝑁𝐼))1/3
• No perfect substitutability - reduced substitutability
• Awards well-rounded performance
• Encourages improvements in the weakest dimension
• Changing of maxima does not impact ranking by HDI
• Higher discriminatory power
(0.6, 0.6, 0.6)HDI=0.600,
(0.5, 0.6, 0.7)HDI=0.594,
(0.4, 0.6, 0.8) HDI=0.577
• Accounts for inequality across dimensions

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Aggregation: Geometric mean
Critiques:
• A well rounded performance across dimensions is not a
requirement within the human development approach
• Development/government policies should not be focused on
maximizing the HDI
• Changing of aspiration levels should be done infrequently and if it
is done proportionally (a slope-invariant linear transformation),
maxima do not impact ranking by the arithmetic mean based HDI
• High discrimination power is based on the accounted inequality
across dimensions which is not as important as the inequality
within dimension and across population
• No decomposition by dimension nor by subpopulation

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Aggregation: Arithmetic mean
𝐻𝐷𝐼Σ =
1
3
𝐼𝐿𝐸 +
1
3
1
2
𝐼𝑀𝑌𝑆 +
1
2
𝐼𝐸𝑌𝑆 +
1
3
𝐼ln(𝐺𝑁𝐼)
• Easy interpretation
• Decomposability by dimension
• Perfect substitutability:
- a low achievement in one dimension is linearly compensated
for by a high achievement in another dimension.
Ex. HDI=0.6: (0.6, 0.6, 0.6), (0.5, 0.6, 0.7), (0.4, 0.6, 0.8)
- Constant tradeoffs between non-income dimension
• Low discriminatory power

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• Changing the functional form may cause big changes in the HDI values
and ranks especially in the lower end of distribution.
Example:
LE EDU GNI Stdev HDI
(geometric)
HDI
(arithmetic)
Mali .496 .270 .346 .115 .359 (175) .371 (176)
Liberia .580 .439 .140 .225 .329 (182) .386 (175)

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Summary of recommendations1
• Revert to the original arithmetic formula
• With fixed minima (zeroes)
• With aspirational cut-offs constrained and updated
infrequently
• With log of income component
• With fixed cut-offs between groups
__________
1 2nd Conference on measuring human progress, March 4-5, New York

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Thanks
Milorad.kovacevic@undp.org