Reflections on the Human Development Index
James Foster
George Washington University and OPHI
2nd Conference on Measuring Human Progress
4-5 March 2013, New York
Introduction
• HDI
– Remarkable accomplishment
– Attracted criticism
• Arbitrary decisions
• Purpose of this short talk
– Focus on aspects of HDI that might be improved
– Consider alternatives
– Offer suggestions
• View as less arbitrary
Desiderata
(Ia) It must understandable and easy to describe
(Ib) It must conform to a common sense notion of
what is being measured
(II) It must fit the purpose for which it is being
developed
(III) It must be technically solid
(IVa) It must be operationally viable
(IVb) It must be easily replicable
Desiderata
• (I) corresponds to strong policy needs
– Understandable at a deeper level including cutoffs
– Measuring absolute size of HD
• Atkinson’s independence of other countries – not relative
– Anchored in underlying variables
– Numbers mean something
• (II) concerns the intended purpose of the measure
–
–
–
–
Compete with GNI per capita
Compare HD achievements across countries
Monitoring progress across time for a given country
Drilling in or out (subgroups or dimensions)
Desiderata
• (III) is is theoretical justification
– Axioms to make sure measure conforms to purpose
– Theoretical framework (say within welfare economics)
• (IV) concerns practicality
– Does it work with existing data?
– Can it be updated in time?
• These are benchmarks to compare and evaluate
particular versions of HDI
• Contrast with GNI per capita
– Poor in (II), better in others?
Outline of Paper
• Reconsider frequent recalibration of top and bottom
goalposts
– Confounds understanding over time
– Gives countries unclear signals
• Reconsider HDI demarcations into relative groups
– Purely relative to deflect criticism
– But ends up deflecting incentives
• Reconsider functional form
– New geometric has certain characteristics
– Old arithmetic has others
– Which is best?
Outline of Paper
• Other themes
– How to anchor HDI values
• Through normalized variables or through original variables?
– Purely data driven goalposts
• Cause much confusion
• Ought to have firm normative basis
• Not just a (relative) function of observed achievements
– Differentiate purposes of goalposts
• Upper (aspiration) vs. lower (natural zeroes)
• Lower should stay fixed
• Upper may change periodically
– Are irrelevant for new HDI, can be made so for old
Lower Goalposts: Natural Zeroes
• Fixed natural zeroes
– Why should they change over time?
– Conflicts with description of HDI as measure of
absolute size
– Need to satisfy measurement properties
– Analogous to poverty cutoff for countries
• Desiderata
– Needed for measure to be simple and easy to explain
– Needed to conform to measurement of HD
– Fits purpose to compare over time and space
Understanding the HDIs
• Gist in 2-dimensional graphs
– From original variables
– To bottom normalized data (net variables)
• Each measured from natural zeroes
Original
Variable 2
Original Variables
natural zero
natural zero
Original Variable 1
Net Variable x2
0
0
Net Variables
Net Variable x1
Upper Goalposts: Aspiration Levels
Net Variable x2
Aspiration level
0
0
Aspiration level
Net Variable x1
New HDI
Net Variable x2
Wx = x11/2 x21/2
Aspiration level
x
WA
Wx
0
0
Aspiration level
Net Variable x1
New HDI
Net Variable x2
HDIN = Wx/WA
Aspiration level
x
WA
Wx
0
0
Aspiration level
Net Variable x1
New HDI
Net Variable x2
HDIN = Wx/WA
Aspiration level
x
WA
Wx
0
0
Aspiration level
Net Variable x1
New HDI
Net Variable x2
HDIN = Wx/WA
Only uses reference level WA
x
WA
Wx
0
0
Net Variable x1
Functional Form
• HDIN can be viewed as a social evaluation
function of net variables, normalized by a
reference level.
– No need for upper goalposts or aspiration levels
• But can use to set reference level
– New ref level yields a multiple of previous HDIN
• Same rankings
• Same rates of growth
• Other convenient properties
Functional Form
• HDIO: Arithmetic mean is used
– But exactly how?
– Return to graph
Upper Goalposts: Aspiration Levels
Net Variable x2
Aspiration level
0
0
Aspiration level
Net Variable x1
Upper Goalposts: Aspiration Levels
Net Variable x2
Set the slope of HDIO indifference
Aspiration level
0
0
Aspiration level
Net Variable x1
Upper Goalposts: Aspiration Levels
Net Variable x2
Set the slope of HDIO indifference
Aspiration level
0
0
Aspiration level
Net Variable x1
Upper Goalposts: Aspiration Levels
Net Variable x2
What if aspiration levels change?
Aspiration level
0
0
Aspiration level
Net Variable x1
Upper Goalposts: Aspiration Levels
Net Variable x2
What if aspiration levels change?
Slopes change - inconsistent
Aspiration level
0
0
Old
New
Aspiration level Aspiration level
Net Variable x1
Upper Goalposts: Aspiration Levels
Net Variable x2
Always?
Aspiration level
0
0
Aspiration level
Net Variable x1
Upper Goalposts: Aspiration Levels
Net Variable x2
Slope unchanged if new
levels are proportionate
Slope unchanged if new
levels are proportionate
Aspiration level
0
0
Aspiration level
Net Variable x1
Upper Goalposts: Aspiration Levels
Net Variable x2
HDIO = Wx/WA
Aspiration level
0
x
Wx
0
Aspiration level
WA
Net Variable x1
Functional Form
• HDIO can be viewed as a social evaluation
function of net variables, normalized by a
reference level – if aspiration levels stay in
proportion
– New ref level yields a multiple of previous HDIO
• Same rankings
• Same rates of growth
• Other convenient properties
Summary of Suggestions
– Leave natural zeroes as natural zeroes
– Alter aspiration levels only infrequently
• 5 – 10 years normative targets
• In a constrained way (or proportionate)
• All past inconsistencies will then be caused by data
updates
– Not by HDRO
Summary of Suggestions
– Fix absolute demarcation cutoffs for categorizing
countries
• Alternative 1: choose relatively, then fix absolutely
• Alternative 2: Look within variables for natural cutoffs
– Note: They will be arbitrary
• Like poverty lines, like middle class ranges
• But if fixed over time, countries can progress
• And given above recalibration methods
– Consistent cutoffs can be maintained over time
Summary of Suggestions
– Go back to original arithmetic formula
• With fixed zeroes
• With aspirations cutoffs constrained and updated
infrequently
– Normative, not positive
Summary of Suggestions
– Why arithmetic?
•
•
•
•
Simple and understandable
With above calibrations, similar properties to HDIN
Decomposability by dimension (as in MPI)
Potential for decomposability by subgroup if data
permits
» Mean of log individual incomes
» Rather than log of mean incomes
Summary of Suggestions
– What about inequality across dimensions?
• HDIN accounts for it
• HDIO does not
– Note the Atkinson Inequality measure: IA = (HDIO – HDIN)/HDIO
• But this form of inequality is not the priority!
• Within dimension inequality is key!
– Focus: Need data to move to IHDI as the standard
Summary of Suggestions
– Alternative transformations for variables?
• Careful to maintain simplicity!
• Chakravarty: HDI0 form but with all variables
transformed by a common concave function
• Of course this is possible
– Simplicity? Lose the close connection between variable and
measure – it is a function of the normalized variable!
» But can decompose by dimension
– No possibility for subgroup decomposition
» Even if alter data
– Why transform income and others identically?
Thank you!