“Reflections on the Human Development Index” (paper by J. Foster) Additional Considerations

Michaela Saisana Second Conference on Measuring Human Progress

New York, 4-5 March 2013

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“Reflections on the Human Development

Index” (paper by J. Foster)

Additional Considerations Michaela Saisana

[email protected]

European CommissionJoint Research Centre

Econometrics and Applied Statistics Unit



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Introduction• Achieveme

nts• The

challenge• The

measure• Popularity

It is exactly the “unobserved” nature of composite indicators that is their main limitation and their raison d'être.

180

4,460

7,730

12,600

16,20017,80018,600

21,300

0

5,000

10,000

15,000

20,000

25,000

1985 1990 1995 2000 2005 2010 2015

Year

Scho

lar G

oogl

e hi

ts o

n "H

uman

dev

elop

men

t ind

ex"

~5-fold increase since

2000

180

4,460

7,730

12,600

18,600

21,300

77,100

115,000

0

5,000

10,000

15,000

20,000

25,000

1985 1990 1995 2000 2005 2010 2015

Year

Scho

lar G

oogl

e hi

ts o

n "H

uman

dev

elop

men

t ind

ex"

0

50,000

100,000

150,000

200,000

250,000

Scho

lar G

oogl

e hi

ts o

n "G

ross

do

mes

tic p

rodu

ct"

“Yet the dimensions of the HDI do not easily meld into one. And without a systematic method […prices…] the index could prove difficult to explain and defend” (J. Foster, 2013)



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• Calibration• Goalposts• Gaterories • Cobb-Douglas HDI

Main points



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• Calibration• Goalposts• Categories • Aggregation• New HDI

Main points“Frequent recalibration gives the strong suggestion that HDI values are contingent and temporary and depend importantly on arbitrary constructs”

Foster’s suggestion: 1) ~ 10 year recalibration (as for

poverty)2) Crossover between calibration

periods: process outlined explicitly and transparently

Source: Global Innovation Index



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Source: Global Innovation Index



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• Calibration• Goalposts• Categories • Cobb-Douglas HDI

Main points“The HDI is typically cast and interpreted as a multidimensional measure of size and hence is seen to be an absolute measure. […] Yet in actual implementation, this is not necessarily the way the HDI behaves.”

Life expectancy at birth Bounds in the HDIAfter 2010: 20y – observed (83.2 y, JN) Before : 25y – 85y

Source: Wikipedia



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34.6 32.8

39.844.0

47.8

76.7 79.082.3 83.4

30354045505560657075808590

1970 1980 1990 2000 2010 2020

Life

exp

ecta

ncy

at b

irth

(yea

rs)


Main pointsMinimum and Maximum across 194 countries

85.6

Life expectancy at birth Suggestion: Fixed bounds30y (Early 20th Century) – 87 years

Similarly for the other indicators



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Main pointsCategories of Human DevelopmentRelative (since 2010) versus Absolute (before 2010)+ progress against other countries, rather than arbitrary numerical cutoffs whose meaning may vary with each new calibration. - fuzzy incentives, less practical value for the

country- many factors enter into the determination of

progress (e.g. different calibrations, performance of other countries, policies of the country, or inclusion of new countries).

- a country can not set a meaningful numerical target to achieve over time.

Foster’s suggestion: 1) A staggered recalibration schedule &2) Fixed numerical cutoffs for the four HD categories (e.g. WB grouping by income)



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Main points

HDI Life expectancy at birth (years)

Mean years of

schooling

Expected years of

schooling

GNI per capita (PPP$)

…

0.6 58.2 7.9 10.8 6,487

0.8 …

Further recommendation: To present the fixed cutoffs for the HDI with respect to the raw data (assuming an even performance)




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Main points•Calibration•Goalposts•Categories • Cobb-Douglas HDI

3/13/13/1 YELW “[…] attempt to view the HDI more as a social evaluation function that aggregates across dimensional variables directly”

3/13/13/1 YELW

L= life expectancy - 20 yearsE =1/2 (mean years of schooling + expected years of schooling)Y= ln (GNI per capita) – ln (100)

*/WWH W*= target social evaluation level



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Advantages of the geometric mean versus the arithmetic mean for the HDI1) implies only partial compensability, i.e. poor performance in one HD dimension cannot be fully compensated by good performance in another, 2) rewards balance by penalizing uneven performance between dimensions, 3) encourages improvements in the weak dimensions, i.e. the lower the performance in a particular HD dimension, the more urgent it becomes to improve in that dimension.

Life Edu GNI stdevHDI

(arithmetic)HDI 2011

(geometric)Liberia’s

improvement

Mali .496 .270 .346 .115 .371 (176) .359 (175)

Liberia .580 .439 .140 .225 .386 (175) .329 (182)

Option A .680 .439 .140 .419 .347 5.5%

Option B .580 .439 .240 .419 .394 19.8%

More on the geometric mean in the case of the HDI…



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More on the “quality” of the HDI… (Implicit Weights) We suggest to use as a measure of

importance of a variable in an index what is known as:

‐ Pearson’s correlation ratio‐ First order effect‐ Top marginal variance- Main effect…

Source: Paruolo, Saisana, Saltelli, 2013, J.Royal Stat. Society A

Using these points we can compute a statistics that tells us: How much (on average) would the variance of the HDI scores be

reduced if one could fix “Life expectancy”?

HDI

Life Expectancy



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𝑆 𝑖=𝑉 𝑋 𝑖

(𝐸𝑋 𝑖 (𝑌|𝑋 𝑖 ))𝑉 (𝑌 )

More on the “quality” of the HDI… (Implicit Weights)

HDI

Life Expectancy

HDI 2011 NominalWeights (wi)

Implicit Weights (Si)

Life expectancy .333 .83 [.81 .85]

Education .333 .88 [.83 .87]

GNI .333 .90 [.88 .91]We could reduce the variation of the HDI scores by 83% by fixing ‘Life expectancy”.

Quality check: The HDI is balanced in its three underlying dimensions (Si values are very similar)



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More on the “quality” of the HDI… (Marginal weights)

Recommendation: To plot life expectancy instead to evidence that countries with low life expectancy are more encouraged to improve

Marginal Weights=



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Some recent criticism…

Source: M. Ravallion (2012) Troubling tradeoffs in the HDI, J. Dev. Economics, 99:201-209

Tradeoffs = marginal rate of substitution, i.e. how much of one dimension must be given up for an extra unit of another, keeping the index constant.

Previous HDI

The new HDI has devalued longevity, especially in poor countries.



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Final considerations Simply take the log of GNI just once (now logged twice) Take the arithmetic average the two education indicators (now geometric) Use two indicators per dimension (now only in case of education) Use the generalized mean of the three dimensions (a compromise solution between arithmetic-geometric averaging) /1)( YELHDI

mean arithmetic,1mean geometric,0

mean arithmetic ,1mean geometric ,0

5.0



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Assess any new calibration formula in terms of: Implicit weights (reduction in the HDI variance by

fixing one dimension at a time) Marginal weights (impact on HDI of 1% increase

in one of the dimensions) Marginal rate of substitution (how much of one

component must be given up for an extra unit of another, keeping the index constant)

More reading at:http://composite-indicators.jrc.ec.europa.eu(first Google hit on “composite indicators” over the last 10 years!)



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1. Paruolo P., Saisana M., Saltelli A., 2013, Ratings and Rankings: voodoo or science?. J Royal Statistical Society A 176(2).

2. Saisana M., Saltelli A., 2012, JRC audit on the 2012 WJP Rule of Law Index, In Agrast, M., Botero, J., Martinez, J., Ponce, A., & Pratt, C. WJP Rule of Law Index® 2012. Washington, D.C.: The World Justice Project.

3. Saisana M., Philippas D., 2012, Sustainable Society Index (SSI): Taking societies’ pulse along social, environmental and economic issues, EUR 25578, Joint Research Centre, Publications Office of the European Union, Italy.

4. Saisana M., D’Hombres B., Saltelli A., 2011, Rickety Numbers: Volatility of university rankings and policy implications. Research Policy 40, 165–177.

5. Saisana M., Saltelli A., Tarantola S., 2005, Uncertainty and sensitivity analysis techniques as tools for the analysis and validation of composite indicators. J Royal Statistical Society A 168(2), 307-323.

6. OECD/JRC, 2008, Handbook on Constructing Composite Indicators. Methodology and user Guide, OECD Publishing, ISBN 978-92-64-04345-9.

References and Related Reading

“Reflections on the Human Development Index” (paper by J. Foster) Additional Considerations

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