paper by J Foster Additional Considerations Michaela Saisana michaelasaisanajrceceuropaeu European Commission Joint Research Centre Econometrics and Applied Statistics Unit Introduction ID: 296857
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“Reflections on the Human Development Index” (paper by J. Foster)Additional Considerations Michaela Saisanamichaela.saisana@jrc.ec.europa.euEuropean CommissionJoint Research CentreEconometrics and Applied Statistics UnitSlide2
IntroductionAchievementsThe challengeThe measurePopularity It is exactly the “unobserved” nature of composite indicators that is their main limitation and their raison d'être.
~5-fold increase since 2000
“
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)Slide3
CalibrationGoalpostsGaterories Cobb-Douglas HDIMain pointsSlide4
CalibrationGoalpostsCategories AggregationNew HDIMain 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 IndexSlide5
Source: Global Innovation IndexSlide6
CalibrationGoalpostsCategories Cobb-Douglas HDIMain 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 HDI
After 2010:
20y
– observed (83.2 y, JN) Before : 25y – 85y
Source: WikipediaSlide7
CalibrationGoalpostsCategories Cobb-Douglas HDIMain points
Minimum and Maximum across 194 countries
85.6
Life expectancy at birth
Suggestion
: Fixed bounds
30y (Early 20th Century) – 87 years
Similarly for the other indicatorsSlide8
CalibrationGoalpostsCategories Cobb-Douglas HDI Main points
Categories of Human Development
Relative (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)Slide9
Main pointsHDILife 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)
Calibration
Goalposts
Categories
Cobb-Douglas HDI
Slide10
Main pointsCalibrationGoalpostsCategories Cobb-Douglas HDI
“[…] attempt to view the HDI more as a
social evaluation function
that aggregates across
dimensional variables
directly”
L= life expectancy - 20 years
E =1/2 (mean years of schooling + expected years of schooling)
Y= ln (GNI per capita) – ln (100)
W*= target social evaluation levelSlide11
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
stdev
HDI
(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…Slide12
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 ExpectancySlide13
More on the “quality” of the HDI… (Implicit Weights)
HDI
Life Expectancy
HDI 2011
Nominal
Weights (w
i
)
Implicit
Weights (S
i
)
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 (S
i
values are very similar)Slide14
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=Slide15
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.Slide16
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)Slide17
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!)Slide18
Paruolo P., Saisana M., Saltelli A., 2013, Ratings and Rankings: voodoo or science?. J Royal Statistical Society A 176(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.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.Saisana M., D’Hombres B., Saltelli A., 2011, Rickety Numbers: Volatility of university rankings and policy implications. Research Policy 40, 165–177.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. OECD/JRC, 2008, Handbook on Constructing Composite Indicators. Methodology and user Guide
, OECD Publishing, ISBN 978-92-64-04345-9.
References and Related Reading