New method (2010 HDI onwards)

HDI trends between 1990 and 2021

World   OECD countries

Developing countries:   Arab States   East Asia and the Pacific   Europe and Central Asia   Latin America and the Caribbean   South Asia   Sub-Saharan Africa

Published on 4 November 2010 (and updated on 10 June 2011), the 2010 Human Development Report calculated the HDI combining three dimensions:^[7][8]

• A long and healthy life: Life expectancy at birth
• Education: Mean years of schooling and expected years of schooling
• A decent standard of living: GNI per capita (PPP international dollars)

In its 2010 Human Development Report, the UNDP began using a new method of calculating the HDI. The following three indices are used:

1. Life Expectancy Index (LEI) ${\displaystyle ={\frac {{\textrm {LE}}-20}{85-20}}}$${\displaystyle ={\frac {{\textrm {LE}}-20}{65}}}$

LEI is equal to 1 when life expectancy at birth is 85 years, and 0 when life expectancy at birth is 20 years.

2. Education Index (EI) ${\displaystyle ={\frac {{\textrm {MYSI}}+{\textrm {EYSI}}}{2}}}$^[9]

2.1 Mean Years of Schooling Index (MYSI) ${\displaystyle ={\frac {\textrm {MYS}}{15}}}$^[10]

Fifteen is the projected maximum of this indicator for 2025.

2.2 Expected Years of Schooling Index (EYSI) ${\displaystyle ={\frac {\textrm {EYS}}{18}}}$^[11]

Eighteen is equivalent to achieving a master's degree in most countries.

3. Income Index (II) ${\displaystyle ={\frac {\ln({\textrm {GNIpc}})-\ln(100)}{\ln(75,000)-\ln(100)}}}$${\displaystyle ={\frac {\ln({\textrm {GNIpc}})-\ln(100)}{\ln(750)}}}$

II is 1 when GNI per capita is $75,000 and 0 when GNI per capita is $100.

Finally, the HDI is the geometric mean of the previous three normalized indices:

${\displaystyle {\textrm {HDI}}={\sqrt[{3}]{{\textrm {LEI}}\cdot {\textrm {EI}}\cdot {\textrm {II}}}}.}$

LE: Life expectancy at birth
MYS: Mean years of schooling (i.e. years that a person aged 25 or older has spent in formal education)
EYS: Expected years of schooling (i.e. total expected years of schooling for children under 18 years of age, incl. young men and women aged 13–17)
GNIpc: Gross national income at purchasing power parity per capita

Old method (HDI before 2010)

The HDI combined three dimensions last used in its 2009 report:

• Life expectancy at birth, as an index of population health and longevity to HDI
• Knowledge and education, as measured by the adult literacy rate (with two-thirds weighting) and the combined primary, secondary, and tertiary gross enrollment ratio (with one-third weighting).
• Standard of living, as indicated by the natural logarithm of gross domestic product per capita at purchasing power parity.

HDI trends between 1975 and 2004

OECD   Europe (not in the OECD), and CIS   Latin America and the Caribbean   East Asia

Arab League   South Asia   Sub-Saharan Africa

This methodology was used by the UNDP until their 2011 report.

The formula defining the HDI is promulgated by the United Nations Development Programme (UNDP).^[12] In general, to transform a raw variable, say ${\displaystyle x}$, into a unit-free index between 0 and 1 (which allows different indices to be added together), the following formula is used:

• ${\displaystyle x{\text{ index}}={\frac {x-a}{b-a}}}$

where ${\displaystyle a}$ and ${\displaystyle b}$ are the lowest and highest values the variable ${\displaystyle x}$ can attain, respectively.

The Human Development Index (HDI) then represents the uniformly weighted sum with 1⁄3 contributed by each of the following factor indices:

• Life Expectancy Index ${\displaystyle ={\frac {LE-25}{85-25}}}$${\displaystyle ={\frac {LE-25}{60}}}$
• Education Index = ${\displaystyle {\frac {2}{3}}\times ALI+{\frac {1}{3}}\times GEI}$
  • Adult Literacy Index (ALI)${\displaystyle {\frac {ALR-0}{100-0}}}$${\displaystyle ={\frac {ALR}{100}}}$
  • Gross Enrollment Index (GEI) ${\displaystyle {\frac {CGER-0}{100-0}}}$${\displaystyle ={\frac {CGER}{100}}}$
• GDP ${\displaystyle ={\frac {\log \left(GDPpc\right)-\log \left(100\right)}{\log \left(40000\right)-\log \left(100\right)}}}$${\displaystyle ={\frac {\log \left(GDPpc\right)-\log \left(100\right)}{\log \left(400\right)}}}$

In each original HDI

The year represents the time period from which the statistics for the index were derived. In parentheses is the year when the report was published.

Sources of data error

Economists Hendrik Wolff, Howard Chong and Maximilian Auffhammer discuss the HDI from the perspective of data error in the underlying health, education and income statistics used to construct the HDI. They have identified three sources of data error which are: (i) data updating, (ii) formula revisions and (iii) thresholds to classify a country's development status. They conclude that 11%, 21% and 34% of all countries can be interpreted as currently misclassified in the development bins due to the three sources of data error, respectively. Wolff, Chong and Auffhammer suggest that the United Nations should discontinue the practice of classifying countries into development bins because the cut-off values seem arbitrary, and the classifications can provide incentives for strategic behavior in reporting official statistics, as well as having the potential to misguide politicians, investors, charity donors and the public who use the HDI at large.^[17]

In 2010, the UNDP reacted to the criticism by updating the thresholds to classify nations as low, medium, and high human development countries. In a comment to The Economist in early January 2011, the Human Development Report Office responded^[18] to an article published in the magazine on 6 January 2011^[19] which discusses the Wolff et al. paper. The Human Development Report Office states that they undertook a systematic revision of the methods used for the calculation of the HDI, and that the new methodology directly addresses the critique by Wolff et al. in that it generates a system for continuously updating the human-development categories whenever formula or data revisions take place.

In 2013, Salvatore Monni and Alessandro Spaventa emphasized that in the debate of GDP versus HDI, it is often forgotten that these are both external indicators that prioritize different benchmarks upon which the quantification of societal welfare can be predicated. The larger question is whether it is possible to shift the focus of policy from a battle between competing paradigms to a mechanism for eliciting information on well-being directly from the population.^[20]

Indices

Other