New method (2010 HDI onwards) Published on 4 November 2010 (and updated on 10 June 2011), the 2010 Human Development Report calculated the HDI combining three dimensions: • 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) = \frac{\textrm{LE} - 20}{85-20} = \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) = \frac{{\textrm{MYSI} + \textrm{EYSI}}} {2} :2.1 Mean Years of Schooling Index (MYSI) = \frac{\textrm{MYS}}{15} :: Fifteen is the projected maximum of this indicator for 2025. :2.2 Expected Years of Schooling Index (EYSI) = \frac{\textrm{EYS}}{18} :: Eighteen is equivalent to achieving a
master's degree in most countries. 3. Income Index (II) = \frac{\ln(\textrm{GNIpc}) - \ln(100)}{\ln(75,000) - \ln(100)} = \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: : \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. 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). In general, to transform a raw
variable, say x, into a unit-free
index between 0 and 1 (which allows different indices to be added together), the following
formula is used: • x\text{ index} = \frac{x - a}{b - a} where a and b are the
lowest and highest values the variable x can attain, respectively. The Human Development Index (HDI) then represents the uniformly weighted sum with contributed by each of the following factor indices: •
Life Expectancy Index = \frac{\text{LE} - 25} {85-25} = \frac{\text{LE} - 25} {60} •
Education Index = \frac{2} {3} \times \text{ALI} + \frac{1} {3} \times \text{GEI} •
Adult Literacy Index (ALI) = \frac{\text{ALR} - 0} {100 - 0} = \frac{\text{ALR}} {100} •
Gross Enrollment Index (GEI) = \frac{\text{CGER} - 0} {100 - 0} =\frac{\text{CGER}} {100} •
GDP = \frac{\log(\text{GDPpc}) - \log(100)} {\log(40000) - \log(100)} = \frac{\log(\text{GDPpc}) - \log(100)} {\log(400)} == 2023 Human Development Index (2025 report) ==