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Technical Notes Technical notes Calculating the human development indices—graphical presentation Human Development DIMENSIONS Long and healthy life Knowledge A decent standard of living Index (HDI) INDICATORS Life expectancy at birth Expected years Mean years GNI per capita (PPP $) of schooling of schooling DIMENSION Life expectancy index Education index GNI index INDEX Human Development Index (HDI) Inequality-adjusted DIMENSIONS Long and healthy life Knowledge A decent standard of living Human Development Index (IHDI) INDICATORS Life expectancy at birth Expected years Mean years GNI per capita (PPP $) of schooling of schooling DIMENSION Life expectancy Years of schooling Income/consumption INDEX INEQUALITY- Inequality-adjusted Inequality-adjusted Inequality-adjusted ADJUSTED life expectancy index education index income index INDEX Inequality-adjusted Human Development Index (IHDI) Gender Development Female Male Index (GDI) DIMENSIONS Long and Standard Long and Standard healthy life Knowledge of living healthy life Knowledge of living INDICATORS Life expectancy Expected Mean GNI per capita Life expectancy Expected Mean GNI per capita years of years of (PPP $) years of years of (PPP $) schooling schooling schooling schooling DIMENSION INDEX Life expectancy index Education index GNI index Life expectancy index Education index GNI index Human Development Index (female) Human Development Index (male) Gender Development Index (GDI) Gender Inequality DIMENSIONS Health Empowerment Labour market Index (GII) INDICATORS Maternal Adolescent Female and male Female and male shares Female and male mortality birth population with at least of parliamentary seats labour force ratio rate secondary education participation rates DIMENSION Female reproductive Female empowerment Female labour Male empowerment Male labour INDEX health index index market index index market index Female Male gender index gender index Gender Inequality Index (GII) Multidimensional DIMENSIONS Health Education Standard of living Poverty Index (MPI) INDICATORS Nutrition Child mortality Years School Cooking Sanitation Drinking Electricity Housing Assets of schooling attendance fuel water POVERTY Intensity Headcount MEASURES of poverty ratio Multidimensional Poverty Index (MPI) TECHNICAL NOTES 1 Technical note 1. Human Development Index The Human Development Index (HDI) is a summary The justification for placing the natural zero for measure of achievements in three key dimensions of life expectancy at 20 years is based on historical ev- human development: a long and healthy life, access to idence that no country in the 20th century had a life knowledge and a decent standard of living. The HDI expectancy of less than 20 years (Maddison 2010; is the geometric mean of normalized indices for each Oeppen and Vaupel 2002; Riley 2005). Maximum of the three dimensions. This technical note describes life expectancy is set at 85, a realistic aspirational the data sources, steps to calculating the HDI, and the target for many countries over the last 30 years. Due methodology used to estimate missing values. to constantly improving living conditions and medi- cal advances, life expectancy has already come very Data sources close to 85 years in several economies: 84.9 years in Hong Kong, China (Special Administrative Region) • Life expectancy at birth: UNDESA (2019). and 84.6 years in Japan. • Expected years of schooling: UNESCO Institute Societies can subsist without formal education, jus- for Statistics (2020), ICF Macro Demographic tifying the education minimum of 0 years. The maxi- and Health Surveys (2008–2020), United Nations mum for expected years of schooling, 18, is equivalent Children’s Fund (UNICEF) Multiple Indicator to achieving a master’s degree in most countries. The Cluster Surveys (2008–2020) and OECD (2019). maximum for mean years of schooling, 15, is the pro- • Mean years of schooling: UNESCO Institute for jected maximum of this indicator for 2025. Statistics (2020), Barro and Lee (2018), ICF Macro The low minimum value for gross national income Demographic and Health Surveys (2008–2020), (GNI) per capita, $100, is justified by the considera- UNICEF Multiple Indicator Cluster Surveys ble amount of unmeasured subsistence and nonmar- (2008–2020) and OECD (2019). ket production in economies close to the minimum, • GNI per capita: World Bank (2020), IMF (2020), which is not captured in the official data. The maxi- United Nations Statistics Division (2020). mum is set at $75,000 per capita. Kahneman and De- aton (2010) have shown that there is virtually no gain Steps to calculate Human in human development and wellbeing from annual Development Index values income above $75,000 per capita. Currently, only three countries (Liechtenstein, Qatar and Singapore) There are two steps to calculating HDI values. exceed the $75,000 income per capita ceiling. Having defined the minimum and maximum val- Step 1. Creating the dimension indices ues, the dimension indices are calculated as: actual value – minimum value Dimension index = . (1) Minimum and maximum values (goalposts) are set maximum value – minimum value in order to transform the indicators expressed in dif- ferent units into indices between 0 and 1. These For the education dimension, equation 1 is first goalposts act as “the natural zeros” and “aspiration- applied to each of the two indicators, and then the al targets”, respectively, from which component indi- arithmetic mean of the two resulting indices is taken. cators are standardized (see equation 1 below). They Using the arithmetic mean of the two education indi- are set at the following values: ces allows perfect substitutability between expected years of schooling and mean years of schooling, which Dimension Indicator Minimum Maximum seems to be right given that many developing coun- Health Life expectancy (years) 20 85 tries have low school attainment among adults but are Education Expected years of schooling (years) 0 18 very eager to achieve universal primary and second- Mean years of schooling (years) 0 15 ary school enrolment among school-age children. Standard of Because each dimension index is a proxy for ca- living GNI per capita (2017 PPP$) 100 75,000 pabilities in the corresponding dimension, the 2 HUMAN DEVELOPMENT REPORT / 2020 transformation function from income to capabilities per capita in local currency from current to constant is likely to be concave (Anand and Sen 2000) — that terms using two steps. First, the value of GNI per cap- is, each additional dollar of income has a smaller ef- ita in current terms is converted into PPP terms for fect on expanding capabilities. Thus for income the the base year (2017). Second, a time series of GNI per natural logarithm of the actual, minimum and maxi- capita in 2017 PPP constant terms is constructed by mum values is used. applying the real growth rates to the GNI per capita in PPP terms for the base year. The real growth rate Step 2. Aggregating the dimensional indices is implied by the ratio of the nominal growth of GNI per capita in current local currency terms to the GDP The HDI is the geometric mean of the three dimen- deflator. sional indices: For several countries without a value of GNI per capita in constant 2017 PPP terms for 2019 reported HDI = (I . I . I ) 1/3 Health Education Income in the World Development Indicators database, real growth rates of GDP per capita available in the World Example: Sudan Development Indicators database or in the Interna- tional Monetary Fund’s Economic Outlook database Indicator Value are applied to the most recent GNI values in constant Life expectancy at birth (years) 65.3 PPP terms. Expected years of schooling (years) 7.9 Official PPP conversion rates are produced by the Mean years of schooling (years) 3.8 International Comparison Program, whose surveys Gross national income per capita (2017 PPP $) 3,829 periodically collect thousands of prices of matched goods and services in many countries. The last Note: Values are rounded. round of this exercise refers to 2017 and covered 176 65.3 – 20 economies. Health index = = 0.6971 85 – 20 Estimating missing values 7.9 – 0 Expected years of schooling index = = 0.4380 18 – 0 For a small number of countries missing one of the four indicators, the HDRO estimated the missing val- 3.8 – 0 Mean years of schooling index = = 0.2513 15 – 0 ues using cross-country regression models. In this Report expected years of schooling were es- 0.4380 + 0.2513 timated for Bahamas, Congo, Equatorial Guinea, Fiji, Education index = = 0.3447 2 Gabon, Haiti, Liberia, Libya and Vanuatu, and mean years of schooling were estimated for Comoros, Dji- ln(3,829) – ln(100) Income index = = 0.5506 bouti, Eritrea, Grenada, Lebanon, Madagascar, Fed- ln(75,000) – ln(100) erated States of Micronesia, Saint Kitts and Nevis, South Sudan and Syrian Arab Republic. Human Development Index = (0.6971 . 0.3447 . 0.5506)1/3 = 0.510 Human development categories Methodology used to express income The 2014 Human development Report introduced a system of fixed cutoff points for the four categories of The World Bank’s 2020 World Development Indica- human development achievements. The cutoff points tors database contains estimates of GNI per capita in (COP) are the HDI values calculated using the quar- constant 2017 purchasing power parity (PPP) terms tiles (q) from the distributions of the component indi- for many countries. For countries missing this indica- cators averaged over 2004–2013: tor (entirely or partly), the Human Development Re- port Office (HDRO) calculates it by converting
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