Human Assets Index: Insights from a Retrospective Series Analysis

Abstract

We build retrospective series for the Human Assets Index from the United Nations—Committee for Development Policy data. The HAI is a composite index which includes health and education components. Our series cover 145 developing countries for the period 1990–2014. The analysis provides insights into the changes in the HAI and its distribution for different groups of Developing Countries. We discuss the importance of the HAI’s components by considering the weight given to them in the index. We propose a new weighting scheme which is optimized based on the correlation ratio and linearity (nonlinearity) relationship between components, and we present the country ranking changes due to the optimized HAI.

Appendix: Methods for Constructing Retrospective Series

1.1 Percentage of Population Undernourished

1.1.1 Definition

The percentage of population undernourished is computed and regularly reported by the Food and Agriculture Organization of the United Nations (FAO). It estimates the proportion of the population with a calorie intake below the minimum necessary for an active and healthy life. The FAO uses the cutoff of 1800 calories as the average minimum energy requirement per person per day.⁹

1.1.2 Calculation Principles of the Undernourishment Index Retrospective Series

Primary data on the prevalence of undernourishment is retrieved from the official dataset FAOSTAT (data available at http://faostat3.fao.org/home/E). Data are complete over all the 25 years except for 28 countries for which there is no information available on undernourishment, which represent 19% of the sample.¹⁰ To deal with this, we resort to econometric regressions to predict undernourishment prevalence from available information on strong correlates, income distribution measured by the Gini index, and gross national income per capita (GNIpc).

1.1.2.1 Method 1: Using GNIpc, GINI and Region Fixed Effects

This method is used to impute missing data on undernourishment to countries with complete series on GNIpc and GINI. The first step consists in estimating the following OLS regression on the sample of countries/years for which undernourishment, GNIpc and GINI data are available, which also exploit region fixed effects:

$$ U_{1it} = \alpha_{1} + \beta_{1} *{ \ln }(GNIpc_{it} ) + \gamma_{1 } *{ \ln }\left( {Gini_{it} } \right) + \delta_{1} *t_{t} + \mu_{1i} *region + \varepsilon_{1it} $$

With U undernourishment, FAO primary data; ${\text{GNIpc}}_{ }$ Gross national income per capita, World Development Indicators—World Bank; Gini: Gini index, World Development Indicators—The World Bank; region: a set of dummies Middle East and North Africa (MENA), Sub Saharan Africa (SSA), South Asia (SA), East Asia and Pacific (EAP), Latin America and Caribbean (LAC) and Europe and Central Asia (ECA).

Coefficient are taken out and used to calculate values for countries where data on U are missing but data on GNIpc and GINI are available:

$$ \widehat{{U_{1it} }} = +_{1} *{ \ln }(GNIpc_{it} ) + *{ \ln }\left( {Gini_{it} } \right) + *t_{t} + * region $$

Data have been generated using this method for Burundi, Comoros, Democratic Republic of Congo, Papua New Guinea, Federated States of Micronesia (for the 1993–2014 period), Saint Lucia, Seychelles, Syria (1990–2007) and Sudan (2008–2014).

1.1.2.2 Method 2: Using GNI and Region Fixed Effects

This method is used to impute missing data on undernourishment to countries (-years) for which only series on GNIpc are available. The first step consists in estimating the following OLS regression:

$$ U_{2it} = \alpha_{2} + \beta_{2} *{ \ln }(GNIpc_{it} ) + \delta_{2} *t_{t} + \mu_{2i} *region + \varepsilon_{2it} $$

Coefficient are taken out and used to calculate missing values:

$$ \widehat{{U_{2it} }} = + *{ \ln }(GNIpc_{it} ) + *t_{t} + * region $$

This Method 2 has been used to produce data for Antigua and Barbuda, Bhutan, Dominica, Equatorial Guinea, Eritrea (for the 1994–2011 period), Grenada, Libya (2001–2014), Marshall Island (1995–2014), Palau (1993–2014), Saint Kitts and Nevis, South Sudan (2010–2014), Tonga and Tuvalu (2001–2014).

1.1.2.3 Special Cases

For some countries, the use of methods 1 and 2 is not possible because data on GINI and GNIpc are missing. Thus:

• Data for Somalia are obtained from the 2012 retrospective series of Undernourishment; and extrapolated on 2012–2014.

• Former Sudan data prior to 2008 are used for Sudan and South Sudan;

• Data for Nauru are obtained from the source indicated by the UN-CDP (from Statistics for Development Division-Secretariat of the Pacific Community: http://www.spc.int/nmdi/poverty).

After the use of these imputation methods, only 27 data are still missing, representing 0.7% of the sample of 145 countries over 1990–2014: Marshall Islands (1990–1994), Federated States of Micronesia (1990–1992), Nauru (1990–2005), and Palau (1990–1992).

1.1.3 Normalization and Bounds

Undernourishment, which is negatively related to human assets, is normalized through the following inversed formula (the higher the undernourishment, the lower the index):

$$ U_{Index} = \left\{ {\begin{array}{ll} {100*\frac{Max - x}{Max - min} } & { if\, min < x < max} \\ 0 & { if\, x > Max} \\ {100} & {if \,x < min} \\ \end{array} } \right. $$

With x is the country/year undernourishment prevalence value.

Lower bound (Min): 5 Upper bound (Max): 65

1.2 Under-Five Mortality Index

1.2.1 Definition

As explained in UN-DESA definitions, the Under-5 mortality rate “expresses the probability of dying between birth and age five. It is expressed as deaths per 1000 births”. The under-five mortality rate provides comprehensive information on the health impact of social, economic and environmental conditions in a country. It is influenced by poverty, education; by the availability, accessibility and quality of health services; by environmental risks including access to safe water and sanitation; and by nutrition. Following the UN-CDP, we use the under-five mortality rate from the United Nations Inter-agency Group for Child Mortality Estimation (CME), CME Info, available from http://childmortality.org.

1.2.2 Calculation Principles of the Under-Five Mortality Index Retrospective Series

The estimates of Under-five mortality rates from the United Nations—CME are generated with a regression model for assessing levels and trends for all countries in the world over a long time period (Alkema and New 2014). Thus, primary data on under-five mortality rates are fully complete over 1990–2015.

1.2.3 Normalization and Bounds

The Under-five mortality rate, which is negatively related to human assets, is normalized so as to get the index to enter the HAI through the following inversed formula (the higher the under-five mortality rate, the lower the index):

$$ U5M_{Index} = \left\{ {\begin{array}{ll} {100*\frac{Max - x}{Max - min}} & {if \, min < x < max} \\ 0 & {if\, x > Max} \\ {100} & {if \,x < min} \\ \end{array} } \right. $$

With x under-five mortality rate value.

Lower bound (Min): 10 Upper bound (Max): 175

1.3 Adult Literacy Rate Index

1.3.1 Definition

As defined by the UN-DESA, the adult literacy rate “measures the number of literate persons aged fifteen and above expressed as a percentage of the total population in that age group. A person is considered literate if he/she can read and write, with understanding, a simple statement related to his/her daily life”.¹¹ The indicator shows the accumulated achievement of primary education and literacy programs in imparting basic literacy skills to the population, thereby enabling them to apply such skills in life, contributing to the economic and socio-cultural development. The adult literacy rate is regularly reported by the UNESCO Institute for Statistics at http://www.uis.unesco.org/.

1.3.2 Calculation Principles of the Adult Literacy Index Retrospective Series

Despite significant improvement in terms of data coverage, a large number of missing data still exist in the adult literacy rate database provided by the UNESCO Institute for Statistics. For our sample of 145 countries over 1990–2014, 3160 data out of 3625 are missing (about 87%). We first resort to simple linear interpolation and extrapolation to estimate data for countries where intermediate, beginning or end-of period data are scarcely missing (no more than 5 missing data). After this step, 992 missing data remain (about 27%), as the interpolation method is not relevant for 18 countries for which data are widely missing. We then rely on econometric methods of imputation.

1.3.2.1 Method 1: Using GNI and Country Fixed Effects

This method is used for countries for which data on LR exist but are too scarce to use simple inter or extrapolation. It is based on a regression that links Literacy rate to GNI per capita, time and country fixed effects (using the within estimator):

$$ LR_{1it} = \alpha_{1} + \beta_{1} *\ln \left( {GNIpc_{it} } \right) + \delta_{1} * t_{t} + \mu_{1i } + \varepsilon_{1it} $$

With $GNIpc_{ }$: Gross national income per capita, World Development Indicators.

Literacy rate is then generated by:

$$ \widehat{{LR_{1it} }} = \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\alpha }_{1} + \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\beta }_{1} *\ln (GNIpc_{it} ) + \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\delta }_{1} * t_{t} + \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\mu }_{1i } $$

This method is used to generate data for Solomon Islands over 1992–2014.

1.3.2.2 Method 2: Using GNIpc and Region Fixed Effects

This method is used for countries which have only one observation over the period 1990–2014. For these countries, it is not relevant to run country fixed-effects estimates using within estimator. Therefore, we introduce region fixed effects and provide estimates using OLS estimator:

$$ LR_{2it} = \alpha_{2} + \beta_{2} *\ln \left( {GNIpc_{it} } \right) + \delta_{2} * t_{t} + \mu_{2i } *Region_{i} + \varepsilon_{2it} $$

With $GNIpc_{ }$: Gross national income per capita, World Development Indicators- World Bank; Region: dummies Middle East and North Africa (MENA), Sub Saharan Africa (SSA), South Asia (SA), East Asia and Pacific (EAP), Latin America and Caribbean (LAC) and Europe and Central Asia (ECA).

The predicted value for Literacy rate is then:

$$ \widehat{{LR_{2it} }} = \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\alpha }_{2} + \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\beta }_{2} *{ \ln }(GNIpc_{it} ) + \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\delta }_{2} *t_{t} + \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\mu }_{2i } * Region_{i} $$

This method is used to generate data for Djibouti over 1992–2005, and over the entire period for Bahamas, Barbados, Dominica, Fiji, Grenada, Israel, Kiribati, Marshall Islands, Federated States of Micronesia, Korea Republic, Saint Kitts and Nevis, Saint Lucia, Saint Vincent and the Grenadines and Tuvalu.

1.3.2.3 Special Cases

Due to incomplete data on GNIpc, both imputation methods are not applicable for a couple of countries:

• For Somalia, we use data from the last previous retrospective series;

• To complete data for Djibouti (2006–2014), we use data from the last previous retrospective series; and extrapolated over 2012–2014.

After the use of these imputation methods, only 20 data are still missing, representing 0,6% of the sample of 145 countries over 1990–2014: Marshall Islands (1990–1994), Federated States of Micronesia (1990–1991), Solomon Islands (1990–1991), Tuvalu (1990–2000).

1.3.3 Normalization and Bounds

The Adult literacy rate, which is positively related to human assets, is normalized using the following min–max formula (the higher the literacy rate, the higher the index; the literacy index is merely the adult literacy rate multiplied by 100):

$$ LR_{Index} = \left\{ {\begin{array}{ll} {100*\frac{x - min}{Max - min}} & { if \,min < x < max} \\ {100} & { if\, x > Max} \\ 0 & { if\, x < min} \\ \end{array} } \right. $$

With x Adult literacy rate value.

Lower bound (Min): 25 Upper bound (Max): 100

1.4 Gross Secondary School Enrolment Ratio Index

1.4.1 Definition

The secondary education, which is one of the greatest challenges in poor countries, is usually measured by the gross secondary school enrolment ratio. As defined by the UNDP-DESA-DPAD, this indicator “measures the number of pupils enrolled in secondary schools, regardless of age, expressed as a percentage of the population in the theoretical age group for the same level of education”.¹² It provides information on the share of population with the level of skills deemed to be necessary for development. The indicator is regularly reported by the United Nations Educational, Scientific and Cultural Organization (UNESCO), Institute for Statistics (available at http://www.uis.unesco.org).

1.4.2 Calculation Principles for the Retrospective Series of the Gross Secondary Enrolment Ratio Index

The raw data downloaded from the UNESCO website are missing for 1406 observations out of 3625 (39%). For intermediate and end-of period missing data, when no more than 5 data are missing, we use linear interpolation and extrapolation to fill them. After this step, 511 missing data remain (14%). For the other cases, we use imputation based on econometric regression.

1.4.2.1 Method 1: Beginning of Period, Using GNIpc and Country Fixed Effects

This method is used for values missing at the beginning of the series. We use the following model which includes income level, 1 year lead value of gross secondary school enrolment ratio, and time and country fixed effects. The Within estimator is used:

$$ SE_{1it} = \alpha_{1} + \beta_{1} *\ln \left( {GNIpc_{it} } \right) + \gamma_{1} SE_{i,t + 1} + \delta_{1} * t_{t} + \mu_{1i } + \varepsilon_{1it} $$

The gross secondary school enrolment ratio is then generated, anti-chronologically and year after year:

$$ \widehat{{SE_{1it} }} = \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\alpha }_{1} + \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\beta }_{1} *\ln \left( {GNIpc_{it} } \right) + \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\gamma }_{1} SE_{i,t + 1} + \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\delta }_{1} * t_{t} + \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\mu }_{1i } $$

This method has been used sporadically to generate data for some countries, but more widely for Equatorial Guinea (2006–2014); Gabon (2003–2014); Cambodia (2009–2014); Bahrain (2007–2014); Guinea-Bissau (2007–2014); Haiti (1990–2014; Kiribati (2009–2014); Palau (1990–2002), Nauru (1990–1999); Federated States of Micronesia (2006–2014); Marshall Islands (1990–1998; 2010–2014); Libya (2007–2014); Maldives (2005–2014); Timor-Leste(1990–2000); Trinidad and Tobago (2005–2014); Tuvalu (1990–2000); United Arab Emirates (2000–2014).

1.4.2.2 Special Cases

Due to missing data on SE and GNIpc, data remain missing for the entire period for Singapore, South Sudan, Turkmenistan (except the year 2014), and Democratic People’s Republic of Korea (except for the year 2009). This represents 98 data or 2.7% of the sample.

1.4.3 Normalization and Bounds

The gross secondary school enrolment ratio, which is positively related to human assets, is normalized using the following min–max formula (the higher the gross secondary school enrolment ratio, the higher the index):

$$ SE_{Index} = \left\{ {\begin{array}{ll} {100*\frac{x - min}{Max - min} } & { if \,Min < x < max} \\ {100} & { if\, x > Max} \\ 0 & { if \,x < min} \\ \end{array} } \right. $$

With x Gross secondary school enrolment ratio value.

Lower bound (Min): 10 Upper bound (Max): 100