Испанские ученые посчитали Индекс человеческого развития

Испанский образовательный фонд Rafael del Pino опубликовал индекс, складывающийся из таких компонентов, как продолжительность жизни, образование и доходы на душу населения. Индекс просчитан для периода с 1870 по 2007 год.

Historical Index of Human Development

Human wellbeing is widely viewed as a multidimensional phenomenon, in which income is only one facet. Human development, originally defined as a process of enlarging people’s choices, namely, enjoying a healthy life, acquiring knowledge and achieving a decent standard of living, provides a multidimensional measure of wellbeing.

These achievements provide individuals with freedom to choose and the opportunity to lead their own lives. Thus, human development can be depicted as positive freedom by which individuals are granted access to resources, including property, that allow them to develop their personal potential.

Dimensions of human development

In order to provide a synthetic measure of human development, its different dimensions are expressed in index form,

life expectancy at birth as a proxy for a healthy life,
education measures (literacy, schooling) for access to knowledge,
and discounted GDP per head as a surrogate for wellbeing dimensions other than education and health.

Life expectancy is defined as the average number of years of life which would remain for males and females reaching the ages specified if they continued to be subjected to the same mortality experienced in the year(s) to which these life expectancies refer.

The rate of adult literacy is defined as the percentage of the population aged 15 years or over who is able to read and write.

Gross total enrolment rate provides the percentage of population in the relevant age cohort enrolled in primary, secondary, and tertiary education.

GDP per head is expressed in 1990 dollars adjusted for its purchasing power adjusted , that it, for the difference in price level across countries (the so-called Geary-Khamis [G-K] 1990 $).

As social variables (longevity and education) have upper and lower bounds (unlike GDP per head that has not known upper bound), they are transformed non-linearly in order to allow for two main facts: that increases of the same absolute size represent greater achievements the higher the level at which they take place; and that quality improvements are associated to increases in quantity. Thus,

I = f (x, Mo, M) = (log (M – Mo) – log (M – x)) / log (M – Mo),

Where I is the dimension index, x is an indicator of a country’s standard of living, M and Mo are the maximum and minimum values, respectively, or goalposts, that facilitate comparisons over time and log stands for the natural logarithm. The index for each dimension ranges between 0 and 1.

In the case of GDP per head, as it is intended as crude proxy for those dimensions of wellbeing other than education and health, logarithmic transformation has been introduced. The log transformation implies that, in terms of human development, returns of per capita income decline as it reaches higher levels. Given its non-bounded nature, without this transformation, GDP per head would dominate the human development index rendering it redundant. In order to get the income index I have used the following expression, in which x, M, and Mo are expressed in logs.

I = (x – Mo) / (M – Mo),

Goalposts are set for human development’s different dimensions. For life expectancy at birth, the maximum and the minimum values were established at 83.2 and 20 years, respectively. For education, adult literacy and gross enrolment (primary, secondary, and tertiary) rates, maximum and minimum values of 100 and 0 were fixed. Then, they were combined into a single education index using an unweighted geometric average. In the case of per capita GDP, the maximum and minimum values over 1870-2007 were G-K 1990 $42,916 and $206, respectively.

The Historical Index of Human Development

The indices for each dimension are, then, combined using equal weights into an index of human development.

In an attempt to reduce the substitutability between its different dimensions -namely, to avoid that a high achievement in one dimension linearly compensates for a low achievement in another-, the indices for each dimension are combined into a historical index of human development using a geometric average.

If we denote the non-linearly transformed values of life expectancy and education as LEB and EDU, and the adjusted per capita income as UNY, the historical index of human development can be expressed as,

HIHD = LEB^1/3 EDU^1/3 UNY^1/3

Time and Spatial Coverage

As regards the time span considered, the initial date, 1870, has been as the starting point because it is when large scale improvements in health, helped by the diffusion of the germ theory of disease since the 1880s, and mass education began in Western Europe and the European Offshoots. It is also in the late nineteenth century when, along the advance in medical knowledge, social spending started expanding in Western Europe and its offshoots. The final year, 2007, represents the eve of the Great Recession.

Over the entire time span, 1870-2007, 96 countries are considered, and its number rises up to 104, 137, and 157 countries for the samples starting in 1913, 1950, and 1990, respectively. These samples represent above 90 per cent of the world population (and practically 100 per cent after 1950).

Referencias bibliográficas

Prados de la Escosura, L. (2015), “World Human Development, 1870-2007”, Review of Income and Wealth 61 (2): 220-247

United Nations Development Programme (UNDP) (2014), Human Development Report 2014, New York: United Nations Development Programme.

Как выглядит Российская империя, затем СССР, а затем и РФ в сравнении с другими странами и по годам с 1870 до 2007 года можно увидеть на графиках.