Describe the different indicators that are used by UNDP to construct the Human Development Index (HDI). Why is a logarithmic transformation applied only to per capita income in the calculation of HDI?

Indicators Used in Constructing the HDI

The HDI is constructed using three primary indicators, one for each dimension of human development:

• Health: Life Expectancy at Birth: This indicator reflects the number of years a newborn infant would be expected to live if prevailing patterns of mortality at the time of their birth remain the same throughout their life. It is a key measure of health and longevity.
• Education: This dimension is measured using two sub-indicators:
  • Mean Years of Schooling: Average number of years of education received by people ages 25 and older.
  • Expected Years of Schooling: Number of years of schooling children are expected to receive if current enrolment rates continue.
  Prior to the 2010 revision, Gross Enrollment Ratio (GER) was used.
• Standard of Living: Gross National Income (GNI) per capita: This represents the average income of a country’s citizens, adjusted for purchasing power parity (PPP) to account for differences in the cost of goods and services across countries. It reflects the economic resources available to individuals.

Calculation of the HDI

Each dimension index is calculated as follows:

1. Dimension Index = (Actual Value – Minimum Value) / (Maximum Value – Minimum Value)

The HDI is then calculated as the geometric mean of the three dimension indices:

HDI = (Dimension Index for Health * Dimension Index for Education * Dimension Index for Standard of Living)^(1/3)

Logarithmic Transformation of GNI per Capita

A crucial aspect of the HDI calculation is the application of a logarithmic transformation to the GNI per capita. This transformation is *not* applied to the life expectancy or education indices. The rationale behind this lies in the concept of diminishing marginal utility of income. This economic principle states that as income increases, the additional satisfaction or well-being derived from each additional unit of income decreases.

Here's a breakdown of why this is important:

• Preventing Income Dominance: Without the logarithmic transformation, GNI per capita, being a relatively large number, could disproportionately influence the overall HDI value. Small changes in income could lead to significant changes in the HDI, overshadowing improvements in health and education.
• Reflecting Diminishing Returns: The logarithmic transformation compresses the range of income values, reducing the impact of very high incomes. This aligns with the idea that improvements in health and education have a greater impact on well-being at lower income levels than at higher income levels. For example, increasing income from $1,000 to $2,000 has a much larger impact on well-being than increasing it from $100,000 to $101,000.
• Ensuring Sensitivity to Lower Income Levels: The transformation makes the HDI more sensitive to improvements in the standard of living for those at the lower end of the income spectrum.

The specific formula used for the logarithmic transformation is:

Log(GNI per capita) = ln(GNI per capita) / ln(1000)

This ensures that the GNI per capita index is scaled appropriately and does not unduly influence the overall HDI value.

Implications of the Logarithmic Transformation

The logarithmic transformation contributes to a more balanced and nuanced assessment of human development. It ensures that the HDI reflects not only economic prosperity but also progress in health and education, giving a more holistic picture of a country’s development achievements. However, it's important to note that the HDI, even with this transformation, is still a simplification of a complex reality and should be used in conjunction with other indicators to gain a comprehensive understanding of development challenges and opportunities.