composite indicators: Human Development Index (HDI)

Economic Development – Composite Indicators

1. Why Use Composite Indicators?

• Single‑variable measures (e.g., per‑capita GDP) capture only the monetary side of development.
• Human development is multi‑dimensional – health, education and living standards all matter.
• A composite indicator combines several relevant outcomes into one comparable figure, making it easier to rank countries, to track progress over time and to evaluate the impact of policies.

2. Monetary Indicators (the “income” side of development)

Indicator	Definition (Cambridge syllabus)	Role in Development Analysis	Typical Data Source
GDP (Gross Domestic Product)	Total market value of all final goods and services produced within a country in a given year.	Measures overall economic activity; usually expressed per‑capita.	World Bank – World Development Indicators (WDI)
GNI (Gross National Income)	GDP plus net primary income (remittances, dividends, interest) received from abroad.	Reflects the total income available to residents; the HDI uses GNI PPP.	World Bank – WDI; IMF
NNI (Net National Income)	GNI minus depreciation of the capital stock.	Shows the net amount of income that can be used for consumption and investment.	World Bank – WDI
PPP (Purchasing‑Power Parity)	Adjustment that equalises the purchasing power of different currencies by using a common basket of goods.	Allows meaningful comparison of real living standards across countries; the HDI uses GNI PPP.	World Bank – International Comparison Program (ICP)

3. Non‑Monetary Indicators (the “human” side of development)

The Cambridge syllabus expects students to be familiar with the following core social‑development variables. They are used either directly in the HDI or in extended indices such as the MPI.

Indicator	What it measures	Typical Data Source
Life expectancy at birth (years)	Average number of years a newborn is expected to live if current mortality rates continue.	World Health Organization (WHO); UNDP Human Development Report
Infant mortality rate (deaths per 1 000 live births)	Indicator of health services and living conditions for the youngest.	WHO; World Bank
Maternal mortality ratio (deaths per 100 000 live births)	Quality of maternal health care.	WHO
Literacy rate (adult, %)	Proportion of people aged 15+ who can read and write a short simple statement.	UNESCO Institute for Statistics (UIS)
Primary, secondary & tertiary enrolment ratios (%)	Extent to which school‑age populations are in school.	UIS
Mean years of schooling (MYS)	Average number of years of education received by people aged 25 +.	UIS
Expected years of schooling (EYS)	Number of years a child of school‑entering age can expect to receive.	UIS
Access to safe water, sanitation & electricity (% of population)	Basic infrastructure and living‑standard dimension.	World Bank – WDI; WHO/UNICEF Joint Monitoring Programme

4. Classification of Economies (UN‑DP Income Groups)

These thresholds are used throughout the UNDP reports and are a frequent exam requirement when a question asks you to “classify” a country’s level of development.

Group	2024 GNI per capita (PPP $)
High‑income	> 20 000
Upper‑middle‑income	8 001 – 20 000
Lower‑middle‑income	1 001 – 8 000
Low‑income	≤ 1 000

Example: In 2023 the GNI PPP of Kenya was US$ 4 850, placing it in the **lower‑middle‑income** group.

5. Human Development Index (HDI)

The HDI is the flagship composite statistic used by the UNDP to rank countries on three fundamental dimensions of human well‑being.

5.1 Components, Indicators & Data Sources

Dimension	Indicator(s)	Typical Data Source
Health	Life expectancy at birth (years)	WHO; UNDP Human Development Report
Education	Mean years of schooling (MYS) & Expected years of schooling (EYS)	UNESCO Institute for Statistics (UIS)
Standard of living	GNI per capita (PPP $)	World Bank – International Comparison Program (ICP)

5.2 Normalisation (Min‑Max Method)

Each raw indicator is transformed to a dimension index between 0 and 1:

$$ I_{j}= \frac{X_{j}-X_{j}^{\min}}{X_{j}^{\max}-X_{j}^{\min}} $$

• $X_{j}$ – observed value of indicator $j$.
• $X_{j}^{\min}$ and $X_{j}^{\max}$ – fixed bounds set by the UNDP (see table).

Indicator	Minimum	Maximum
Life expectancy (years)	20	85
Mean years of schooling	0	15
Expected years of schooling	0	18
GNI per capita (PPP $)	100	75 000

5.3 Income Index – Logarithmic Transformation

Because the marginal benefit of income falls as people become richer, the income component is log‑transformed before normalisation:

$$ I_{IN}= \frac{\ln (GNI)-\ln (100)}{\ln (75\,000)-\ln (100)} $$

5.4 Education Index

$$ I_{ED}= \frac{I_{MYS}+I_{EYS}}{2} $$

$I_{MYS}$ and $I_{EYS}$ are each obtained with the min‑max formula above.

5.5 Aggregation – Geometric Mean

The three dimension indices are combined using a geometric mean, which penalises a low score in any one dimension:

$$ \text{HDI}= \sqrt[3]{I_{HE}\times I_{ED}\times I_{IN}} $$

• $I_{HE}$ – Health (life expectancy) index
• $I_{ED}$ – Education index
• $I_{IN}$ – Income (GNI) index

5.6 Worked Example – Real 2023 Data (Norway)

Data taken from the UNDP Human Development Report 2024 (2023 reference year).

Indicator	2023 Value	Normalised Index
Life expectancy (years)	82.9	$I_{HE}= \frac{82.9-20}{85-20}=0.962$
Mean years of schooling (MYS)	12.7	$I_{MYS}= \frac{12.7-0}{15-0}=0.847$
Expected years of schooling (EYS)	18.0	$I_{EYS}= \frac{18.0-0}{18-0}=1.000$
GNI per capita (PPP $)	66 900	$I_{IN}= \frac{\ln(66\,900)-\ln(100)}{\ln(75\,000)-\ln(100)}\approx0.986$

Education index:

$$ I_{ED}= \frac{0.847+1.000}{2}=0.924 $$

Overall HDI:

$$ \text{HDI}= \sqrt[3]{0.962 \times 0.924 \times 0.986}=0.958 $$

Interpretation: Norway falls in the “Very high human development” band (≥ 0.800).

6. Inequality‑Adjusted HDI (IHDI)

• Why it exists: The standard HDI treats each country as if every citizen enjoys the same level of health, education and income. The IHDI discounts each dimension for within‑country inequality (using a Gini‑type measure).
• Calculation (simplified): For each dimension a “loss” due to inequality is estimated, then the three adjusted dimension indices are combined with the same geometric mean.
• Numerical illustration (2023 Brazil):
  • HDI = 0.765 (from the UNDP table).
  • Inequality loss = 0.10 (overall).
  • IHDI = HDI × (1 – loss) = 0.765 × 0.90 ≈ 0.689.
  The drop from 0.765 to 0.689 shows that inequality reduces the effective level of human development.

7. Gender Development Index (GDI)

• Calculates separate HDI values for males and females using gender‑specific data for life expectancy, education and income.
• GDI = Female HDI ÷ Male HDI. A value < 1 indicates that women are disadvantaged.
• Example (2023 India): Male HDI = 0.714, Female HDI = 0.636 → GDI = 0.636 / 0.714 ≈ 0.89.
• Useful in exam questions that ask you to “evaluate gender disparities in development”.

8. Multidimensional Poverty Index (MPI)

The MPI measures acute deprivation across three equally‑weighted dimensions: health, education and living standards. Ten indicators are used (e.g., child mortality, nutrition, school attendance, electricity, sanitation, etc.).

• Each household is assigned a deprivation score (0–10). A score ≥ 33 % counts the household as “multidimensionally poor”.
• MPI = Headcount ratio × Average intensity of deprivation.
• Exam tip: when a question asks you to “compare poverty and development”, contrast the income‑based poverty line with the MPI’s broader view.

9. Mean Years of Schooling – Weighted (MEW)

MEW refines the education component by weighting mean years of schooling by enrolment rates at each level (primary, secondary, tertiary). It is useful when the exam explicitly asks for an “education‑focused” composite indicator.

10. Interpreting HDI Scores (UNDP 2024 bands)

• Very high human development: HDI ≥ 0.800
• High human development: 0.700 ≤ HDI < 0.800
• Medium human development: 0.550 ≤ HDI < 0.700
• Low human development: HDI < 0.550

11. Limitations of the (Standard) HDI

1. Data quality and coverage: Many low‑income countries have incomplete or outdated statistics on schooling and health, leading to estimates or gaps.
2. Equal weighting assumption: The HDI gives each of the three dimensions the same weight (1/3). Policy priorities differ – a country may value health far more than income.
3. Omission of inequality and gender: The standard HDI masks within‑country disparities. This is why the IHDI and GDI were introduced.
4. Aggregation bias: The geometric mean reduces the impact of an extreme value but still hides the distribution of outcomes (e.g., a very high income can compensate for very low education).
5. Conceptual simplification: Reducing multidimensional welfare to a single number inevitably loses nuance; complementary indices (IHDI, GDI, MPI, MEW) are required for a fuller picture.
6. Choice of bounds: The min‑max limits are arbitrary and are periodically revised, which can affect comparability over time.

12. The Kuznets Curve and Composite Indicators

• Kuznets hypothesis: As a country’s GNI per capita rises, inequality first increases (industrialisation, urban‑rural migration) and then falls (redistributive policies, education). The resulting relationship is an inverted‑U.
• Link to HDI/IHDI:
  • When income rises, the HDI generally improves because health and education also tend to increase.
  • The IHDI may reveal a turning point: if income growth is accompanied by rising inequality, the IHDI can plateau or even decline while the HDI continues to rise.
• Exam‑style evaluation:
  1. State the Kuznets curve and its relevance to development.
  2. Explain how the HDI reflects the “up‑ward” part of the curve.
  3. Use the IHDI to illustrate the “down‑ward” part (inequality erodes gains).
  4. Discuss empirical evidence (e.g., many East Asian economies show a muted Kuznets pattern because of strong education investment).

13. Suggested Diagram (for revision)

14. Exam Tips & Key Take‑aways

• When asked to “calculate” an index, always:
  1. State the raw data and its source.
  2. Show the normalisation step (including the log transformation for income).
  3. Combine the indices using the geometric mean.
• Structure evaluation answers in three parts:
  1. Outline the construction of the indicator (strength).
  2. Discuss the main limitations (data, weighting, omission of inequality/gender, aggregation).
  3. Mention complementary indices (IHDI, GDI, MPI, MEW) that address those weaknesses.
• Remember the UNDP income‑group thresholds – they often appear in “classify the country” questions.
• Use real‑world examples (e.g., Norway – very high HDI; Brazil – HDI vs IHDI gap; India – GDI < 1) to demonstrate depth of knowledge.
• Link the Kuznets curve to composite indicators when the question asks you to “evaluate the relationship between economic growth and human development”.