IA idea · Finance & economics
Measuring inequality: fitting Lorenz curves and computing the Gini coefficient
Research question
Which function best fits the Lorenz curve of income in [two countries], and how close is the Gini coefficient calculated by integrating that function to the officially published value?
Adapt it: change the place, the data or the comparison until the question is yours.
Why it makes a good exploration
The Gini coefficient is quoted in the news but rarely explained. It is an area between two curves — a direct use of integration — and fitting the Lorenz curve is a genuine modelling decision.
The mathematics you'll need
- Lorenz curves from income shares by quintile
- Fitting a function such as L(x) = xᵏ or other forms
- Definite integration: G = 1 − 2∫₀¹ L(x) dx
- Trapezoidal rule comparison
Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.
Where the data comes from
Income shares by quintile or decile from the World Bank or Our World in Data.
- World Bank Open Data — Development indicators (GDP, life expectancy, mortality, internet use) for every country, usually from 1960.
- Our World in Data — Clean country-level time series (CO₂, population, health, energy, education) with CSV download on every chart.
Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.
A possible outline
- Explain the Lorenz curve and the Gini coefficient.
- Plot the cumulative shares for two countries.
- Fit models and choose the best.
- Integrate to find G; compare with the trapezoidal estimate and official figures.
- Reflect on what the Gini hides.
Pitfalls that cost marks
- Models that do not pass through (0,0) and (1,1).
- Mixing income and wealth data.
- Not explaining why the trapezoidal estimate differs.
Showing personal engagement
- Compare your own country with another you know.
- Discuss a policy change and its effect on the curve.
- Explain Gini to a family member.
See Criterion C: personal engagement for what examiners look for.
Taking it further
Compare the trend in Gini over 30 years and discuss whether your model's parameter is a better measure.