Gini Coefficient (G): Measuring Income and Wealth Inequality

Definition and Mathematical Foundations

The Gini coefficient quantifies the average absolute difference between every pair of observations, divided by twice the mean. Formally, for a population with values x₁, x₂, …, xₙ and mean μ, G = (1/(2n²μ)) Σ₁ⁿ Σ₁ⁿ |xᵢ − xⱼ|. When income is equally distributed, all pairwise differences vanish and G = 0. Concentration of income in a single individual maximises differences, pushing G toward 1.

A more intuitive geometric interpretation uses the Lorenz curve, which plots cumulative population share on the horizontal axis against cumulative income share on the vertical axis, after ordering individuals by income. The Gini coefficient equals twice the area between the Lorenz curve and the 45° equality line: G = 1 − 2 ∫₀¹ L(p) dp, where L(p) denotes the Lorenz curve at percentile p. Discretely, summing trapezoids under the curve yields G = 1 − Σ (Lᵢ + Lᵢ₋₁) · Δp, with Δp representing population share increments.

Because the Gini coefficient depends solely on relative shares, multiplying every observation by a constant leaves G unchanged. This scale invariance makes it suitable for comparing countries with vastly different income levels. However, adding a constant to all incomes reduces G, highlighting that transfers such as universal basic income can, in theory, lower inequality even without changing rank ordering.

Data Preparation and Calculation

Accurate Gini estimation begins with clean, representative data. Household surveys typically collect income components (wages, transfers, capital income) along with sampling weights. Apply weights when constructing Lorenz curves to ensure each observation reflects its population share. Adjust for household size using equivalence scales if the goal is to measure individual welfare rather than household totals.

Sorting observations in ascending order enables cumulative sum calculations. Spreadsheet implementations can compute Gini by combining sorted arrays with cumulative totals, but scripting languages or statistical packages offer greater transparency and reproducibility. Document handling of negative incomes, zero values, and outliers: options include truncating to zero, offsetting with a constant, or treating losses separately. These choices affect G, especially in datasets with entrepreneurs or capital gains.

Sampling variability matters. For complex survey designs, use replicate weights or bootstrap methods to estimate standard errors and confidence intervals. Publishing G alongside uncertainty builds trust and allows significance testing between regions or time periods. When comparing administrative data with survey-based estimates, reconcile definitions (pre-tax vs. post-tax, individual vs. household) to avoid misleading conclusions.

Applications

Public policy. Governments use Gini trends to evaluate tax reforms, social protection, and labour-market interventions. Progressive taxation or targeted cash transfers often appear as declines in G, while regressive policy shifts push it upward. International organisations benchmark member states to guide aid allocation and sustainable development strategies.

Corporate strategy and ESG. Companies assess internal pay structures by computing Gini coefficients for wages or bonuses. Supply-chain managers use the metric to gauge concentration risk among vendors, while investors monitor Gini-based sustainability scores when screening portfolios for social impact.

Urban planning and housing. City planners analyse neighbourhood-level Gini coefficients derived from property values or rent burdens to prioritise affordable housing and transit investments. Utility regulators examine energy-bill inequality to design rate structures that protect low-income households.

Education and health. School districts evaluate Gini coefficients of funding per pupil to ensure equitable resource distribution. Public-health agencies use the measure to study disparities in insurance coverage, vaccine access, or environmental exposure.

Governance and Best Practices

Transparency is essential when publishing inequality metrics. Provide reproducible code snippets or methodological appendices that describe weighting, data cleaning, and variance estimation. Version-control datasets and scripts so revisions can be audited. When releasing corporate or regional Gini coefficients, include independent assurance or third-party reviews where feasible.

Integrate inequality monitoring with broader performance frameworks. For example, municipalities can tie Gini targets to housing affordability or climate resilience metrics, ensuring that social outcomes complement environmental goals. Organisations should revisit calculations annually, capturing the impact of new policies or economic shocks.