Ginikoefficient

The Ginikoefficient, commonly referred to as the Gini coefficient, is a statistical measure of inequality in a distribution such as income or wealth. It summarizes how far a distribution deviates from perfect equality, where everyone has the same amount, and how much of the total is held by different individuals or groups.

The coefficient ranges between 0 and 1 (or 0 to 100 if expressed as a percentage). A value of 0 indicates perfect equality, while a value of 1 (or 100) indicates maximal inequality under the chosen distribution. In practice, real-world values typically fall between these extremes and vary by country, year, and data source.

Calculation can be done via the Lorenz curve or directly from data. If the observations x_(i) are sorted in ascending order and μ is the mean, the discrete formula commonly used is:

G = (1 / (n μ)) ∑_{i=1}^n (2i − n − 1) x_(i),

where n is the number of observations. Equivalently, G can be defined as one minus twice the area under the Lorenz curve, with the Lorenz curve plotting the cumulative share of income against the cumulative share of people.

Applications and interpretation: the Gini coefficient is widely used to compare inequality across countries or over time, and to study links between inequality and other socioeconomic outcomes. It is employed in economics, development research, and policy analysis by organizations such as the World Bank and OECD.

Limitations: the Gini coefficient depends on how a population is defined and measured, can be sensitive to data quality and top-coding, and does not reveal who is advantaged or the specific shape of the distribution. Different definitions of income or wealth and sampling methods can affect comparability.

History: the measure is named after Corrado Gini, an Italian statistician who introduced it in the early 20th century.