Theil Index

The Theil Index is a statistical measure of inequality developed by Dutch econometrician Henri Theil in his 1967 book Economics and Information Theory. It applies Shannon's concept of information entropy to income or wealth distributions, quantifying how far an observed distribution diverges from a perfectly equal one.

The index ranges from 0 (perfect equality, where every unit holds an identical share) upward, with higher values indicating greater inequality. Its theoretical maximum equals ln(N), where N is the number of individuals or units in the population, so the bound depends on sample size. For interpretation, Theil values are often normalized or compared across similarly sized populations.

Its defining advantage over the more famous Gini coefficient is additive decomposability. A national Theil Index can be split cleanly into:

• a within-group component (inequality inside regions, ethnic groups, or sectors), and
• a between-group component (inequality between the group means).

This property makes it especially useful for researchers studying regional or spatial inequality. The World Bank, UNU-WIDER, and the OECD have used Theil decompositions to analyze, for example, how much of China's national income inequality stems from coastal-versus-interior gaps versus inequality within provinces, or how EU-wide inequality breaks down into between-country and within-country shares.

Two common variants exist. The Theil T index weights by income shares and is more sensitive to changes at the top of the distribution. The Theil L index (also called the mean log deviation) weights by population shares and is more sensitive to changes at the bottom. Both belong to the broader family of Generalized Entropy (GE) measures, corresponding to GE(1) and GE(0) respectively.

Limitations include lack of an intuitive scale (unlike Gini's 0–1 range), sensitivity to zero or negative incomes, and dependence on the quality of disaggregated data. Despite this, the Theil Index remains a standard tool in development economics, regional science, and inequality research where group structure matters.