The multi-decomposition of the Hirschman-Herfindahl index: measuring household inequality in Cameroon, 1996-2001

This research proposes a new decomposition of the Hirschman-Herfindahl index (which is equal to half the square of the coefficient of variation) into subgroup and income source. The method for decomposing into subgroups is similar to that used by Dagum when decomposing Gini's index. This bidimensional decomposition helps measure the contributions of income sources taken independently and the contributions arising from links between pairs of these income sources within and between subgroups. This approach gives rise to new components of the total inequality. The method is used here to break down and analyse the evolution of household expenditure inequality in Cameroon during the period 1996 to 2001. The analysis reveals that the inequality has substantially increased in the urban areas, a situation blamed to a large extent on expenditures on equipment-furniture-goods and services; while inequality declined in the rural areas.