Estimation of inequality indices with decomposition by subgroup

Inequality indices which are decomposable by population subgroup are increasingly used to analyze the anatomy of (income) inequality and also for analysis of secular trends. Examples of subgroup partitions include: age group of household head; work attachment; family type. Particularly useful are the class of additively decomposable indices, for which total inequality can be written as the weighted sum of inequality within each subgroup, plus inequality between groups. It is now well known that the only indices with this property belong to the so-called Generalized Entropy (GE) class, which includes the two Theil indices and the coefficient of variation. The so-called Atkinson class of indices is decomposable but not additively (and the Gini coefficient is neither). This talk introduces the author's program ineqdeco for calculating GE, Atkinson, and Gini inequality indices with options for weighted data and decompositions by population subgroup, and gives an empirical illustration and mentions several Stata programming issues. Time permitting, the talk will also introduce the following related programs: geivars which calculates sampling variances for GE inequality measures with (f)weighted data; povdeco which calculates three Foster, Greer and Thorbecke poverty indices with options for weighted data and decompositions by population subgroup; sumdist, a utility for summarising quantiles and (generalized) Lorenz ordinates of a distribution; and smfit and dagumfit which fit the Singh–Maddala (Burr Type 12) and Dagum (Burr Type 3) 3-parameter distributions to unit-record data by ML with options to calculate the predicted income quantiles and inequality indices.