The Theil Index in Sequences of Nested and Hierarchic Grouping Structures: Implications for the Measurement of Inequality through Time with Data Aggregated at Different Levels of Industrial Classification

This paper discusses the implications of the decomposition property of the Theil index in sequences of nested and hierarchic grouping structures, formalizing general results applicable to a generic sequence of grouping structures. A specific application to data on wages and employment by industrial classification to measure the evolution of wage inequality through time will be explored, analyzing the links between Theil indexes computed at different levels of n-digit SIC codes. A dynamic analysis shows the extent to which a between group Theil statistic tracks the evolution of inequality within industries, and estimations are provided as to the amount of information gained by using ever more disaggregated grouping structures to assess the dynamics of overall inequality. The empirical illustration provides a monthly time-series for industrial earnings inequality in the US is computed at 2, 3 and 4-digit SIC codes from January of 1947 to March of 1999.