Constructing Long and Dense Time-Series of Inequality Using the Theil Index

Year-to-year economy-wide measures of income distribution, such as the Gini coefficient, are rarely available for long periods except in a few developed countries, and as a result few analyses of year-to-year changes in inequality exist. But wage and earnings data by industrial sectors are readily available for many countries over long time frames. This paper proposes the application of the between-group component of the Theil index to data on wages, earnings, and employment by industrial classification in order to measure the evolution of wage or earnings inequality through time. We provide formal criteria under which such a between-group Theil statistic can reasonably be assumed to give results that also track the (unobserved) evolution of inequality within industries. While the evolution of inequality in manufacturing earnings cannot be taken as per se indicating the larger movements of inequality in household incomes, including those outside the manufacturing sector, we argue on theoretical grounds that the two will rarely move in opposite directions. We conclude with an empirical application to the case of Brazil, an important developing country for which economy-wide Gini coefficients are scarce, but for which a between-industries Theil statistic may be computed on a monthly basis as far back as 1976.