A practical log-linear aggregation method with examples: Heterogeneous income growth in the USA

Abstract

A practical aggregation method for heterogeneous log-linear functions is presented. Inequality measures are employed in the construction of an exact representation of the aggregate behavior of an economy formed by heterogeneous log-linear agents. The exact aggregate representation derived here is relatively simple and intuitive. It can be used thereafter in applied issues and in teaching, easing the solving and understanding of aggregation problems. Three macroeconomic applications are discussed: the aggregation of the Lucas supply function, the time-inconsistent behavior of an egalitarian social planner facing heterogeneous discount rates, and the case of a simple heterogeneous growth model. The latter application, which leads to a decomposition of growth rates of the mean into means of growth rates plus inequality changes, is explored empirically. Aggregate CPS data is used to show that, when inequality changes are taken in consideration, the slowdown that followed the first oil shock appears to be worse than usually thought. Additionally, the new economy growth resurgence seems less impressive when compared to the growth performance of the period that preceded the first oil shock.

Keywords: log-linear, aggregation, heterogeneity, inequality, household income, income distribution, heterogeneous growth

JEL Classification: C43, O47