Staring at Economic Aggregators through Information Lenses

Abstract: It is hard to exaggerate the role of economic aggregators -- functions that summarize numerous and / or heterogeneous data -- in economic models since the early XX$^{th}$ century. In many cases, as witnessed by the pioneering works of Cobb and Douglas, these functions were information quantities tailored to economic theories, i.e. they were built to fit economic phenomena. In this paper, we look at these functions from the complementary side: information. We use a recent toolbox built on top of a vast class of distortions coined by Bregman, whose application field rivals metrics' in various subfields of mathematics. This toolbox makes it possible to find the quality of an aggregator (for consumptions, prices, labor, capital, wages, etc.), from the standpoint of the information it carries. We prove a rather striking result. From the informational standpoint, well-known economic aggregators do belong to the \textit{optimal} set. As common economic assumptions enter the analysis, this large set shrinks, and it essentially ends up \textit{exactly fitting} either CES, or Cobb-Douglas, or both. To summarize, in the relevant economic contexts, one could not have crafted better some aggregator from the information standpoint. We also discuss global economic behaviors of optimal information aggregators in general, and present a brief panorama of the links between economic and information aggregators. Keywords: Economic Aggregators, CES, Cobb-Douglas, Bregman divergences