Staring at Economic Aggregators through Information Lenses

TL;DR

This paper analyzes economic aggregators through an information-theoretic lens, showing that well-known functions like CES and Cobb-Douglas are optimal from an informational perspective, especially under common economic assumptions.

Contribution

It introduces a novel information-based framework for evaluating economic aggregators, demonstrating their optimality and exact fit to classical forms like CES and Cobb-Douglas under certain conditions.

Findings

Economic aggregators are optimal from an information standpoint.

Classical aggregators like CES and Cobb-Douglas emerge as the best fits.

The set of optimal aggregators shrinks to classical forms under typical assumptions.

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