Cash Flow Entropy

TL;DR

This paper introduces a novel entropy-based measure for assessing the diversity of cash flows among agents in an economy, linking it to inequality and agent behavior.

Contribution

It develops a hierarchical inequality measure based on information entropy, encompassing the Theil index, and formalizes constraints on agent cash flow entropies.

Findings

Introduces a new entropy-based diversity measure for cash flows.

Includes the Theil index as a special case within the new framework.

Formalizes the balance between cash flow aggregating and diversifying agents.

Abstract

In this paper we aim to find a measure for the diversity of cash flows between agents in an economy. We argue that cash flows can be linked to probabilities of finding a currency unit in a given cash flow. We then use the information entropy as a natural measure of diversity. This leads to a hirarchical inequality measure, which includes the well-known Theil index as a special case, and a constraint on agent entropy differentials, i.e., the difference between cash inflow and outflow entropies. The last result is particularly intriguing as it formalises the fact that an economy must contain both, cash flow aggregating and cash flow diversifying agents.