Keynesian chaos revisited: odd period cycles and ergodic properties

TL;DR

This paper analyzes two Keynesian macroeconomic models to characterize chaos and demonstrates that, despite chaos, future GDP levels can be statistically predicted using ergodic theory, offering a new approach for complex economic systems.

Contribution

It provides a complete characterization of chaos in two Keynesian models and applies ergodic theory to predict long-term GDP behavior, introducing a novel analytical method.

Findings

Existence of topological chaos in both models

Ergodic theory enables prediction of average GDP levels

Method applicable to other complex economic models

Abstract

In this paper, we study two standard (Keynesian) dynamic macroeconomic models (one is piecewise linear and the other is nonlinear). Our purpose is twofold: (1)~For each model, we give a complete characterisation for the existence of a topological chaos (of the GDP levels), (2)~Even if a chaos exists, using ergodic theory, we show that it is possible to predict the future GDP levels "on average". This paper gives a new application of a celebrated result in ergodic theory by A. Avila (2014 fields medalist). We believe that our method/strategy in this paper is generic enough to be used to analyse many other (seemingly untractable) chaotic economic models.