Computing Economic Chaos

TL;DR

This paper explores the discrepancy between theoretical chaos in economic models and the rapid convergence observed in computational simulations, attributing it to digital approximation effects and emphasizing the importance of both approaches in understanding real economic data.

Contribution

It explains why computational models often fail to exhibit true chaos due to digital approximation, highlighting the importance of considering both theoretical and numerical perspectives.

Findings

Digital approximation causes convergence to cycles in simulations.

Both theoretical and numerical analyses are crucial for understanding economic dynamics.

Computational models can misrepresent chaotic behavior due to discretization effects.

Abstract

Existence theory in economics is usually in real domains such as the findings of chaotic trajectories in models of economic growth, tatonnement, or overlapping generations models. Computational examples, however, sometimes converge rapidly to cyclic orbits when in theory they should be nonperiodic almost surely. We explain this anomaly as the result of digital approximation and conclude that both theoretical and numerical behavior can still illuminate essential features of the real data.