Deterministic chaos in government debt dynamics with mechanistic primary balance rules

TL;DR

This paper demonstrates that government debt dynamics governed by simple primary balance rules can exhibit deterministic chaos, implying unpredictable debt-to-GDP ratios due to sensitive dependence on initial conditions.

Contribution

It reveals that under certain assumptions, debt dynamics follow the logistic map, leading to chaotic behaviour in government debt evolution.

Findings

Debt dynamics can become chaotic under simple rules.

Deterministic chaos implies high sensitivity to initial conditions.

The logistic map models debt behaviour effectively.

Abstract

This paper shows that with mechanistic primary budget rules and with some simple assumptions on interest rates the well-known debt dynamics equation transforms into the infamous logistic map. The logistic map has very peculiar and rich nonlinear behaviour and it can exhibit deterministic chaos with certain parameter regimes. Deterministic chaos means the existence of the butterfly effect which in turn is qualitatively very important, as it shows that even deterministic budget rules produce unpredictable behaviour of the debt-to-GDP ratio, as chaotic systems are extremely sensitive to initial conditions.