Scale invariant properties of public debt growth

TL;DR

This paper investigates the scale-invariant properties of public debt growth across countries, revealing convergence phenomena and modeling debt ratios with Gamma distributions to inform sustainable debt thresholds.

Contribution

It introduces a quantitative analysis of public debt and debt-to-GDP ratio dynamics, highlighting scale-invariant properties and proposing a probabilistic framework for debt sustainability.

Findings

Countries with lower initial debt grow faster in debt levels.

Debt-to-GDP ratios tend to converge, with smaller ratios increasing more rapidly.

Gamma distribution effectively models the probability density of debt ratios.

Abstract

Public debt is one of the important economic variables that quantitatively describes a nation's economy. Because bankruptcy is a risk faced even by institutions as large as governments (e.g. Iceland), national debt should be strictly controlled with respect to national wealth. Also, the problem of eliminating extreme poverty in the world is closely connected to the study of extremely poor debtor nations. We analyze the time evolution of national public debt and find "convergence": initially less-indebted countries increase their debt more quickly than initially more-indebted countries. We also analyze the public debt-to-GDP ratio R, a proxy for default risk, and approximate the probability density function P(R) with a Gamma distribution, which can be used to establish thresholds for sustainable debt. We also observe "convergence" in R: countries with initially small R increase their R more quickly than countries with initially large R. The scaling relationships for debt and R have practical applications, e.g. the Maastricht Treaty requires members of the European Monetary Union to maintain R < 0.6.