Long-Run Sovereign Debt Composition: An Analytic Ergodic Framework with Explicit Maturity Structure

TL;DR

This paper develops an analytic ergodic framework for modeling sovereign debt dynamics with explicit maturity structure, providing steady-state conditions, closed-form metrics, and insights into stochastic interest rate and deficit effects.

Contribution

It introduces a novel discrete-time model incorporating granular maturity and stochastic factors, deriving conditions for ergodic convergence and analytical formulas for key debt metrics.

Findings

Steady-state conditions for debt sustainability identified.

Closed-form expressions for portfolio shares and cost-risk metrics derived.

Stochastic interest-rate and deficit correlation effects analyzed.

Abstract

This paper describes a discrete-time model of regularly-issued sovereign debt dynamics under a deficit-driven nominal debt growth regime that explicitly accounts for granular maturity. New issuance follows fixed allocations across a finite maturity ladder, and the government budget constraint determines total borrowing endogenously. In the deterministic baseline, we identify a sustainability condition for convergence to a steady-state and derive closed-form steady portfolio shares, as well as key metrics for steady cost and risk (proxied as one-period rollover ratio). Extending the model to a stochastic recurrence equation (SRE) driven by interest rates and (normalized) deficits that are stationary and mean-reverting, and using a future-cashflow state representation of debt, we identify an analogous condition for ergodic convergence to a unique invariant distribution. This implies that metrics calculated by Monte Carlo debt simulations driven by factors with these properties will recover the ergodic means of the underlying system, independently of initial conditions, provided the simulation horizon is sufficiently long. Analytical formulae for expectations of certain key metrics under this invariant distribution are derived, and agreement with simulation is observed. We find that the introduction of stochastic interest-rate/deficit correlation into the framework leads to intuitive correction terms to their deterministic-baseline counterparts.