The Spectral Topology of Global Imbalances:A Graph-Theoretic Framework for Systemic Risk in the Balance of Payments

TL;DR

This paper introduces a spectral graph-theoretic framework to analyze systemic risk in global imbalances, revealing how network topology influences financial stability and contagion risk.

Contribution

It develops a spectral stability criterion and a systemic-risk index based on eigenvector centrality, offering new tools for macroprudential policy targeting network spectral properties.

Findings

Systemic risk correlates with spectral radius of the global exposure matrix.

Eigenvector centrality identifies nodes critical to systemic stability.

Spectral gaps indicate thresholds for sovereign debt contagion.

Abstract

Traditional balance-of-payments (BoP) analysis treats national external positions as largely idiosyncratic time series. This misses an essential structural fact: global imbalances are jointly realized on a directed, weighted network of cross-border current-account and financial claims. We propose a network-theoretic paradigm in which the world economy is a directed graph whose edge weights encode net bilateral exposures. In this setting, systemic fragility is an emergent property of the spectral topology of the global exposure matrix. We develop (i) a mathematically explicit construction of a BoP adjacency operator, (ii) a \textbf{Spectral Stability Criterion} proving that the system is globally asymptotically stable if and only if the spectral radius $\rho(A) < 1$, and (iii) a \textbf{Spectral Stability Margin} ($\delta = 1 - \rho(B)$) that quantifies the proximity of the global economy to a ``Critical Slowing Down'' phase transition. Furthermore, we define a systemic-risk index using eigenvector centrality to identify nodes whose failure is mathematically indistinguishable from global collapse. Finally, we employ a \textbf{Non-backtracking (Hashimoto) operator} to derive a precise \textbf{topological threshold} for sovereign debt contagion, filtering bilateral ``noise'' to isolate deep-network circulation. Our results demonstrate that systemic risk is a latent property of the global spectral topology, requiring macroprudential interventions targeted at the network's spectral gaps rather than individual debt-to-GDP ratios.