Candidacy and Trigger: A Two-Phase Empirical Model of Hierarchical Collapse

TL;DR

This paper develops an empirical model to predict hierarchical collapse in countries, identifying risk factors and timing signals, and demonstrating the importance of external shocks over endogenous dynamics.

Contribution

It introduces a two-phase model distinguishing structural risk from trigger events, validated through a classifier with high accuracy in predicting collapses.

Findings

The classifier achieves an AUC of 0.91 in distinguishing collapsing countries.

Structural variables indicate high-risk countries a decade before collapse.

External shocks, not internal dynamics, primarily set collapse timing.

Abstract

We test a dynamic ODE model of hierarchical asymmetry on a panel of 260 countries over 1960-2023, drawing on World Bank, Penn World Table, V-Dem and World Inequality Database sources. In cross-section the model holds partially: trade openness and bottom-of-distribution health suppress within-country asymmetry. The annual time-evolution equation fails, with out-of-sample R^2 at or below zero across five functional forms. The same state vector, augmented with market, debt and trajectory features, is much more successful as a discriminator: a four-layer leave-one-collapse-out classifier separates 29 historical collapses from 60 stable controls at a nested cross-validated AUC of 0.91. The signal splits into a chronic risk profile visible a decade before the event and an acute inflection three to five years before. Three independent tests reject the endogenous-drift reading of collapse. What remains is a candidacy-and-trigger picture in which structural variables identify the high-risk countries while collapse timing is set by shocks outside the modelled system. A separate strand documents a lagged co-movement between global fertility and global asymmetry on a single n=63 aggregate series; taken alone this would suggest a selection-pool channel. The same pattern is then tested within countries, within demographic strata, inside a two-way fixed-effects panel and through a migration-mediated cross-country interaction model, and the directional reading fails in each. The aggregate co-movement is a compositional effect rather than a causal channel. A global event-study on 7,316 peer-event observations confirms regional spillover in asymmetry and a novel post-collapse degradation of bottom-of-distribution health in regional neighbours. A pre-registered forward-look produces a top-20 / bottom-20 ranking to be evaluated over 2026-2036.