Identifiability of Contagion Components amid Environmental Fluctuations in Aggregated Default Counts

Shintaro Mori

Papers from arXiv.org

Abstract: Can contagion components be identified in aggregated default counts when default probabilities fluctuate with the economic environment? We study this question as an identifiability problem for coarse-grained default-count distributions. Three dependence mechanisms are compared: cumulative contagion in the Davis--Lo model, threshold-type contagion in the Torri model, and common-factor dependence in the Vasicek model. Under an i.i.d. specification, the Vasicek model gives the best overall fit, indicating that a smooth mixture induced by environmental fluctuations can reproduce much of the observed annual default clustering. We then introduce a hierarchical specification in which the baseline default probability varies across years. This extension separates cross-year environmental fluctuations from within-year contagion. Most of the variance of annual default counts is explained by fluctuations in default conditions. The remaining component, however, depends on the contagion mechanism. Threshold-type contagion is largely absorbed into environmental heterogeneity, whereas cumulative contagion leaves a small but persistent signature in both variance decomposition and tail behavior. These results clarify when contagion remains identifiable after aggregation and when it becomes indistinguishable from environmental fluctuations.

Date: 2026-04, Revised 2026-05
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