Identifiability of Contagion Components amid Environmental Fluctuations in Aggregated Default Counts

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.