Contagion or Macroeconomic Fluctuations? Identifiability in Aggregated Default Data

TL;DR

This paper investigates whether contagion effects can be distinguished from macroeconomic fluctuations in aggregated default data, using different dependence models and hierarchical extensions.

Contribution

It compares three dependence structures to determine when contagion can be identified in aggregate default counts and how macroeconomic factors influence default clustering.

Findings

Vasicek model best fits tail behavior in aggregated default data.

Most variation in default counts is due to macroeconomic factors rather than contagion.

Threshold contagion does not produce a stable component after aggregation, unlike the Lo-Davis model.

Abstract

Can contagion be inferred from aggregated default data? We study this as a problem of identifiability, asking whether contagion generates components in default count distributions that remain distinct from those induced by macroeconomic fluctuations. We compare three dependence structures: cumulative contagion in the Lo-Davis 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 provides the best overall fit, especially in the tail, indicating that a smooth mixture structure captures annual default clustering more effectively than threshold-type contagion at the aggregate level. We then allow the default probability to vary across years through a hierarchical specification. Under this extension, most of the variation in annual default counts is explained by cross-year movements in default conditions rather than by within-year contagion. What remains, however, depends on the interaction mechanism. In the Torri model, threshold-type contagion does not leave a stable component that can be separated from macroeconomic heterogeneity after aggregation. In the Lo-Davis model, by contrast, a small but persistent component remains visible in both the variance decomposition and the tail behavior. These results clarify when contagion can still be inferred from coarse-grained data and when it is effectively absorbed into macroeconomic variation.