Causal motifs and existence of endogenous cascades in directed networks with application to company defaults

TL;DR

This paper introduces a framework using causal motifs to detect endogenous cascades in directed networks, applied to company defaults, revealing endogenous spreading periods in real economic data.

Contribution

It develops a novel motif-based detection method for endogenous cascades and demonstrates its effectiveness on both synthetic and real-world company default data.

Findings

Small motifs can reliably identify endogenous spreading events.

The method successfully detected likely endogenous cascades in Croatian company defaults.

Synthetic simulations validate the robustness of the motif-based detection.

Abstract

Motivated by the detection of cascades of defaults in economy, we developed a detection framework for an endogenous spreading based on causal motifs we define in this paper. We assume that the change of state of a vertex can be triggered by an endogenous or an exogenous event, that the underlying network is directed and that times when vertices changed their states are available. In addition to the data of company defaults, we also simulate cascades driven by different stochastic processes on different synthetic networks. We show that some of the smallest motifs can robustly detect endogenous spreading events. Finally, we apply the method to the data of defaults of Croatian companies and observe the time window in which an endogenous cascade was likely happening.