Non-Normal Interactions Create Socio-Economic Bubbles

Abstract

We present a generic new mechanism for the emergence of collective exuberance among interacting agents in a general class of Ising-like models that have a long history in social sciences and economics. The mechanism relies on the recognition that socioeconomic networks are intrinsically non-symmetric and hierarchically organized, which is represented as a non-normal adjacency matrix. Such non-normal networks lead to transient explosive growth (a “bubble”) in a generic domain of control parameters, in particular in the subcritical regime. Contrary to previous models, here the coordination of opinions and actions and the associated global macroscopic order do not require the fine-tuning close to a critical point. This is illustrated in the context of financial markets theoretically, numerically via agent-based simulations and empirically through the analysis of so-called meme stocks. It is shown that the size of the bubble is directly controlled through the Kreiss constant which measures the degree of non-normality in the network. This mapping improves conceptually and operationally on existing methods aimed at anticipating critical phase transitions, which do not take into consideration the ubiquitous non-normality of complex system dynamics. Our mechanism thus provides a general alternative to the previous understanding of instabilities in a large class of complex systems, ranging from ecological systems to social opinion dynamics and financial markets.

Keywords: financial bubbles, non-normal matrices, social networks, sub-criticality, hierarchical networks, anticipating tipping points

JEL Classification: C02, C46, G01, G17