Financial Interactions and Collective States: Part II. Banks, Investors and Firms

TL;DR

This work extends a field-theoretic framework of capital allocation to include banks as money-creating agents alongside investors and firms. It shows that money creation does not inherently resolve systemic instability; stability outcomes depend on how banks allocate credit (toward firms vs. investors) and on the sectoral distribution of capital and risk. The model yields a rich landscape of collective states, with potential unique or dual sectoral-return solutions and complex default propagation through intermediation networks. It highlights that highly capitalized, high-return banks and investors can be sources of endogenous fragility, underscoring limitations of macroprudential regulation in fully mitigating systemic risk. Overall, the paper emphasizes that financial interdependence and endogenous capital flows generate intrinsic fragility and complex transition dynamics between equilibria, including default states.

Abstract

In a previous paper, we applied a field formalism to analyze capital allocation and accumulation within a microeconomic framework of investors and firms. The financial connections were modeled by a field of stakes, representing the links between agents. We showed that the resulting collective states were composed of interconnected groups of agents defined by their connections, their returns and disposable capital. However, within this framework, the collective states exhibited structural instability, as capital shortages in specific sectors could trigger cascades of defaults. The present model refines this framework by introducing a third type of agent, banks, a type of investor that can create money through loans. We show that money creation neither eliminates systemic instability nor prevents the emergence of defaults. In fact, the effect of banks on system stability and defaults is ambiguous: When banks favor firms over investors, money creation stabilizes the system by providing the necessary capital to prevent initial defaults, whereas when banks favor investors over firms, investors' influence is strengthened, potentially amplifying instability and defaults. Moreover, regardless of whether they favor investors or firms, banks may facilitate the propagation of defaults once they have started. Ultimately, because banks are themselves investors, the emergence of highly capitalized, high-return banks can directly generate instability in the system. Beyond these mechanisms, the analysis reveals the structural limits of macroprudential regulation. Highly capitalized, high-return investors and banks may appear more diversified and resilient, yet they constitute the primary source of endogenous instability. The model thus highlights that systemic fragility is inherent to the very structure of financial interdependence and capital flows.