Financial Interactions and Capital Accumulation
Résumé
In a series of precedent papers, we have presented a comprehensive methodology, termed
Field Economics, for translating a standard economic model into a statistical field-formalism
framework. This formalism requires a large number of heterogeneous agents, possibly of different
types. It reveals the emergence of collective states among these agents or type of agents while
preserving the interactions and microeconomic features of the system at the individual level. In
two prior papers, we applied this formalism to analyze the dynamics of capital allocation and
accumulation in a simple microeconomic framework of investors and firms.
Building upon our prior work, the present paper refines the initial model by expanding its
scope. Instead of considering financial firms investing solely in real sectors, we now suppose that
financial agents may also invest in other financial firms. We also introduce banks in the system
that act as investors with a credit multiplier. Two types of interaction are now considered
within the financial sector: financial agents can lend capital to, or choose to buy shares of, other
financial firms. Capital now flows between financial agents and is only partly invested in real
sectors, depending on their relative returns. We translate this framework into our formalism
and study the di¤usion of capital and possible defaults in the system, both at the macro and
micro level.
At the macro level, we find that several collective states may emerge, each characterized
by a distinct level of average capital and investors per sector. These collective states depend
on external parameters such as level of connections between investors or firms' productivity.
The multiplicity of possible collective states is the consequence of the nature of the system
composed of interconnected heterogeneous agents. Several equivalent patterns of returns and
portfolio allocation may emerge. The multiple collective states induce the unstable nature of
nancial markets, and some of them include defaults may emerge. At the micro level, we study
the propagation of returns and defaults within a given collective state. Our findings highlight
the significant role of banks, which can either stabilize the system through lending activities or
propagate instability through loans to investors.
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