Financial Fragility, Mean-Field Interaction and Macroeconomic Dynamics: A Stochastic Model

Abstract

The links between aggregate financial indicators and business fluctuations have been widely addressed in literature while the same interest has not been devoted to the role of microeconomic financial variables in determining macroeconomic results. One of the causes may be individuated in the lack of suitable analytical tools. Firms are different each other as regards, at least, financial structure and size. Therefore, their responses to shocks come out to be different and asymmetric. Moreover, firms are reciprocally linked, and their diverse reactions influence the whole system at micro, macro and meso level. The uncertainty about the final outcome is amplified by feedback effects from aggregate level to firms. In this work we model an economic system populated by heterogeneous firms that, reacting to stochastic shocks to maximize their profit, modify the ratio among liabilities and equities. These variations influence the financial environment and the demography of firms population, endogenously generating business fluctuations. Using a stochastic aggregation method we define a system of coupled dynamic equations that describe long run path and cycles of aggregate output.