Financial Markets and the Real Economy: A Statistical Field Perspective on Capital Allocation and Accumulation

This paper provides a general method to directly translate a classical economic framework with a large number of agents into a field-formalism model. This type of formalism allows the analytical treatment of economic models with an arbitrary number of agents, while preserving the system's interactions and microeconomic features of the individual level.We apply this methodology to model the interactions between financial markets and the real economy, described in a classical framework of a large number of heterogeneous agents, investors and firms. Firms are spread among sectors but may shift between sectors to improve their returns. They compete by producing differentiated goods and reward their investors by paying dividends and through their stocks' valuation. Investors invest in firms and move along sectors based on firms' expected long-run returns.The field-formalism model derived from this framework allows for collective states to emerge. We show that the number of firms in each sector depends on the aggregate financial capital invested in the sector and its firms' expected long-term returns. Capital accumulation in each sector depends both on short-term returns and expected long-term returns relative to neighbouring sectors.For each sector, three patterns of accumulation emerge. In the first pattern, the dividend component of short-term returns is determinant for sectors with small number of firms and low capital. In the second pattern, both short and long-term returns in the sector drive intermediate-to-high capital. In the third pattern, higher expectations of long-term returns drive massive inputs of capital.Instability in capital accumulation may arise among and within sectors. We therefore widen our approach and study the dynamics of the collective configurations, in particular interactions between average capital and expected long-term returns, and show that overall stability crucially depends on the expectations' formation process.Expectations that are highly reactive to capital variations stabilize high capital configurations, and drive low-to-moderate capital sectors towards zero or a higher level of capital, depending on their initial capital. Inversely, low-to moderate capital configurations are stabilized by expectations moderately reactive to capital variations, and drive high capital sectors towards more moderate level of capital equilibria.Eventually, the combination of expectations both highly sensitive to exogenous conditions and highly reactive to variations in capital imply that large fluctuations of capital in the system, at the possible expense of the real economy.