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

This paper provides a general method to 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 at the individual level. We apply this methodology to model the interactions between financial markets and the real economy. We start with 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 they reward their investors through dividends and better stock valuation. Investors invest in firms based on firms' expected long-run returns. They may also gradually reallocate their capital along the sectors space. From this framework, we derive a field-formalism model in which collective states 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 the sector's short-term returns and relative expected long-term returns. For each sector, three patterns of accumulation emerge. In the first pattern, sectors with a relatively large number of low-capitalized firms woo investors with dividends. 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. Since instability in capital accumulation may arise among and within sectors, we widen our study to the dynamics of the collective configurations, in particular interactions between average capital and expected long-term returns, and show that the expectations formation process is crucial to overall stability. Expectations highly reactive to capital variations stabilize high capital configurations. Depending on their initial capital, they may drive low-to-moderate capital sectors towards zero or a higher level of capital. Inversely, expectations moderately reactive to capital variations stabilize low-to-moderate capital configurations and drive high capital sectors towards a more moderate level of capital equilibria. Eventually, expectations that are both highly sensitive to exogenous conditions and highly reactive to variations in capital induce large fluctuations of capital in the system, possibly at the expense of the real economy.