 A Statistical Field Perspective on Capital Allocation and Accumulation: Individual dynamicsPierre Gosselin () and
Aïleen Lotz
Working Papers from HAL Abstract: We have shown, in a series of articles, that a classical description of a large number of economic agents can be replaced by a statistical fields formalism. To better understand the accumulation and allocation of capital among di¤erent sectors, the present paper applies this statistical fields description to a large number of heterogeneous agents divided into two groups. The first group is composed of a large number of firms in di¤erent sectors that collectively own the entire physical capital. The second group, investors, holds the entire financial capital and allocates it between firms across sectors according to investment preferences, expected returns, and stock prices variations on financial markets. In return, firms pay dividends to their investors. Financial capital is thus a function of dividends and stock valuations, whereas physical capital is a function of the total capital allocated by the financial sector. Whereas our previous work focused on the background fields that describe potential long-term equilibria, here we compute the transition functions of individual agents and study their probabilistic dynamics in the background field, as a function of their initial state. We show that capital accumulation depends on various factors. The probability associated with each firm's trajectories is the result of several contradictory e¤ects: the firm tends to shift towards sectors with the greatest long-term return, but must take into account the impact of its shift on its attractiveness for investors throughout its trajectory. Since this trajectory depends largely on the average capital of transition sectors, a firm's attractiveness during its relocation depends on the relative level of capital in those sectors. Thus, an under-capitalized firm reaching a high-capital sector will experience a loss of attractiveness, and subsequently, in investors. Moreover, the firm must also consider the effects of competition in the intermediate sectors. An under-capitalized firm will tend to be ousted out towards sectors with lower average capital, while an over-capitalized firm will tend to shift towards higher averagecapital sectors. For investors, capital allocation depends on their short and long-term returns. These returns are not independent: in the short-term, returns are composed of both the firm's dividends and the increase in its stock prices. In the long-term, returns are based on the firm's growth expectations, but also, indirectly, on expectations of higher stock prices. Investors' capital allocation directly depends on the volatility of stock prices and …rms'dividends. Investors will tend to reallocate their capital to maximize their short and long-term returns. The higher their level of capital, the stronger the reallocation will be. Keywords: Interactions.; Financial Markets Real Economy Capital Allocation Statistical Field Theory Background …elds Collective states Multi-Agent Model Interactions. JEL Classi…cation: B40 C02 C60 E00 E1 G10; Financial Markets; Real Economy; Capital Allocation; Statistical Field Theory; Background fields; Collective states; Multi-Agent Model; Financial Markets Real Economy Capital Allocation Statistical Field Theory Background fields Collective states Multi-Agent Model Interactions. JEL Classification: B40 C02 C60 E00 E1 G10; Interactions. JEL Classification: B40; C02; C60; E00; E1; G10 (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-04301351 Access Statistics for this paper More papers in Working Papers from HAL |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.