Model of “secular” cycle of financial capital accumulation

Crises hitting the world economy since the end of the previous century need a deeper explanation than effects of numerous sudden shocks. According to G. Arrighi’s theory, they manifest the final phase of North-American cycle of capital accumulation. Although analytically promising, the theory doesn’t meet broad recognition. A reason could be its weak formalization. This article addresses this problem by developing a mathematical model of capital growth rates. They are measured by nominal yield and interest rates which represent increments of capital in its general, financial form. If capital level follows a logistic path then its growth rate should be described by logistic differential equation. The model is brought to data on government bonds yields in Great Britain in XVIII– XIX centuries and USA — in XX century up to now. The study provides evidence for the pivotal role of financial-capital accumulation in systemic cycles and its S-shaped form. Besides, it reveals importance of trade balance in specifying cycle phases of domestic and global capital expansion.