Gross domestic product growth rates as confined Lévy flights: Towards a unifying theory of economic growth rate fluctuations

Abstract

A new model that combines economic growth rate fluctuations at the microscopic and macroscopic level is presented. At the microscopic level, firms are growing at different rates while also being exposed to idiosyncratic shocks at the firm and sector level. We describe such fluctuations as independent Lévy-stable fluctuations, varying over multiple orders of magnitude. These fluctuations are aggregated and measured at the macroscopic level in averaged economic output quantities such as GDP. A fundamental question is thereby to what extend individual firm size fluctuations can have a noticeable impact on the overall economy. We argue that this question can be answered by considering the Lévy fluctuations as embedded in a steep confining potential well, ensuring nonlinear mean-reversal behavior, without having to rely on microscopic details of the system. The steepness of the potential well directly controls the extend towards which idiosyncratic shocks to firms and sectors are damped at the level of the economy. Additionally, the theory naturally accounts for business cycles, represented in terms of a bimodal economic output distribution, and thus connects two so far unrelated fields in economics. By analyzing 200 years of US GDP growth rates, we find that the model is in good agreement with the data.

Escape from the potential well: accelerating by shaping and noise tuning

“…The α-stable noise is a generalization of the Gaussian white noise to the nonequilibrium realms [24], where heavy tailed fluctuations are abundant [42,[60][61][62][63][64][65]. The noise produces independent increments which follow a heavy-tailed α-stable density [24,27].…”

Deterministic force-free resonant activation

“…Well-developed theory and desired mathematical properties, for example, self-similarity, infinite divisibility and generalized central limit theorem, ensure α-stable noises are widely applied in various out-of-equilibrium models and setups displaying anomalous fluctuations. Non-Gaussian, heavy-tailed fluctuations have been recorded in diverse experimental setups ranging from rotating flows [20], optical systems and materials [21,22], physiological applications [23], disordered media [24], biological systems [25], financial time series [26][27][28], the dispersal patterns of humans and animals [29,30], and laser cooling [31] to gaze dynamics [32] and search strategies [33,34]. Lévy noise systems are also extensively studied theoretically [35][36][37][38][39][40][41][42].…”

Underdamped, anomalous kinetics in double-well potentials

“…Moreover, non-negligible probability of extreme events produces multimodal stationary states in single-well potentials steeper than parabolic [18][19][20]. Non-Gaussian, heavy-tailed fluctuations have been observed in plenitude of experimental setups ranging from disordered media [21], biological systems [22], rotating flows [23], optical systems and materials [24,25], physiological applications [26], financial time series [27][28][29], dispersal patterns of humans and animals [30,31], laser cooling [32] to gaze dynamics [33] and search strategies [34,35]. They are studied both theoretically [36][37][38][39][40][41] and experimentally.…”