Out-of-Equilibrium Dynamics and Excess Volatility in Firm Networks

59 Pages Posted: 5 Jan 2021 Last revised: 3 Nov 2021

See all articles by Théo Dessertaine

Théo Dessertaine

University of Paris-Saclay - Ecole Polytechnique

José Moran

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School; University of Oxford - Mathematical Institute

Michael Benzaquen

Ecole Polytechnique, Palaiseau; Capital Fund Management

Jean-Philippe Bouchaud

Capital Fund Management

Date Written: December 9, 2020

Abstract

We study the conditions under which input-output networks can dynamically attain a competitive equilibrium, where markets clear and profits are zero. We endow a classical firm network model with minimal dynamical rules that reduce supply/demand imbalances and excess profits. We show that the time needed to reach equilibrium diverges to infinity as the system approaches an instability point beyond which the Hawkins-Simons condition is violated and competitive equilibrium is no longer admissible. We argue that such slow dynamics is a source of excess volatility, through accu- mulation and amplification of exogenous shocks. Factoring in essential physical constraints absent in our minimal model, such as causality or inventory management, we then propose a dynamically consistent model that displays a rich variety of phenomena. Competitive equilibrium can only be reached after some time and within some restricted region of parameter space, outside of which one observes spontaneous periodic and chaotic dynamics, reminiscent of real business cycles. This suggests an alternative explanation of excess volatility in terms of purely endogenous fluctuations. Diminishing return to scale and increased perishability of goods are found to ease convergence towards equilibrium.

Suggested Citation

Dessertaine, Théo and Moran, José and Benzaquen, Michael and Benzaquen, Michael and Bouchaud, Jean-Philippe, Out-of-Equilibrium Dynamics and Excess Volatility in Firm Networks (December 9, 2020). Available at SSRN: https://ssrn.com/abstract=3745898 or http://dx.doi.org/10.2139/ssrn.3745898

Théo Dessertaine

University of Paris-Saclay - Ecole Polytechnique ( email )

55 Avenue de Paris
Versailles, 78000
France

José Moran

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School ( email )

Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

University of Oxford - Mathematical Institute ( email )

Radcliffe Observatory, Andrew Wiles Building
Woodstock Rd
Oxford, Oxfordshire OX2 6GG
United Kingdom

Michael Benzaquen (Contact Author)

Ecole Polytechnique, Palaiseau ( email )

Route de Saclay
Palaiseau, 91128
France

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France

Jean-Philippe Bouchaud

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France
+33 1 49 49 59 20 (Phone)

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