New York Office

Dynamic Solow model

Research Project

Capital Demand Driven Business Cycles

Mechanism and Effects

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karl naumann-woleske

Principal Investigator: Karl Naumann-Woleske

Chair of Econophysics and Complex Systems, Ecole Polytechnique

Project Summary

We develop a tractable macroeconomic model that captures dynamic behaviors across multiple timescales, including business cycles. The model is anchored in a dynamic capital demand framework reflecting an interaction-based process whereby firms determine capital needs and make investment decisions on a micro level. We derive equations for aggregate demand from this micro setting and embed them in the Solow growth economy. As a result, we obtain a closed-form dynamical system with which we study economic fluctuations and their impact on long-term growth. For realistic parameters, the model has two attracting equilibria: one at which the economy contracts and one at which it expands. This bi-stable configuration gives rise to quasiperiodic fluctuations, characterized by the economy’s prolonged entrapment in either a contraction or expansion mode punctuated by rapid alternations between them. We identify the underlying endogenous mechanism as a coherence resonance phenomenon. In addition, the model admits a stochastic limit cycle likewise capable of generating quasiperiodic fluctuations; however, we show that these fluctuations cannot be realized as they induce unrealistic growth dynamics. We further find that while the fluctuations powered by coherence resonance can cause substantial excursions from the equilibrium growth path, such deviations vanish in the long run as supply and demand converge.


Working Paper

Captial Demand Driven Business Cycles: Mechanism and Effects

Karl Naumann-Woleske, Michael Benzaquen, Maxim Gusev, and Dimitri Kroujiline | November 23, 2021