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Stable Periodic Economic Cycles from Controlling

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Nonlinearities in Economics

Part of the book series: Dynamic Modeling and Econometrics in Economics and Finance ((DMEF,volume 29))

Abstract

When a system becomes unstable or noise becomes excessive, often regulations of the form of limiters (barriers obstructing excursion into undesired areas of the phase space) are imposed. It is hoped that by the influence of this element, the system can be calmed and its behaviour can be optimised. In what follows below, we consider a simple noisy nonlinear economics model that self-organises towards criticality. We demonstrate that the inherent effect of limiters is the emergence of stable cycles and that limiters need to be implemented with care in order to obtain an optimised system response. In particular, the implementation of the limiter around the maximal system response has generally a suboptimal effect, whereas the placement of the limiter in the vicinity of a period-one cycle will generally yield the optimal effect. We also show that, as a downside of the proposed approach, in order to control on period-one cycles, generally strong interventions are required. In democratic countries, a transparent control policy would therefore be an indispensable for its implementation. The discussed framework may prove helpful for this purpose.

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Notes

  1. 1.

    For g(0) = 1 one also could use the ansatz gn(x) = 1 + bx 2n and take the limit for n →∞. Again, the solution is a square wave with b = −2. Using g(1) = −α yields α = 1 and δ −1 = 0.

  2. 2.

    Scaling laws for ‘stars’ and ‘windows’ observed in the bifurcation diagram for h > h ∞ of the logistic map were already described by Sinha [38]. They both depend on the derivative of the map at the origin and are therefore not universal. The scaling factor for ‘stars’ and ‘windows’ of the tent map is 2.

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Authors and Affiliations

  1. Institute of Neuroinformatics, ETHZ/University of Zürich, Zürich, Switzerland

    Ruedi Stoop

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  1. Ruedi Stoop
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Correspondence to Ruedi Stoop .

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Editors and Affiliations

  1. Department of Economics & Finance, University of Bari Aldo Moro, Bari, Italy

    Giuseppe Orlando

  2. Technical University of Madrid Center for Biomedical Technology, Campus Montegancedo, Pozuelo de Alarcón, Madrid, Spain

    Alexander N. Pisarchik

  3. Institute of Neuroinformatics, Swiss Federal Institute of Technology, Zürich, Switzerland

    Ruedi Stoop

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Stoop, R. (2021). Stable Periodic Economic Cycles from Controlling. In: Orlando, G., Pisarchik, A.N., Stoop, R. (eds) Nonlinearities in Economics. Dynamic Modeling and Econometrics in Economics and Finance, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-030-70982-2_15

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