A Non-Linear Synchronization Model

  • Bernd Süssmuth
Part of the Contributions to Economics book series (CE)


The model outlined in the following essentially takes up the track of the model by Weser (1992) to portray and explain the interacting US manufacturing sectors’ investing behaviors, empirically described in t he preced ing chapte rs of the pr esent par t of the monograph. The original st ructure is in several parts maintained. Nevertheless, central innovations necessary:
  1. 1.

    to take a natural rate of damping of the observed sectoral investment cycles into account,

  2. 2.

    to allow for heterogeneous degrees of interaction between the interacting sectors,

  3. 3.

    to take exogenous (stochastic) shocks into accout, and

  4. 4.

    to simulate it, for the first time, on the base of real world data and estimations,


are under taken to ensure that the model exhibits the synchronization of behavior across economic sectors that is observed and documented in the preceding two chapters of the present part of the monograph. In a first step the model is related to an argumentation based on the recent literature on herding. Proceedingly, it is stringently and reasonably calibrated on the base of the empirical findings reported in chapter 6 and 7. Finally, the model in its stochastic version is Monte Carlo (MC-) simulated to assess an agreement between model and data.


Root Mean Square Error Capital Stock Generalize Synchronization Business Cycle Model Capital Deficit 
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  1. 1.
    Since uncertainty grows and the relatively more distant future has relatively less impact on actual decisions, the inequality ps > pm holds.Google Scholar
  2. 2.
    In modern game theory, similar scenarios are well-known as ‘chicken games’ in combination with ‘vicious circle games’, cf. Iwanaga and Namatame (2000). 3 In the context of modeling aggregate fluctuations in financial markets by means of herding.Google Scholar
  3. 5.
    This kind of classification, as originally suggested for the present model by Weser (1992), is also common practice in dynamic systems of statistical physics. See for example Kuramoto and Nishikawa (1987), who note: “A notable feature of our system is that it clearly splits into two subsystems in the presence of collective oscillation, namely a synchronized part of the population and a desynchxonized one.” p. 571.Google Scholar
  4. 6.
    In order to operationalize the simulation and optimize the simulation outputs according to this parameter.Google Scholar
  5. 7.
    Which showed in previously conducted preliminary simulation runs good fits both on the sectoral and aggregate level.Google Scholar
  6. 8.
    Corresponding prognostic measures are MSE = 0.124, MAE = 0.121, RMSE = 0.353.Google Scholar
  7. 9.
    Confirmed in a series of previous experiments in the early experimental phase of the simulation study, the simulated and empirical sectoral series move closely in line for a wide range of [γ,ϑ]-combinations. So I decided to concentrate the simulation’sobjective primarily on discrepancies of the two aggregate series. A sample demonstration of how well the sectoral series are captured by the model is given in the proceeding section of the present chapter.Google Scholar
  8. 10.
    A further argument for the importance of this measure is the following: Since the linear models investigated in section 6 of the present work clearly failed to replicate the variance of the empirical aggregate manufacturing investment series, one should be especially concerned with the replication of the volatility of the actual series.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Bernd Süssmuth
    • 1
  1. 1.Department of Economics (Economic Policy)University of BambergBambergGermany

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