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Book contents
- Frontmatter
- Contents
- Preface
- Part I Introduction
- Part II Modeling Interactions
- Part III Hierarchical Dynamics and Critical Phenomena
- 7 Sluggish Dynamics and Hierarchical State Spaces
- 8 Self-organizing and Other Critical Phenomena in Economic Models
- Elaborations and Future Directions of Research
- Appendix
- References
- Index
7 - Sluggish Dynamics and Hierarchical State Spaces
Published online by Cambridge University Press: 05 May 2010
- Frontmatter
- Contents
- Preface
- Part I Introduction
- Part II Modeling Interactions
- Part III Hierarchical Dynamics and Critical Phenomena
- 7 Sluggish Dynamics and Hierarchical State Spaces
- 8 Self-organizing and Other Critical Phenomena in Economic Models
- Elaborations and Future Directions of Research
- Appendix
- References
- Index
Summary
This chapter discusses dynamics on state spaces that are hierarchically structured. As the examples in Sections 2.5.3 and 5.12 suggest, dynamics with such structured state spaces may exhibit sluggish responses, much slower than the exponential decays associated with ordinary dynamics.
In this chapter, we introduce the notion of the “renormalization group” into hierarchically structured state spaces as a method of aggregation, that is, as a procedure for trimming the level of branches of tree hierarchies. This aggregation scheme is different from the one we introduced via the master equation in Chapter 5, and potentially useful, but not standard in the macroeconomic literature.
We also address the question of sensitivity of macromodels with respect to details of microeconomic unit specification. By means of several examples, we show that the sluggishness of dynamic responses of hierarchically structured systems is robust, or insensitive to details of micromodel specifications.
Examples of hierarchically structured state spaces
Some examples of hierarchically structured models are presented in Chaper 2. Here are some more examples to serve as additional evidence of the relevance of hierarchically structured models in macroeconomic modeling.
Further discussion of the notion of ultrametrics, and dynamics with transition rates (probabilities) that are functions of ultrametrics follow this section.
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- Information
- New Approaches to Macroeconomic ModelingEvolutionary Stochastic Dynamics, Multiple Equilibria, and Externalities as Field Effects, pp. 184 - 212Publisher: Cambridge University PressPrint publication year: 1996