7 - On formal dynamics: From Lundberg to chaos analysis

Summary

The Stockholm School and its vital contribution to sequence analysis played a key role in the transition of economic dynamics from the intuitive approaches of earlier business cycle theory to the powerful and rigorous analytics that is the hallmark of theoretical writings in the area since World War II. Erik Lundberg provided a vital contribution to this evolution. Though formal dynamic models had been contributed earlier by Ragnar Frisch, Lundberg's research showed well before Paul Samuelson's profound contributions on the subject how such models could be grounded firmly in the logic of sequence analysis and the pertinent macroeconomic considerations.

Lundberg's basic contribution to the field does not make any use of the now commonplace mathematical tools that sometimes offer general solutions to dynamic relationships; instead, it relies on numerical time sequences generated with the aid of particular illustrative values of the parameters of his dynamic equations. But I will show that this is not as restrictive a procedure as it may appear to be. Rather, there is a trade-off between the abstraction and deemphasis of the details of the underlying economic processes that the more formal procedures engender and the insights offered by the painstaking calculations that are vital for Lundberg's numerical time paths. Indeed, it will be pointed out that the ostensible superiority of the formal approaches in terms of the greater generality of their results is to a considerable degree an illusion, because the mathematical techniques are fully effective in providing analytic solutions for dynamic models only when those models take the most elementary (linear) forms.