Knife-edge conditions in the modeling of long-run growth regularities∗

Balanced (exponential) growth cannot be generalized to a concept which would not require knife-edge conditions to be imposed on dynamic models. Already the assumption that a solution to a dynamical system (i.e. time path of an economy) satisfies a given functional regularity imposes at least one knife-edge assumption on the considered model. In particular, regular (quasi-arithmetic) growth requires knife-edge conditions as well, and so does logistic growth, “generalized regular growth” which we introduce herein, and their consecutive generalizations. Furthermore, it is always possible to find divergent qualitative changes in dynamic behavior of the model if a certain parameter is infinitesimally manipulated. In this sense, dynamics of all growth models are fragile and “unstable”. Our results imply that either (i) all models designed to replicate empirically observed macro-scale regularities are methodologically flawed because slightest deviations in parameter settings could change their predictions strongly enough to invalidate them, or (ii) the concept of knife-edge conditions should not be used as means of discrimination between competing models, or (iii) the standard understanding of “long run” is irrelevant.