Stable balanced expansion in homogeneous dynamic models

This paper examines the stability of balanced paths of expansion or contraction in closed macroeconomic models as typical cases of homogeneous dynamical systems. Examples of known two-dimensional deterministic and stochastic models are discussed. The appendix presents the mathematical tools and concepts to prove the stability of expanding/contracting paths in homogeneous systems. These are described by so-called Perron-Frobenius solutions. Since convergence of orbits of homogeneous systems in intensive form is only a necessary condition for convergence in state space additional requirements are derived for the general n-dimensional case. For deterministic dynamic economies, as in most models of economic growth, of international trade, or monetary macro, conditions of existence and stability are obtained applying the features of the non-linear generalization of the Perron-Frobenius Theorem. In the stochastic case, the conditions for the stability of balanced paths are derived using a recent extension of the Perron-Frobenius Theorem provided by Evstigneev & Pirogov (2010) and Babaei, Evstigneev & Pirogov (2018).