A Chaotic Map Arising in the Theory of Endogenous Growth

Growth theorists have almost always adopted the assumption of balanced growth in their investigations of development phenomena. In reality countries growth rates oscillate, sometimes wildly, around some average value. The latter is often taken to represent the balanced rate to which the development dynamics spontaneously tends to return after each perturbation. In this paper we try a different interpretation: the growth rate of capital stock in a developing economy oscillates within some bounded interval of feasible values and the balanced growth is in fact unstable. These oscillations may be persistent and endogenously determined by the accumulation process itself and they generate a non-trivial, invariant distribution of growth rates. We study a class of two-sector models displaying this feature in the prescence of a positive external effect. The qualitative properties of a specific example are analyzed by means of analytical and numerical methods. Our simulations reveal that, while the artificial economy is certainly able to display rather impressive endogenous growth cycles, they occur only when the external effects is unreasonably strong. Similarly to previous tentatives of modeling endogenous oscillations by means a chaotic map, we suceed at the theoretical level but fail short of reproducing some crucial empirical properties of the growth cycles experienced by modern market economies.