Global analysis and indeterminacy in a two-sector growth model with human capital

The purpose of the present paper is to highlight some features of global dynamics of the two-sector growth model with accumulation of human and physical capital analyzed by Brito and Venditti, which is a specialization of the model proposed by Mulligan and Sala-i-Martin. In particular, our analysis focuses on the context in which the Brito-Venditti system admits two balanced growth paths, each corresponding, after a change of variables, to an equilibrium point of a three-dimensional system, and proves the possible existence of points (P) over bar such that in any neighborhood of (P) over bar lying on the plane corresponding to fixed values of the state variables there exist points (Q) over bar whose positive trajectories tend to either equilibrium point. This implies that equilibrium selection in the Brito-Venditti system may depend on the expectations of economic agents rather than on the history of the economy. That is, economies with identical technologies and preferences, starting from the same initial values of the state variables (history), may follow rather different equilibrium trajectories according to the economic agents' choices of the initial values of the jumping variables (expectations). Moreover, we prove that the basins of attraction (two or three-dimensional) of locally indeterminate equilibrium points may be very large, as they can extend up to the boundary of the system phase space.