History Dependence and Global Dynamics in Models with Multiple Equilibria

A wealth of literature, reviewed in the first section of this paper, is concerned with the occurence of multiple equilibria in economic optimization models and with the resulting history dependence of optimal solutions. Typically, the existence of multiple equilibria is associated with market imperfections, expectational phenomena, and the like. Less known is that this phenomenon is also possible in efficient, perfect foresight intertemporal optimization models, and that: (1) it can also occur in strictly concave efficient models; (2) the threshold separating the optimal trajectories towards the one or the other long-run optimal outcome does not necessary coincide with an unstable steady-state; (3) unstable steady-states may generically be non-optimal; (4) the policy function at the thresholds is frequently not continuous; and (5) local stability analysis may yield information on the occurence of these properties. In the paper, we demonstrate and discuss these properties in the case of a one-dimensional state space, with an extension to the two-dimensional case. Since in most cases, the first four properties (1)-(4) cannot be addressed analytically, we present three numerical methods for their investigation.