Abstract
This paper innovates the literature on endogenous discounting in environmental economics, by studying the global properties of the equilibrium outside the small neighborhood of the steady state. The internalization of individual consumption in the social discount rate is rich of powerful consequences from the economic point of view, for it leads to a qualitative change in the steady state and its transitional dynamics, so that the perfect foresight equilibrium may not be unique, and thus both local and global indeterminacy can eventually emerge. The main implication for decision making is that if indeterminacy occurs, public policies become not sufficient to drive the economy towards the long-run equilibrium. In particular, we show that the onset of parametric restrictions for which both global indeterminacy in the full R3 vector field, and a quasi-periodic dynamics with trajectories wrapped around an invariant torus, may eventually emerge.
Highlights
In the last two decades an increasing interest has been devoted to studying the impact of endogenous discounting in economic growth models
A bulk of literature postulates that, in sharp contrast with standard neoclassical assumptions, the subjective rate of time preference is not constant, but may depend on some aggregate economic variables, such as individual consumption. The internalization of these external social factors is rich of powerful consequences from the economic point of view, for it leads to a qualitative change in the steady state and its transitional dynamics, so that the perfect foresight equilibrium may not be unique, and both local and global indeterminacy can eventually emerge [1,2]
This issue is meaningful in the field of environmental economics, where the economic implications behind global indeterminacy can be interpreted as the way two identically endowed economies may start at some point to follow completely different equilibrium paths towards the long-run steady state
Summary
In the last two decades an increasing interest has been devoted to studying the impact of endogenous discounting in economic growth models. A bulk of literature postulates that, in sharp contrast with standard neoclassical assumptions, the subjective rate of time preference is not constant, but may depend on some aggregate economic variables, such as individual consumption The internalization of these external social factors is rich of powerful consequences from the economic point of view, for it leads to a qualitative change in the steady state and its transitional dynamics, so that the perfect foresight equilibrium may not be unique, and both local and global indeterminacy can eventually emerge [1,2]. The novelty of this paper relies on a deep investigation of the global behavior of the economy studied in [24], where indeterminacy may occur for a less stringent set of parametric restrictions To tackle this problem, we use the principles of bifurcation theory to gain hints on the global properties of the equilibrium, and to investigate the whole set of conditions which lead to the emergence of a quasi-periodic dynamics along an invariant torus.
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