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Self-Control, Saving, and the Low Asset Trap

We examine a class of intertemporal consumption allocation models in which time inconsistent preferences create self-control problems. Behavior corresponds to an equilibrium of a game played by successive incarnations of the single decision-maker, and the scope for self-control is defined by the set of subgame perfect equilibria. We study the features of this set computationally. A reasonably robust feature of the equilibrium set is the existence of a threshold asset level, below which no self-discipline is possible (the individual simply consumes assets down to zero), and above which it is possible to sustain positive asset accumulation. We investigate the sensitivity of the equilibrium set to various parameters. For example, we show that when credit becomes more readily available, self-control becomes easier to impose, and fewer individuals are caught in the low asset trap.