Interacting mechanisms of time inconsistency

• We model the interaction of hyperbolic discounting with short planning horizons.
• Hyperbolic discounting does not affect actual consumption with short, fixed horizons.
• Hyperbolic discounting affects allocations if horizon equals the remaining life span.
• Findings are robust to the form of the utility function and to the model time grid.
• Findings are robust to how transfer programs redistribute income over the life cycle.

We interact two prominent behavioral mechanisms of time inconsistency that have been used to study inadequate saving: hyperbolic discounting and short-term planning. Hyperbolic discounting is a conventional way to model impulsive decision making, and short planning horizons have been used to represent myopia. One might expect that interacting both mechanisms within the same model would compound the inadequacy of saving. However, our key finding takes the form of a paradox: hyperbolic discounting does not affect consumption and saving allocations if the planning horizon is short and fixed, although it will affect allocations if the planning horizon is equal to the remaining life span. We demonstrate analytically that this finding is robust to the shape of the disposable income path, to the coarseness of the time grid, and to alternative forms of the period utility function.