How the Future Shapes Consumption with Time-Inconsistent Preferences

Time-inconsistent preferences, which are modeled by relative discount functions, are a common explanation for the empirical finding that lifecycle profiles of household consumption are typically hump-shaped rather than monotonic. More precisely, time-inconsistent preferences that are present-biased often generate a hump-shaped consumption profile over the lifecycle. We develop a general framework for understanding present bias in consumption through a future weighting factor that perturbs the discount factor of utility at future periods away from exponential discounting. Using our framework we derive necessary and sufficient conditions on the future weighting factors for the log consumption profile to be locally concave. We find that these conditions, which are necessary for the consumption profile to be hump-shaped, are stronger than just assuming a present bias. Furthermore, we explore the conditions under which the consumption profile determined in the first period of life Pareto dominates the realized consumption profile. Lastly, we explore the interconnections between these two sets of conditions, elucidating the linkages between the determinants of hump-shaped consumption profiles and the conditions necessary for the initial consumption path to achieve Pareto dominance.