Equivalent representations of non-exponential discounting models

I characterize the entire class of consumption rules for finite-horizon models in which consumption is proportional to lifetime wealth. Any such rule can be obtained from a preference model with CRRA period utility. In a steady state with constant interest rates, a proportional consumption rule can be derived from a model with time-consistent preferences or from a model with possibly time-inconsistent preferences in which a household continually reoptimizes future utility discounted relative to the present instant. These two preference models will only coincide for the special case when the discount function is exponential. More generally, there will be two distinct yet observationally equivalent preference models. Hyperbolic-like discounting may arise because that is a simpler way for the brain to process a standard exponential discount function after accounting for mortality risk.