Uncertainty under hyperbolic discounting: the cost of untying your hands

The relevance of present consumption bias on personal finance has been confirmed in several studies and has important theoretical and practical implications. It has important, measurable implications when analyzing commitment or self-control, adherence to healthy habits (e.g. exercising or dieting), procrastination tendencies or savings. The purpose of this paper is to contribute to our understanding of these issues by postulating a model of income uncertainty within a hyperbolic discounting framework that measures the cost of financial intertemporal inconsistencies related to this bias. The emphasis is on the analysis of this cost. We also propose experimental designs and consistent estimationmethods, as well as agent-based modelling extensions. The authors develop a finite-horizon model with hyperbolic preferences. Individuals have a present bias distinct from their discount rate so their choices face intertemporal inconsistencies. The authors further extend the analysis with uncertainty about future incomes. Specifically, individuals live for three periods, and the authors find the optimal consumption levels in the perfect-information benchmark by backward induction. They then proceed to add biases and uncertainty to characterize their implications and measure the costs of the intertemporal inconsistencies they cause. The authors measure how an agent’s utility is greater when they “tie their hands” than when they are free to re-evaluate and change their consumption schedule. This “cost of being vulnerable to falling into temptation” only depends (increasingly) on the measure of the present bias and (decreasingly) on the discount factor. They analyze the varying effects on utility and consumption of changes in impatience and optimism. They conclude by discussing theoretical and practical implications; they also propose agent-based simulations, as well as empirical and experimental designs, to further test the relevance and applications of the results.