Self-Control Problems in Consumption-Saving Models: A Tractable Continuous-Time Approach
This paper studies the consumption-saving decisions of "present-biased" consumers who face self-control problems when making these choices. I show that continuous-time methods allow for present bias to be tractably incorporated into rich consumption-saving models featuring stochastic income, credit card borrowing, and illiquid assets like houses and retirement accounts. In this rich economic environment I present closed-form expressions characterizing the effect of present bias on consumption, the demand for illiquid assets, and welfare. This welfare analysis specifies the channels through which present bias can matter for policymakers, and leads to what I call the present-bias dilemma: present bias has large welfare costs, but individuals have little ability to alleviate these costs without government intervention.