By augmenting the continuous-time specification of Harris and Laibson (2013) with the assumption that hard borrowing constraints do not bind in equilibrium, present bias can be tractably incorporated into rich consumption-saving models featuring stochastic income, risky and illiquid assets, and costly borrowing. I present closed-form expressions characterizing how present bias affects consumption, illiquid asset demand, and welfare. This welfare analysis specifies the channels through which present bias can matter for policy and uncovers the present-bias dilemma: present bias can have large welfare costs, but individuals have little ability to alleviate these costs using financial commitment devices like illiquid assets.

We study the effect of monetary and fiscal policy in a heterogeneous-agent model where households have present-biased time preferences and naive beliefs. The model features a liquid asset and illiquid home equity, which households can use as collateral for borrowing. Because present bias substantially increases households’ marginal propensity to consume (MPC), present bias increases the effect of fiscal policy. Present bias also amplifies the effect of monetary policy, but at the same time, slows down the speed of monetary transmission. Interest rate cuts incentivize households to conduct cash-out refinances, which become targeted liquidity injections to high-MPC households. Present bias also introduces a motive for households to procrastinate refinancing their mortgages, which slows down the speed with which this monetary channel operates.