David Laibson and Peter Maxted. In Preparation. “
The β–δ–Δ Sweet Spot”.
AbstractWhen agents have present-biased discount functions and are partially or fully sophisticated, equilibria in infinite-horizon problems are non-unique. In addition, the unique equilibrium selected by backward induction features strategic motives that induce pathological properties, including policy function discontinuities and non-monotonicities. Harris and Laibson (2013) show that continuous-time methods can be used to eliminate pathological equilibria. This paper proposes a discrete-time alternative in consumption models that is simple and computationally tractable: use monthly (or shorter) period lengths, which, when combined with calibrated levels of background noise, effectively eliminates the strategic mechanisms that plague present-biased models. The numerical solution to a discrete-time model with monthly periods approximates its well-behaved continuous-time counterpart. Accordingly, economists can work in discrete time while gaining the tractability afforded by continuous time. This paper formalizes these methods and provides numerical examples.
David Laibson, Sean Chanwook Lee, Peter Maxted, Andrea Repetto, and Jeremy Tobacman. In Preparation. “
Estimating Discount Functions with Consumption Choices over the Lifecycle”.
AbstractThis paper estimates time preferences using a structural lifecycle consumption-saving model. The model includes stochastic labor income, liquid and illiquid assets, revolving credit, child and adult dependents, bequests, and discount functions that allow short-term and long-term discount rates to differ. Data on wealth accumulation and credit card borrowing over the lifecycle identify the parameters in the model. In almost all specifications we reject the restriction to a constant discount factor (i.e., exponential discounting). Our benchmark estimates imply a short-term discount factor of beta=0.5 and a long-term annualized discount factor of delta=0.99.