David Laibson, Harvard University
Joint with Macro Seminar.
ABSTRACT: When agents have present-biased discount functions and are partially or fully sophisticated, intra-personal strategic motives induce equilibria with pathological properties, including non-uniqueness, policy function discontinuities and policy-function non-monotonicities. Harris and Laibson (2013) propose a continuous-time model with an instantaneously short 'present', which eliminates such pathologies. The current paper provides a bridge between this continuous-time approach and traditional discrete-time models. Calibrated buffer-stock consumption models with discrete time periods that are no longer than one month are pathology-free and feature policy functions that are nearly identical to the policy functions associated with the continuous-time model. Researchers working on consumption models with present bias should use discrete time models with time periods that are no longer than one month (and calibrated levels of background noise), or the continuous-time model, whichever framework is computationally more tractable. Within this family of discrete- and continuous-time buffer-stock models, the predictions are indistinguishable and pathology-free.