Working Paper: NBER ID: w24257
Authors: Dan Cao; Ivan Werning
Abstract: Is the standard hyperbolic-discounting model capable of robust qualitative predictions for savings behavior? Despite results suggesting a negative answer, we provide a positive one. We give conditions under which all Markov equilibria display either saving at all wealth levels or dissaving at all wealth levels. Moreover, saving versus dissaving is determined by a simple condition comparing the interest rate to a threshold made up of impatience parameters only. Our robustness results illustrate a well-behaved side of the model and imply that qualitative behavior is determinate, dissipating indeterminacy concerns to the contrary (Krusell and Smith, 2003). We prove by construction that equilibria always exist and that multiplicity is present in some cases, highlighting that our robust predictions are not due to uniqueness. Similar results may be obtainable in related dynamic games, such as political economy models of public spending.
Keywords: Hyperbolic Discounting; Savings Behavior; Equilibria
JEL Codes: D03; D15; D7; E21
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| interest rate (r) (E43) | savings behavior (D14) |
| interest rate (r) > 1 (E43) | agents will save (L85) |
| interest rate (r) < 1 (E43) | agents will dissave (L85) |
| wealth increases (D31) | no reversal from dissaving to saving (E21) |
| savings behavior (D14) | broader applicability in dynamic games (C73) |