Naive Agents with Quasi-hyperbolic Discounting and Perfect Foresight

We consider the Ramsey growth model with quasi-hyperbolic discounting where the agent cannot commit to future actions and is naive about her time inconsistency. We study the problem of observational equivalence, i.e., whether consumption paths are the same under quasi-hyperbolic and exponential discounting. To describe the behavior of a naive agent in a general equilibrium framework, we introduce the notion of a sliding equilibrium path and distinguish between two natural types of expectations: pseudo-prefect foresight and perfect foresight. Under pseudo-prefect foresight an agent at each date recalculates both her consumption path and expectations about prices, while under perfect foresight an agent correctly foresees prices on a sliding equilibrium path and is naive only about her time inconsistency. The main contribution of this paper is the study of a sliding equilibrium path under perfect foresight. We prove its existence for a general isoelastic utility function and show that, except for the well-known cases of a constant interest rate or logarithmic utility, there is no observational equivalence in general. In a number of important cases we also compare sliding equilibria under pseudo-perfect and perfect foresight in terms of long-run macroeconomic variables, and show that perfect foresight implies a higher capital stock and a higher consumption level than pseudo-perfect foresight.