(1) Objectives
Recently some literatures reported anomalies that contradict with standard discounted utility models. For example, Frederick, Loewenstein, and O’Donoghue (2002) provide survey these anomalies and suggest that consumers’ behaviors indicate time inconsistent and the preference for improving sequences. To explain these anomalies, recent literatures deviate from the standard discounted utility models. Laibson (1997) assumes the decreasing discount rate and shows that naïve consumers tend to revise their saving plan downward. Loewenstein (1987) This paper extends Loewenstein (1987) to a dynamic model and analyzes optimal consumption choices of sophisticated consumers. Next, the present paper derives implied discount factor from optimal consumption profile by using standard Euler equation and investigates the relation between actual discount factor and the implied discount factor. (2) Methods There exist single consumption good and a representative consumer with felicities from current consumption and from anticipation of future consumptions. The time is discrete and lasts for T period. There exists only one riskless asset with constant interest rate. The consumer determines consumption/savings in order to maximize life-time utility. To derive optimal consumption strategy, this paper provides the generalized Euler equation which associates marginal utilities of consumption at three periods. (3) Results Consumers can savor distant future consumption for a longer time than near future consumption, which makes consumers to be patient. Furthermore, the positive effect on discount factor depends on time distant. In particular, if consumers strongly concern the felicity from anticipation, the distant future consumption is less discounted than near future consumption, that is, discount factor is increasing in time distant and their time preference exhibit future bias. Consumers with increasing discount factor (i.e., future bias) tend to revise their saving plan upward, which leads to time-inconsistency for saving/consumption choices. Consumers with increasing discount factor tend to choose upward sloping consumption profile. This is consistent with preference for improving sequences suggested by empirical literatures (i.e., Loewenstein and Sicherman, 1991). Furthermore, implied discount factor derived from consumption profile for consumers with future bias exhitis the property of decreasing in time distance. An empirical implication for this is as follows. If observers estimate implied discount factor from actual consumption data by using standard discount model, they conclude that discount factor is decreasing in time distant, which opposes to an actual property of discount factor.