Time Discounting and Time Consistency

Time discounting is the phenomenon that a desired result in the future is perceived as less valuable than the same result now. Economic theories can take this psychological fact into account in several ways. In the economic literature the most widely used type of additive time discounting is exponential discounting. In exponential discounting, the fall of valuation depends by a constant factor on the length of the delay period. It is well known, however, that exponential time discounting often does not describe well how people actually behave. Most people are averse to short delays in gratification now, while their future selves may not mind a bit of extra waiting. This behaviour can be described well by non-exponential discounting functions such as hyperbolic discounting. In hyperbolic discounting, valuations fall rapidly for small delay periods, but the fall gets slower for longer delay periods. Hyperbolic discounting captures phenomena such as procrastination, addiction and in general inconsistency over time. This chapter investigates whether forms of non-exponential discounting, in particular close to the so called Quasi-Hyperbolic model, could also be characterized in terms of dynamically consistent choices when individuals discount the welfare of future selves as well as their payoffs

Optimal Conservation Policy under Imperfect Intergenerational Altruism

In this paper we study the optimal forest conservation policy by a hyperbolically discounting society. Society comprises a series of non-overlapping imperfectly altruistic generations each represented by its own government. Under uncertainty about future pay-offs we determine, as solution of an intergenerational dynamic game, the optimal timing of irreversible harvest. Earlier harvest occurs and the option value attached to the forest clearing decision is eroded under both the assumptions of naïve and sophisticated belief about future time-preferences. This results in a bias toward the current generation gratification which affects the intergenerational allocation of benefits and costs from harvesting and conserving a natural forest.Imperfect altruism, Real Options, Hyperbolic Discounting, Time Inconsistency, Natural Resources Management, Resource /Energy Economics and Policy, D81, C70, Q23, Q58,

Time discounting and time consistency

Time discounting is the phenomenon that a desired result in the future is perceived as less valuable than the same result now. Economic theories can take this psychological fact into account in several ways. In the economic literature the most widely used type of additive time discounting is {\em exponential discounting}. In exponential discounting, the fall of valuation depends by a constant factor on the length of the delay period. It is well known, however, that exponential time discounting often does not describe well how people actually behave. Most people are averse to short delays in gratification now, while their future selves may not mind a bit of extra waiting. This behaviour can be described well by non-exponential discounting functions such as {\em hyperbolic discounting}. In hyperbolic discounting, valuations fall rapidly for small delay periods, but the fall gets slower for longer delay periods. Hyperbolic discounting captures phenomena such as procrastination, addiction and in general inconsistency over time. This chapter investigates whether forms of non-exponential discounting, in particular close to the so called Quasi-Hyperbolic model, could also be characterized in terms of dynamically consistent choices when individuals discount the welfare of future selves as well as their payoffs

INDETERMINACY IN A LOG-LINEARIZED NEOCLASSICAL ROWTH MODEL WITH QUASI-GEOMETRIC DISCOUNTING

This paper studies the properties of solutions to a log-linearized version of the neoclassical growth model with quasi-geometric discounting. We show that after the log-linearization, the model has indeterminacy and multiplicity of equilibria even though the original non-linear model has a unique interior solution. Specifically, in both the deterministic and stochastic cases, the log-linearized model has a continuum of steady states. In the deterministic case, there is a unique log-linear policy function leading to each steady state, while in the stochastic case, there is a continuum of log-linear policy functions, associated with each steady state. Hence, the standard log-linearization method cannot be applied for solving models with quasi-geometric discounting.quasi-geometric (quasi-hyperbolic) discounting, time inconsistency, neoclassical growth model

Cultural Neuroeconomics of Intertemporal Choice

According to theories of cultural neuroscience, Westerners and Easterners may have distinct styles of cognition (e.g., different allocation of attention). Previous research has shown that Westerners and Easterners tend to utilize analytical and holistic cognitive styles, respectively. On the other hand, little is known regarding the cultural differences in neuroeconomic behavior. For instance, economic decisions may be affected by cultural differences in neurocomputational processing underlying attention; however, this area of neuroeconomics has been largely understudied. In the present paper, we attempt to bridge this gap by considering the links between the theory of cultural neuroscience and neuroeconomic theory\ud of the role of attention in intertemporal choice. We predict that (i) Westerners are more impulsive and inconsistent in intertemporal choice in comparison to Easterners, and (ii) Westerners more steeply discount delayed monetary losses than Easterners. We examine these predictions by utilizing a novel temporal discounting model based on Tsallis' statistics (i.e. a q-exponential model). Our preliminary analysis of temporal discounting of gains and losses by Americans and Japanese confirmed the predictions from the cultural neuroeconomic theory. Future study directions, employing computational modeling via neural networks, are briefly outlined and discussed

Some Common Confusions about Hyperbolic Discounting

There is much confusion over what "hyperbolic discounting" means. I argue that what matters is the use of relativistic instead of objective time, not the shape of the discount function.time inconsistency, hyperbolic discounting

A neuroeconomic theory of rational addiction and\ud nonlinear time-perception.

Neuroeconomic conditions for “rational addiction” (Becker and Murphy, 1988) have\ud been unknown. This paper derived the conditions for “rational addiction” by utilizing a\ud nonlinear time-perception theory of “hyperbolic” discounting, which is mathematically\ud equivalent to the q-exponential intertemporal choice model based on Tsallis' statistics. It\ud is shown that (i) Arrow-Pratt measure for temporal cognition corresponds to the degree\ud of irrationality (i.e., Prelec’s “decreasing impatience” parameter of temporal\ud discounting) and (ii) rationality in addicts is controlled by a nondimensionalization\ud parameter of the logarithmic time-perception function. Furthermore, the present theory\ud illustrates the possibility that addictive drugs increase impulsivity via dopaminergic\ud neuroadaptation without increasing irrationality. Future directions in the application of\ud the model to studies in neuroeconomics are discussed