Interacting mechanisms of time inconsistency

We interact two prominent behavioral mechanisms of time inconsistency that have been used to study inadequate saving: hyperbolic discounting and short-term planning. Hyperbolic discounting is a conventional way to model impulsive decision making, and short planning horizons have been used to represent myopia. One might expect that interacting both mechanisms within the same model would compound the inadequacy of saving. However, our key finding takes the form of a paradox: hyperbolic discounting does not affect consumption and saving allocations if the planning horizon is short and fixed, although it will affect allocations if the planning horizon is equal to the remaining life span. We demonstrate analytically that this finding is robust to the shape of the disposable income path, to the coarseness of the time grid, and to alternative forms of the period utility function.     

A General Formula for Valuing Defaultable Securities

Previous research has shown that under a suitable no‐jump condition, the price of a defaultable security is equal to its risk‐neutral expected discounted cash flows if a modified discount rate is introduced to account for the possibility of default. Below, we generalize this result by demonstrating that one can always value defaultable claims using expected risk‐adjusted discounting provided that the expectation is taken under a slightly modified probability measure. This new probability measure puts zero probability on paths where default occurs prior to the maturity, and is thus only absolutely continuous with respect to the risk‐neutral probability measure. After establishing the general result and discussing its relation with the existing literature, we investigate several examples for which the no‐jump condition fails. Each example illustrates the power of our general formula by providing simple analytic solutions for the prices of defaultable securities.     

Intergenerational and International Discounting

A discount rate for the consumption of future generations is typically composed of two parts. One is a "pure" time preference for immediate over postponed consumption, the other a declining marginal utility as consumption increases. The costs of greenhouse abatement, however, for at least the first 50 years, will be borne by the developed countries; the benefits will accrue to the presently undeveloped. Pure time preference always relates to one's own consumption; it has no relevance here. Consumption transfers over time will be from richer to poorer, from lower to higher marginal utility. It is a foreign aid program and it ought to have to compete with more direct foreign aid, which can benefit the very poor rather than their much-better-off descendants.     

Impulsivity as a Risk Factor for HIV Transmission in Men Who Have Sex with Men: A Delay Discounting Approach

Delay discounting (DD) is a measure of impulsivity that describes the subjective decline in value of a consequence as the delay to that consequence increases. We sought to assess whether the results of a monetary DD task would be predictive of sexual risk-taking in a group of Internet-using men who have sex with men (MSM). 1402 participants completed an online survey that included questions about the participant’s demographics, sexual history and behavior, drug use, sexual compulsivity, and a monetary DD task. High DD was associated with increased odds of reporting >2 UAI partners in the past 12 months [aOR = 1.5 (1.1–2.1)]. Future studies should examine the utility of DD as a predictor of risky sexual behavior, as well as explore the possibility of HIV prevention interventions targeting DD.     

Awareness of low self-control: Theory and evidence from a homeless shelter

Survey measures of self-control provide a potential low-cost alternative to incentivized elicitation. However, asking respondents to introspect on their self-control problems may instead measure their awareness of them, especially in populations with low self-control. We illustrate this with the Ameriks, Caplin, Leahy, and Tyler (2007) survey, which captures self-control problems through the deviation between self-reported ideal and predicted behavior (Expected Deviation, ED). Previous empirical evidence from high income or highly educated populations correlates larger ED with worse outcomes. We theoretically show that the reverse will be true in settings where awareness can play a large role: when self-control is low and costly commitment devices are available. We empirically show that, for residents of a homeless shelter, ED is positively correlated to savings in shelter lockboxes, a costly commitment device. This correlation is stronger for those likely to experience more self-control problems: individuals with past addiction problems.     

Decision-Making, Time Horizons, and Risk in the Very Long-Term Perspective

Some decisions made today have far-reaching consequences as exemplified by those concerning nuclear power and spent nuclear fuel. The investigation presented here uses a decision theoretic framework in which time horizons and the discounting of negative consequences play significant roles. The results indicated wide variations in the lengths of the planning horizons judged to be adequate not only across a number of activities, including nuclear waste management, but also across groups of subjects (e.g., engineering students, retired people, and nuclear fuel experts). The paper reports typical judgments and correlations between different variables for different groups of subjects. The differences across groups reflect potential sources of conflict, depending in part on different values and different perceptions of more or less uncertain facts. Discounting functions for negative consequences in the future were also established. A range in differences in the speed of discounting were found and illustrated. Furthermore, it was found that substantial proportions in all groups regarded negative consequences related to nuclear waste as nondiscountable. When asked about the effect of time until outcome on acceptable probability of a negative outcome, many subjects used the probability concept in an incoherent way, illustrating the great difficulty in communicating small probabilities in a long-term risk context.     

Regional efficacy evaluation in multi-regional clinical trials using a discounting factor weighted Z test

Multi-regional clinical trial (MRCT) is an efficient design to accelerate drug approval globally. Once the global efficacy of test drug is demonstrated, each local regulatory agency is required to prove effectiveness of test drug in their own population. Meanwhile, the ICH E5/E17 guideline recommends using data from other regions to help evaluate regional drug efficacy. However, one of the most challenges is how to manage to bridge data among multiple regions in an MRCT since various intrinsic and extrinsic factors exist among the participating regions. Furthermore, it is critical for a local agency to determine the proportion of information borrowing from other regions given the ethnic differences between target region and non-target regions. To address these issues, we propose a discounting factor weighted Z statistic to adaptively borrow information from non-target regions. In this weighted Z statistic, the weight is derived from a discounting factor in which the discounting factor denotes the proportion of information borrowing from non-target regions. We consider three ways to construct discounting factors based on the degree of congruency between target and non-target regions either using control group data, or treatment group data, or all data. We use the calibrated power prior to construct discounting factor based on scaled Kolmogorov–Smirnov statistic. Comprehensive simulation studies show that our method has desirable operating characteristics. Two examples are used to illustrate the applications of our proposed approach.     

Is Time-Discounting Hyperbolic or Subadditive?

Subadditive time discounting means that discounting over a delay is greater when the delay is divided into subintervals than when it is left undivided. This may produce the most important result usually attributed to hyperbolic discounting: declining impatience, or the inverse relationship between the discount rate and the magnitude of the delay. Three choice experiments were conducted to test for subadditive discounting, and to determine whether it is sufficient to explain declining impatience. All three experiments showed strong evidence of subadditive discounting, but there was no evidence of declining impatience. I conclude by questioning whether hyperbolic discounting is a plausible account of time preference.     

Air Pollution and Mortality: Quantification and Valuation of Years of Life Lost

To analyze the loss of life expectancy (LLE) due to air pollution and the associated social cost, a dynamic model was developed that took into account the decrease of risk after the termination of an exposure to pollution. A key parameter was the time constant for the decrease of risk, for which estimates from studies of smoking were used. A sensitivity analysis showed that the precise value of the time constant(s) was not critical for the resulting LLE. An interesting aspect of the model was that the relation between population total LLE and PM2.5 concentration was numerically almost indistinguishable from a straight line, even though the functional dependence was nonlinear. This essentially linear behavior implies that the detailed history of a change in concentration does not matter, except for the effects of discounting. This model was used to correct the data of the largest study of chronic mortality for variations in past exposure, performed by Pope et al. in 1995; the correction factor was shown to depend on assumptions about the relative toxicity of the components of PM2.5. In the European Union, an increment of 1 microg/m3 of PM2.5 for 1 year implies an average LLE of 0.22 days per person. With regard to the social cost of an air pollution pulse, it was found that for typical discount rates (3% to 8% real) the cost was reduced by a factor of about 0.4 to 0.6 relative to the case with zero discount rate, if the value of a life year was taken as given; if the value of a life year was calculated from the "value of statistical life" by assuming the latter as a series of discounted annual values, the cost varied by at most +/-20% relative to the case with zero discount rate. To assess the uncertainties, this study also examined how the LLE depended on the demographics (mortality and age pyramid) of a population, and how it would change if the relative risk varied with age, in the manner suggested by smoking studies. These points were found to have a relatively small effect (compared to the epidemiological uncertainties) on the calculated LLE.     

Commitment vs. Flexibility

We study the optimal trade‐off between commitment and flexibility in a consump‐ tion–savings model. Individuals expect to receive relevant information regarding tastes and thus they value the flexibility provided by larger choice sets. On the other hand, they also expect to suffer from temptation, with or without self‐control, and thus they value the commitment afforded by smaller choice sets. The optimal commitment problem we study is to find the best subset of the individual's budget set. This problem leads to a principal–agent formulation. We find that imposing a minimum level of savings is always a feature of the solution. Necessary and sufficient conditions are derived for minimum‐savings policies to completely characterize the solution. We also discuss other applications, such as the design of fiscal constitutions, the problem faced by a paternalist, and externalities.