Discounting Across Generations: Necessary, not Suspect

Periodically, ethical objections are raised against the practice of discounting for future effects. Concerns about the potential effects on future generations from long-term nuclear waste disposal and global climate change have caused these ethical objections to recur. This article rebuts the various ethical objections to future discounting on practical, ethical, and analytic grounds. Discounting for future effects is a ubiquitous practice that cannot be practically prevented. In the event that public policy would dictate against future discounting in public decisions, such a constraint could never be successfully imposed on markets. Market values will always reflect the full, discounted streams of future effects even if governments prohibited the practice among individuals. Ethically, there is no basis for choosing an upper-bound time horizon beyond which discounting should be rejected. Any proposed horizon is arbitrary and has no obvious foundation. All decisions are fundamentally irreversible, so opponents of future discounting also must define a degree of irreversibility beyond which normal discounting should not apply, and defend on ethical grounds the basis for this demarcation. This task is further complicated by the likelihood that choices are rarely, if ever, as irreversible as opponents suggest. Typical examples given to prove future discounting is inappropriate overstate the degree of irreversibility actually present and understate subsequent opportunities for modifications. Finally, opposition to distant-future discounting on the ground that burdens are shifted to future generations must face the fact that such shifts are characteristic of intergenerational transfers now practiced widely and with great public support.     

时间偏好不一致委托代理问题的优化与决策

现有讨论委托代理问题涉及将不同时点收益和成本折现时,几乎毫无例外的选择唯一能代表时间偏好一致的折现函数—指数折现.本文放松时间偏好一致这一假设,选择能反映时间偏好不一致的准双曲折现函数一ββδ作为代理人折现函数,分析收益由努力程度和外部因素共同作用,代理人的成本和收益发生在不同时点时,委托人如何制定激励合同使得代理人努力工作且委托人获得最大利润.研究发现,最优合同与代理人的现期偏好参数β和对未来现期偏好参数的认知β有关,委托人从时间偏好一致的代理人获取的利润高于时间偏好不一致的代理人,从悲观部分幼稚型获取利润小于成熟型,但从成熟型和乐观部分幼稚型获取的利润相同.     

Behavioral Perspectives on Variability in Human Behavior as Part of Process Safety

ABSTRACT

Process safety involves worker decisions at various points in an extended process, and much remains unknown regarding sources of variability in worker behavior at these decision points. This paper seeks to explain why some workers may be deviating from sanctioned policies and procedures. Risky choice is analyzed through discussion of positive and negative reinforcement, habituation in terms of respondent and operant behavior, risk discounting, and consequence dimensions that include a review of prospect theory, heuristics, and behavioral decision theory. Recommendations are made for improving our understanding of sources of variability in process safety by conducting systematic research on the perspectives reviewed.     

Dispositional Factors Affecting Choices Surrounding the Purchase of Insurance and the Taking of Mitigating Measures Against Flooding

This research investigated the role of dispositional factors in decisions to purchase insurance and to take mitigating measures against flooding. Two dispositional factors—risk aversion in the domain of losses and time discounting rate—were found to be predictors of the decision to acquire flood insurance. The observation of a relationship between experiment-based risk attitudes and the decision to insure oneself against flooding replicates a finding of Petrolia et al. The finding that impatience negatively impacts decisions to take out insurance against flooding is novel. However, support was not found for analogous hypotheses concerning relationships between the two dispositional variables and decisions to take mitigating measures. Evidently, factors other than individual risk aversion and time discounting rate play a crucial role in this behavior.     

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.     

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.     

On Intergenerational Equity and Its Clash with Intragenerational Equity and on the Need for Policies to Guide the Regulation of Disposal of Wastes and Other Activities Posing Very Long-Term Risks

This article begins with some history of the derivation of 40 CFR Part 191, the U.S. Environmental Protection Agency (EPA) standard that governs the geologic disposal of spent nuclear fuel and high-level and transuranic radioactive wastes. This is followed by criticisms of the standard that were made by a Sub-Committee of the EPA Science Advisory Board, by the staff of the U.S. Nuclear Regulatory Commission, and by a panel of the National Academies of Science and Engineering. The large disparity in the EPA approaches to regulation of disposal of radioactive wastes and disposal of hazardous, long-lived, nonradioactive chemical waste is illustrated. An examination of the intertwined matters of intergenerational equity and the discounting of future health effects follows, together with a discussion of the conflict between intergenerational equity and intragenerational equity. Finally, issues related to assumptions in the regulations concerning the future state of society and the biosphere are treated, as is the absence of any national philosophy or guiding policy for how to deal with societal activities that pose very long-term risks.     

Is Eradication of the Pinewood Nematode (Bursaphelenchus xylophilus) Likely? An Evaluation of Current Contingency Plans

The pinewood nematode (PWN) is one of the worst tree‐killing exotic pests in East‐Asian countries. The first European record of establishment in Portugal in 1999 triggered extensive surveys and contingency plans for eradication in European countries, including immediate removal of large areas of conifer host trees. Using Norway as an example, we applied a simulation model to evaluate the chance of successful eradication of a hypothetical introduction by the current contingency plan in a northern area where wilting symptoms are not expected to occur. Despite a highly variable spread of nematode infestations in space and time, the probability of successful eradication in 20 years was consistently low (mean 0.035, SE 0.02). The low success did not change significantly by varying the biological parameters in sensitivity analyses (SA), probably due to the late detection of infestations by the survey (mean 14.3 years). SA revealed a strong influence of management parameters. However, a high probability of eradication required unrealistic measures: achieving an eradication probability of 0.99 in 20 years required 10,000 survey samples per year and a host tree removal radius of 8,000 m around each detection point.     

Spatial Stochastic Simulation Offers Potential as a Quantitative Method for Pest Risk Analysis

Pest risk analysis represents an emerging field of risk analysis that evaluates the potential risks of the introduction and establishment of plant pests into a new geographic location and then assesses the management options to reduce those potential risks. Development of new and adapted methodology is required to answer questions concerning pest risk analysis of exotic plant pests. This research describes a new method for predicting the potential establishment and spread of a plant pest into new areas using a case study, Ralstonia solanacearum, a bacterial disease of potato. This method combines current quantitative methodologies, stochastic simulation, and geographic information systems with knowledge of pest biology and environmental data to derive new information about pest establishment potential in a geographical region where a pest had not been introduced. This proposed method extends an existing methodology for matching pest characteristics with environmental conditions by modeling and simulating dissemination behavior of a pest organism. Issues related to integrating spatial variables into risk analysis models are further discussed in this article.     

Discounting Compensation for Injuries

The reasons commonly given for discounting future costs and benefits are doubtfully applicable to future injuries: in particular, time preference justifies neither inter- nor intragenerational discounting. The cost of future injuries could be discounted on grounds that a smaller sum, invested at interest, is needed to pay a given level of ex post monetary compensation the further in the future the injury occurs. This effect is offset, however, by the diminishing marginal utility of compensation, if consumption is otherwise increasing. Depending on the elasticity of marginal utility of consumption, on whether consumption is growing at an optimal rate, and on the time period considered, the implicit discount rate may be positive, zero, or negative (even indefinitely so). There is no prospect of conventional discounting dealing appropriately with the cost of injuries to either future or present generations.     

A free gift card alternative to price discounts in the newsvendor problem

In this paper, we develop a newsvendor model in which the retailer gives “free” gift cards to consumers who purchase a regularly priced product at the end of the selling season instead of discounting the product. The model is developed for a market with patient consumers. We derive the sufficient optimality condition for the retailer's stocking level in the first period and the optimal gift card value in the second period. We also investigate the conditions under which giving gift cards results in higher expected profits than discounting the product. We find that five factors determine the effectiveness of gift cards. The first three factors are consumers' valuation per $1 of gift card, gift card redemption rates, and the average gross margin of the retailer. The last two factors are the degree to which consumers use gift cards to pay for products which they would have purchased from the retailer in the future with cash, and the additional spending above the gift card value consumers make when they redeem the card. The last two factors have a strong interaction. We also find that gift cards can be profitable when patient consumers consistently value each $1 by their redemption probability, even with 100% redemption. Numerical analysis shows that in the presence of patient consumers, increases in the redemption rate may lead to an increase in the expected profit. Similar counter-intuitive behavior of the expected profit occurs with changes in other problem parameters. The analysis also shows that gift cards' profit advantage over discounting increases with the variability of demand. The analysis also indicates that gift cards are most effective for low to medium priced products sold by high margin retailers.     

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.     

ON THE POSSIBILITY OF INFORMATIONALLY EFFICIENT MARKETS

This paper presents conditions for a resolution of the Grossman–Stiglitz paradox of informationally efficient markets. We display a market with asymmetric information where a privately revealing equilibrium obtains in a competitive framework and where incentives to acquire information are preserved as long as the correlation in traders’ valuations is not too large. The equilibrium is efficient, and the problems associated with fully revealing rational expectations equilibria are precluded without resorting necessarily to noise traders. The robustness of the results to general information structures is established and the effect of market power is examined in a large market approximation to the competitive economy. The model is applied to explain changes in bidding behavior in central bank liquidity auctions in the crisis period. (JEL: D82, D84, G14, E59)     

Assortative Matching with Explicit Search Costs

In this paper, I analyze a decentralized search and matching economy with transferable utility composed of heterogeneous agents. I explore whether Becker's assortative matching result generalizes to an economy where agents engage in costly search. In an economy with explicit additive search costs, complementarities in joint production (supermodularity of the joint production function) lead to assortative matching. This is in contrast to previous literature, which had shown that in a search economy with discounting, assortative matching may fail even when the joint production function is supermodular.     

Cooperation and Punishment

We show that, in repeated common interest games without discounting, strong ‘perturbation implies efficiency’ results require that the perturbations must include strategies that are ‘draconian’ in the sense that they are prepared to punish to the maximum extent possible. Moreover, there is a draconian strategy whose presence in the perturbations guarantees that any equilibrium is efficient. We also argue that the results of Anderlini and Sabourian (1995) using perturbation strategies that are cooperative (and hence nondraconian) are not due to computability per se but to the further restrictions they impose on allowable beliefs.     

Strategic Management of Distressed Inventory

It is well known that maximizing revenue from a fixed stock of perishable goods may require discounting prices rather than allowing unsold inventory to perish. This behavior is seen in industries ranging from fashion retail to tour packages and baked goods. A number of authors have addressed the markdown management problem in which a seller seeks to determine the optimal sequence of discounts to maximize the revenue from a fixed stock of perishable goods. However, merchants who consistently use markdown policies risk training customers to “wait for the sale.” We investigate models in which the decision to sell inventory at a discount will change the future expectations of customers and hence their buying behavior. We show that, in equilibrium, a single‐price policy is optimal if all consumers are strategic and demand is known to the seller. Relaxing any of these conditions can lead to a situation in which a two‐price markdown policy is optimal. We show using numerical simulation that if customers update their expectations of availability over time, then optimal sales limit policies can evolve in a complex fashion.     

Eliciting Risk and Time Preferences

We design experiments to jointly elicit risk and time preferences for the adult Danish population. Since subjects are generally risk averse, we find that joint elicitation provides estimates of discount rates that are significantly lower than those found in previous studies and more in line with what would be considered as a priori reasonable rates. The statistical specification relies on a theoretical framework that involves a latent trade‐off between long‐run optimization and short‐run temptation. Estimation of this specification is undertaken using structural, maximum likelihood methods. Our main results based on exponential discounting are robust to alternative specifications such as hyperbolic discounting. These results have direct implications for attempts to elicit time preferences, as well as debates over the appropriate domain of the utility function when characterizing risk aversion and time consistency.     

EOQ FORMULA: IS IT VALID UNDER INFLATIONARY CONDITIONS?

The classical analysis of the economic order quantity (EOQ) problem ignores the effect of inflation. When a firm's cost factors are expected to rise at an annual rate of 10 percent or more, what adjustments in order quantities should the firm make to control its lot-size inventory (or cycle stock)? Using a model that includes both inflationary trends and time discounting, it is concluded that inflation brings no incentive either to increase or to decrease order quantities. In addition, order quantities can be computed using the classical EOQ formula under inflationary conditions, provided that the cost of capital invested in inventory is interpreted as an inflation-free cost. This interpretation implies that changes in the inflation rate should not affect the cost of capital that is utilized in the EOQ formula for determining order quantities.     

Small Theories and Large Risks—Is Risk Analysis Relevant for Epistemology?

Ought we to take seriously large risks predicted by “exotic” or improbable theories? We routinely assess risks on the basis or either common sense, or some developed theoretical framework based on the best available scientific explanations. Recently, there has been a substantial increase of interest in the low‐probability “failure modes” of well‐established theories, which can involve global catastrophic risks. However, here I wish to discuss a partially antithetical situation: alternative, low‐probability (“small”) scientific theories predicting catastrophic outcomes with large probability. I argue that there is an important methodological issue (determining what counts as the best available explanation in cases where the theories involved describe possibilities of extremely destructive global catastrophes), which has been neglected thus far. There is no simple answer to the correct method for dealing with high‐probability high‐stakes risks following from low‐probability theories that still cannot be rejected outright, and much further work is required in this area. I further argue that cases like these are more numerous than usually assumed, for reasons including cognitive biases, sociological issues in science and the media image of science. If that is indeed so, it might lead to a greater weight of these cases in areas such as moral deliberation and policy making.     

Heterogeneous Submission Behavior and its Implications for Success in Innovation Contests with Public Submissions

Innovation contests are increasingly adopting a format where submissions are viewable by all contestants and the information structure changes during the contest. In such an “unblind” format, contestants must weigh the costs of revealing their submissions against the benefits of improving their submissions through emerging information. We take a closer look at how contestants solve problems in innovation contests with public submission of solutions—that is, unblind contests, by examining the implications of their submission behavior for contest outcomes. We analyze the submission behavior in terms of three dimensions: the position of first submission by the contestant, the number of submissions the contestant makes, and the length of active participation by the contestant. The econometric analysis of a large dataset of unblind innovation contests and participating contestants indicates that, despite the potential for free riding and intellectual property loss from disclosure of submissions, contestants who have a lower position of first submission are more likely to succeed in the contest. Further, we find some evidence of a curvilinear relationship between a contestant's number of submissions and her likelihood of success, indicating a potential “quality–quantity” trade‐off in unblind innovation contests. Finally, our findings indicate that increasing the length of participation in a contest has a positive effect on a contestant's likelihood of success. Departing from prior studies on innovation contests, where a contestant's success is assumed to be a function of her prior experience and problem‐solving skills, our study provides new empirical evidence that, in innovation contests with public submissions, the submission behavior of a contestant also plays an explanatory role in a contestant's success.