The implications of hyperbolic discounting for project evaluation

The neoclassical theory of project evaluation is based on models in which agents discount the future at a constant exponential rate. But there is strong empirical evidence that people discount the future hyperbolically, applying larger annual discount rates to near-term returns than to returns in the distant future. This has led some policymakers to argue that, in evaluating programs with benefits spread over decades (such as subway systems and abatement of greenhouse gases), a low long-term discount rate should be used. In fact, some economists have suggested that higher discount rates be applied in the present and lower rates in the future. The authors demonstrate that this is incorrect. The problem with hyperbolic discounting is that it leads to time-inconsistent plans -- a person who discounts the future hyperbolically will not carry out the consumption plans he makes today. The authors note that if social decisionmakers were to use people's 1998 hyperbolic rates of time preferences, plans made in 1998 would not be followed -- because the low discount rate applied to returns in, say, 2020, will become a high discount rate as the year 2020 approaches. Since it makes sense to analyze only plans that will actually be followed, the authors characterize the equilibrium of an intertemporal game played by an individual who discounts the future hyperbolically. Along an equilibrium consumption path, the individual will behave as though he were discounting the future at a constant exponential rate. The individual's consumption path is, however, Pareto inferior: He would be better off if he could force himself to consume less and save more. This provides a rationale for government subsidization of interest rates or, equivalently, lowering the required rate of return on investment projects. Although hyperbolic discounting provides a rationale for lowering the required rate of return on investment projects, it does not provide justification for those who seek to treat environmental projects differently from other investment projects.Environmental Economics&Policies,Economic Theory&Research,Payment Systems&Infrastructure,International Terrorism&Counterterrorism,Financial Intermediation,Banks&Banking Reform,ICT Policy and Strategies,Inequality,Economic Theory&Research,Environmental Economics&Policies

Discounting in Strategy Logic

Discounting is an important dimension in multi-agent systems as long as we want to reason about strategies and time. It is a key aspect in economics as it captures the intuition that the far-away future is not as important as the near future. Traditional verification techniques allow to check whether there is a winning strategy for a group of agents but they do not take into account the fact that satisfying a goal sooner is different from satisfying it after a long wait. In this paper, we augment Strategy Logic with future discounting over a set of discounted functions D, denoted SLdisc[D]. We consider "until" operators with discounting functions: the satisfaction value of a specification in SLdisc[D] is a value in [0, 1], where the longer it takes to fulfill requirements, the smaller the satisfaction value is. We motivate our approach with classical examples from Game Theory and study the complexity of model-checking SLdisc[D]-formulas.Comment: Extended version of the paper accepted at IJCAI 202

On Depth and Retrospect: “I Forget, and Forgive – but I Discount”

The discounting of future felicity flows transposes to the intertemporal optimization context the assumption of interest-bearing wealth or savings. The validity of the hypothesis has been challenged by several empirical (ir)regularities and by the theoretical implications for human decision processing. In particular, it implies a very special weight of past decisions on current welfare prospects, which appears largely inconsistent with forgetfulness – even if not with learning – and memory effects, often stressed or embedded in behavioral science studies. In this article, we explore the modifications induced by generalizing the typical welfare function in order to accommodate such retrospective influences. The idea is simple – and can be thought inspired in felicity functions encompassing habit formation: to allow for accumulated welfare – of hypothetically “compounded” but also depreciating past-to-current felicity streams – to affect the periodic utility function – which therefore enjoy some durable good properties. Sensitivity of the Ramsey optimal path to the new formulation is also inspected. The mathematical principle has useful production theory applications: in supply chain modelling. Then the optimal depth of a production process stems from a standard problem that now also embeds delay evaluation – discounting; a rationale for a particular pattern of the term structure of interest rates was also forwarded. Growth – general equilibrium - models are extended to allow for the hypothesis.Time Discount, Time Preference, Interest, Retrospect Theory, Durable Goods, Durable Felicity Functions, Vertical Production Systems, Intertemporal Economies of Depth, Supply Chains, Networks, Complexity, Consistency, Term Structure of Interest Rates.

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

Discounting and catastrophic risk management

The risk management of complex coupled human-environmental systems essentially relies on discounting future losses and gains to their present values. These evaluations are used to justify catastrophic risks management decisions which may turn into benefits over long and uncertain time horizons. The misperception of proper discounting rates critically affects evaluations and may be rather misleading. Catastrophes are not properly treated within conventional economic theory. The lack of proper evaluations dramatically contributes to increasing the vulnerability of our society to human-made and natural disasters. Underestimation of rare low probability - high consequences potentially catastrophic scenarios (events) have led to the growth of buildings and industrial land and sizable value accumulation in flood (and other disaster) prone areas without paying proper attention to flood mitigations. A challenge is that an extreme event, say a once-in-300-year flood which occurs on average only once in 300 years, may have never occurred before in a given region. Therefore, purely adaptive policies relying on historical observations provide no awareness of the risk although, a 300-year flood may occur next year. For example, floods in Austria, Germany and the Czech Republic in 2002 were classified as 1000-, 500-, 250-, and 100-year events. Chernobyl nuclear disaster was evaluated as 106-year event. Yet common practice is to ignore these types of events as improbable events during a human lifetime. This paper analyzes the implications of potentially catastrophic events on the choice of discounting for long-term catastrophic risk management. It is shown that arbitrary discounting can be linked to "stopping time" events, which define the discount-related random horizon ("end of the world") of valuations. In other words, any discounting compares potential gains and losses only within a finite random discount-related stopping time horizon. The expected duration of this horizon for standard discount rates obtained from capital markets does not exceed a few decades and, as such, these rates cannot properly evaluate impacts of 1000-, 500-, 250-, 100- year catastrophes. The paper demonstrates that the correct discounting can be induced by the concept of stopping time, i.e. by explicit modelling of arrival time scenarios of potential catastrophes. In general, catastrophic events affect the induced discount rates, which alter the optimal mitigation efforts that, in turn, change events. The paper shows that stopping-time related discounting calls for the use of stochastic optimisation methods. Combined with explicit spatio-temporal catastrophe modelling, this induces the discounting which allows to properly focus risk management solutions on arrival times of potential catastrophic events rather then horizons of capital markets

High temporal discounters overvalue immediate rewards rather than undervalue future rewards : an event-related brain potential study

Impulsivity is characterized in part by heightened sensitivity to immediate relative to future rewards. Although previous research has suggested that "high discounters" in intertemporal choice tasks tend to prefer immediate over future rewards because they devalue the latter, it remains possible that they instead overvalue immediate rewards. To investigate this question, we recorded the reward positivity, a component of the event-related brain potential (ERP) associated with reward processing, with participants engaged in a task in which they received both immediate and future rewards and nonrewards. The participants also completed a temporal discounting task without ERP recording. We found that immediate but not future rewards elicited the reward positivity. High discounters also produced larger reward positivities to immediate rewards than did low discounters, indicating that high discounters relatively overvalued immediate rewards. These findings suggest that high discounters may be more motivated than low discounters to work for monetary rewards, irrespective of the time of arrival of the incentives

Encoding of Marginal Utility across Time in the Human Brain

Marginal utility theory prescribes the relationship between the objective property of the magnitude of rewards and their subjective value. Despite its pervasive influence, however, there is remarkably little direct empirical evidence for such a theory of value, let alone of its neurobiological basis. We show that human preferences in an intertemporal choice task are best described by a model that integrates marginally diminishing utility with temporal discounting. Using functional magnetic resonance imaging, we show that activity in the dorsal striatum encodes both the marginal utility of rewards, over and above that which can be described by their magnitude alone, and the discounting associated with increasing time. In addition, our data show that dorsal striatum may be involved in integrating subjective valuation systems inherent to time and magnitude, thereby providing an overall metric of value used to guide choice behavior. Furthermore, during choice, we show that anterior cingulate activity correlates with the degree of difficulty associated with dissonance between value and time. Our data support an integrative architecture for decision making, revealing the neural representation of distinct subcomponents of value that may contribute to impulsivity and decisiveness

Technology assessment between risk, uncertainty and ignorance

The use of most if not all technologies is accompanied by negative side effects, While we may profit from today’s technologies, it is most often future generations who bear most risks. Risk analysis therefore becomes a delicate issue, because future risks often cannot be assigned a meaningful occurance probability. This paper argues that technology assessement most often deal with uncertainty and ignorance rather than risk when we include future generations into our ethical, political or juridal thinking. This has serious implications as probabilistic decision approaches are not applicable anymore. I contend that a virtue ethical approach in which dianoetic virtues play a central role may supplement a welfare based ethics in order to overcome the difficulties in dealing with uncertainty and ignorance in technology assessement