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.     

资金约束下损失规避零售商的订购和广告协同策略

在损失规避下,探讨了零售商的订购和广告协同决策问题。零售商的初始资金状态存在三种情形：资金充足、资金相对短缺（不需融资）、资金短缺（对外融资）,分别在三种情形下刻画了零售商的最优运营策略,结果表明：零售商用于商品采购和广告的资金产生的边际效用与边际负效用之比相等,且介于1与单位融资资金的使用成本之间;用于两项活动的最后一单位资金产生的边际效用相等。探讨了损失规避、初始资金、融资利率、商品价格及广告促销的敏感性对运营策略的影响：在资金充足或资金短缺下,商品订购量和广告强度随影响因素的变动方向通常相同;在资金相对短缺下,商品订购量和广告强度随影响因素的变动方向则相反。讨论中揭示了一些管理启示。     

A Theory of Intergenerational Altruism

Modeling intergenerational altruism is crucial to evaluate the long‐term consequences of current decisions, and requires a set of principles guiding such altruism. We axiomatically develop a theory of pure, direct altruism: Altruism is pure if it concerns the total utility (rather than the mere consumption utility) of future generations, and direct if it directly incorporates the utility of all future generations. Our axioms deliver a new class of altruistic, forward‐looking preferences, whose weight put on the consumption of a future generation generally depends on the consumption of other generations. The only preferences lacking this dependence correspond to the quasi‐hyperbolic discounting model, which our theory characterizes. Our approach provides a framework to analyze welfare in the presence of altruistic preferences and addresses technical challenges stemming from the interdependent nature of such preferences.     

Optimal and Acceptable Technical Facilities Involving Risks

Economic cost-benefit optimization of technical facility requires suitable "life saving cost" and/or an appropriate acceptance criterion if human life and limb are at risk. Traditionally, acceptance criteria implicit in codes of practice, standards, or regulations for well-defined fields of application are calibrated against past and present practice. This is all but satisfying. It is unclear whether present rules are already optimal. Extrapolations into new fields of application are extremely difficult. Direct cost-benefit analysis is proposed as an alternative. Based on the recently proposed "life quality index" (LQI), a rational acceptance criterion and so-called life saving cost are derived. The classical life quality index is reviewed, modified, and imbedded in modern economics theory. The results are then applied to technical facilities. The relation between optimization and the LQI-based acceptance criterion is discussed. The relevant economics literature is reviewed with respect to discount rates applicable for long-term investments into risk reduction. They should be as low as possible according to a recent mathematical result. Modern economic growth theory decomposes the output growth rate into the rate of time preference of consumption and the rate of economical growth multiplied by the elasticity of marginal utility of consumption. It is found that the rate of time preference of consumption should be a little larger than the long-term population growth rate. The public benefit rate (output growth rate) on the other hand should be smaller than the sum of the population growth rate and the long-term growth rate of a national economy, which is around 2% for most industrial countries. Accordingly, the rate of time preference of consumption is about 1%, which is also intergenerationally acceptable from an ethical point of view. Given a certain output growth rate there is a corresponding maximum financial interest rate in order to maintain nonnegativity of the objective function at the optimum. Finally, a simple demonstration example is added.     

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.     

WHAT GOOD IS WEALTH WITHOUT HEALTH? THE EFFECT OF HEALTH ON THE MARGINAL UTILITY OF CONSUMPTION

We estimate how the marginal utility of consumption varies with health. To do so, we develop a simple model in which the impact of health on the marginal utility of consumption can be estimated from data on permanent income, health, and utility proxies. We estimate the model using the Health and Retirement Study's panel data on the elderly and near‐elderly, and proxy for utility with measures of subjective well‐being. Across a wide range of alternative specifications and assumptions, we find that the marginal utility of consumption declines as health deteriorates, and we are able to clearly reject the null of no state dependence. Our point estimates indicate that a one‐standard‐deviation increase in the number of chronic diseases is associated with a 10%–25% decline in the marginal utility of consumption relative to this marginal utility when the individual has no chronic diseases. We present some simple, illustrative calibration results that suggest that state dependence of the magnitude we estimate can have a substantial effect on important economic problems such as the optimal level of health insurance benefits and the optimal level of life‐cycle savings.     

Measuring the Dynamic Efficiency Costs of Regulators' Preferences: Municipal Water Utilities in the Arid West

Evidence suggests that municipal water utility administrators in the western US price water significantly below its marginal cost and, in so doing, inefficiently exploit aquifer stocks and induce social surplus losses. This paper empirically identifies the objective function of those managers, measures the deadweight losses resulting from their price‐discounting decisions, and recovers the efficient water pricing policy function from counterfactual experiments. In doing so, the estimation uses a “continuous‐but‐constrained‐ control” version of a nested fixed‐point algorithm in order to measure the important intertemporal consequences of groundwater pricing decisions.     

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.     

Evaluating time streams of income

When a decision maker considers possible returns from a business project or investment, he often faces the problem that these returns are not all received at the same time, and thus he must make some adjustments to take account of his time preference for money. After a review of discounting, a utility theory approach is made by developing a two-attribute utility function u(x, t) which represents the desirability of an income of x at a time t in the future. Assumptions to simplify the assessment of this function are considered. Then u(x, t) is used to form a criterion for evaluating infinite time streams of income.     

A Simple Intertemporal Model of Retirement Estimated On Italian Cross‐Section Data

Abstract. We develop and estimate a simple structural intertemporal model of retirement, using cross‐section Italian data. Under certain assumptions, the condition for being in retirement or alternatively in employment status at a certain date reduces to a static comparison between the instantaneous utility as employed and the instantaneous utility as retired (minus the future opportunity cost of retiring) at that date. Forward‐looking versus myopic versions of the model are obtained by including or dropping the term measuring the future loss of retiring. The model can easily be formulated under two opposite hypotheses — no savings and no borrowing versus perfect credit market (perfect consumption smoothing). The implications of the estimates are illustrated by simulating the effects of changes in the parameters of the pension system or in the demographic variables. In particular, the elasticity of the number of individuals in retirement status with respect to the pension turns out to be small but not irrelevant from the perspective of the long‐term design and evaluation of the pension system.     

INFORMATION AND THE EQUITY PREMIUM

We determine how better information affects the average equity premium in a standard representative‐agent exchange economy. Perfect information obviously eliminates the equity premium, and a particular kind of information about the level of future consumption always lowers the average equity premium. Surprisingly, information sometimes raises the average equity premium, no matter what the preferences of the representative agent. Information purely about the volatility either of consumption or the marginal utility of consumption raises the equity premium for a wide class of preferences. Moreover, information can raise the average equity premium by an arbitrarily large percentage (while still matching important magnitudes, such as average growth and the risk‐free rate). We consider two different economies: a two‐period economy with arbitrary preferences for the representative agent; and an infinite horizon economy, in which we restrict both preferences and the endowment distribution.     

Using Asset Prices to Measure the Persistence of the Marginal Utility of Wealth

We derive a lower bound for the volatility of the permanent component of investors' marginal utility of wealth or, more generally, asset pricing kernels. The bound is based on return properties of long‐term zero‐coupon bonds, risk‐free bonds, and other risky securities. We find the permanent component of the pricing kernel to be very volatile; its volatility is about at least as large as the volatility of the stochastic discount factor. A related measure for the transitory component suggest it to be considerably less important. We also show that, for many cases where the pricing kernel is a function of consumption, innovations to consumption need to have permanent effects.     

人口结构变动对时间偏好的影响分析

本文从经济学角度定义了老龄化率，以便更好地刻画社会进入老龄化且老龄化程度不断变化这一现象，并将人口结构参数定义为老龄化率与人口增长率的比例。人口结构变动除影响技术进步率外，还影响家庭对未来的看法，将人口结构参数引进Ramsey模型分析对经济的影响，发现在鞍型的平衡增长路径上，人均产出增长率取决于技术进步率与老龄化率之差，而由于人口结构参数影响时间偏好，经济增速最大化与社会福利最大化所要求的人口结构参数出现了不一致，本文给出了两种情形下的必要条件，并进行数值模拟。     

Persistent Private Information

This paper studies the design of optimal contracts in dynamic environments where agents have private information that is persistent. In particular, I focus on a continuous‐time version of a benchmark insurance problem where a risk‐averse agent would like to borrow from a risk‐neutral lender to stabilize his utility. The agent privately observes a persistent state variable, typically either income or a taste shock, and he makes reports to the principal. I give verifiable sufficient conditions showing that incentive‐compatible contracts can be written recursively, conditioning on the report and two additional state variables: the agent's promised utility and promised marginal utility of the private state. I then study two examples where the optimal contracts can be solved in closed form, showing how persistence alters the nature of the contract. Unlike the previous discrete‐time models with independent and identically distributed (i.i.d.) private information, the agent's consumption under the contract may grow over time. Furthermore, in my setting the efficiency losses due to private information increase with the persistence of the private information, and the distortions vanish as I approximate an i.i.d. environment.     

Two Backorder Compensation Mechanisms in Inventory Systems with Impatient Customers

We study a compensation mechanism design problem with customer‐choice behavior in a continuous review setting where the production and demand processes are stochastic. When a stockout occurs, the firm controls backorders on the basis of certain compensation policies. Customers make decisions to maximize their utility, which is decreasing in the price, the waiting time, and the customer's impatience factor. We assume that the impatience factor is private information held by the customer only. Two compensation mechanisms are designed to control backorders, namely uniform compensation and priority auction with an admission price. Under uniform compensation, the firm offers the same discount to all customers, whereas under auction compensation, priority is granted according to the customers' bid prices. We obtain the optimal stockout price and base stock level under each mechanism, and analyze the properties of the respective optimal policies. Assuming linear waiting costs with uniformly distributed impatience factor, we find that the auction mechanism (1) maintains a lower base stock level and results in greater profit and (2) benefits customers with relatively lower or higher impatience factors, but customers with a medium impatience factor may be rendered worse off. We further show that both compensation mechanisms are suitable for products with a high unit profit, a high lost sales penalty cost, and a high holding cost.     

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.     

CAPACITY AND PRODUCTION DECISIONS IN STOCHASTIC MANUFACTURING SYSTEMS: AN ASYMPTOTIC OPTIMAL HIERARCHICAL APPROACH

We present a new paradigm of hierarchical decision making in production planning and capacity expansion problems under uncertainty. We show that under reasonable assumptions, the strategic level management can base the capacity decision on aggregated information from the shopfloor, and the operational level management, given this decision, can derive a production plan for the system, without too large a loss in optimality when compared to simultaneous determination of optimal capacity and production decisions. The results are obtained via an asymptotic analysis of a manufacturing system with convex costs, constant demand, and with machines subject to random breakdown and repair. The decision variables are purchase time of a new machine at a given fixed cost and production plans before and after the purchase. The objective is to minimize the discounted costs of investment, production, inventories, and backlogs. If the rate of change in machine states such as up and down is assumed to be much larger than the rate of discounting costs, one obtains a simpler limiting problem in which the random capacity is replaced by its mean. We develop methods for constructing asymptotically optimal decisions for the original problem from the optimal decisions for the limiting problem. We obtain error estimates for these constructed decisions.     

基于活动方法的瓶颈模型与拥挤收费问题研究

Vickrey提出的基于出行的瓶颈模型以出行作为分析单位,没有考虑出行与活动之间的相互关联.本文对Vickrey的瓶颈模型进行了拓展,提出了基于活动的瓶颈模型来研究通勤者早晨上班出发时间决策问题,模型考虑了通勤者对出行负效用与活动效用之间的权衡.在基于活动的瓶颈模型的基础上,分别研究了常数和线性边际活动效用下瓶颈动态拥挤收费和阶梯收费问题,并与传统的瓶颈模型的解进行比较.结果表明,当活动的边际效用为线性函数时,瓶颈处最优动态收费曲线不再呈分段线性关系,而是分段二次曲线;与基于活动的瓶颈模型相比,传统的基于出行的瓶颈模型将高估瓶颈处的排队延误、阶梯收费水平,以及早高峰的开始和结束时间;基于出行的瓶颈模型和常数边际活动效用下的瓶颈模型导致的最优阶梯收费是最优动态收费最大值的一半,并且刚好消除瓶颈处排队延误的一半;与线性边际活动效用下的瓶颈模型相比较,两者低估了阶梯收费能消除的瓶颈排队,从而低估了阶梯收费的效率.     

Leader–follower equilibria to examine investment decisions in grid resilience-enhancing measures

Large-area, long-duration power outages are increasingly common in the United States, and cost the economy billions of dollars each year. Building a strategy to enhance grid resilience requires an understanding of the optimal mix of preventive and corrective actions, the inefficiencies that arise when self-interested parties make resilience investment decisions, and the conditions under which regulators may facilitate the realization of efficient market outcomes. We develop a bi-level model to examine the mix of preventive and corrective measures that enhances grid resilience to a severe storm. The model represents a Stackelberg game between a regulated utility (leader) that may harden distribution feeders before a long-duration outage and/or deploy restoration crews after the disruption, and utility customers with varying preferences for reliable power (followers) who may invest in backup generators. We show that the regulator's denial of cost recovery for the utility's preventive expenditures, coupled with the misalignment between private objectives and social welfare maximization, yields significant inefficiencies in the resilience investment mix. Allowing cost recovery for a higher share of the utility's capital expenditures in preventive measures, extending the time horizon associated with damage cost recovery, and adopting a storm restoration compensation mechanism shift the realized market outcome toward the efficient solution. If about one-fifth of preventive resilience investments is approved by regulators, requiring utilities to pay a compensation of $365 per customer for a 3-day outage (about seven times the level of compensation currently offered by US utilities) provides significant incentives toward more efficient preventive resilience investments.     

Optimal Taxes on Fossil Fuel in General Equilibrium

We analyze a dynamic stochastic general‐equilibrium (DSGE) model with an externality—through climate change—from using fossil energy. Our central result is a simple formula for the marginal externality damage of emissions (or, equivalently, for the optimal carbon tax). This formula, which holds under quite plausible assumptions, reveals that the damage is proportional to current GDP, with the proportion depending only on three factors: (i) discounting, (ii) the expected damage elasticity (how many percent of the output flow is lost from an extra unit of carbon in the atmosphere), and (iii) the structure of carbon depreciation in the atmosphere. Thus, the stochastic values of future output, consumption, and the atmospheric CO₂ concentration, as well as the paths of technology (whether endogenous or exogenous) and population, and so on, all disappear from the formula. We find that the optimal tax should be a bit higher than the median, or most well‐known, estimates in the literature. We also formulate a parsimonious yet comprehensive and easily solved model allowing us to compute the optimal and market paths for the use of different sources of energy and the corresponding climate change. We find coal—rather than oil—to be the main threat to economic welfare, largely due to its abundance. We also find that the costs of inaction are particularly sensitive to the assumptions regarding the substitutability of different energy sources and technological progress.