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.     

Dynamic Valuation Decomposition Within Stochastic Economies

I explore the equilibrium value implications of economic models that incorporate responses to a stochastic environment with growth. I propose dynamic valuation decompositions (DVD's) designed to distinguish components of an underlying economic model that influence values over long investment horizons from components that impact only the short run. A DVD represents the values of stochastically growing claims to consumption payoffs or cash flows using a stochastic discount process that both discounts the future and adjusts for risk. It is enabled by constructing operators indexed by the elapsed time between the trading date and the date of the future realization of the payoff. Thus formulated, methods from applied mathematics permit me to characterize valuation behavior and the term structure of risk prices in a revealing manner. I apply this approach to investigate how investor beliefs and the associated uncertainty are reflected in current‐period values and risk‐price elasticities.     

Can We Use Human Judgments to Determine the Discount Rate?

It has been suggested that the long-term discount rate for environmental goods should decrease at longer delays. One justification for this suggestion is that human judgments support it. This article presents an experiment showing that judgments concerning discount rates are internally inconsistent. These results point to potential problems with the use of judgments referenda for determining discount rates in cost-benefit analyses.     

Gambling Reputation: Repeated Bargaining With Outside Options

We study the role of incomplete information and outside options in determining bargaining postures and surplus division in repeated bargaining between a long‐run player and a sequence of short‐run players. The outside option is not only a disagreement point, but reveals information privately held by the long‐run player. In equilibrium, the uninformed short‐run players' offers do not always respond to changes in reputation and the informed long‐run player's payoffs are discontinuous. The long‐run player invokes inefficient random outside options repeatedly to build reputation to a level where the subsequent short‐run players succumb to his extraction of a larger payoff, but he also runs the risk of losing reputation and relinquishing bargaining power. We investigate equilibrium properties when the discount factor goes to 1 and when the informativeness of outside options diffuses. In both cases, bargaining outcomes become more inefficient and the limit reputation‐building probabilities are interior.     

What Happens When Wal‐Mart Comes to Town: An Empirical Analysis of the Discount Retailing Industry

In the past few decades multistore retailers, especially those with 100 or more stores, have experienced substantial growth. At the same time, there is widely reported public outcry over the impact of these chain stores on other retailers and local communities. This paper develops an empirical model to assess the impact of chain stores on other discount retailers and to quantify the size of the scale economies within a chain. The model has two key features. First, it allows for flexible competition patterns among all players. Second, for chains, it incorporates the scale economies that arise from operating multiple stores in nearby regions. In doing so, the model relaxes the commonly used assumption that entry in different markets is independent. The lattice theory is exploited to solve this complicated entry game among chains and other discount retailers in a large number of markets. It is found that the negative impact of Kmart's presence on Wal‐Mart's profit was much stronger in 1988 than in 1997, while the opposite is true for the effect of Wal‐Mart's presence on Kmart's profit. Having a chain store in a market makes roughly 50% of the discount stores unprofitable. Wal‐Mart's expansion from the late 1980s to the late 1990s explains about 40–50% of the net change in the number of small discount stores and 30–40% for all other discount stores. Scale economies were important for Wal‐Mart, but less so for Kmart, and the magnitude did not grow proportionately with the chains' sizes.     

The Role of Discount Vouchers in Market with Customer Valuation Uncertainty

Online discount voucher market In the discount voucher market, customers usually face two types of valuation uncertainty, namely, preference uncertainty and consumption state uncertainty. Preference uncertainty is related to the customer's lack of relevant experience with the merchant, whereas consumption state uncertainty is related to the advance selling nature of the discount voucher mechanism. By taking a comprehensive perspective (i.e., considering revenue management and promotion effect at the same time), we find (i) no show of voucher buyers may not be a good thing for the merchant, especially for those large or start‐up ones; (ii) offering refund may always hurt the merchant's profit and the PayPal model may not be optimal in terms of maximizing social welfare; and (iii) market segmentation is not necessary for the profitability of promotion.     

Discount Rates in Risk Versus Money and Money Versus Money Tradeoffs

We use data from a survey of residents of five Italian cities conducted in late spring 2004 to estimate the discount rates implicit in (1) money versus future risk reductions and (2) money versus money tradeoffs. We find that the mean personal discount rate is 0.3-1.7% in (1) and 8.7% in (2). The latter is lower than the discount rates estimated in comparable situations in many recent studies, greater than market interest rates in Italy at the time, and exhibits modest variation with age and gender. The discount rate implicit in money versus risk tradeoffs is within the range of estimates from studies in the United States and Europe, and does not depend on observable individual characteristics. We use split samples to investigate whether a completely abstract risk reduction - one where the risk reduction delivery has been stripped of all specifics, so that respondents should focus on the risks without being distracted by details - results in WTP and discount figures comparable to those from an identified delivery mechanism (a medical test). We find that while WTP for an immediate risk reduction is 42-73% higher with the abstract risk reduction, the discount rate in the money versus risk tradeoffs and the variance of the error term in the WTP equation are the same across the two variants of the questionnaire.     

Coordinating Sales and Raw Material Discounts in a Global Supply Chain

In this paper, the supplier of a key component to a global manufacturer offers a one‐time price discount; we study the firm's optimal response to the discount under two different strategies. In the first strategy, the firm does not pass along the discount to its customers (sales subsidiaries); the firm simply coordinates purchasing and production among the different factories to take advantage of this one‐time price discount. In the second strategy, the firm offers price discounts for its most profitable products in different sales subsidiaries to increase their demand. We carried out experiments for the two strategies based on a mathematical programming model, built around Toshiba's global notebook supply chain. Model constraints include, among others, material constraints, bill‐of‐materials, capacity and transportation constraints, minimum lot size constraints, and a constraint on minimum fill rate (service level constraint). Unlike most models of this type in the literature, which define variables in terms of single arc flows, we employ path variables, which allow for direct identification and manipulation of profitable and non‐profitable products.     

A Model of Utility Smoothing

Experimental studies have found that a decision maker prefers spreading good and bad outcomes evenly over time. We propose, in an axiomatic framework, a new model of discount factors that captures this preference for spread. The model provides a refinement of the discounted utility model while maintaining dynamic consistency. The derived discount factors incorporate gain/loss asymmetry recursively: the difference between average future utility and current utility defines a gain or a loss, and gains are discounted more than losses. This notion of utility smoothing can induce a preference for spread: if bad outcomes are concentrated on future periods, moving one of the bad outcomes to today would be beneficial because such an operation eliminates a large loss and replaces it with a small gain.     

EOQ model for imperfective items under a one-time-only discount

In practice, when a supplier is confronted with extreme completion in markets, unanticipated surplus in inventory, or change in the production run of a product, he/she may offer a special price discount to motivate buyers to order a special quantity. The purpose of the present paper is to investigate an inventory model for imperfective items under a one-time-only discount, where the defectives can be screened out by a 100% screening process and then can be sold in a single batch by the end of the 100% screening process. The optimal order policies associated with three kinds of effective times of the reduced price are obtained. Finally, a numerical example is provided to illustrate the proposed model.     

面向动态风险评价及投资决策的IRRV模型

建立了跨期相对风险-价值(Inter-temporal Relative Risk-Value,简称IRRV)模型,首次整合了时间-概率权衡与风险-价值权衡。面向结果非负的复杂风险事件,在偏好公理的基础上推导出时间-概率权衡关系的显性表达式,将时间具有内在不确定性这一植根于"心理距离"的直觉思想形式化,最终用关于时间的内在折扣率刻画跨期对决策者效用的影响。内在折扣率取决于决策者的时间偏好,也可能依赖结果的量值,是决定时间-概率权衡的核心因素。借助时间-概率权衡理论,将静态意义上的相对风险-价值模型扩展成为动态意义上的跨期相对风险-价值模型。该模型在同一个空间内综合考虑了价值、时间和概率三个基本的决策维度,为动态风险决策提供了一个规范化框架。     

PRICE‐DEPENDENT INVENTORY MODELS WITH DISCOUNT OFFERS AT RANDOM TIMES*

We consider an inventory model with a supplier offering discounts to a reseller at random epochs. The offer is accepted when the inventory position is lower than a threshold level. We compare three different pricing policies in which demand is induced by the resellers price variation. Policy 1 is the EOQ policy without discount offers. Policy 2 is a uniform price, stock‐independent policy. Policy 3 is a stock level‐dependent, discriminated price policy. Assuming constant demand rates, expressions are obtained for the optimal order quantities, prices, and profits. The numerical experiments show that if it is better to accept a suppliers discount, then it benefits the reseller to transfer the discount to downstream customers.     

WHO IS ‘BEHAVIORAL’? COGNITIVE ABILITY AND ANOMALOUS PREFERENCES

In this paper, we ask whether variation in preference anomalies is related to variation in cognitive ability. Evidence from a new laboratory study of Chilean high‐school students with similar schooling backgrounds shows that small‐stakes risk aversion and short‐run discounting are less common among those with higher standardized test scores. The relationship with test scores survives controls for parental education and wealth. We find some evidence that elementary‐school GPA is predictive of preferences measured at the end of high school. Two laboratory interventions provide suggestive evidence of a possible causal impact of cognitive resources on expressed preferences.     

考虑捐赠行为的食品动态定价策略研究

由于质量控制不当和库存过多导致的浪费是企业管理易腐食品面临的主要挑战。针对当前食品浪费严重的问题，建立考虑变质率的动态定价模型，研究捐赠行为下单一定价、两次定价与多级折扣定价三种定价策略对食品企业最优决策的影响。通过数值分析，发现捐赠行为能够提升企业利润且在多级折扣定价策略下效果更为显著，但当折扣次数较少时，单一定价策略对考虑捐赠的企业而言更优；食品最初质量、变质率、打折时间点、捐赠时间点、税收返回比率均是影响企业定价决策的重要因素；若质量差异越大，企业在多级折扣定价策略下的利润会减少，而考虑捐赠行为会使得企业利润呈上升趋势；在变质率越高时，考虑捐赠的单一定价策略会降低企业的利润，但对多级折扣定价策略下的利润影响不大；当折扣时间越接近于捐赠时间点时，基于捐赠行为的多级折扣定价策略会更优；当捐赠时间点越接近于保质期时，考虑捐赠的价格策略会优于不考虑捐赠时的价格策略。此外，研究还表明增加税收返回比率对考虑捐赠下的定价策略不一定是有利的。     

中国A股市场增发效应与投资者保护

国内学者对增发效应的研究主要集中在董事会拟增发公告效应上,对增发的中长期效应较少涉及,虽然对增发公告效应的研究也很有意义,但对于倡导理性的投资者而言,则其重要性不如增发的中长期效应。本文在一个比较长的时间窗口内考察了我国A股市场1998—2004年间获准增发上市公司增发的中长期效应和增发上市日效应,实证分析结果表明,在拟增发公告效应出现5%-10%负效应基础上,流通股股东增发的中长期效应继续出现显著的负效应,并且流通股股东的超额收益率与上市公司利润增长率和增发价格折扣率显著正相关,与其它因素不存在显著的相关关系。     

Bargaining and Reputation

The paper develops a reputation based theory of bargaining. The idea is to investigate and highlight the influence of bargaining ‘postures’ on bargaining outcomes. A complete information bargaining model a la Rubinstein is amended to accommodate ‘irrational types’ who are obstinate, and indeed for tractability assumed to be completely inflexible in their offers and demands. A strong ‘independence of procedures’ result is derived: after initial postures have been adopted, the bargaining outcome is independent of the fine details of the bargaining protocol so long as both players have the opportunity to make offers frequently. The latter analysis yields a unique continuous‐time limit with a war of attrition structure. In the continuous‐time game, equilibrium is unique, and entails delay, consequently inefficiency. The equilibrium outcome reflects the combined influence of the rates of time preference of the players and the ex ante probabilities of different irrational types. As the probability of irrationality goes to zero, delay and inefficiency disappear; furthermore, if there is a rich set of types for both agents, the limit equilibrium payoffs are inversely proportional to their rates of time preference.     

讨价还价过程与供应链的利润最大化均衡

是否存在一组贴现因子使得轮流出价的讨价还价的完美子博弈均衡刚好实现供应链总体利润最大?本文研究表明当博弈双方的贴现率都趋近于1,各企业利润之和将收敛于供应链的总体利润最大化均衡.接着,证明了当双方的贴现率严格地小于1时,供应链的总体利润不可能达到利润最大化均衡.最后,通过具体的算例来说明所得到的结论.     

Quantity Discount‐Based Inventory Coordination: Effectiveness and Critical Environmental Factors

It is understood that quantity discounts provide a practical foundation for coordinating inventory decisions in supply chains. The primary objective of this research is to test, under a variety of environmental conditions, the effectiveness of quantity discounts as an inventory coordination mechanism between a buyer and a supplier. A comprehensive simulation experiment with anova has been designed to investigate the impacts of (1) choice of quantity discount‐based inventory coordination policies, (2) magnitude of demand variation, (3) buyer's and supplier's relative inventory cost structure, and (4) buyer's economic time‐between‐orders on the effectiveness of supply chain inventory coordination. The analytical results confirm that the quantity discount policies have managerial properties as a mediator for inventory coordination. The results also show that the performance of quantity discount‐based inventory coordination policies is influenced significantly by environmental factors, such as the magnitude of demand variation, the buyer's and the supplier's inventory cost structure, and the buyer's economic time‐between‐orders.     

Optimal Sourcing and Lead‐Time Reduction under Evolutionary Demand Risk

We develop a real‐options model for optimizing production and sourcing choices under evolutionary supply‐chain risk. We model lead time as an endogenous decision and calculate the cost differential required to compensate for the risk exposure coming from lead time. The shape of the resulting cost‐differential frontier reveals the term structure of supply‐chain risk premiums and provides guidance as to the potential value of lead‐time reduction. Under constant demand volatility, the break‐even cost differential increases in volatility and lead time at a decreasing rate, making incremental lead‐time reduction less valuable than full lead‐time reduction. Stochastic demand volatility increases the relative value of incremental lead‐time reduction. When demand has a heavy right tail, the value of lead‐time reduction depends on how extreme values of demand are incorporated into the forecasting process. The cost‐differential frontier is invariant to discount rates, making the cost of capital irrelevant for choosing between lead times. We demonstrate the managerial implications of the model by applying it first to the classic Sport‐Obermeyer case and then to a supplier‐selection problem faced by a global manufacturer.     

Accuracy of Numerical Solutions Using the Euler Equation Residuals

This paper is concerned with asymptotic properties on the accuracy of numerical solutions. It is shown that the approximation error of the policy function is of the same order of magnitude as the size of the Euler equation residuals. Moreover, for bounding this approximation error the most relevant parameters are the discount factor and the curvature of the return function. These findings provide theoretical foundations for the construction of tests to assess the performance of alternative computational methods.