A dynamic two country Heckscher–Ohlin model with non-homothetic preferences

We examine the properties of a two-country dynamic Heckscher–Ohlin model that allows for preferences to be non-homothetic. We show that the model has a continuum of steady state equilibria under free trade, with the initial conditions determining which equilibrium will be attained. We establish conditions under which a static Heckscher–Ohlin theorem will hold in the steady state, and also conditions for a dynamic Heckscher–Ohlin theorem to hold. If both goods are normal, each country will have a unique autarkic steady state, and all steady state equilibria are saddle points. We also consider the case in which one good is inferior, and show that this can lead to multiple autarkic steady states, violations of the static Heckscher–Ohlin theorem in the steady state. Furthermore, there may exist steady state equilibria that Pareto dominate other steady states. These steady states will be unstable if discount factors are the same in each country, although they may exhibit dynamic indeterminacy if discount factors differ.     

Public goods,voting, and growth

We study a parametric politico‐economic model of economic growth with productive public goods and public consumption goods. The provision of public goods is funded by a proportional tax. Agents are heterogeneous in their initial capital endowments, discount factors, and the relative weights of public consumption in overall private utility. They vote on the shares of public goods in gross domestic products (GDP). We propose a definition of voting equilibrium, prove the existence and provide a characterization of voting equilibria, and obtain a closed‐form solution for the voting outcomes. Also we introduce a “fictitious” representative agent and interpret the outcome of voting as a choice made by a central planner for his benefit. Finally, we undertake comparative static analysis of the shares of public goods in GDP and of the rate of balanced growth with respect to the discount factors and the preferences for public consumption. The results of this analysis suggest that the representative‐agent version of our model is capable of capturing the interaction between many voting heterogeneous agents only if the heterogeneity is one‐dimensional.     

Patience auctions: the impact of time vs. money bidding on elicited discount rates

We introduce, test, and compare two auction-based methods for eliciting discount rates. In these “patience auctions”, participants bid the smallest future sum they would prefer -or- the longest time they would wait for a reward, rather than receive a smaller, immediate payoff. The most patient bidder receives the delayed reward; all others receive the immediate payoff. These auctions allow us to compare discounting when participants’ attention is focused on the temporal versus monetary dimension of delayed rewards. We find that the estimated parameters in the three most commonly used discount functions (exponential, hyperbolic, and quasi-hyperbolic) differ across these two bidding methods (time-bids vs. money-bids). Specifically, our participants tend to show more impatience under time-bids. Furthermore, we find that people are more likely to exhibit exponential (as opposed to hyperbolic) discounting and exhibit less present bias under time-bids, compared to money-bids. To our knowledge, this paper is the first to directly compare time versus money preference elicitations, within the same subjects, using an incentive-compatible mechanism.     

Oligopsony Distortions and Welfare Implications of Trade*

While imperfect competition in the output market has garnered extensive focus in the new trade theory literature, input market imperfection has received considerably less attention. Since market power in input purchase has been growing in recent years, it is worth examining the welfare implications of trade arising from oligopsony power. We develop a model consisting of two final goods, one intermediate good, and two primary factors (capital and labor). One final good and the intermediate good employ primary factors, whereas the other final good uses labor and the intermediate input. All markets operate under perfect competition except for the intermediate input, which is oligopsonistic. Using this model, we show that oligopsony can lead to some anomalies such as an increase in the oligopsony output, reward to the intensive‐factor in the oligopsony sector, national welfare, and deterioration of terms of trade, but it always decreases the reward to the intermediate input.     

Regionalism and Multilateral Trade Liberalization with Asymmetric Countries

The paper examines the impact of regionalism on the process of multilateral trade liberalization when countries are asymmetric. The author uses a three‐country, three‐good, competing exporters model, with countries being symmetric in everything but their discount factors. The equilibrium regional agreement is found to be a customs union between a patient and an impatient country and that the impact of regionalism depends on the discount factors. The impact of regionalism on multilateral trade liberalization depends critically on which countries engage in regionalism.     

TOUGH LOVE AND INTERGENERATIONAL ALTRUISM*

This article develops and studies a tough love model of intergenerational altruism. We model tough love by modifying the Barro‐Becker standard altruism model in two ways. First, the child’s discount factor is endogenously determined, so lower childhood consumption leads to a higher discount factor later in life. Second, the parent evaluates the child’s lifetime utility with a constant high discount factor. Our model predicts that parental transfers will fall when the child’s discount factor falls. This is in contrast with the standard altruism model, which predicts that parental transfers are independent of exogenous changes in the child’s discount factor.     

HETEROGENEOUS RISK ATTITUDES IN A CONTINUOUS‐TIME MODEL*

We prove that every continuous‐time model in which all consumers have time‐homogeneous and time‐additive utility functions and share a common probabilistic belief and a common discount rate can be reduced to a static model. This result allows us to extend some of the existing results of the representative consumer and risk‐sharing rules in static models to continuous‐time models. We show that the equilibrium interest rate is lower and more volatile than in the standard representative consumer economy, and that the individual consumption growth rates are more dispersed than in the absence of uncertainty.     

项目导向型供应链跨组织合作行为激励机制

在假定项目型组织平等合作的基础上,运用委托-代理理论和博弈论,纳入总承包商给予专业分包商基于监控信号的奖惩结构,构建了基于监控信号的项目导向型供应链跨组织合作激励模型,并与传统激励模型进行比较,通过数据模拟与模型算例,研究了监控信号对激励契约设计的影响。研究表明：通过引入监控信号,总承包商可以收集到更多有关专业分包商行为选择的信息,通过调整对专业分包商的奖励和惩罚力度,可以促进专业分包商采取合作行为,降低其机会主义行为,也可以降低总承包商对专业分包商激励的盲目性。     

From the Shadow Price of Capital to the Marginal Cost of Funds: In Search of the Implementation of a Principle

The “folk principle” for multi‐period project evaluation states that if all the costs and benefits of a project are expressed as withdrawals from and increments to private consumption at different time points, then the appropriate discount rate is the consumer's rate of interest. The shadow price of capital (SPC) approach intends to implement this principle, but faces serious practical difficulties. By taking a utility‐based perspective, this paper explains why the SPC approach cannot fully implement the folk principle even theoretically. Then, it derives, as a complete implementation of the folk principle, a multi‐period cost‐benefit rule that is based on the concept of the marginal cost of funds.     

Strategic take-back programs when consumers have heterogeneous environmental preferences

We look at the strategic introduction of take-back programs (TBPs) which offer consumers a discount on their next purchase (reward) when they drop off previous purchases. In a Hotelling duopoly, consumers are heterogeneous not only in terms of their location on the Hotelling line but also in terms of their recycling preferences. Firms introduce TBPs to obtain a market share advantage (reward effect) and/or to recover the intrinsic value of the recycled units (recycling effect); their choice of the optimal reward balances these two effects: for instance, a firm might be willing to introduce a TBP, even if this means losing money on each recycled unit, in order to prevent the competitor from gaining a too large market share advantage. Comparing the level of TBP uptake at the market equilibrium to the one that maximizes social welfare, we show that a lower or higher TBP uptake can be socially desirable, depending, among other, on the weight that is given to the environmental benefits of TBPs. Several extended producer responsibility policies are discussed in terms of their potential to encourage TBP uptake and their overall impact on social welfare.     

Integrating dynamic pricing and inventory control for fresh‐agri product under consumer choice

In this article, we investigate a joint pricing and inventory problem for a retailer selling fresh‐agri products (FAPs) with two‐period shelf lifetime in a dynamic stochastic setting, where new and old FAPs are on sale simultaneously. At the beginning of each period, the retailer makes ordering decision for new FAP and sets regular and discount prices for new and old inventories, respectively. After demand realisation, the expired leftover is disposed and unexpired inventory is carried to the next period, for continuing selling. Unmet demand of all FAPs is backordered. The objective is to maximise the total expected discount profit over the whole planning horizon. We present a price dependent, stochastic dynamic programming model taking into account zero lead‐time, linear ordering costs, inventory holding and backlogging costs, as well as disposal cost. As the influence of the perishability, each customer selects his preferred choice based on the utility of product price and quality. By the way of constructing demand rate vector, the original formulation can be transferred to be jointly concave and tractable. Finally, we characterise the optimal policy and develop effective methods to solve the problem. We also conduct numerical studies to further characterise the optimal policy, and to evaluate the loss of efficiency under static policies when compared to the optimal dynamic policy.     

A NEW APPROACH TO ASSET INTEGRATION: METHODOLOGY AND MYSTERY

Abstract. This paper develops a new methodology to test financial market integration. Our technique is based on an intertemporal asset‐pricing model, and relies on estimating and comparing expected discount rates across asset markets. Expected discount rates are allowed to vary freely over time, constrained only by the fact that they are equal across assets. Assets are allowed to have very general risk characteristics, and are constrained only by a linear factor model of covariances with the discount rate over short time periods. We provide a variety of domestic and international empirical illustrations of our technique, and find surprisingly little evidence of integration.     

Interlinkage and Generous Tit‐for‐Tat Strategy

We investigate an infinitely‐repeated prisoners' dilemma with imperfect monitoring and consider the possibility that the interlinkage of the players' distinct activities enhances implicit collusion. We show a necessary and sufficient condition for the existence of a generous tit‐for‐tat Nash equilibrium. Such an equilibrium, if it exists, is unique. This equilibrium achieves approximate efficiency when monitoring is almost perfect, where the discount factors are fixed.     

SOCIAL NORMS,LOCAL INTERACTION,AND NEIGHBORHOOD PLANNING*

This article examines optimal social linkage when each individual's repeated interaction with each of his neighbors creates spillovers. Each individual's discount factor is randomly determined. A planner chooses a local interaction network or neighborhood design before the discount factors are realized. Each individual then plays a repeated Prisoner's Dilemma game with his neighbors. A local trigger strategy equilibrium (LTSE) describes an equilibrium in which each individual conditions his cooperation on the cooperation of at least one “acceptable” group of neighbors. Our main results demonstrate a basic trade‐off in the design problem between suboptimal punishment and social conflict. Potentially suboptimal punishment arises in designs with local interactions since in this case monitoring is imperfect. Owing to the heterogeneity of discount factors, however, greater social conflict may arise in more connected networks. When individuals' discount factors are known to the planner, the optimal design exhibits a cooperative “core” and an uncooperative “fringe.”“Uncooperative” (impatient) types are connected to cooperative ones who tolerate their free riding so that social conflict is kept to a minimum. By contrast, when the planner knows only the ex ante distribution over individual discount factors, then in some cases the optimal design partitions individuals into maximally connected cliques (e.g., cul‐de‐sacs), whereas in other cases incomplete graphs with small overlap (e.g., grids) are possible.     

Time discounting for primary and monetary rewards

This paper reports a positive and statistically significant relation between short-term discount rates elicited with a monetary and a primary reward (chocolate). This finding suggests that high short-term discount rates are related to an underlying individual trait.     

Self-fulfilling patience

This paper explores macroeconomic implications of investment in patience in a standard neoclassical growth model with Becker-Mulligan endogenous time preferences. The endogenous discount rate acts as a new margin for inter-temporal decisions, in addition to the standard margin that hinges on the marginal return of capital. This time preference margin alters the equilibrium dynamics and stability of the neoclassical growth model substantially. When the discount rate is positive, there may exist multiple steady states that are either saddle-point stable or unstable. When the discount rate is negative, the unique steady state is locally indeterminate due to self-fulfilling patience investment. Interestingly, the existence of the local indeterminacy does not need any externality. When the discount rate is zero, various types of bifurcations can happen, leading to rich equilibrium dynamics such as limit cycles and chaos. We show that opening up the closed economy can cause aggregate instability.     

Non-parametric test of time consistency: Present bias and future bias

This paper reports the elicited time preference of human subjects in a laboratory setting. The model allows for non-linear utility functions, non-separability between delay and reward, and time inconsistency including future bias in addition to present bias. In particular, the experiment (1) runs a non-parametric test of time consistency and (2) estimates the form of time discount function independently of instantaneous utility functions, and then (3) the result suggests that many subjects exhibiting future bias, indicating an inverse S-curve time discount function.     

Subjective random discounting and intertemporal choice

This paper provides an axiomatic foundation for a particular type of preference shock model called the random discounting representation where a decision maker believes that her discount factors change randomly over time. For this purpose, we formulate an infinite horizon extension of [E. Dekel, B. Lipman, A. Rustichini, Representing preferences with a unique subjective state space, Econometrica 69 (2001) 891-934], and identify the behavior that reduces all subjective uncertainties to those about future discount factors. We also show uniqueness of subjective belief about discount factors. Moreover, a behavioral comparison about preference for flexibility characterizes the condition that one's subjective belief second-order stochastically dominates the other. Finally, the resulting model is applied to a consumption-savings problem.     

On striking for a bargain between two completely informed agents

This paper provides a thorough equilibrium analysis of a wage contract negotiation model where the union must choose between strike and holdout between offers and counter-offers. When the union and the firm have different discount factors, delay in reaching an agreement may Pareto dominate many immediate agreements. We derive the exact bounds of equilibrium payoffs and characterize the equilibrium strategy profiles that support these extreme equilibrium payoffs for all discount factors. In particular, our analysis clarifies open issues on the maximal wage in this model when the union has a higher discount factor than the firm. We would like to thank Wilko Bolt, Gerard van der Laan, Michiel Keyzer, and an associate editor and the referee for their comments and suggestions. Quan Wen is grateful to the Tinbergen Institute and the Vrije Universiteit for their hospitality and generosity. This project is supported by Netherlands Organization for Scientific Research (NWO), grant B45-271.     

Relational Political Contribution under Common Agency

Motivated by commitment problems of contracts in lobbying, this paper studies a model of a repeated common agency where monetary transfers must be voluntary. First, we show that the optimal punishment strategy for a principal takes a two‐phase scheme, which is similar to the punishment characterized by Goldlücke and Kranz. Second, we investigate whether an outcome of standard menu auctions with binding contracts can be supported by implicit contracts. We define the environment to be more preference‐diverse if an efficient decision is less attractive to each principal. We show that the discount factor must be high to support the outcome of the standard menu auction if the environment is preference‐diversified.