Endogenous Fluctuations in Two-Sector Models: Role of Preferences

We consider a discrete-time two-sector CES (constant elasticity of substitution) economy with sector specific external effects and nonlinear preferences. Our goal is to examine carefully the influence of the utility curvature on the occurrence of multiple equilibria. We show that local indeterminacy depends on an interplay between factor substitutability and the elasticity of intertemporal substitution in consumption. Moreover, considering that, when the external effects are set equal to zero, we get a two-sector optimal growth model, we study also the role of the utility curvature on the occurrence of competitive equilibrium cycles. We show that persistent endogenous fluctuations and macroeconomic volatility require a strong enough elasticity of intertemporal substitution in consumption. We thank two anonymous referees for helpful comments and suggestions. External effects are feedbacks from the other agents in the economy who face also identical maximizing problems. See Benhabib and Farmer (Ref. 1) for a survey. Global indeterminacy based on a finite number of equilibria is associated with the existence of thresholds and multiple steady states. See Deissenberg, Feichtinger, Semmler, and Wirl (Ref. 2).     

Overlapping Generations Model with Endogenous Labor Supply: General Formulation

This paper develops a one-sector overlapping generations model with endogenous labor supply and nonseparable preferences. It demonstrates that local indeterminacy arises easily under gross substitutability as soon as there exist multiple steady states. We show also that, depending on whether leisure and second-period consumption are gross substitutes, local indeterminacy holds for very different parameter configurations. If gross substitutability is satisfied, the existence of multiple equilibrium paths requires the share of capital in the total income to be strong enough with respect to the elasticity of capital-labor substitution. On the other hand, if gross substitutability is violated, local indeterminacy necessitates the share of capital in the total income to be weak enough with respect to the elasticity of capital-labor substitution. This paper is dedicated to the memory of Louis-André Gérard-Varet, Director of GREQAM from 1987 to 1999. We thank S. Catania, C. Deissenberg, J. P. Drugeon, L. A. Gérard-Varet, J. M. Grandmont, A. Kirman, T. Lloyd-Braga, P. Michel, P. Pintus,E.Thibault, B.Wigniolle, and two anonymous referees for helpful comments and suggestions. The paper benefited from comments received during a presentation at the Conference on Dynamic Equilibria, Expectations and Indeterminacies, Paris. France, 1999.     

House exchange and residential segregation in networks

This paper considers a Schelling model in an arbitrary fixed network where there are no vacant houses. Agents have preferences either for segregation or for mixed neighborhoods. Utility is non-transferable. Two agents exchange houses when the trade is mutually beneficial. We find that an allocation is stable when for two agents of opposite-color each black (white) agent has a higher proportion of neighbors who are black (white). This result holds irrespective of agents’ preferences. When all members of both groups prefer mixed neighborhoods, an allocation is also stable provided that if an agent belongs to the minority (majority), then any neighbor of opposite-color is in a smaller minority (larger majority).     

Repeated bargaining with reference-dependent preferences

We consider a two-player bargaining model in which one or both players have reference-dependent preferences, but are otherwise perfectly rational. Our behavioural assumption is that players with reference-dependent preferences prefer impasse to consuming strictly less than their current reference points. Reference points adjust each period according to some exogenously specified law of motion. When reference points do not adjust following disagreement, we show that disagreement does not arise in equilibrium, but they do influence the division of the pie. In contrast, when reference points adjust downwards following disagreement, disagreements arise and players may try to manipulate the reference point of their opponent. When reference points adjust downwards following a rejection, for a particular Markov equilibrium, we show that the set of feasible allocations can be divided into agreement and disagreement regions. In particular, there are thresholds such that if one (or more) player’s reference point is above the threshold, disagreement necessarily arises.     

On sequential and simultaneous contributions under incomplete information

When contributors to a common cause (or public good) are uncertain about each others’ valuations, early contributors are likely to be cautious in free-riding on future contributors. Contrary to the case of complete information, when contributors have independent private valuations for the public good, the expected total contribution generated in a sequential move game may be higher than in a simultaneous move game. This is established in a conventional framework with quasi-linear utility where agents care only about the total provision of the public good (rather than individual contribution levels) and there is no non-convexity in the provision of the public good. We allow for arbitrary number of agents and fairly general distribution of types.     

有政府债券的军事花费和经济增长(英文)

本文讨论了军事花费 ,资本积累和政府债券在一个随机内生的增长模型中 ,结果表明 :如果本国有一个低的消费替代弹性 ,则外国财富和军事花费的增长都会导致本国经济的增长 ;但是 ,如果本国有一个高的消费替代弹性时 ,外国军事花费的大的扰动也可导致本国经济的增长 .     

LONG-RUN EQUILIBRIA IN AN ECONOMY WITH A GREENHOUSE EFFECT

This paper examines perfect foresight inter-generational macroeconomic tradeoffs associated with climate change. Consumption of perfectly competitive agents is associated with exacerbation of the climate change problem. Saving and investment reduce exposure to a negative production externality caused by the greenhouse effect, through a non-probabilistic catastrophic threshold. In this overlapping generations economy, saving and investment provide benefits to future generations that current individuals are unable to capture. Two kinds of equilibria are shown to exist. The gas stock may remain at a constant or declining level so the threshold does not matter in steady-state equilibrium even with population growth, where consumption, investment and production are all constant in per capita terms. When the threshold does matter because the gas stock is growing in steady state, agents flirt with catastrophe, make strategic economic decisions based on what other agents are doing, and optimize by walking a knife-edge of disaster at the threshold. Like the private provision of a public good, price-taking agents internalize the public bad. This is the focal point symmetric Nash equilibrium, but the potential for a coordination failure is also shown to exist where agents with perfect foresight would find it optimal not to end the economy, but are unable to avoid doing so.     

Productive public expenditures, expectation formations and nonlinear dynamics

In this paper, we investigate the dynamic properties of an overlapping generations’ model with capital accumulation and publicly funded inventions under three different expectations: perfect foresight, myopic expectations and adaptive expectations. We show that considering productive public expenditures in the model will increase the dimension of the dynamical system. To study the dynamic behavior of a high-dimensional dynamical system, we focus on the case when the elasticity of publicly funded invention to output is small and approximate the system by using a one-dimensional dynamical system. This approximation method provides an efficient way to rigorously prove the existence of chaos in high-dimensional dynamical systems. We show that when agents are perfectly foresighted, there exists a unique, nontrivial steady state which is a global attractor. Cycles or even chaos may occur under myopic and adaptive expectations when the inter-temporal elasticity of substitution of consumption is large enough. Furthermore, we find that the impact of fiscal policy is sensible to the expectation formation.     

Random paths to pairwise stability in many-to-many matching problems: a study on market equilibration

This paper considers a decentralized process in many-to-many matching problems. We show that if agents on one side of the market have substitutable preferences and those on the other side have responsive preferences, then, from an arbitrary matching, there exists a finite path of matchings such that each matching on the path is formed by satisfying a blocking individual or a blocking pair for the previous matching, and the final matching is pairwise-stable. This implies that an associated stochastic process converges to a pairwise-stable matching in finite time with probability one, if each blocking individual or pair is satisfied with a positive probability at each period along the process.     

Unbounded growth in the Neoclassical growth model with non-constant discounting

For a Neoclassical growth model, the literature highlights that exponential discounting is observationally equivalent to quasi-hyperbolic discounting, if the instantaneous discount rate decreases asymptotically towards a positive value. Conversely, in this paper a zero long-run value allows a solution without stagnation. We prove that a less than exponential but unbounded growth can be attained, even without technological progress. The growth rate of consumption decreases asymptotically towards zero, although so slowly that consumption grows unboundedly. The asymptotic convergence towards a non-hyperbolic steady-state which saving rate matches the intertemporal elasticity of substitution and the speed of convergence towards this equilibrium are analyzed.     

Time inconsistency and learning in bargaining games

This paper studies an alternating-offers bargaining game between possibly time-inconsistent players. The time inconsistency is modeled by quasi-hyperbolic discounting and the “naive backwards induction” solution concept is used in order to obtain the results. Both naive agents who remain naive and those who learn about their own preferences are considered. Offers of the players who are naive or partially naive are never accepted by any type of player in either no learning or gradual learning cases. The game between a naive or partially naive player who never learns and a time-consistent agent ends in an immediate agreement if the time-consistent agent is the proposer. A one period delay occurs if the time-consistent agent is the responder. The more naive the player is, the higher the share received. In addition, two naive agents who never learn disagree perpetually. When naive and partially naive agents play against exponential or sophisticated agents and they are able to learn their types over time, there exists a critical date before which there is no agreement. Therefore, the existence of time-inconsistent players who can learn their types as they play the game can be a new explanation for delays in bargaining. The relationship among the degree of naivete, impatience level and bargaining delay is also characterized. Specifically, for sufficiently high discount factors, agreement is always delayed. On the other hand, if the naive agent has sufficiently firm initial beliefs (slow learning or high degree of naivete), agents agree immediately.     

Divide and compromise

We introduce two symmetrized versions of the popular divide-and-choose mechanism for the allocation of a collectively owned indivisible good between two agents when monetary compensation is available. Our proposals retain the simplicity of divide-and-choose and correct its ex-post asymmetry. When there is complete information, i.e., agents know each other well, both mechanisms implement in subgame perfect equilibria a unique allocation that would be obtained by a balanced market. The results hold for general continuous preferences that may not be quasi-linear.     

Consistent conjectures in a dynamic model of non-renewable resource management

We consider a model of non-renewable resource extraction where players do not know their opponents’ utility functions and form conjectures on the behavior of others. Two forms of beliefs are introduced, one based on the state of the resource, the other on this state and on the others’ strategy (their consumption). We focus on consistent equilibria, where beliefs must be consistent with observed past plays. Closed form expressions of the optimal policies are derived. Comparisons are made with the full information benchmark case. With strategy and state based beliefs, the agents may behave more (respectively, less) aggressively than in the non-cooperative benchmark depending on the initial consumption level. When initial consumption is low, the optimal consumption path lies below that of the cooperative benchmark. We conclude the analysis by discussing the impact of public policies on the agents’ choice of consumption patterns, and the robustness of the results for the case of renewable resources.     

Stable and Pareto optimal group activity selection from ordinal preferences

In several situations agents need to be assigned to activities on basis of their preferences, and each agent can take part in at most one activity. Often, the preferences of the agents do not depend only on the activity itself but also on the number of participants in the respective activity. In the setting we consider, the agents hence have preferences over pairs “(activity, group size)” including the possibility “do nothing”; in this work, these preferences are assumed to be strict orders. The task will be to find stable assignments of agents to activities, for different concepts of stability such as Nash or core stability, and Pareto optimal assignments respectively. In this respect, particular focus is laid on two natural special cases of agents’ preferences inherent in the considered model, namely increasing and decreasing preferences, where agents want to share an activity with as many (as few, respectively) agents as possible.     

中国能源消费、碳排放与经济增长的区域差异性研究

基于1990～2010年我国30个省市面板数据,采用面板计量分析方法,考察我国源消费、碳排放与经济增长三者之间相互影响关系对空间区域的依赖性.研究结果表明:能源消费、碳排放与经济增长三者之间不仅存在着相互影响的关系,且具有显著的区域差异性.各省份的经济发展均为各地区能源消费增长的重要诱因之一,这与能源消费与经济增长具有较高关联度的结论保持一致.北京、辽宁、吉林等16个省份碳排放变化与经济增长变化之间的的弹性系数为负值,而天津等其他14个省市碳排放总量还将伴随着经济增长而增长,所以弹性系数为正值,这点隐含说明当区域经济水平较高时,该区域也将拥有更多优势条件来减低碳排放,实现碳减排最终还是需要依赖于发达的经济水平.     

Conditions that cause risk pooling to increase inventory

We say product A is a partial substitute for product B if a fraction of the customers who prefer B are willing to accept A when B is out of stock. When demand is uncertain, it is intuitive and true that a larger “willing to substitute” fraction implies larger expected profits. A higher “willing to substitute” fraction allows one to pool the risk of individual products. It may also be intuitive that a larger “willing to substitute” fraction might result in lower optimal total inventory. For the full substitution structure, several researchers have shown that for certain distributions such as the exponential, this latter intuition is not true. We show that this full substitution anomaly can occur with any right skewed demand distribution. We assume i.i.d. demand distributions unless we indicate otherwise. We also show that the anomaly can occur for a number of realistic situations of partial substitution with commonly used demand distributions such as Normal, exponential, Poisson, and uniform. We also demonstrate the anomaly for more than one period, with backlogging, lost sales, more than two products, and with setup costs.     

Capital–labor substitution and long-run growth in a model with physical and human capital

Most of the literature analyzing the growth-substitutability nexus considers models in which long-run growth is exogenous. We study this link in an endogenous growth model with physical and human capital. We show that for two economies differing uniquely in factor substitutability, the one with the higher elasticity of substitution will have higher long-run growth. This is due to the efficiency effect of a higher factor substitution. Furthermore, if the initial ratio of physical to human capital is below (above) its steady-state value, the economy with the higher elasticity of substitution will have a higher (lower) steady-state physical capital income share.     

Hierarchical optimization: An introduction

Decision problems involving multiple agents invariably lead to conflict and gaming. In recent years, multi-agent systems have been analyzed using approaches that explicitly assign to each agent a unique objective function and set of decision variables; the system is defined by a set of common constraints that affect all agents. The decisions made by each agent in these approaches affect the decisions made by the others and their objectives. When strategies are selected simultaneously, in a noncooperative manner, solutions are defined as equilibrium points [13,51] so that at optimality no player can do better by unilaterally altering his choice. There are other types of noncooperative decision problems, though, where there is a hierarchical ordering of the agents, and one set has the authority to strongly influence the preferences of the other agents. Such situations are analyzed using a concept known as a Stackelberg strategy [13, 14,46]. The hierarchical optimization problem [11, 16, 23] conceptually extends the open-loop Stackelberg model toK players. In this paper, we provide a brief introduction and survey of recent work in the literature, and summarize the contributions of this volume. It should be noted that the survey is not meant to be exhaustive, but rather to place recent papers in context.     

Natural implementation with semi-responsible agents in pure exchange economies

We study Nash implementation by natural price–quantity mechanisms in pure exchange economies when agents have intrinsic preferences for responsibility. An agent has an intrinsic preference for responsibility if she cares about truth-telling that is in line with the goal of the mechanism designer besides her material well-being. A semi-responsible agent is an agent who, given what her opponents do, acts in an irresponsible manner when a responsible behavior poses obstacles to her material well-being. The class of efficient allocation rules that are Nash implementable is identified provided that there is at least one agent who is semi-responsible. The Walrasian rule is shown to belong to that class.     

关于湖北省节能的投入产出分析

运用投入产出法,对湖北省达成"十一五"节能目标的万元GDP综合能耗进行了分能源品种的分解,对湖北省未来五年的能源经济指标进行了预测和分析.首先,本文把64部门的2002年湖北省投入产出表整理成6部门的投入产出表,推测出2005年湖北省能源生产和消费指标,分析了湖北省能源供需的基本形势.其次,本文以实现"十一五"期间万元GDP综合能耗降低20%为目标,对不同GDP增长率下的能源需求情景进行了预测,计算了湖北省2010年分品种的万元GDP综合能耗、能源消费弹性系数等指标,分析了不同能源品种对单位GDP综合能耗下降的贡献程度.最后本文提出了政策建议,并指出模型的发展方向.