Recursive utility with unbounded aggregators

A new framework is presented for the study of the existence and uniqueness of solutions to the Koopmans’ equation in the unbounded case, that is based on the contraction mapping approach. In the bounded below case with bounded consumption streams, uniqueness of the solution in the whole class of weak-star continuous utility functions is obtained. When the aggregator is unbounded below and/or consumption streams are unbounded, existence of a weak-star continuous solution is shown, and a simple criterium to check the sufficient conditions for existence is provided. Juan Pablo Rincón-Zapatero and Carlos Rodríguez-Palmero gratefully acknowledge financial support by the Ministerio de Educación y Ciencia and FEDER funds under Research Projects MTM2005-06534 and SEJ2005-08709/ECON, respectively, and by Consejería de Educación de la Junta de Castilla y León under Research Projects VA99/04 and VA017B05, respectively. This paper has substantially benefited from the comments of an anonymous referee. Particular and special thanks are due to Robert Becker for his very helpful comments and valuable suggestions.     

The interactions between natural and physical capitals in the tourist lifecycle model

This paper presents a model of the interactions between natural resources and physical capital in the evolution of a tourist destination. The projected trajectory of the number of tourists approaches the classical lifecycle pattern. The post-stagnation phase is analyzed within the model, obtaining different patterns which depend on the impacts of physical capital on both demand and environmental degradation. The magnitudes of these impacts are determined by the type of tourism. An empirical application to the case of the tourist industry in the Canary Islands (Spain) is presented, showing that the model can represent the general characteristics of the post-stagnation phase of a tourist destination.     

On the impact of leverage constraints on asset prices and trading volume

Abstract. Researchers have used stylized facts on asset prices and trading volume in stock markets (in particular, the mean reversion of asset returns and the correlations between trading volume, price changes and price levels) to support theories where agents are not rational expected utility maximizers. This paper shows that this empirical evidence is in fact consistent with a standard infinite horizon – perfect information – expected utility economy where some agents face leverage constraints similar to those found in todays financial markets. In addition, and in sharp contrast to the theories above, we explain some qualitative differences that are observed in the price-volume relation on stock and on futures markets. We consider a continuous-time economy where agents maximize the integral of their discounted utility from consumption under both budget and leverage constraints. Building on the work by Vila and Zariphopoulou (1997), we find a closed form solution, up to a negative constant, for the equilibrium prices and demands in the region of the state space where the constraint is non-binding. We show that, at the equilibrium, stock holdings volatility as well as its ratio to stock price volatility are increasing functions of the stock price and interpret this finding in terms of the price-volume relation. We would like to thank the editor and two anonimous referees for valuable substantive comments. Our gratitude also to Franklin Allen, Kerry Back, Domenico Cuoco, Xavier Freixas, Sanford Grossman, Michel Habib, Lutz Hendricks, Richard Kihlstrom, Fernando Restoy, Mary Thomson, Jean-Luc Vila, participants to seminars at Birkbeck College, Carnegie-Mellon, Columbia, ESSEC, HEC, IAE, INSEAD, London Business School, London School of Economics, McGill, Michigan, National University of Singapore, Pompeu Fabra, North Carolina, Washington-St-Louis, Wharton, the Jornadas de Economía Financiera BBV, and the Meetings of the Society for Economic Dynamics and Control and the American Finance Association. Special thanks are due to Süleyman Basak for his enthusiastic support and many helpful suggestions. The usual disclaimer applies. We gratefully acknowledge the support of the BBV and Caja de Madrid Foundations and CREF (both authors) and of the Spanish Ministry of Education under DGICYT grant no. PB93-0388 (first author).     

Behavior in one-shot traveler’s dilemma games: model and experiments with advice

We report results of one-shot traveler’s dilemma game experiments to test the predictions of a model of introspection. The model describes a noisy out-of-equilibrium process by which players reach a decision of what to do in one-shot games. To test the robustness of the model and to compare it to other models of introspection without noise, we introduce non-binding advice. Advice has the effect of coordinating all players’ beliefs onto a common strategy. Experimentally, advice is implemented by asking subjects who participated in a repeated traveler’s dilemma game to recommend an action to subjects playing one-shot games with identical parameters. In contrast to observations, models based on best-response dynamics would predict lower claims than the advised. We show that our model’s predictions with and without advice are consistent with the data.      

Trees and decisions

Summary. The traditional model of sequential decision making, for instance, in extensive form games, is a tree. Most texts define a tree as a connected directed graph without loops and a distinguished node, called the root. But an abstract graph is not a domain for decision theory. Decision theory perceives of acts as functions from states to consequences. Sequential decisions, accordingly, get conceptualized by mappings from sets of states to sets of consequences. Thus, the question arises whether a natural definition of a tree can be given, where nodes are sets of states. We show that, indeed, trees can be defined as specific collections of sets. Without loss of generality the elements of these sets can be interpreted as representing plays. Therefore, the elements can serve as states and consequences at the same time.Received: 23 January 2003, Revised: 2 November 2003, JEL Classification Numbers: C72, D70. Correspondence to: Klaus RitzbergerWe are grateful to Larry Blume, Ariel Rubinstein, Jörgen Weibull, an anonymous referee, and seminar participants at the universities of Vienna, Salamanca, and Heidelberg for helpful comments. Financial support from the Austrian Science Fund (FWF) under project P15281 is also gratefully acknowledged.     

Political Profit: Taxing and Spending in the Hierarchical State

A bstract . The actions of government fall into two types: taxes (the taking of property ) and expenditures (the awarding of gifts ). Politicians profit as long as the value of resources raised from taxation exceeds the cost of expenditures. From their point of view, fiscal efficiency consists in maximizing the support obtained by spending and minimizing the opposition generated by taxing. This is accomplished by spending on well-organized groups and taxing the uninformed public. This results in the "iron law of political redistribution" in which income and wealth are transferred from the latter to the former. In a hierarchical State , it is usually profitable for those at the top to centralize control over taxing and spending, if for no other reason than to make it difficult for politicians at lower levels to compete against them. This gives rise to the "law of hierarchical centralization "—in a hierarchical State, power becomes centralized over time. The greater the power of government, the faster this process takes place. In order to avoid this problem, one could design constitutions which are non-hierarchical in nature, in which each unit of government is completely autonomous from the others, as firms are in a free market.     

Sectoral and aggregate technology growth in Spain

In this paper we analyze technological change in the Spanish economy by constructing adjusted Solow residuals, where the adjustment attempts to correct for the bias associated with the potential presence of imperfect competition, increasing returns, variable input utilization and, especially, sectoral reallocation of inputs across sectors. We refer to this modified Solow residual as a technology index. Sectoral reallocations and variable input utilization are key determinants of the differences between the aggregate Solow residual and the technology index resulting from the aggregation of estimated sectoral technological growth. We show that starting in the mid nineties, there has been a deceleration in the aggregate growth rate of technology which is basically due to the behaviour of the manufacturing sectors. Finally, our results imply that aggregate technology growth is less volatile than aggregate productivity as measured by the Solow residual.     

Strategic Environmental Standards, Wage Incomes and the Location of Polluting Firms

The purpose of this paper is tostudy how the choice of environmental standardsby governments is affected by the existence ofwage incomes when firms locations areendogenous. In developed countries labor isunionized, which allows positive wage incomesto arise. Thus, each government has incentivesto persuade firms to locate in its countrysince social welfare depends on suchincomes. But, as pollution damages theenvironment, each government will only try toattract polluting firms to thecountry, to obtain the wage incomes, whenthe valuation of environmental damage showsthat it is low.