An algebraic theory of portfolio allocation

Summary. Using group and majorization theory, we explore what can be established about allocation of funds among assets when asymmetries in the returns vector are carefully controlled. The key insight is that preferences over allocations can be partially ordered via majorized convex hulls that have been generated by a permutation group. Group transitivity suffices to ensure complete portfolio diversification. Point-wise stabilizer subgroups admit sectoral separability in fund allocations. We also bound the admissible allocation vector by a set of linear constraints the coefficients of which are determined by group operations on location and scale asymmetries in the rate of returns vector. For a distribution that is symmetric under a reflection group, the linear constraints may be further strengthened whenever there exists an hyperplane that separates convex sets. Received: May 15, 2001; revised version: March 20, 2002 RID="*" ID="*" Journal paper No. J-19797 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 3463, and supported by Hatch Act and State of Iowa funds. Correspondence to: D. A. Hennessy     

Is assortative matching efficient?

Summary. This paper develops some general conditions under which complementarities between individual agents imply that assortative matching is efficient. Our analysis has four main findings. First, when agents are organized into equal-sized groups, just as in Becker (1973), the presence of within-group complementarities is sufficient for stratification to be efficient. Second, if group sizes vary, assortative matching may not be efficient even though complementarities are present, unless particular functional form assumptions are imposed. Third, the connection between assortative matching, complementarities and efficiency reemerges if one considers sequences of replications of the economy in which individual coalitions are uniformly bounded in size. Fourth, the presence of feedbacks from the composition of group memberships has important effects on efficient allocations and breaks any simple link between assortative matching and efficiency. Together, these results suggest that the characterization of the cross-section evolution of an efficiently sorted economy is likely to be highly complex. Received: September 25, 2001; revised version: February 26, 2002 RID="*" ID="*" We thank William Brock for many helpful conversations and Scott Page for detailed comments on an earlier draft of this paper. The National Science Foundation, John D. and Catherine T. MacArthur Foundation and Center for Urban Land Economic Research have generously provided financial support. Correspondence to: S. N. Durlauf     

On the constancy of bribe-proof solutions

Summary. We consider the problem of choosing one point in a set of alternatives when monetary transfers are possible. In this context, Schummer (2000) shows that a social choice function must be a constant function if manipulation through bribes is ruled out. But he requires two kinds of domain-richness conditions. One is either smooth connectedness or the finiteness of the set of alternatives and the other is monotonical closedness. However, dispensing with the former condition, we alternatively prove the same result under a weaker condition than monotonical closedness. Received: April 11, 2000; revised version: February 25, 2002 RID="*" ID="*" This paper received the Osaka University Institute of Social and Economic Research Moriguchi Prize in January 2001. I am grateful to Prof. Ryoichi Nagahisa, Prof. Tatsuyoshi Saijo, Prof. Ken-ichi Shimomura, Prof. Ken Urai, and especially two anonymous referees for their useful and helpful comments and suggestions. I am a Research Fellow of the Japan Society for the Promotion of Science.     

Existence and optimality of oligopoly equilibria in linear exchange economies

Summary. We consider a linear exchange economy and its successive replicas. We study the notion of Cournot-Walras equilibrium in which the consumers use the quantities of commodities put on the market as strategic variables. We prove that, generically, if the number of replications is large enough but finite, the competitive behaviour is an oligopoly equilibrium. Then, under a mild condition, which may be interpreted in terms of market regulation and/or market activity, we show that any sequence of oligopoly equilibria of successive replica economies converges to the Walrasian outcome and furthermore that every oligopoly equilibrium of large, but finite, replica is Pareto optimal. Consequently, under the same assumptions on the fundamentals of the economy, one has an asymptotic result on the convergence of oligopoly equilibria to the Walras equilibrium together with a generic existence result for the Cournot-Walras. Received: June 20, 2002; revised version: November 20, 2002 RID="*" ID="*" Part of this paper was written while the second author was visiting the Universidad de Vigo. The support of the department of mathematics is gratefully acknowledged. Correspondence to: J.M. Bonnisseau     

Exact arbitrage and portfolio analysis in large asset markets

Summary. We provide a detailed portfolio analysis for a financial market with an atomless continuum of assets. In the context of an exact arbitrage pricing theory (EAPT), we go beyond the characterization of the existence of important portfolios (normalized riskless, mean, cost, factor and mean-variance efficient portfolios) to furnish exact portfolio compositions in terms of explicit portfolio weights. Such an analysis has not been furnished before in the context of the asymptotic arbitrage pricing theory (APT). We also characterize conditions under which a mean-variance efficient portfolio is a benchmark portfolio used in the EAPT to proxy essential risk. We illustrate our results with several examples of specific financial markets. Received: May 30, 2002; revised version: August 15, 2002 RID="*" ID="*"Some of the results reported here constituted part of Cowles Foundation Discussion Paper– No. 1139 circulated under the title “Hyperfinite Asset Pricing Theory”; additional results were obtained when Sun visited the Department of Economics at Johns Hopkins University during March 2002. This paper was presented at the Conference on Economic Design held at NYU on July 6–9, 2002 Correspondence to: M. A. Khan     

Indeterminacy in a small open economy with endogenous labor supply

Summary. We establish conditions under which indeterminacy can occur in a small open economy business cycle model with endogenous labor supply. Indeterminacy requires small externalities in technologies with social constant returns to scale, independently of the intertemporal elasticities in both consumption and labor. Received: December 12, 2001; revised version: May 17, 2002 RID="*" ID="*"The paper has benefited from discussions with Jess Benhabib and Mark Weder, as well as from the comments of an anonymous referee. Correspondence to: Q. Meng     

A simple axiomatization and constructive representation proof for choquet expected utility

>P>Summary. We provide a set of simple and intuitive set of axioms that allow for a direct and constructive proof of the Choquet Expected Utility representation for decision making under uncertainty. Received: October 29, 2002; revised version: November 13, 2002 RID="*" ID="*" We thank Matthew Ryan for very useful comments and suggestions on related work and for encouraging us to write this note. Correspondence to: S. Grant     

Ranking investment projects

Summary. This paper describes conditions under which one investment project dominates a second project in terms of net present value, irrespective of the choice of the discount rate. The resulting partial ordering of projects has certain similarities to stochastic dominance. However, the structure of the net present value function leads to characterizations that are quite specific to this context. Our theorems use Bernstein's (1915) innovative results on the representation and approximation of polynomials, as well as other general results from the theory of equations, to characterize the partial ordering. We also show how the ranking is altered when the range of discount rates is limited or the rate varies period by period. Received: January 5, 2002; revised version: October 29, 2002 RID="*" ID="*" We thank Robert Driskill, Andrea Maneschi, Roy Radner, and participants of seminars at NYU, Notre Dame, Purdue, and Washington University for helpful comments. The present version of the paper has benefited from comments by a referee and the editor. Foster is grateful for support from the John D. and Catherine T. MacArthur Foundation through its network on Inequality and Poverty in Broader Perspective. Correspondence to: T. Mitra     

Stochastic growth: asymptotic distributions

Summary. This note studies conditions under which sequences of state variables generated by discrete-time stochastic optimal accumulation models have law of large numbers and central limit properties. Productivity shocks with unbounded support are considered. Instead of restrictions on the support of the shock, an “average contraction” property is required on technology. Received: August 27, 2001; revised version: January 9, 2002 RID="*" ID="*"The author thanks John Creedy and Rabee Tourky for helpful comments, and the Economic Theory Center, University of Melbourne for financial support.     

Rate-of-return dominance and efficiency in an experimental economy

Summary. One of the main challenges for monetary economics is to explain the use of assets that are dominated in rate-of-return as media of exchange. We use experimental methods to study how a fiat money might come to be used in transactions when an identically marketable, dividend-bearing asset, a consol, is also available. Our experimental economies, which have an overlapping generations structure, have the property that the only stationary rational expectations equilibria (SREE) require exclusive use of the consol as the medium of exchange. In a baseline treatment, agents use the consol exclusively, as would occur in an SREE. However, in other treatments, we observe episodes of rate-of-return dominance,with consistent use of fiat money as a medium of exchange. The results show that two properties of our economies are associated with the rate of return dominance anomaly. The first is a history of trading with fiat money, prior to the introduction of the consol. The second is the timing of the dividend payment; when the dividend payment follows the execution of trades between generations, hoarding of the consol occurs on the part of the old, who earn dividends by hoarding. In our economies, settling transactions with a dividend-bearing asset does not improve allocations over those resulting from trading with fiat money. Received: July 11, 2002; revised version: July 25, 2002 RID="*" ID="*"We thank Anne Villamil, participants in the 2000 Purdue University Conference on Monetary Economics, the Summer 2000 meetings of the Economic Science Association, and a referee, for very helpful comments. We thank the Krannert School of Management and the Purdue University Center for International Business, Education and Research for financial support and Vivian Lei for research assistance. We also thank Ron Michener for referring us to the historical account of the early introduction of money into the American colonies, as reported by Benjamin Franklin. Correspondence to: G. Camera     

Edgeworth and Walras equilibria of an arbitrage-free exchange economy

Summary. In this paper, we first give a direct proof of the existence of Edgeworth equilibria for exchange economies with consumption sets which are (possibly) unbounded below. The key assumption is that the individually rational utility set is compact. It is worth noticing that the statement of this result and its proof do not depend on the dimension or the particular structure of the commodity space. In a second part of the paper, we give conditions under which Edgeworth allocations can be decentralized by continuous prices in a finite dimensional and in an infinite dimensional setting. We then show how these results apply to some finance models.Received: 15 April 2002, Revised: 25 February 2003, JEL Classification Numbers: C62, D58, G12. Correspondence to: Monique FlorenzanoThis paper was presented at seminars of the Economic Departments of Brown University, The Johns Hopkins University, The University of Alabama, Purdue University and at the Centro de Modelamiento Matematico de la Universidad de Chile at Santiago. The paper has benefitted of the comments of these diverse audiences. Part of this work was done while the authors were visiting respectively Brown University and the Centro de Modelamiento Matematico. We thank them for their hospitality.     

The Lens Condition with Two Factors

The authors give a simple, constructive proof that the lens condition implies the factor price equalization condition when there are only two factors. Taking stock of the conditions under which the lens condition is equivalent to the factor price equalization condition, there are the conditions of two factors or two goods or two countries, or the condition that the rank of the factor‐use matrix is equal to the number of goods. It is shown that, in an essential sense, there are no other such conditions.     

Voluntariness and efficiency in the provision of public goods

This paper presents a characterization of Lindahl allocations which makes no reference to personalized prices. Lindahl equilibria are characterized here by two conditions: Pareto efficiency and a voluntariness condition. Voluntariness requires that no consumer may benefit from a reduction in his contribution if this means that the vector of public goods must be reduced in the same proportion. The intersection of the (large) set of voluntary allocations and that of efficient ones turns out to be (under differentiability) the set of Lindahl allocations.     

Dictatorial domains

Summary. In this paper, we introduce the notion of a linked domain and prove that a non-manipulable social choice function defined on such a domain must be dictatorial. This result not only generalizes the Gibbard-Satterthwaite Theorem but also demonstrates that the equivalence between dictatorship and non-manipulability is far more robust than suggested by that theorem. We provide an application of this result in a particular model of voting. We also provide a necessary condition for a domain to be dictatorial and use it to characterize dictatorial domains in the cases where the number of alternatives is three. Received: July 12, 2000; revised version: March 21, 2002 RID="*" ID="*" The authors would like to thank two anonymous referees for their detailed comments. Correspondence to: A. Sen     

Balancedness and the core in economies with asymmetric information

Summary. A condition is given that is equivalent to balancedness of all NTU-games derived from an exchange economy with asymmetric information when endowments are variable. The condition is applicable to the ex-ante model with expected utilities, but also to the more general model of Arrow-Radner type economies without subjective probabilities. Differences in the interpretation of measurability assumptions between these two models are discussed, and another model with information consistent utility functions is developed in which the result would also hold. Received: December 12, 2001; revised version: November 1, 2002 RID="*" ID="*"I thank two anonymous referees whose comments led to an improvement of the paper.     

General equilibrium with trade balance and real interest rate parity

This paper demonstrates, in the context of a two-sector OLG neoclassical growth model, conditions under which international trade in consumption goods alone may be sufficient for the equalization of real returns to physical capital across countries; that is, under which commodity arbitrage is sufficient for real interest rate parity (RIRP). This role for repeated commodity arbitrage is established via a dynamic extension of the factor price equalization (FPE) theorem which is valid at all dates comprising the equilibrium path as well as its steady state. The results are at odds with the conventional view regarding RIRP which arises from open one-sector growth models, in which case steady state trade balance and RIRP are irreconcilable, and are also a contradiction to frequent assertions of lon-run specialization in two-sector frameworks. An equilibrium path for an integrated world economy yields an endogenous, time-variant cone of diversification which implies sufficient conditions for the dynamic paths of a cross-section of economies to exhibit FPE, and hence RIRP with trade balance, at all points in time. These conditions require that the savings rates and initial capital-labor ratios of individual countries do not deviate too significantly from world averages, and that both sectors absorb capital easily. The first of these requirements is sufficient to establish steady state FPE and RIRP in the general specification. The first two requirements are sufficient for the entire equilibrium path to be characterized by FPE and RIRP in a log-linear example. Received: September 22, 1998; revised version: February 10, 2000     

Incentives in market games with asymmetric information: the core

Summary. This paper examines the ex ante core of a pure exchange economy with asymmetric information in which state-dependent allocations are required to satisfy incentive compatibility. This restriction on players' strategies in the cooperative game can be interpreted as incomplete contracts or partial commitment. An example is provided in which the incentive compatible core with nontransferable utility is empty; the game fails to be balanced because convex combinations of incentive compatible net trades can violate incentive compatibility. However, randomization of such strategies leads to ex post allocations which satisfy incentive compatibility and are feasible on average. Hence, convexity is preserved in such a model and the resulting cooperative games are balanced. In this framework, an incentive compatible core concept is defined for NTU games derived from economies with asymmetric information. The main result is nonemptiness of the incentive compatible core. Received: December 26, 2001; revised version: June 11, 2002 RID="*" ID"*" This work was financed, in part, by contract No 26 of the programme “P?le d'attraction interuniversitaire” of the Belgian government, and, in part, by research grant SBR93-09854 from the U.S. National Science Foundation. Much of my thinking about this topic was developed during a wonderful visit to CORE for the 1991–1992 academic year (on sabbatical from the University of Pennsylvania). This paper was originally circulated in December 1991 as CARESS Working Paper #91-38, Center for Analytic Research in Economics and the Social Sciences, Department of Economics, University of Pennsylvania and in February 1992 as CORE Discussion Paper 9221, Center for Operations Research and Econometrics, Université Catholique de Louvain, Louvain-la-Neuve, Belgium. RID="*" ID="*" At the very start of my research, Jean-Fran?ois Mertens was almost a co-author. Fran?ois Forges provided detailed comments at a later stage, during my visit to THEMA, Université Cergy-Pontoise, in Spring 1997. They are entitled to the customary disclaimer.     

The proper panel econometric specification of the gravity equation: A three-way model with bilateral interaction effects

We argue that the proper specification of a panel gravity model should include main (exporter, importer, and time) as well as time invariant exporter-by-importer (bilateral) interaction effects. In a panel of 11 APEC countries, the latter are highly significant and account for the largest part of variation. First version received: February 2001/Final version received: June 2002 RID="*" ID="*"  We are grateful to two anonymous referees and Robert Kunst for their helpful comments.     

Nash implementation with a private good

Summary. I construct a general model of social planning problems, including mixed production economies and regulatory problems with negative externalities as special cases, and I give simple mechanisms for Nash implementation under three increasingly general sets of assumptions. I first construct a continuous mechanism to implement the (constrained) Lindahl allocations of an economy, and I then extend this to arbitrary social choice rules based on prices. I end with a mechani sm to implement any monotonic social choice rule, assuming only the existence of a private (not necessarily transferable) good. In that general case, each agent simply reports an upper contour set, an outcome, and I need two agents to make binary numerical announcements. I do not require the usual no-veto-power condition. Received: February 19, 1998; revised version: January 30, 2002     

Implementation in teams

Summary. This paper considers a team production model in which the final output is a function of one or more observable intermediate variables that are functions of the actions of the team members. When there is only one intermediate variable, our model essentially reduces to the standard models in which only the final output is observable. We provide a necessary and sufficient condition for implementing an outcome. This condition imposes restrictions on the possible deviations from the outcome that can be caused by every member of the team unilaterally. As a consequence of this characterization, when there are more than one intermediate variable, we are able to show that in a broad class of problems these intermediate variables may be sufficiently informative to allow sharing rules that implement efficient outcomes. Received: March 26, 2001; revised version: August 12, 2002 RID="*" ID="*"I would like to thank Parimal Bag, Craig Brett, Greg Dow, Hugo Hopenhayn, Ashok Kotwal, Dilip Mookherjee, Santanu Roy, Sudhir Shah, Guofu Tan and John Weymark for helpful discussions on earlier versions of this paper. The usual disclaimer applies.