Computing equilibria in finance economies with incomplete markets and transaction costs

Summary. Transaction costs on financial markets may have important consequences for volumes of trade, asset pricing, and welfare. This paper introduces an algorithm for the computation of equilibria in the general equilibrium model with incomplete asset markets and transaction costs. We show that economies with transaction costs can be analyzed with differentiable homotopy techniques and thus in the same framework as frictionless economies despite the existence of non-differentiabilities of agents asset demand functions and the existence of locally non-unique equilibria. We introduce an equilibrium selection concept into the computation of economic equilibria that picks out a specific equilibrium in the presence of a continuum of equilibria.Received: 2 December 2002, Revised: 15 November 2004, JEL Classification Numbers: C61, C62, C63, C68, D52, D58, G11, G12. Correspondence to: P. Jean-Jacques HeringsThis research started when Jean-Jacques Herings enjoyed the generous hospitality of the Cowles Foundation for Research in Economics at Yale University. His research has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences and a grant of the Netherlands Organisation for Scientific Research. We thank audiences at Stanford University, UC San Diego, and Venice for discussions on the subject. We are very grateful to an anonymous referee for very helpful comments on an earlier draft.     

Are incomplete markets able to achieve minimal efficiency?

Summary. We consider economies with incomplete markets, one good per state, two periods, t = 0,1, private ownership of initial endowments, a single firm, and no assets other than shares in this firm. In Dierker, Dierker, Grodal (2002), we give an example of such an economy in which all market equilibria are constrained inefficient. In this paper, we weaken the concept of constrained efficiency by taking away the planners right to determine consumers investments. An allocation is called minimally constrained efficient if a planner, who can only determine the production plan and the distribution of consumption at t = 0, cannot find a Pareto improvement. We present an example with arbitrarily small income effects in which no market equilibrium is minimally constrained efficient.Received: 26 November 2002, Revised: 28 May 2003, JEL Classification Numbers: D2, D52, D61, G1.We are grateful to an anonymous referee for very valuable comments. E. and H. Dierker would like to thank the Institute of Economics, University of Copenhagen, for its hospitality and its financial support.     

Excess price volatility and financial innovation

Summary. In a three-period finite exchange economy with incomplete financial markets and retrading, we study the effects of the degree of incompleteness and of changes in the financial structure on asset price volatility. In what are essentially no aggregate risk economies, asset price volatility is a sunspot-like phenomenon. If markets are completed by financial innovation, asset price volatility reduction is generic. With aggregate risk, changes in the financial structure affect asset price volatility through a pecuniary externality. Financial innovation which decreases equilibrium price volatility can be crafted under conditions of sufficient market incompleteness. Numerical examples illustrate the role of risk aversion for volatility changes and show that, with or without aggregate risk, reducing the degree of incompleteness per se is not necessarily associated with a volatility reduction.Received: 10 October 2003, Revised: 3 June 2004, JEL Classification Numbers: C60, D52, G10. Correspondence to: Alessandro CitannaThis research project stems from and expands previous work circulated as Financial innovation and price volatility, GSIA Working Paper #1996-E30 and Controlling price volatility through financial innovation, Kellogg Working Paper #2002-1338. We thank Herakles Polemarchakis and Chris Telmer for their comments. We are grateful to an anonymous referee for careful reviews of earlier versions. The first author thanks also GSIA - Carnegie Mellon University for the kind hospitality during Fall 2002, when part of this project was completed.     

Crime and social norms

In this paper, we develop a general equilibrium model of crime. It is shown that law and norms are substitutes in achieving a stable equilibrium. Here we offer a new interpretation of different theories of social norms in the context of crime and deterrence. The law and economics theory is presented as an opportunism-limiting approach to norms whereas the evolutionary theory is presented as an opportunity cost approach.Received: January 2003, Accepted: July 2003, JEL Classification: D59, K14, K42Paper presented at the 3rd annual meeting of SPIE Portuguese Association for Research in Economics, June 22-23, 1998, Braga and at the 15th annual meeting of the European Association of Law and Economics, September 24-26, 1998, Utrecht. I am grateful to two referees and the editor for helpful comments that much improved the paper, and to Dorothea Kübler, Eric Posner, Dieter Schmidtchen, and Stergios Skaperdas for suggestions that much improved this paper, and to Kelly Markva for research assistantship. The author acknowledges the financial support of FCT, Lisbon, Portugal. Part of this paper was written while the author visited Stanford Law School. The usual disclaimer applies.     

The core of an economy with satiation

Summary. It has long been known that in economies with satiation, the set of competitive equilibria does not coincide with the limiting core of an economy. In dividend equilibria, introduced independently by a number of authors, the budget excess is allowed to be divided among consumers as dividends and equilibrium existence is restored. In this paper a new notion of blocking which leads to core - dividend equilibrium equivalence is introduced. Specifically, it is shown that an allocation is a dividend equilibrium if and only if a corresponding equal treatment allocation of a large economy is in the core.Received: 21 June 2003, Revised: 3 December 2003, JEL Classification Numbers: D50.Alexander Konovalov: The author would like to thank M. Florig, P. J. J. Herings, V. Marakulin, D. Talman, V. Vasilev, and anonymous referees for helpful comments and suggestions.     

Optimal debt contracts and moral hazard along the business cycle

Summary. We analyze the Pareto optimal contracts between lenders and borrowers in a model with asymmetric information. The model generalizes the Rothschild-Stiglitz pure adverse selection problem by including moral hazard. Entrepreneurs with unequal abilities borrow to finance alternative investment projects which differ in degree of risk and productivity. We determine the endogenous distribution of projects as functions of the amount of loanable funds, when lenders have no information about borrowers ability and technological choices. Then, we embed these results in a dynamic competitive economy and show that the average quality of the selected projects in equilibrium may be high in recessions and low in booms. This phenomenon may generate (a) multiple steady states, (b) a smaller impact of exogenous shocks on output relative to the full information case, (c) endogenous fluctuations.Received: 11 June 2001, Revised: 17 June 2003, JEL Classification Numbers: A10, G14, G20, E32.Correspondence to: Pietro ReichlinPietro Reichlin acknowledges financial support from MURST and Paolo Siconolfi acknowledges financial support from the GSB of Columbia University.     

Managerial risk reduction, incentives and firm value

Summary. Empirical evidence suggests that managers privately alter the risk in their compensation by trading in the financial markets. This paper analyzes the implications of the managers hedging ability on her optimal compensation scheme, incentives and firm value. I allow the manager to reduce her systematic risk exposure by trading the market portfolio. I find that the managers optimal hedge depends on the liquidity of the market. Due to imperfect liquidity, the managers optimal hedge is not complete. The equilibrium pay-performance sensitivity and hence the managers equilibrium incentives and the firm value increases in the liquidity of the market.Received: 24 November 2003, Revised: 22 September 2004, JEL Classification Numbers: G30, G32.I am grateful to a referee whose comments improved the paper. I would also like to thank Gerald Garvey and Li Jin for their helpful comments on an earlier draft.     

A model to analyse financial fragility

Summary. This paper sets out a tractable model which illuminates problems relating to individual bank behaviour, to possible contagious inter-relationships between banks, and to the appropriate design of prudential requirements and incentives to limit ‘excessive’ risk-taking. Our model is rich enough to include heterogeneous agents, endogenous default, and multiple commodity, and credit and deposit markets. Yet, it is simple enough to be effectively computable and can therefore be used as a practical framework to analyse financial fragility. Financial fragility in our model emerges naturally as an equilibrium phenomenon. Among other results, a non-trivial quantity theory of money is derived, liquidity and default premia co-determine interest rates, and both regulatory and monetary policies have non-neutral effects. The model also indicates how monetary policy may affect financial fragility, thus highlighting the trade-off between financial stability and economic efficiency.Received: 6 November 2003, Revised: 6 October 2004 JEL Classification Numbers: D52, E4, E5, G11, G21.C.A.E. Goodhart, P. Sunirand, D.P. Tsomocos: We are grateful to T.F. Bewley, S. Bhattacharya, F. Hahn, C. Mayer, H.S. Shin and seminar participants at the Bank of Austria, Bank of England, Bank of Norway, Bank for International Settlements, Brown University, the 7th Annual Macroeconomic Conference, Crete, EcoMod-IIOA International Conference, Brussels, the 2nd Oxford Finance Summer Symposium and Nuffield, Oxford, the Hong Kong Institute for Monetary Research, Purdue University, the University of Birmingham, the VI SAET Conference, Rhodes, Yale University, and especially an anonymous referee and H.M. Polemarchakis for helpful comments. The views expressed are those of the authors and do not necessarily reflect those of the Bank of England. Correspondence to: D.P. Tsomocos     

非均衡最优规划模型解的经济政策意义

本文根据非均衡理论的最优规划模型 ,探讨了在凯恩斯失业均衡和抑制性通货膨胀均衡下 ,几个主要的经济变量P、W、G、T、M、A对于家庭消费C和产出Y (或就业L)的影响。主要的结论是 :在凯恩斯失业状态下 ,刺激消费的同时 ,积累仍不可忽视 ;计划经济国家长期过分注重积累的传统经济政策思想是不合理的 ;平衡或盈余的财政政策是计划经济国家的明智之举 ;计划经济国家长期实行低工资水平的政策是错误的     

Price leadership in a duopoly with capacity constraints and product differentiation

This paper analyzes Stackelberg price leadership in a duopoly in which firms are capacity constrained and products are imperfect substitutes. Assuming symmetric substitutes, linear demand, and efficient rationing, we characterize the equilibria with an exogenously specified leader. Using the equilibrium profits derived from these games, we argue that over certain ranges of asymmetric capacities an endogenous price leader will emerge. When endogenous leadership does arise, it is the large capacity firm which is the leader. We thus provide a game theoretic model of dominant firm price leadership.Dave Furth's research has been undertaken as a part of the project Competition and Cooperation. Dan Kovenock has benefited from financial support from Erasmus University Rotterdam, the Krannert School of Management, and the Jay N. Ross Young Faculty Research Fellowship. We are grateful to Tom Faith for valuable research assistance. We have benefited from the comments of the editor, two anonymous referees, and participants at the European meetings of the Econometric Society in September 1989 and the North American Winter Meetings of the Econometric Society in December 1989.     

Endogenous fluctuations in unionized economies with productive externalities

Summary. We discuss the effects of unions on steady-state multiplicity and welfare, and on the existence of endogenous fluctuations. We consider an OG economy with productive capital externalities and we focus on underemployment equilibria. We find that for wide regions in the parameter space, including an arbitrarily small degree of externalities and a Cobb-Douglas technology, unions increase steady state employment and welfare, and local indeterminacy (sunspots) emerges. Moreover with a CES technology multiplicity of steady states is only possible in the presence of unions. Our results also show that the role of unions in shaping local dynamics and bifurcations depends on technology (externalities and factors substitutability).Received: 16 January 2002, Revised: 18 March 2004, JEL Classification Numbers: E32, J51, D60, D62. Correspondence to: Leonor ModestoThis paper is a much revised version of our former working paper Unions, Increasing Returns and Endogenous Fluctuations. Financial support from Fundação para a Ciência e Tecnologia under the POCTI, is gratefuly acknowledged.     

Equilibria in a multi-object uniform price sealed bid auction with multi-unit demands

Summary In many existing markets demanders wish to buy more than one unit from a group of identical units of a commodity. Often, the units are sold simultaneously by auction. The vast majority of literature pertaining to the economics of auctions, however, considers environments in which demanders buy at most one object. In this paper we derive necessary and sufficient conditions for a set of bidding strategies to be a symmetric monotone Bayes-Nash equilibrium to a uniform price sealed bid auction using the first rejected bid pricing rule in an independent private values environment with two-unit demands. In any symmetric monotone Bayes-Nash equilibrium, all bidders submit one bid equal to their higher valuation and one bid lower than their lower valuation. We characterize the equilibrium and derive the exact amount of underrevelation in the lower bid.This article is based on chapter 2 of the author's Ph.D. thesis. I would like to acknowledge the financial support of the Clarence Hicks Memorial Fellowship, the California Institute of Technology and the Jet Propulsion Laboratory. I also thank D. Roderick Kiewiet, Richard McKelvey, Charles Plott, David Porter, Annemieke Tromp, participants in the Tinbergen Institute Seminar Series, an anonymous referee and especially John Ledyard for countless enlightening comments.     

Ambiguity aversion and the absence of indexed debt

Summary. Following the seminal works of Schmeidler (1989), Gilboa and Schmeidler (1989), roughly put, an agents subjective beliefs are said to be ambiguous if the beliefs may not be represented by a unique probability distribution, in the standard Bayesian fashion, but instead by a set of probabilities. An ambiguity averse decision maker evaluates an act by the minimum expected value that may be associated with it. In spite of wide and long-standing support among economists for indexation of loan contracts there has been relatively little use of indexation, except in situations of extremely high inflation. The object of this paper is to provide a (theoretical) explanation for this puzzling phenomenon based on the hypothesis that economic agents are ambiguity averse. The paper considers a general equilibrium model based on Magill and Quinzii (1997) with ambiguity averse agents, where both nominal and indexed bond contracts are available for trade and all relevant prices are determined endogenously. We obtain conditions which prompt an endogenous cessation of trade in indexed bonds: i.e., conditions under which there is no trade in indexed bonds in any equilibrium; only nominal bonds are traded.Received: 7 April 2003, Revised: 8 March 2004, JEL Classification Numbers: D81, E31, D52, E44.Correspondence to: Sujoy MukerjiWe thank seminar members at Birkbeck, Oxford, Paris I, Southampton and Tel Aviv, the audience at the 00 European Workshop on General Equilibrium Theory, and especially, E.Dekel, I. Gilboa, D. Schmeidler and A. Pauzner for helpful comments. The first author acknowledges financial assistance from an Economic and Social Research Council of U.K. Research Fellowship (# R000 27 1065). The second author thanks financial support from the French Ministry of Research (Action Concertée Incitative).     

On the continuity of equilibrium and core correspondences in economies with differential information

Summary. We study upper semi-continuity of the private and coarse core and the Walrasian expectations equilibrium correspondences for economies with differential information, with Boylan (1971) topology on agents information fields.Received: 16 January 2004, Revised: 28 October 2004, JEL Classification Numbers: D50, D82, C70. Correspondence to: Ezra EinyWe wish to thank Carlos Herves, Nicholas Yannelis, and an anonymous referee for their helpful comments.     

Sunspots,indeterminacy and Pareto inefficiency in economies with incomplete markets

Summary. We consider two periods economies with both intrinsic and extrinsic uncertainty. Asset markets are incomplete in the certainty economy. If assets are nominal, there are enough commodities and the number of agents is greater than two and smaller than the total number of states of nature tomorrow (minus one), then a sunspot-invariant equilibrium is generically Pareto dominated by some sunspot equilibria. When assets are real, and there are enough commodities, if there are sunspot equilibria, there are sunspot equilibria Pareto dominating sunspot-invariant equilibria under the same restriction on the number of agents (and stronger restrictions on the number of commodities).Received: 20 October 2003, Revised: 1 April 2004, JEL Classification Numbers: D52.I wish to thank Paolo Siconolfi for helpful suggestions and comments. I aknowledge the financial support of M.I.U.R. and the kind hospitality of C.C.D.R. in Summer 2003.     

The distribution of money and prices in an equilibrium with lotteries

Summary. We construct a tractable fundamental model of money with equilibrium heterogeneity in money balances and prices. We do so by considering randomized monetary trades in a standard search-theoretic model of money where agents can hold multiple units of indivisible tokens and can offer lotteries on monetary transfers. By studying a simple trading pattern, we can analytically characterize the monetary distribution. Interestingly, such distributions match those observed in numerically simulated economies with fully divisible money and price heterogeneity.Received: 16 April 2003, Revised: 11 February 2004JEL Classification Numbers: D30, D83, E40.A. Berentsen, G. Camera, C. Waller: The paper has benefitted from insightful comments of two anonymous referees, whom we thank. We also thank participants at the conference Recent Developments in Money and Finance, held at Purdue University in May 2003, and the EPRI/University of Western Ontario Money Conference held in October 2003. Correrspondence to: G. Camera     

The structure of the set of sunspot equilibria in economies with incomplete financial markets

Summary This paper considers the set of equilibria of two-period, sunspot economies withS purely extrinsic states of nature in the second period andI assets with linearly independent nominal payoffs. The span of the payoff matrix contains the vector [1, ... , 1] (i.e., inside money). The set of economies is described in terms of (sunspot-invariant) utility functions. IfS>I> 0, there is an open, dense set of economies such that, given a vector of no arbitrage asset prices, the set of equilibrium allocations contains a smooth manifold of dimensionS—I. Such a manifold contains at least one nonsunspot equilibrium (and at most a finite number of such equilibria).The paper was written while I was a visitor at C.O.R.E., Universitè Catholique de Louvain, with the financial support of a S.P.E.S. fellowship. I would like to thank D. Cass, H. Polemarchakis and P. Siconolfi for their helpful comments.     

Decentralizing lottery allocations in markets with indivisible commodities

Summary In economies with indivisible commodities, consumers tend to prefer lotteries in commodities. A potential mechanism for satisying these preferences is unrestricted purchasing and selling of lotteries in decentralized markets, as suggested in Prescott and Townsend [Int. Econ. Rev.25, 1–20]. However, this paper shows in several examples that such lottery equilibria do not always exist for economies with finitely many consumers. Other conditions are needed. In the examples, equilibrium and the associated welfare gains are realized if consumptions are bounded or if lotteries are based upon a common sunspot device as defined by Shell [mimeo, 1977] and Cass and Shell [J. Pol. Econ.91, 193–227]. The paper shows that any lottery equilibrium is either a Walrasian equilibrium or a sunspot equilibrium, but there are Walrasian and sunspot equilibria that are not lottery equilibria.This paper is based on Chapter 3 of my doctoral dissertation, written while I was a student at Cornell University. I thank Larry Blume, Yue Yun Chen, David Easley, Aditya Goenka, John Marshall, Bruce Smith, John Wooders and an anonymous referee. I am particularly grateful to Karl Shell and Cheng-Zhong Qin. I thank the Academic Senate at UCSB for financial support.     

Institutions and economic growth in Portugal: a quantitative exploration

This paper presents a broad diagnostic of the level of institutional development in Portugal in the legal, corporate governance and financial systems. A comparative assessment suggests that Portuguese institutions are less developed than their European Union and East Asian counterparts, more developed than Greek institutions and on a level similar to that of Spanish institutions. We use data for a wide cross-section of countries since 1960 and correlate indicators of institutional development with the long-term average growth rate, identifying issues where reform is likely to significantly affect economic growth. We construct three new indices that measure the potential of institutional reform - the impact of reform on growth, the required reform effort and the efficiency of reform index - by taking into consideration the institutional distance between Portugal and the European Union. These indices measure, respectively, which reforms have the most payoff in terms of growth, which are less costly to undertake and which deliver the most growth per required effort. Our results strongly suggest that in a large number of issues, institutional reform may translate into substantially higher rates of economic growth. Of the ten most promising reforms, six are in the legal area, irrespective of which of the indices is considered. Whereas legal reform is promising at the aggregate and the microeconomic levels, in the financial sector aggregate indicators offer the wider scope for productive reform, while in the corporate governance area it is indices at the micro level that hold the most promise. These results support the view that a comprehensive reform effort is likely to deliver higher rates of growth in Portugal, allowing faster real convergence with the rest of the European Union.Received: January 2003, Accepted: February 2004, JEL Classification: O0, O5, K00, K4, G2, G3This paper is based on Firms, Financial Markets and the Law: Institutions and Economic Growth in Portugal, prepared for the conference Desenvolvimento Económico Português no Espaço Europeu: Determinantes e Políticas, organized by the Banco de Portugal. Financial support by the Banco de Portugal, NOVA FORUM and FUNDAÇÃO Para a Ciência e tecnologia and Polti through feder are gratefully acknowledged. Comments from Marcelo Rebelo de Sousa, two anonymous referees and the editor are sincerely appreciated. The usual disclaimer applies.     

Non-existence of recursive equilibria on compact state spaces when markets are incomplete

This paper analyzes one-good exchange economies with two infinitely lived agents and incomplete markets. It is shown that there are no recursive (Markov) equilibria for which borrowing (debt) constraints never bind if the state space of exogenous and endogenous variables is a compact subset of . Moreover, for large enough (but finite) borrowing limits, no recursive equilibrium with compact state space exists. These non-existence results hold for any economy satisfying the following standard assumptions: preferences are additively separable across time and states; the one-period utility function is time- and state-independent and unbounded from below; endowments are bounded and follow a Markov chain with stationary transition matrix; there is some idiosyncratic risk and no aggregate risk.