The Borda rule,Condorcet consistency and Condorcet stability

Summary. The Borda rule is known to be the least vulnerable scoring rule to Condorcet inconsistency, Saari (2000). Such inconsistency occurs when the Condorcet winner (the alternative which is preferred to any other alternative by a simple majority) is not selected by the Borda rule. This note exposes the relationship between the Borda rule and the Condorcet q-majority principle as well as the Condorcet q-majority voting rule. The main result establishes that the Borda rule is Condorcet q-majority consistent when where k is the number of alternatives. The second result establishes that is the minimal degree of majority decisiveness corresponding to the Borda rule under sincere voting. The same majority is required to ensure decisiveness under the Borda rule and to ensure that a q-rule (the generalized q-majority Condorcet rule) is a voting rule. Received: April 8, 2002; revised version: July 17, 2002 Correspondence to:S. Nitzan     

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).     

Schumpeter and the revival of evolutionary economics: an appraisal of the literature

During the last two decades we have seen a revival of interest in the works of Joseph Schumpeter and “evolutionary” ideas in economics more generally. A professional society honouring Schumpeter's name has been founded, and linked to it we have had for more than fifteen years now a professional journal devoted to this stream of thought. However, it has been argued that, despite these developments, the link between Schumpeter's own work and the more recent contributions to evolutionary economics is in fact rather weak. This paper considers this claim. Based on an analysis of Schumpeter's contribution to economics the paper presents an overview and assessment of the more recent literature in this area. It is argued that although there are important differences between Schumpeter's work and some of the more recent contributions, there nevertheless remains a strong common core that clearly distinguishes the evolutionary stream from other approaches (such as, for instance, so-called “new growth theory”). RID="*" ID="*" Many people have contributed to this paper in various ways. Jon Hekland at the Norwegian Research Council started it all by asking me to make an overview of the contribution from “evolutionary economics” to our understanding of contemporary economies. Several people helped me on the way by supplying written material, comments and suggestions, and I am indebted to all of them. Brian Arthur, Stan Metcalfe, Keith Pavitt, Erik Reinert, Paolo Saviotti and Bart Verspagen may be particularly mentioned. A preliminary version was presented at the conference “Industrial R&D and Innovation Policy Learning – Evolutionary Perspectives and New Methods for Impact Assessment” organised by the Norwegian Research Council (“SAKI”) at Leangkollen, Asker, April 18–19.2002. I wish to thank the discussant, Tor Jakob Klette, and the participants at the conference for useful feedback. Moreover I have benefited from comments and suggestions from the editors and referees of this journal. The final responsibility is mine, however. Economic support from the Norwegian Research Council (“SAKI”) is gratefully acknowledged.     

Probability of survival in a random exchange economy with dependent agents

Summary. In this paper I analyze the general equilibrium in a random Walrasian economy. Dependence among agents is introduced in the form of dependency neighborhoods. Under the uncertainty, an agent may fail to survive due to a meager endowment in a particular state (direct effect), as well as due to unfavorable equilibrium price system at which the value of the endowment falls short of the minimum needed for survival (indirect terms-of-trade effect). To illustrate the main result I compute the stochastic limit of equilibrium price and probability of survival of an agent in a large Cobb-Douglas economy. Received June 7, 2001; revised version: January 7, 2002 RID="*" ID="*" I would like to thank Mukul Majumdar and Thomas DiCiccio for helpful discussion and an anonymous referee for valuable comments and suggestions.     

Candidate stability and nonbinary social choice

Summary. The requirement that a voting procedure be immune to the strategic withdrawal of a candidate for election can be formalized in different ways. Dutta, Jackson, and Le Breton (Econometrica, 2001) have recently shown that two formalizations of this candidate stability property are incompatible with some other desirable properties of voting procedures. This article shows that Grether and Plott's nonbinary generalization of Arrow's Theorem can be used to provide simple proofs of two of their impossibility theorems. Received: August 15, 2001; revised version: March 11, 2002 RID="*" ID="*" Parts of this article were previously circulated in somewhat different form in a working paper with the same title by the second author. We are grateful to Michel Le Breton and an anonymous referee for their comments. Correspondence to:J.A. Weymark     

Is capital a collusion device?

Summary. We examine how irreversible capital reduces the possibility of a duopoly to sustain implicit collusion by grim strategies, when the product is homogenous and firms compete in quantities. Compared with the case of reversible capital, there are two countervailing effects: Deviation from an existing collusion is less attractive, because capital once installed causes costs forever. But the punishment will also be less severe due to the high capacity the deviating firm can build before punishment starts. The last effect dominates, meaning that the commitment value of capital is negative for all firms. If capital is irreversible, collusion breaks down for realistic magnitudes of interest rates. Received: April 30, 1999; revised version: November 30, 2001     

Delegation and polarization of platforms in political competition

Summary. We consider a model of political competition among two ideological parties who are uncertain about the distribution of voters. The distinguishing feature of the model is that parties can delegate electoral decisions to candidates by nomination. It is shown that if the credible platform commitments of the candidates is feasible, then at least one of the parties nominates in equilibrium to a candidate who has an ideology that is more radical than the delegating party's ideology. In a variety of circumstances, this, in turn, yields a polarization of equilibrium policy choices of the candidates. It is thus argued formally here that strategic nomination of the candidates may well be one of the major reasons behind the well documented observation that the platforms associated with the political parties in two-party democracies are often surprisingly polarized. Received: January 10, 2002; revised version: May 8, 2002 RID="*" ID="*" We thank Alberto Alesina, Levent Ko?kesen, Antonio Merlo, Ronny Razin, Vijay Krishna, Alessandro Lizzeri, and seminar participants at Alicante, Columbia, Copenhagen, and NYU for helpful comments. We also thank an anonymous referee for its useful suggestions. A good fraction of this research was conducted while Ok was a visitor in the Department of Economics at University of Alicante; he thanks for the kind hospitality of this institution. We gratefully acknowledge the financial support from the Spanish Ministry of Education through grant CICYT BEC2001-0535 (Faulí-Oller) and BEC2001-0980 (Ortu?o-Ortín). Correspondence to:I. Ortu?o-Ortin     

Capital asset pricing models with default risk: Theory and application in insurance

The Capital Asset Pricing Model has been used frequently to derive a fair price of insurance. But the use of this model overestimates insurance premiums because it does not account for the insolvency risk of insurers. This paper examines how the insurance price should be fairly adjusted when insurers' default risk is considered. It develops a model which shows that fair insurance premiums are lower when insurance firms have a positive probability of being insolvent. Using data of property liability insurers during the period from 1943–99, the paper further estimates the effects of the insolvency risk on insurers' underwriting profit rate. It shows that the incorporation of the default risk of insurers in the model, by significantly reducing the required price for insurance, would lead to lower profit potentials. Some writers argue that including the insolvency risk when calculating insurance premiums is not so necessary because of the existence of states' guaranty insurance funds which protect consumers. However, as shown in the paper, these funds have provided inadequate protection to consumers. Therefore, because of the increase in the number of insolvencies in recent years, and because of the limited coverage provided by states' guaranty funds, it seems that considering the insolvency risk in insurance pricing has become very necessary.     

Budget deficits and interest rates in Germany

This study uses the basic tools of cointegration to determine whether there exists a long-term relationship between budget deficits and nominal interest rates in Germany. Maximum eigenvalue, trace, and likelihood ratio tests all affirm that there does apparently exist a long-term relationship between the budget deficit and the nominal interest rate. Accordingly, regression studies and formal causality tests have a reasonable basis for investigating whether budget deficits lead to higher interest rates in Germany.     

A new proof of the maximum principle

Summary. We offer a new proof of the maximum principle, by using the envelope theorem that is frequently used in the standard microeconomic theory. Received: April 11, 2002; revised version: June 26, 2002 Correspondence to: K. Shimomura