Medical insurance with rank-dependent utility

Summary. A well-known result in the medical insurance literature is that zero co-insurance is never second-best for insurance contracts subject to moral hazard. We replace the usual expected utility assumption with a version of the rank-dependent utility (RDU) model that has greater experimental support. When consumers exhibit such preferences, we show that zero co-insurance may in fact be optimal, especially for low-risk consumers. Indeed, it is even possible that the first-best and second-best contracts are identical. In this case, there is no “market failure”, despite the informational asymmetry. We argue that these RDU results are in better accord with the empirical evidence from US health insurance markets. Received: February 26, 2001; revised version: October 4, 2002 RID="*" ID="*"The authors would particularly like to thank Simon Grant, John Quiggin, Peter Wakker and an anonymous referee for valuable comments and suggestions on earlier drafts. The paper has also benefitted from the input of seminar audiences at The Australian National University, University of Auckland, University of Melbourne and University of Sydney. Ryan also gratefully acknowledges the financial support of the ARC, through Grant number A000000055. Correspondence to:R. Vaithianathan     

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     

Alternating-offer bargaining over menus under incomplete information

Summary. This paper considers bargaining with one-sided private information and alternating offers where an agreement specifies both a transfer and an additional (sorting) variable. Moreover, both sides can propose menus. We show that for a subset of parameters the alternating-offer game has a unique equilibrium where efficient contracts are implemented in the first period. This stands in sharp contrast to the benchmarks of contract theory, where typically only the uninformed side proposes, and bargaining theory, where typically the agreement only specifies a transfer. Received: September 10, 2001; revised version: March 25, 2002 RID="*" ID="*" I benefitted from discussions with Benny Moldovanu, Holger Müller, and Roland Strausz, and from comments made by an anonymous referee.     

Corporate insurance with optimal financial contracting

Summary. This paper attemps to rationalize the use of insurance covenants in financial contracts, and shows how external financing generates a demand for insurance by risk-neutral entrepreneurs. In our model, the entrepreneur needs external financing for a risky project that can be affected by an accident during its realization. Accident losses and final returns are private information to the firm, but they can be evaluated by two costly auditing technologies. We derive the optimal financial contract: it is a bundle of a standard debt contract and an insurance contract with franchise, trading off bankruptcy costs vs auditing costs. We then analyze how this optimal contract can be achieved by decentralized trading on competitive markets when insurance and credit activities are exogenously separated. With additive risks, the insurance contract involves full coverage above a straight deductible. We interpret this result by showing how our results imply induced risk aversion for risk-neutral firms. Received: December 14, 1998; revised version: August 11, 1999     

Optimal design of pension funds: a mission impossible?

Summary. Nowadays many employers offer their employees the possibility of an insurance against too large losses in income when retiring or becoming disabled. This paper models the optimization problem of the employer when setting up such a so-called pension fund. Not surprisingly, it turns out that the optimal solution depends on the premium the employees are willing to pay at most for such an insurance. Since this is private information for an employee and hence not known to the employer, he needs to collect information regarding these maximum premiums. It is shown that if employees' characteristics only differ in the maximum premium they are willing to pay, the employer is unable to perfectly inform himself on these maximum premiums, i.e. he cannot create the right incentives for his employees to reveal their maximum premiums truthfully. Received: March 20, 2000; revised version: March 11, 2002 RID="*" ID="*" The authors acknowledge the helpful comments and suggestions of an anonymous referee. The research of J. Suijs is made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences (KNAW). Correspondence to: J. Suijs     

A common trends model of UK core inflation

In this paper the long-run trend in RPI inflation (core inflation) for the UK over the 1961–1997 period is estimated within the framework of a multivariate common trends model which extends the bivariate VAR approach of Quah and Vahey (1995). In this context core inflation is directly linked to money and wage growth and interpreted as the long-run forecast of inflation from a small-scale, cointegrated macroeconomic system. First version received: September 1999/Final version received: October 2001 RID="*" ID="*"  We thank two anonymous referees for many helpful comments and suggestions. Work on this paper was partially conducted when C. Morana was at Heriot-Watt University.     

A generalized additive Tobit model

This paper proposes a semi-parametric approach to estimation in Tobit models. A generalized additive Tobit model of residential local long distance (intra-LATA) telephone demand is estimated on a cross-section of residential telephone consumers across twenty-eight states. While past studies of telecommunications demand have used fully parametric models, the model presented here is non-parametric in two dimensions: first no distributional assumption is made for the error distribution, and second, the demand equation is non-parametric with respect to price. We find that the elasticity of demand is substantially lower (in absolute value) that found in previous studies for a 40% cut in tariffs. First version received: July 2000/Final version received: March 2001 RID="*" ID="*"  I thank the referee and Associate Editor for suggestions which improved the paper. The views expressed here are of the author and not Analysis Group | Economics.     

Insurance with Frequency Trading: A Dynamic Analysis of Efficient Insurance Markets

This paper extends existing insurance results on the type of insurance contracts needed for insurance market efficiency to a dynamic setting. It introduces continuously open markets that allow for more efficient asset allocation. It also estimates the role of preferences and endowments in the classification of risks, which is done primarily in terms of the actuarial properties of the underlying risk process. The paper further extends insurability to include correlated and catastrophic events. Under these very general conditions the paper defines a condition that determines whether a small number of standard insurance contracts (together with aggregate assets) suffice to complete markets or one needs to introduce such assets as mutual insurance. Journal of Economic Literature Classification Numbers: D81, D99, G11.     

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     

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     

On the geography of conventions

Summary. We study an evolutionary model in which heterogenous boundedly rational agents interact locally in order to play a coordination game. Agents differ in their mobility with mobile agents being able to relocate within a country. We find that mobile agents enjoy a higher payoff and always benefit from increased mobility, while immobile agents benefit from increased mobility at low levels of mobility only. This wedge in payoffs weakly increases as mobility increases. Some extensions are discussed. Received: January 10, 2001; revised version: December 4, 2002 RID="*" ID="*" We thank, without implicating in any way, George Mailath for helpful discussions. Some of the ideas in this paper were developed during the V Conference of the Society for the Advancement of Economic Theory in Ischia, Italy. The NSF provided financial support. Correspondence to: T. Temzelides     

Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment

Summary. We prove existence of a competitive equilibrium in a version of a Ramsey (one sector) model in which agents are heterogeneous and gross investment is constrained to be non negative. We do so by converting the infinite-dimensional fixed point problem stated in terms of prices and commodities into a finite-dimensional Negishi problem involving individual weights in a social value function. This method allows us to obtain detailed results concerning the properties of competitive equilibria. Because of the simplicity of the techniques utilized our approach is amenable to be adapted by practitioners in analogous problems often studied in macroeconomics. Received: September 13, 2001; revised version: December 9, 2002 RID="*" ID="*" We are grateful to Tapan Mitra for pointing out errors as well as making very valuable suggestions. Thanks are due to Raouf Boucekkine and Jorge Duran for additional helpful discussions. We also thank an anonymous referee for his/her helpful comments. The second author acknowledges the financial support of the Belgian Ministry of Scientific Research (Grant ARC 99/04-235 “Growth and incentive design”) and of the Belgian Federal Goverment (Grant PAI P5/10, “Equilibrium theory and optimization for public policy and industry regulation”). Correspondence to: C. Le Van     

The sale of small firms: a multidimensional analysis

Summary. This paper endogeneizes the security voting structure in an auction mechanism used to sell a small firm. The design of security voting structure allows the seller to choose between two objectives which are not mutually consistent. If the seller wants to maximize his revenue, he should retain some shares to benefit from the future dividends generated by the acquirer. At the opposite, if he wants to sell his firm to the most efficient candidate, he should sell all the shares. Received: July 4, 2001; revised version: October 31, 2002 RID="*" ID="*" The paper has benefited from a number of comments from the anonymous referees. Correspondence to: C. At     

A strategy-proofness characterization of majority rule

Summary. A feasible alternative x is a strong Condorcet winner if for every other feasible alternative y there is some majority coalition that prefers x to y. Let (resp., denote the set of all profiles of linear (resp., merely asymmetric) individual preference relations for which a strong Condorcet winner exists. Majority rule is the only non-dictatorial and strategy-proof social choice rule with domain , and majority rule is the only strategy-proof rule with domain . Received: August 29, 2000; revised version: November 13, 2002 RID="*" ID="*"We are grateful to Wulf Gaertner and our two referees for insightful comments on a previous draft. Correspondence to: D. E. Campbell     

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     

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.     

A two-sector overlapping generations model with heterogeneous capital

Summary. This paper characterizes the existence and stability properties of steady state solutions as well as the nature of transition paths of a two-sector growth model with heterogeneous capital. It compares the properties of a Cobb-Douglas–Leontief economy with heterogeneous capital with the properties of the same economy with homogeneous capital. The model with heterogeneous capital reveals a set of characteristics different to those of the model with homogeneous capital. These include the saddle-path stability of the non-trivial steady state as well as the possibility of overshooting and in contrast to the homogeneous capital case, the possibility of damped oscillations along the transition path for realistic parameter values. Received: September 21, 2001; revised version: November 21, 2002 RID="*" ID="*" We thank Costas Azariadis, and Laurie Conway for helpful comments on a previous draft. The paper has substantially benefited from the feedback of an anonymous referee. Correspondence to: R. Wendner     

Double Moral Hazard,Monitoring, and the Nature of Contracts

generalized double-sided moral-hazard model, with risk-averse parties who mutually monitor each other (to get a reasonable idea of outcome/effort). The model considers trade-off between monitoring costs and moral hazard costs, which are endogenously determined by the extent of monitoring. Using this model, we formally prove a generalized version of Coase's conjecture – that the optimal contract minimizes the agency and risk costs. We then show how varying assumptions about the feasibility or cost of monitoring of the outcome or the worker's effort lead to different contracts being optimal. The analysis is then used to explain the nature of contracts observed in practice under many different situations. We will give an explanation as to why industrial workers typically work under wage contracts, while share contracts are common in agriculture and will explain why profit sharing is more common for senior managers than for the production workers. Received September 19, 2000; revised version received October 30, 1997     

On extensive form implementation of contracts in differential information economies

Summary. In the context of differential information economies, with and without free disposal, we consider the concepts of Radner equilibrium, rational expectations equilibrium, private core, weak fine core and weak fine value. We look into the possible implementation of these concepts as perfect Bayesian or sequential equilibria of noncooperative dynamic formulations. We construct relevant game trees which indicate the sequence of decisions and the information sets, and explain the rules for calculating ex ante expected payoffs. The possibility of implementing an allocation is related to whether or not it is incentive compatible. Implementation through an exogenous third party or an endogenous intermediary is also considered. Received: November 19, 2001; revised version: April 17, 2002 RID="*" ID="*" This paper comes out of a visit by Nicholas Yannelis to City University, London, in December 2000. We are grateful to Dr A. Hadjiprocopis for his invaluable help with the implementation of Latex in a Unix environment. We also thank Leon Koutsougeras and a referee for several, helpful comments. Correspondence to: N.C. Yannelis