Pareto efficient insurance contracts when the insurer's cost function is discontinuous

Summary. We consider the problem of efficient insurance contracts when the cost structure includes a fixed cost per claim. We prove existence of efficient insurance contracts and that the indemnity function in such contracts is non-decreasing in the damage. We further show that either there is no insurance, or the indemnity is positive for all losses, or efficient insurance contracts have a unique jump. We study variants of the model and provide a generalization to the case of non expected utilities. Our results are then applied to Townsend's model of deterministic auditing. Received: November 8, 2000; revised version: March 12, 2002 RID="*" ID="*" We are grateful to F. Salanié for pointing out an error in the previous version of the paper and for suggesting Proposition 6 to us. Correspondence to: R.-A. Dana     

When vagueness induces indirect competition: strategic incompleteness of contracts

Summary. A class of employment contracts entailing production targets and consequent rewards is studied. In a nondiscriminatory environment, a principal hiring many agents faces the problem of writing a common contract which induces the highest possible effort from each one of his agents. While a very high target may get the best out of highly skilled agents, low skilled ones tend to shirk. On the other hand, although low targets make every agent put positive effort, there are efficiency losses from the high skilled agents. Also, in such environments the principal often has better information regarding the skills of all his agents than what each agent has regarding the rest of the agents at work. We show that if skills of agents are sufficiently close, the informed principal earns strictly higher profits by offering incomplete contracts as against being specific, as incomplete contracts reduce flow of information and induce indirect competition amongst agents. Received: May 19, 2000; revised version: August 28, 2001     

Firm-provided training and temporary contracts

This paper analyses the relationship between workers type of contract and the probability of receiving firm-provided training. In particular, we raise the following question: do workers with temporary contracts face the same probability of receiving training as workers with permanent contracts, once we account for the fact that both types of workers have different probabilities of being employed in a firm providing training? The results from our empirical analysis using data from the Spanish labour market suggest that workers with temporary contracts not only are less likely to be employed in training firms but, once they are in those firms, they also have a lower probability of being chosen to participate in firm-provided training activities.JEL Classification: J23, M53Authors gratefully acknowledge financial support from Universidad de Alcalá under research project La relación entre temporalidad y formación en la empresa: un análisis comparativo entre los países de la Unión Europea (award no. UAH2002/022) and from the Spanish Ministry of Science and Technology under research project Observatorio del mercado de trabajo (SEC2001-0061). We have also benefited from our participation in the research project Estudio sobre la situación actual de la contratación temporal e indefinida en España financed by the Spanish Employment Office (INEM). We are grateful to participants in the XXVII Simposio de Análisis Económico (Salamanca), V Jornadas de Economía Laboral (Reus-Tarragona), and a seminar in the Istituto de Ricerca Sociale (Milano), and to one anonymous referee. The usual disclaimer applies.     

Approximation by finite horizons of the undiscounted one-sector growth model

Summary. In this paper I give a method for finding long-run-average policies in the undiscounted economic growth problem using approximations by finite horizons. Required hypothesis is the strong interiority of T-horizon solutions. Received: March 25, 1996; revised version: July 29, 1997     

Risk aversion and incentive compatibility with ex post information asymmetry

Summary. The paper extends Diamond's (1984) analysis of financial contracting with information asymmetry ex post and endogenous “bankruptcy penalties” to allow for risk aversion of the borrower. The optimality of debt contracts, which Diamond obtained for the case of risk neutrality, is shown to be nonrobust to the introduction of risk aversion. This contrasts with the costly state verification literature, in which debt contracts are optimal for risk averse as well as risk neutral borrowers. Received: December 7, 1998; revised version: June 9, 1999     

Non-commitment and savings in dynamic risk-sharing contracts

Summary. We characterize the solution to a dynamic model of risk sharing under non-commitment when saving is possible. Savings can play two important roles. First savings can be used to smooth aggregate consumption across different periods. Second, when savings are observable, they can act as a collateral that can be seized in the case of default. This relaxes the non-commitment constraint. When the aggregate income is fixed or when one of the agent is risk neutral, the allocation tends to first-best consumption. When one of the agent is risk neutral, this convergence occurs in an expected finite number of periods.Received: 17 March 2004, Revised: 8 March 2005, JEL Classification Numbers: C7, D9.Michel Poitevin: Correspondence toWe gratefully acknowledge financial support from F.C.A.R., C.R.S.H. and C.I.R.A.N.O.     

Indivisible labor implies chaos

Summary. We study a simple infinite horizon model with indivisible labor. We characterize the optimal plans under the assumptions that and that , where R is the gross interest rate and is the discount factor. We show that under those assumptions, optimal plans are almost always asymptotically nonperiodic unless initial wealth is excessively small or large. Received: May 25, 1999; revised version: June 24, 1999     

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     

Recursive structure and equilibria in games with private monitoring

Summary. In each stage of a repeated game with private monitoring, the players receive payoffs and privately observe signals which depend on the players' actions and the state of world. I show that, contrary to a widely held belief, such games admit a recursive structure. More precisely, I construct a representation of the original sequential problem as a sequence of static games with incomplete information. This establishes the ground for a characterization of strategies and, hence, of behavior in interactive-decision settings where private information is present. Finally, the representation is used to give a recursive characterization of the equilibrium payoff set, by means of a multi-player generalization of dynamic programming. Received: February 11, 2002; revised version: July 22, 2002 RID="*" ID="*" I am very grateful to In-Koo Cho, Larry Epstein, Denis Gromb, Stephen Morris, Paolo Siconolfi, Lones Smith and Max Stinchcombe for several insights and suggestions. A referee's comments helped improving the exposition. Finally, I wish to thank the participants to the seminars at MEDS, NYU, Columbia University, Caltech, UCLA, University of Rochester, University of Texas-Austin, Northwestern Summer Microeconomics Conference 98, Summer in Tel Aviv 98, and NASM98.     

A simple proof of Ekeland and Scheinkman's result on the necessity of a transversality condition

Summary. Ekeland and Scheinkman (1986) prove the necessity of a standard transversality condition under certain technical conditions. Their result is one of the most powerful on the necessity of a transversality condition currently available in the literature, and their proof involves numerous estimations and relies on Ekeland's variational principle and Fatou's lemma. This note relaxes some of their assumptions and provides a simple proof that uses neither Ekeland's principle nor a convergence result like Fatou's lemma. Received: April 24, 1998; revised version: September 8, 1998     

The convergence of least squares learning in stochastic temporary equilibrium models

Summary. This paper provides conditions for the almost sure convergence of the least squares learning rule in a stochastic temporary equilibrium model, where regressions are performed on the past values of the endogenous state variable. In contrast to earlier studies, (Evans and Honkapohja, 1998; Marcent and Sargent, 1989), which were local analyses, the dynamics are studied from a global viewpoint, which allows one to obtain an almost sure convergence result without employing projection facilities. Received: April 7, 2001; revised version: September 5, 2001     

Optimal contracts in a dynamic costly state verification model

Summary. This paper describes optimal contracts in a dynamic costly state verification model with stochastic monitoring. An agent operates a risky project on behalf of a principal who can observe the projects revenues at a cost. We show that an optimal contract exists such that, at any history, either the principal claims the projects entire revenues or promises to claim nothing in the future. In particular, the agents expected income rises with time. Moreover, except in at most one period, the principal claims all revenues when audit occurs. We provide conditions under which all optimal contracts satisfy these properties.Received: 4 February 2004, Revised: 4 June 2004, JEL Classification Numbers: D8, C7. Correspondence to: Cyril MonnetWe wish to thank Patrick Bolton, Vitor Gaspar, Mark Guzman, Martin Hellwig, Narayana Kocherlakota, Thorsten Koeppl, Albert Marcet, Benny Moldovanu, Ernst-Ludwig von Thadden and seminar participants at the University of Mannheim, the University of Minnesota, the Society for Economics Dynamics Meetings in New York and the Society for the Advancement in Economic Theory in Rhodos for helpful comments and discussions. The views expressed herein are those of the authors and may not reflect the views of the European Central Bank, the Eurosystem, the Federal Reserve Bank of Dallas or the Federal Reserve System.     

Capacity constrained firms in (labor) markets with adverse selection

Summary. We discuss a competitive (labor) market where firms face capacity constraints and individuals differ according to their productivity. Firms offer two-dimensional contracts like wage and task level. Then workers choose firms and contracts. Workers might be rationed if the number of applicants exceeds the capacity of the firm. We show that under reasonable assumptions on the distribution of capacity an equilibrium in pure strategies (by the firms) exists. This result stands in contrast to the case of unlimited capacity. The utility level is uniquely determined in equilibrium. No rationing occurs in equilibrium, but it does off the equilibrium path. Received: December 29, 1999; revised version: November 30, 2000     

Aggregate fluctuations, financial constraints and risk sharing

Summary. Private information and costly state verification often result in credit rationing in models with smooth investment, affecting both loan size and total investment. The optimal contract is derived in a dynamic stochastic growth model with capital for two types of models: one with symmetric information and the other with asymmetric information and costly state verification. When all information is observed costlessly, the equilibrium optimal contract provides complete insurance to risk-averse savers against aggregate fluctuations. When information is asymmetric and there is costly state verification, the equilibrium optimal contract provides only partial insurance against aggregate shocks. The extent of insurance is measured by the marginal rate of transformation of consumption between borrowers and lenders which is closely linked to the user cost of capital. The deadweight monitoring costs create a wedge between a borrower's cost of capital and a lender's stochastic discount factor, with two results: (i) fluctuations in the user cost of capital provides a mechanism by which aggregate shocks can be␣propagated; (ii) the distribution of capital's share of output among borrowers, lenders, and monitoring costs varies even if capital's share is constant. Capital market frictions not only amplify aggregate fluctuations but also generate cross-sectional fluctuations that may not be observable in aggregate data. Received: November 17, 1997; revised version: April 20, 1998     

Exclusive contracts and the institution of bankruptcy

Summary. The paper studies the institution of bankruptcy when exclusive contracts cannot be enforced ex ante, e.g., a bank cannot monitor whether the borrower enters into contracts with other creditors. The institution of bankruptcy enables the bank to enforce its claim to any funds that the borrower has above a fixed bankruptcy protection level. Bankruptcy improves on non-exclusive contractual relationships but is not a perfect substitute for exclusivity ex ante. We characterize the effect of bankruptcy provisions on the equilibrium contracts which borrowers use to raise financing.Received: 6 December 2004, Revised: 15 January 2005, JEL Classification Numbers: D82, G33, K29. Correspondence to: Adriano A. RampiniWe thank the seminar participants at Carnegie Mellon, Columbia, Illinois, Minnesota, Northwestern, Pompeu Fabra, Stanford, the CEPR European Summer Symposium in Financial Markets, the NBER Corporate Finance Program Meeting, the SED Annual Meeting, the Texas Finance Festival, the WFA Annual Conference, the Workshop on Information, Financial Markets and the Business Cycle in Rome and the Federal Reserve Bank of Richmond and in particular Marco Bassetto, Alberto Bennardo, Philip Bond, Peter DeMarzo, Andrea Eisfeldt, Michael Fishman, Zsuzsanna Fluck, Denis Gromb, Oliver Hart, Eugene Kandel, John Kareken, Narayana Kocherlakota, Stephan Krasa, Arvind Krishnamurthy, Deborah Lucas, Thomas Noe, Onur Ozgur, Mitchell Petersen, Artur Raviv, Anne Villamil, Jeffrey Zwiebel, and an anonymous referee for helpful comments, and Nisan Langberg for research assistance. Bisin gratefully acknowledges the research support of the National Science Foundation under Grant No. SES-9818844 and the C.V. Starr Center for Applied Economics.     

Saving behavior in stationary equilibrium with random discounting

Summary. We study the implications of random discount rates of future generations for saving behavior and capital holdings in a steady state competitive equilibrium with heterogeneous population. A well-known difficulty in deterministic economies with heterogeneous households is that in steady state only the most patient households hold capital. In this paper we state conditions under which this random discounting is sufficient for households other than the most patient ones to save. We thus provide a simple and natural way of overcoming the aforementioned difficulty. Received: December 28, 1998; revised version: May 19, 1999     

The set of sunspot equilibria in economies with incomplete financial markets: variable asset prices

Summary. I consider the set of equilibria of two-period economies with S extrinsic states of nature in the second period and I assets with linearly independent nominal payoffs. Asset prices are variable. If the number of agents is greater than (S-I), the payoff matrix is in general position and S 2I, the set of equilibrium allocations generically (in utility function space) contains a smooth manifold of dimension (S-1). Moreover, the map from states o f nature to equilibrium allocations (restricted to this manifold) is one-to-one at each equilibrium. Received: February 23, 1998; revised version: June 1, 2000     

Nominal wage contracts, labor adjustment costs and the business cycle

Previous work of monetary dynamic stochastic general equilibrium models with nominal rigidity a la Taylor, particularly the Cho–Cooley model, was abandoned in favor of the New-Keynesian analysis due to the model's failure to deliver business cycle statistics that match the U.S. economy along some key dimensions. In this paper, we take a step in revitalizing the Cho–Cooley avenue of research. We add empirically plausible labor adjustment costs into a model with nominal wage rigidity and find that with labor adjustment costs our model is able to overcome some of the shortcomings otherwise present in the Cho–Cooley framework, specifically high standard deviations of real variables and a countercyclical productivity.     

An experimental study of decisions in dynamic optimization problems

Summary. We study decisions of subjects who are given an incentive to solve dynamic optimization problems with the structure of a single-agent, one-sector, closed economy macroeconomic model. The decision task involves a sequence of choices of consumption and investment levels. Treatment variables consist of the initial endowment of capital stock, the production technology available to the economy, and the method of creating the structure of an infinite-horizon model. The study includes and contrasts data from both American and Japanese participants. We find that whether over- or underinvestment relative to the optimum occurs depends on the production technology, but not on the initial endowment of capital stock, nor the subject pool used, nor the method of implementing the infinite horizon. Sudden episodes of maximal consumption called binges, which are always suboptimal, are widely observed. Received: December 7, 1998; revised version: March 12, 1999     

Credit contracting and bidding under wealth constraints

Summary. We model credit contracting and bidding in a first-price sealed-bid auction when bidder valuation and wealth are private information. An efficient separating equilibrium exists only if the wealth levels of both bidder types are sufficiently different. If not, high-valuation bidders signal by borrowing more and using less of their wealth – this is inefficient as wealth is a cheaper source of funds. An increase in the amount of borrowing required to signal does not necessarily decrease seller expected revenue. In contrast to separating equilibria, high-valuation bidders adopt pure strategy bids in pooling equilibria. Conditions are identified under which the lower bound on winning bids is higher in pooling than separating equilibria. Received: January 22, 2001; revised version: August 28, 2001