A costly state verification model with diversity of opinions

Summary. In simple models of borrowing and lending with ex-post asymmetric information, Gale and Hellwig (1985) and Williamson (1986) have shown that optimal debt contracts are simple debt contracts where borrowers repay a fixed interest rate whenever possible and lenders seize all the profit when borrowers default. In this note, we depart from their works by assuming that borrowers and lenders have heterogeneous beliefs, and show that simple debt contracts do not necessarily survive as optimal contracts.JEL Classification Numbers: G3, D8.     

Dynamic costly state verification

Summary. I study a model of dynamic risk sharing with costly state verification (CSV). In the model, a risk neutral agent enters an infinitely repeated relationship with a risk averse agent. In each period, the risk averse agent receives a random income which is observed only by himself, unless the risk neutral agent engages in costly monitoring. I provide a set of characterizations for the optimal contract, and I show that CSV has interesting effects on the long run distribution of the agents expected utilities.Received: 19 February 2003, Revised: 11 February 2004, JEL Classification Numbers: D8.This research was initially joint work with Bruce Smith. I thank Bruce for the inspiration. I thank Fernando Alvarez, Narayana Kocherlakota, Steve Spear, and an anonymous referee for helpful comments. I also thank seminar participants at Carnegie Mellon University, Federal Reserve Banks of Minneapolis, Federal Reserve bank of Richmond, Duke University, SUNY Buffalo, University of Rochester, University of Pittsburgh, University of Western Ontario, the 1998 Econometric Society winter meeting, the 1999 SED meeting, and the 1999 SITE workshop at Stanford University for discussions.     

Costly state verification and debt contracts: a critical resume

This paper presents a critical review of the Costly State Verification framework starting from the basic model by Gale and Hellwig [Review of Economic Studies 52 (1985) 647] and further examining the most recent developments. It aims both at discussing the optimality of debt contract in alternative contexts and at offering a reply to the critiques usually moved to this approach within a unified framework.     

Optimal audit policies with correlated types

Summary. We propose a version of Townsends [17] model of costly audits where the agents types are correlated. Audits are used because agents have a limited ability to bear risk so that the Full Surplus Extraction (FSE) scheme á la Crémer and McLean [5,6] and McAfee and Reny [13] are suboptimal. It is shown that Townsends result is a special case of our model when agent types are uncorrelated. The performed numerical simulation of the model using two agents and two types offers interesting insights into what we call the Townsend Ridge. Indeed, the optimal contract which specifies wages to be paid and the audit strategy are remarkably different from one side of the ridge to the next. The observed discontinuity at the ridge reflects a discreet change from a single to a dual audit policy.Received: 11 November 2002, Revised: 10 September 2003JEL Classification Numbers: C63, D82.Correspondence to: M. Martin BoyerWe wish to thank seminar participants at the CEA-Toronto, SCSE-Montréal and WCES-Seattle meetings for discussions and comments on an earlier version of the paper, as well as an anonymous referee for this journal. This paper was financially supported by an Emerging Scholar grant from the American Compensation Association, and by the Fonds FCAR-Québec. The continuing financial support of CIRANO is also appreciated. We remain responsible for any error.     

Complementarities and costly investment in a growth model

We develop a one-sector growth model whose key aspect is the combination of the assumptions of internal costly investment in capital and complementarities between capital goods in the production function. Despite the nonlinearity generated by these assumptions, the model delivers a single equilibrium.      

Debt contracts with ex-ante and ex-post asymmetric information: an example

Summary. We consider a simple model of lending and borrowing combining two informational problems: adverse selection and costly state verification. Our analysis highlights the interaction between these two informational problems. We notably show that the higher the monitoring cost, the less discriminating the optimal menu of contracts is.Received: 24 September 2004, Revised: 5 April 2005, JEL Classification Numbers: C7, D8, G3.L. Renou: Correspondence toWe thank Anne Villamil for insightful comments.     

Dynamic labor contracts with temporary layoffs and permanent separations

Summary. We study the implications of optimal dynamic contracts in private information environments for fluctuations in effort and employment across time and productivity states. To this end, we incorporate temporary layoffs and permanent separations as well as on-the-job effort variations into a dynamic model of moral hazard. We consider two different “commitment” environments. In a “full commitment” environment, although the firm can temporarily lay a worker off, neither party can dissolve the contractual relationship once it has been initiated. On the other hand, in a “limited commitment” environment, both parties can dissolve the relationship at the beginning of any period in order to pursue an outside option. We use our model to study the implications of optimal contracts for incentives, employment histories, layoffs and separations across full information, full commitment and limited commitment settings. We compute solutions to the relevant principal-agent problems, endogenously determining the set of states in which separations occur and the domain of the firm's value function, as well as the value function itself. Received: February 28, 2000; revised version: January 21, 2001     

Bounding the benefits of stochastic auditing: The case of risk-neutral agents

Summary. In the context of a costly-state-verification model with a risk-neutral agent having limited liability, it has been postulated that allowing stochastic auditing reduces the asymmetric information problem to a trivial one: i.e., the first best can be approached arbitrarily closely with feasible contracts. This paper proves the postulate to be false: the surplus from feasible contracts is bounded strictly below the first-best surplus level. The bound is straightforward to compute in examples. The paper thus removes a justification for the restriction to deterministic auditing commonly made in the literature. Received: July 18, 1997; revised version: February 23, 1998     

Inequalities and fluctuations in a dynamic general equilibrium model

   Summary. In the present paper a tractable two-sector neo-classical growth model with heterogeneous agents is considered. The local dynamic properties of the equilibrium path are analyzed in relation with the underlying characteristics of the economy. In particular, the existence of fluctuations is related to the degree of heterogeneity in labor and in capital endowments. When applied to international trade theory, the analysis shows that free trade may distabilize a world economy that is originally stable under the regime of autarky. Received: December 28, 1998; revised version: October 29, 1999     

Demographic processes in a model of innovation diffusion with dynamic market

In this paper we study a binomial innovation diffusion model for a variable size market by modelling the demographic process of entrance-exit from each market compartment. We examine from a theoretical point of view the effect of the simultaneous presence of economic and demographic parameters under the exponential market growth hypothesis, by presenting some general results on the adoptions and sales time path. We also enlighten the relevance of considering these variables in relative terms and show how, in presence of a dynamic, the diffusion process never saturates the market. Finally, we test our model on a data set for cellular phones market in different countries.     

Market and underground activities in a two-sector dynamic equilibrium model

Summary. In this paper a two sector dynamic general equilibrium model is developed in order to evaluate the implications of the underground economy from a business cycle perspective. There are three main results. First, introducing an underground sector improves the fit of the model to the data, especially along several important labor market dimensions. Second, the model produces substantial internal propagation of temporary shocks. Third, it is shown that underground activities offer risk sharing opportunities by allowing households to smooth income through a proper labor allocation between the two sectors.Received: 17 June 2002, Revised: 25 April 2003, JEL Classification Numbers: E320, E260, J22, H200.We have benefited from the comments and suggestions of John Donaldson. We would also like to thank Paolo Siconolfi, Jean Pierre Danthine, Fausto Gozzi, Edmund Phelps, Gustavo Piga, Domenico Tosato, and the participants in the seminars at various universities, David Giles and Stefano Pisani for providing useful information on the underground data, Francesca Caponi for the comments and the information concerning the legal and fiscal aspects involved in the calibration, and Glenn Williams for the research assistance. Finally, we thank two anonymous referees for helpful comments on this and on earlier versions of the paper. Chiarini acknowledges financial support from the Ateneo Research fund of the University of Rome, La Sapienza, Dinamiche dell'integrazione europea e scelta di politica economica. All errors are ours. Correspondence to: F. Busato     

Stochastic convexity in dynamic programming

Summary. This paper explores sufficient conditions for a continuous stationary Markov optimal policy and a concave value function in stochastic dynamic programming problems. Also, the paper addresses conditions needed for the differentiability of the value function. The paper uses conditions such as first order stochastic dominance, second order stochastic dominance and concave stochastic dominance that are widely applied in economics. Received: February 23, 2001; revised version: May 19, 2002 RID="*" ID="*" I am deeply indebted to Prajit Dutta for patient assistance and advice. This paper has benefited from discussions with Tsz Cheong Lai, Tackseung Jun, Werner Stanzl and Satyajit Bose as well as feedback from an anonymous referee.     

Optimal fiscal policy in the Uzawa-Lucas model with externalities

Summary. This paper devises a fiscal policy by means of which the first-best optimum equilibrium is attained as a market equilibrium in the Uzawa-Lucas model when average human capital has an external effect on productivity. The optimal policy requires the use of a subsidy to investment in human capital which can be financed by a tax on labor income. Lump-sum taxation is not required to balance the government budget either in the steady state or in the transitional phase. Physical capital income should not be taxed. Alternatively, the optimal growth path can be attained by means of a subsidy to human capital. Received: March 21, 2002; revised version: September 4, 2002 RID="*" ID="*" Financial support from the Spanish Ministry of Science and Technology through PNICDYIT grant SEC2002-03663 is gratefully acknowledged.     

The effect of inflation uncertainty on inflation: Stochastic volatility in mean model within a dynamic framework

This paper investigates the effect of inflation uncertainty innovations on inflation over time by considering the monthly United States data for the time period 1976–2006. In order to investigate the effect of inflation uncertainty innovation on inflation, a Stochastic Volatility in Mean model (SVM) has been employed. SVM models are generally used to capture the innovation to inflation uncertainty, which cannot be achieved in the framework of popular deterministic ARCH type of models. Empirical evidence provided here suggests that innovations in inflation volatility increases inflation persistently. This evidence is robust across various definitions of inflation and different sub-periods.     

Pricing, learning, and strategic behavior in a single-sale model

Summary. We analyze an infinite horizon model where a seller who owns an indivisible unit of a good for sale has incomplete information about the state of the world that determines not only the demand she faces but also her own valuation for the good. Over time, she randomly meets potential buyers who may have incentives to manipulate her learning process strategically. We show that i) the seller's incentives to post a high price and to experiment are not necessarily monotonic in the information conveyed by a buyer's rejection; and ii) as the discount factors tend to one, there are equilibria where the seller always ends up selling the good at an ex-post individually rational price. Received: January 6, 1999; revised version: July 15, 2000     

Prudent expectations equilibrium in economies with uncertain delivery

In an economy with private information, we introduce the notion of objects of choice as lists of bundles out of which the market selects one for delivery. This leads to an extension of the model of Arrow–Debreu that is used to study trade ex ante with private state verification. Under the assumption that agents are prudent, equilibrium is characterized by the fact that agents consume bundles with the same utility in states that they do not distinguish. This is a weaker condition than the restriction of equal consumption imposed by Radner (Econometrica 36(1), 31–58, 1968), therefore, some no trade situations are avoided and the efficiency of trade increases.     

The value of money in a dynamic equilibrium model

Summary. This paper studies the pricing of money in an infinite-horizon economy with heterogeneous agents, incomplete financial markets and arbitrary borrowing restrictions. Purchases of the consumption good are subject to a cash-in-advance constraint. Under general conditions I show that the price of money is equal to its fundamental value, where this value is defined over all state-price processes that are compatible with the existence of no-arbitrage opportunities. This equality implies that the cash-in-advance constraint is binding infinitely often for all agents in the economy. The analysis highlights certain differences in the determination of the price of money with respect to models with money in the utility function that bear on the optimal implementation of economic policies.Received: 23 October 2003, Revised: 26 August 2004 JEL Classification Numbers: D52, E44, G12.M.S. Santos: This paper is an outgrowth of an earlier collaboration with Michael Woodford. I have also benefitted from various discussions with Eduardo Gimenez, Alejandro Hernandez, and Miguel Iraola. Some very useful comments by an anonymous referee are greatly appreciated.