Equilibria in incomplete assets economies with infinite dimensional spot markets

The paper studies the two period incomplete markets model where assets are claims on state contingent commodity bundles and there are no bounds on portfolio trading. The important results on the existence of equilibrium in this model assume that there is a finite number of commodities traded in each spot market and that preferences are given by smooth utility functions. With these assumptions an equilibrium exists outside an “exceptional” set of assets structures and initial endowments. The present paper extends these results by allowing for general infinite dimensional commodity spaces in each spot market. These include all the important commodity spaces studied in the literature on the existence of Walrasian equilibrium—in each spot market the consumption sets are the positive cone of an arbitrary locally solid Riesz space or of an ordered topological vector space with order unit or of a locally solid Riesz space with quasi-interior point. The paper establishes that even with our very general commodity spaces there exists an equilibrium for a “very” dense set of assets structures. Our approach is in the main convex analytic and the results do not require that preferences be smooth or complete or transitive. The concepts and techniques studied in this paper have important finite as well as infinite dimensional applications. This paper has benefited from the comments of Martine Quinzii, Wayne Shafer, Manuel Santos and Yeneng Sun. The research of C. D. Aliprantis is supported by the NSF Grants SES-0128039, DMS-0437210, and ACI-0325846. The research of R. Tourky is funded by the Australian Research Council Grant A00103450.     

Public debt and welfare in a quantitative Schumpeterian growth model with incomplete markets

This paper quantifies the welfare effects of counterfactual public debt policies using an endogenous growth model with incomplete markets. The economy features public debt, Schumpeterian growth, infinitely-lived agents, uninsurable income risk, and discount factor heterogeneity. Two versions of the model are specified, one with households holding equity in the group of innovating firms. The model is calibrated to the U.S. economy to match the degree of wealth inequality, the share of R&D expenditure in GDP, the firms’ exit rate, the average growth rate, and other standard long-run targets. When comparing balanced growth paths, I find large welfare gains in equilibria characterized by governments accumulating public wealth. The result is robust to the mechanism used to generate a highly concentrated wealth (i.e., preference heterogeneity or “superstar” income shocks). Welfare effects decompositions show that level effects and growth effects reinforce each other. The responses of both the intermediate goods and their market conditions are key in explaining the large level effects. The version of the model without equity is computationally easier to solve, allowing to consider transitional dynamics. Taking into account the dynamic adjustment to the new long-run equilibrium, I show that the transitional welfare costs are not large enough to change the sign of the welfare effects stemming from a change in public debt. I find that eliminating public debt would lead to a 0.8% increase in welfare, while moving to a debt/GDP ratio of 100% would entail a welfare loss of 0.5%. A decomposition analysis shows that growth accounts for approximately 50% of the overall welfare effects.     

Generic inefficiency of equilibria in the general equilibrium model with incomplete asset markets and infinite time

Summary. We consider a Lucas asset-pricing model with heterogeneous agents, exogenous labor income, and a finite number of exogenous shocks. Although agents are infinitely lived, endowments and dividends are time-invariant functions of the exogenous shock alone and are thus restricted to lie in a finite-dimensional space; genericity analysis can be conducted on sets of zero Lebesgue measure. When financial markets are incomplete, that is, there are fewer financial securities than shocks, we show that generically in individual endowments all competitive equilibria are Pareto inefficient. Received: November 22, 1999; revised version: March 4, 2002 RID="*" ID="*" We are grateful to an anonymous referee for very insightful comments on earlier drafts.     

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.     

Creditworthiness and thresholds in a credit market model with multiple equilibria

Summary. The paper studies creditworthiness in a model with endogenous credit cost and debt constraints. Such a model can give rise to multiple candidates for steady state equilibria. We use new analytical techniques such as dynamic programming (DP) with flexible grid size to find solutions and to locate thresholds that separate different domains of attraction. More specifically, we (1) compute present value borrowing constraints and thus creditworthiness, (2) locate thresholds where the dynamics separate to different domains of attraction, (3) show jumps in the decision variable, (4) distinguish between optimal and non-optimal steady states, (5) demonstrate how creditworthiness and thresholds change with change of the credit cost function of the debtor and (6) explore the impact of debt ceilings and consumption paths on creditworthiness.JEL Classification Numbers: C61, C63, D91, D92, E51, G12, G32.An earlier version of this paper has been prepared for the 1998 North American Winter Meeting of the Econometric Society, January 1998, Chicago. We want to thank Jess Benhabib, Buz Brock, Gustav Feichtinger, Franz Wirl, Michael Woodford, Wolf-Jürgen Beyn and Thorsten Pampel for helpful discussions and comments on various versions of the paper. We also want to thank participants in a workshop at the University of Technology, Vienna, the Macroeconomic Workshop at Columbia University, and the SCE conference, at Yale University, June 2001. We are also grateful for comments from a referee of the journal.