Recursive equilibrium in endogenous growth models with incomplete markets

This paper analyzes the existence of recursive equilibria in a class of convex growth models with incomplete markets. Households have identical CRRA-preferences, production displays constant returns to scale with respect to physical and human capital, and all markets are competitive. There are aggregate productivity shocks that affect aggregate returns to physical and human capital investment (stock returns and wages), and there are idiosyncratic shocks to human capital (idiosyncratic depreciation shocks) that only affect individual human capital returns. Aggregate and idiosyncratic shocks follow a joint Markov process. Conditional on the aggregate state, idiosyncratic shocks are independently distributed over time and identically distributed across households. Finally, households have the opportunity to trade assets in zero net supply with payoffs that depend on the aggregate shock, but markets are incomplete in the sense that there are no assets with payoffs depending on idiosyncratic shocks. It is shown that there exists a recursive equilibrium for which equilibrium prices (returns) only depend on the exogenous aggregate shock variable (the wealth distribution is not a relevant state variable). Moreover, the allocation associated with this recursive equilibrium is identical to the equilibrium allocation of an economy in which households live in autarky and face both aggregate and idiosyncratic risk.I would like to thank for helpful comments Peter Howitt, Bob Lucas, Michael Magill, Tomo Nakajima, Herakles Polemarchakis, Martine Quinzii, Kevin Reffett, an anonymous referee, and seminar participants at various universities and conferences.     

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.     

The welfare cost of monopolistic competition: a quantitative assessment

This paper quantifies the welfare cost of monopolistic competition in a simple parametric class of endogenous growth models, embedding the neoclassical growth framework as a special case. We put particular emphasis on taking transitional dynamics into account. In doing so, we develop an original two-step numerical procedure to compute the value function. We find for conservative calibrations that the welfare cost of monopolistic competition can be anywhere between 0.4 and 1.2% of consumption, depending on whether labor is elastically or inelastically supplied.     

Complete and incomplete markets with short-sale constraints

Summary. This paper argues that the introduction of a short-sale constraint in the Arrow-Radner framework invalidates standard definitions of complete and incomplete markets. Two threshold values with familiar properties arise in this constrained set-up. If short sales are not allowed on some security, then financial markets will be incomplete in the standard sense. Beyond a particular level of the short-sale bound, financial markets are “complete”, since the short-sale constraint is not effective. For intermediate bounds the distinction between complete and incomplete financial markets is blurred. Although some technical definitions hold, agents can not fully transfer wealth among states. These intermediate cases, called “technically incomplete markets”, exhibit interesting welfare properties. For instance, the resulting equilibrium allocations may not be Pareto-dominated by those of the non-restricted complete markets equilibrium. Received: November 28, 2000; / revised version: November 9, 2001     

Endogenous longevity,public debt and endogenous growth

This study explores the mechanism that causes an inverted U-shaped relationship between the public debt to GDP ratio and the economic growth rate which is observed in empirical studies. We show that this relationship is caused even when the government does not introduce the golden rule of public finance, and government health care expenditure has important role in generating this relationship.     

A Schumpeterian model of endogenous innovation and growth

A disequilibrium model of endogenous innovation and growth is presented. The behaviour of the agents is supposed to be governed by routines, not by maximization. The entrepreneurs are assumed to invest a fraction of their operating profits in real capital accumulation, and another fraction in R&D. The latter leads to an increase in labour productivity via a R&D production function. In this Schumpeterian model, not only the R&D processes of innovations are considered, but the diffusion processes as well. As in Schumpeter's theory of economic development the economic impact of technical change is considered a disequilibrium phenomenon. Thus, in a capitalist economy characterized by ongoing diffusion processes of innovations, time averages are more important than steady state values even in a long run perspective.     

Information, trade and incomplete markets

The no-trade result of Milgrom and Stokey, J Econ Theory 26:17–27 (1982), states that if rational traders begin with an ex-ante Pareto optimal allocation then the arrival of information cannot generate trade. This paper allows traders to trade before and after the arrival of information. If there are enough securities to hedge against all payoff relevant risk, then the preinformation-arrival allocation is Pareto optimal and information arrival has no effect. This no-retrade result is the competitive analog of the no-trade result of (1982). However, information generically generates trade when markets are state-contingent incomplete.We thank seminar participants at Cambridge, Carnegie Mellon,Cornell, Essex, London, Maastricht, USC, and York and participants at the 2003 SITE, the 2003 SAET and the Fall 2002 Cornell–Penn State Macro Conference. We also thank Karl Shell and a referee for this journal for useful comments     

A model for international capital markets closure in an economy with incomplete markets and short sales

Using a two-country dynamic optimization model, we investigate the impact of exchange risk, incomplete information and short sales constraints on international portfolio decisions around market closure. Using optimal control theory, we provide solutions and simulation results. Our model can be applied to solve several problems in financial economics in the presence of market closure, information asymmetry and short sales constraints.     

Strategic market games with a finite horizon and incomplete markets

Summary. We study a strategic market game associated to an intertemporal economy with a finite horizon and incomplete markets. We demonstrate that generically, for any finite number of players, every sequentially strictly individually rational and default-free stream of allocations can be approximated by a full subgame-perfect equilibrium. As a consequence, imperfect competition may Pareto-dominate perfect competition when markets are incomplete. Moreover - and this contrasts with the main message conveyed by the market games literature - there exists a large open set of initial endowments for which full subgame-perfect equilibria do not converge to -efficient allocations when the number of players tends to infinity. Finally, strategic speculative bubbles may survive at full subgame-perfect equilibria.Received: 24 January 2002, Revised: 21 February 2003, JEL Classification Numbers: C72, D43, D52. Correspondence to: Gaël GiraudWe thank Tim Van Zandt for his comments.     

Balanced budget vs. Tax smoothing in a small open economy: A welfare comparison

The objective of this paper is to investigate the effect of lending and borrowing constraints on the dynamics of public debt and optimal taxation policy in the context of a general equilibrium model with tax smoothing. The results from the numerical simulation of the model show significant welfare gains, provided that the policymaker is allowed to borrow and lend in order to smooth taxes across time instead of maintaining a balanced budget at all times. Moreover, for a specific process for asset prices, it is also shown that if the government can issue state-contingent debt then overall welfare can be further improved substantially.     

An empirical characterization of the effects of public debt on economic growth

Based on a data set of 115 economies, this article empirically investigates the relation between public debt and economic growth. Using the World Bank’s classification for income groups, we initially find that those countries that present the lowest public debt are characterized by the highest economic growth, while the smallest growth rates are associated with the highest public debt. Nevertheless, this conclusion is tempered when we analyse the countries by income level: low-income countries have a different behaviour with respect to lower-middle, upper-middle and high-income countries. When using the IMF’s country classification, the results do not suggest a clear pattern in the public debt–economic growth nexus across different countries, but indicate a heterogeneous relationship between such key macroeconomic variables.     

Public debt and economic growth: what do neoclassical growth models teach us?

This paper aims to quantify the crowding-out effect of public debt and the related loss in long-run output in neoclassical growth models. To accomplish this task, we incorporate the government sector into the Ramsey–Cass–Koopmans (RCK) model, the Blanchard model and the Solow model, which differ only in their assumptions concerning the consumption behaviour of households. We also introduce a general framework that is capable of gauging the burden of public debt in a neoclassical world in the case of any type of consumption behaviour. Our results are threefold. First, contrary to the RCK model, public debt reduces long-run output in the Blanchard model and the Solow model, although to a different extent: the crowding-out effect is marginal in the former, whereas it can be very large in the latter. Second, the burden of public debt is country-specific depending crucially on the saving rate and the population growth rate. Finally, in developed countries the upper limit of the output loss related to public debt is moderate at best even if distortionary taxes are taken into account.     

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.     

Disaggregation of excess demand and comparative statics with incomplete markets and nominal assets

Summary. We prove that locally, Walras' law and homogeneity characterize the structure of market excess demand functions when financial markets are incomplete and assets' returns are nominal. The method of proof is substantially different from all existing arguments as the properties of individual demand are also different. We show that this result has important implications and is part of a more general result that excess demand is an essentially arbitrary function not just of prices, but also of the exogenous parameters of the economy as asset returns, preferences, and endowments. Thus locally the equilibrium manifold, relating equilibrium prices to these parameters has also no structure. Received: September 17, 1996; revised version: November 7, 1997     

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.     

Understanding the welfare effects of unemployment insurance policy in general equilibrium

This paper analyzes the welfare effects of unemployment insurance reforms in a general equilibrium incomplete market model. In particular, it decomposes the total welfare effect for each individual into different factors. I consider a model where the consumers face an uninsurable unemployment risk, can save in an interest-bearing asset, and are subject to a borrowing constraint. The labor market is modeled using a Diamond–Mortensen–Pissarides style search and matching model. The decomposition exercises reveal how each factor contributes to the heterogeneity of welfare effects among different consumers.     

Endogenous growth, welfare and budgetary regimes

Within an optimizing endogenous growth model with productive public capital and government debt, we derive and characterize on the balanced growth path a set of welfare-maximizing fiscal rules under different budgetary regimes. It is shown that optimal fiscal policy depends on the specific budgetary stance considered.     

Credit quality, the intensity of regulation and the segmentation of debt markets

Some debt markets have a “competitive advantage” over others due to easier regulatory requirements. Our model explains changes in the market shares of different debt markets. In particular, borrowers may choose between highly regulated and relatively unregulated placement of debt so as to minimize borrowing costs. Borrowers in the highly regulated market incur higher regulatory cost, but are also able to signal accurately their true risk class. In unregulated markets there is an asymmetric information problem. This results in an equilibrium where the debt market is segmented between less regulated and other, more strictly regulated, placements. Raising regulatory costs will lead to an expansion of the market share of unregulated debt. It will also lead to an increase in the overall default rate on corporate debt.     

Fertility,income and welfare in an OLG model with regulated wages

We analyse the effects of the regulation of wages in a standard one-sector OLG model of neoclassical growth extended to account for endogenous fertility decisions of households and unemployment benefit policies financed at balanced budget. In contrast with the prevailing literature, which has failed to pay due attention to inter-temporal contexts, our conclusion is that minimum wages may be introduced not only for equity reasons, that is, to increase the income of low-paid workers, but under suitable conditions—i.e., if production is sufficiently capital oriented and the unemployment benefits are high enough—minimum wage legislation might be considered as a source of increased economic performance despite unemployment, i.e. a regulated-wage economy performs better than a market-wage economy. As a consequence, since higher minimum wages raise per capita income together with increasing unemployment, our results imply that a positive correlation between unemployment and long-run income per-capita may exist. Further, the lifetime welfare of the representative generation may be increased as well. Finally, the wage rate may also be treated as a policy instrument for the control of population growth.

Autonomous government expenditure growth,deficits, debt,and distribution in a neo-Kaleckian growth model

This article is linked to some recent attempts at including a noncapacity creating autonomous expenditure category as the driver and determinant of growth into Kaleckian distribution and growth models. Whereas previous contributions have focussed on taming Harrodian instability, generated by the deviation of the goods market equilibrium rate of capacity utilization from a normal or target rate, we rather focus on the so-far neglected issues of deficit, debt, and distribution dynamics in such models. For this purpose, we treat the growth of government expenditures on goods and services, financed by credit creation, as the exogenous growth rate driving the system. We examine the long-run convergence of the system toward such a growth rate, analyze the related debt dynamics, and deal with stability and income distribution issues. Finally, we touch upon the economic and, in particular, fiscal policy implications of our model results.