The role of limited contract enforcement in dynamic general equilibrium has been explored extensively in key papers by Eaton and Gersovitz (1981), Kehoe and Levine (1993), Kocherlakota (1996), and Kiyotaki and Moore (1997), all of which seek to explain why individual consumption, aggregate output and asset prices fluctuate more than aggregate consumption, productivity or dividends . Limited commitment has been used to investigate anomalies in asset pricing (Alvarez and Jermann (2000, 2001), Azariadis and Kaas (2007)), international business cycles (Kehoe and Perri (2002)), economic growth (Marcet and Marimon (1992)), consumption patterns and social security issues (Krueger and Perri (2005, 2006)). All these models describe environments in which a shortage of collateral rules out complete risk sharing or consumption smoothing.

One institution that improves the distribution of consumption over households is unsecured credit backed by limiting defaulters’ subsequent trading in asset markets. The literature typically assumes that an omnipotent credit authority or auctioneer excludes defaulting agents for the rest of their lives from any asset trade. Such a penalty is clearly the strongest possible punishment in the absence of collateral. It is no surprise that even the Arrow–Debreu allocation, which corresponds to perfect enforcement, can be achieved as a competitive equilibrium provided that agents are sufficiently patient or sufficiently risk averse.

This paper explores the consequences of weaker punishment arrangements. For example, Bulow and Rogoff (1989) and Hellwig and Lorenzoni (2007) impose one–sided exclusion which permits defaulters to accumulate assets but banishes them permanently from all borrowing. This paper works out the consequences of temporary exclusion from both sides of asset markets. To this end, we consider a two–agent, two–state pure–exchange economy in which defaulters can be excluded from all asset trading for a given finite number of periods. When the punishment period is over, bankrupt households regain full access to all markets. We maintain the common assumption in the literature of a complete market of state–contingent claims supported by default–deterring credit limits. We believe that temporary exclusion is an important feature since real–world bankruptcy procedures never come close to perpetual market exclusion.

It is not surprising that temporary exclusion permits less risk sharing than everlasting punishment. Indeed, first–best allocations are more difficult to enforce, and autarky2 is more likely to be the unique equilibrium outcome. Under permanent market exclusion, Alvarez and Jermann (2000) prove two results: one, autarky is the unique, constrained–efficient equilibrium if it is dynamically efficient (i.e. when the yield on a safe portfolio of claims exceeds the economy’s growth rate). Two, when autarky is dynamically inefficient, there is a better equilibrium with improved risk sharing. In stark contrast to these results, a short exclusion of defaulters permits many stationary equilibria to coexist; the first–best allocation may be one of them.

Whenever multiple steady states exist, one of them is indeterminate and debt limits bind on borrowers. As is well known, indeterminate states give rise to volatile dynamics, that is, to “sunspot” cycles, driven by self–fulfilling prophecies. Thus short exclusion arrangements not only inhibit risk sharing, but they also have the potential to raise the volatility of asset returns and consumption.

To understand why multiple equilibria occur under temporary exclusion even if they are impossible under permanent exclusion, we note that short–sale constraints must react strongly to changes in future security prices when exclusion lasts only a few periods. More specifically, with temporary exclusion there is a dynamic complementarity in security prices. To see why, suppose that security prices increase in period t. Then an agent with high income in t has a stronger incentive to default on loans due at t because losing the ability to trade securities is a less severe punishment. Consequently, default–deterring credit limits in t ? 1 tighten and the volume of security trading in period t ? 1 falls. To induce high–income agents in period t ? 1 to buy fewer securities, security prices must increase. Hence the dynamic complementarity between security prices with short exclusion. Permanent exclusion weakens or removes this positive linkage between two consecutive security prices. We present a more formal discussion of this argument in Section 5.

Equilibrium multiplicity is not the only difference between permanent and temporary exclusion penalties. The other is that the role of the discount factor is altered decisively. With permanent exclusion, there is a “folk theorem” (Proposition 2 of Kehoe and Levine (1993)): when the common discount factor is sufficiently large, a first–best allocation can always be enforced. With temporary exclusion, however, enforceability of a first–best allocation requires, in addition, that risk aversion be sufficiently strong, even when agents are very patient. Moreover, we find that in stochastic economies with one–period exclusion, the first best is never an equilibrium when the discount factor approaches unity, although there can be perfect risk sharing at lower values of the discount factor. Intuitively, very patient households do not care about temporary exclusion penalties but are rather interested in maximizing long–run consumption which proves to be higher after deviating from the first–best allocation. At lower values of the discount factor, however, the first best is enforceable when risk aversion is strong enough.

We are aware of only a few contributions dealing with temporary asset market exclusion of defaulting borrowers. Athreya (2002) and Chatterjee, Corbae, Naka-jima, and Rios-Rull (2007) develop quantitative equilibrium models with incomplete asset markets, characterizing optimal default behavior and equilibrium loan price schedules; Scholl (2005) considers temporary market exclusion in a pure–endowment version of Kehoe and Perri (2002) to explore international risk sharing. However, these contributions neither discuss multiplicity nor the role of discounting which are central themes of this paper. Azariadis and Lambertini (2003) consider a deterministic overlapping–generations economy with three–period lived individuals, also demonstrating the existence of multiple and indeterminate equilibria. However, in their paper endogenous debt constraints are based on one–period exclusion by construction since individuals die in the period after default. Our paper shows that a similar result can be obtained in both deterministic and stochastic economies with infinitely–lived agents.

The paper is organized as follows. After introducing the economic environment and equilibrium concepts in Section 2, we discuss first–best allocations in Section 3 and steady–state equilibria with constrained borrowers in Section 4. Section 5 analyzes the local dynamics near stationary equilibria, establishing indeterminacy results. While the main part of this paper focuses on a deterministic income process, we show in Section 6 how the results can be extended to a stochastic environment with complete markets.

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