Endogenous credit limits with small default costs

Abstract

We analyze an exchange economy of unsecured credit where borrowers have the option to declare bankruptcy in which case they are temporarily excluded from financial markets. Endogenous credit limits are imposed that are just tight enough to prevent default. Economies with temporary exclusion differ from their permanent exclusion counterparts in two important properties. If households are extremely patient, then the first-best allocation is an equilibrium in the latter economies but not necessarily in the former. In addition, temporary exclusion permits multiple stationary equilibria, with both complete and with incomplete consumption smoothing.

Introduction

The role of limited contract enforcement in dynamic general equilibrium has been explored extensively in key papers by Eaton and Gersovitz [11], Kehoe and Levine [14], Kocherlakota [17], and Kiyotaki and Moore [16], 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 [1], [2], Azariadis and Kaas [6]), international business cycles (Kehoe and Perri [13]), economic growth (Marcet and Marimon [20]), consumption patterns and social security issues (Krueger and Perri [18], [19], Andolfatto and Gervais [3]). 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 defaultersʼ 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.

This paper explores the consequences of weaker punishment arrangements. For example, Bulow and Rogoff [8] and Hellwig and Lorenzoni [12] 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 stochastic pure-exchange economy in which defaulters are readmitted to asset trading with positive probability. 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.

Under permanent market exclusion, Alvarez and Jermann [1] prove two results: one, autarky is the unique (and constrained efficient) equilibrium if the autarkic interest rate exceeds the economyʼs growth rate. Two, when the autarky equilibrium is inefficient, there is a better equilibrium with improved risk sharing. Moreover, Kehoe and Levine [14, Proposition 2] establish a kind of “folk theorem”: this constrained efficient equilibrium is first best provided that the common discount factor is sufficiently large. This paper considers a particular equilibrium refinement, namely, the robustness to small explicit default costs. For our class of pure-exchange economies we find that permanent market exclusion gives rise to a unique robust equilibrium. In particular, autarky is not robust to this refinement, unless it is the unique equilibrium.

We show that economies with temporary exclusion differ from their permanent exclusion counterparts in two important ways. First, a higher discount factor does not necessarily help to implement the first best allocation. With temporary exclusion of defaulters and no matter how low the (positive) readmission probability is, the first-best allocation is not self-enforcing, even when agents are extremely patient, unless they are also sufficiently risk averse. Intuitively, very patient households care less about temporary exclusion penalties but are more interested in the expected value of consumption after they are readmitted to asset trade. Default raises both consumption risk during the punishment phase but also the expected value of consumption in the long run (i.e. after readmission to financial markets).

Second, temporary exclusion can give rise to the existence of multiple robust equilibria. In particular, we prove that autarky is always a robust equilibrium if the readmission probability is sufficiently high (i.e. punishment is sufficiently weak). Besides the robust autarky equilibrium, additional stationary equilibria can emerge; the first-best allocation may be one of them. To understand why multiple robust equilibria occur under temporary exclusion although they are impossible under permanent exclusion, we note that temporary exclusion introduces a dynamic complementarity between future and current asset prices. Consider the example of a defaulter who loses the ability to save in the default period but is readmitted to trade in all subsequent periods. Then an increase in future interest rates reduces the continuation value from default (because the agent forgoes asset trade in the default period) which relaxes credit constraints today. In turn, a higher volume of borrowing necessitates a higher current interest rate to clear the credit market today. This dynamic complementarity can trigger equilibrium multiplicity provided that the impact of future market prices on the value of default is sufficiently strong. Note that such a link is absent in economies with infinite market exclusion where default leads to permanent autarky whose payoff is independent of future prices. We present a more elaborate discussion of this argument in Section 4.

We are aware of only a few contributions dealing with temporary asset market exclusion of defaulting borrowers. Athreya [5] and Chatterjee et al. [9] develop quantitative equilibrium models with incomplete asset markets, characterizing optimal default behavior and equilibrium loan price schedules. In the sovereign default literature, temporary market exclusion of defaulting international borrowers is also a common assumption (Arellano [4], Cuadra, Sanchez and Sapriza [10]). However, these contributions neither discuss equilibrium multiplicity nor the role of discounting which are the focus of this paper.¹ Azariadis and Lambertini [7] consider a deterministic overlapping-generations economy with three-period lived individuals, also demonstrating the existence of multiple equilibria. 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 similar results can be obtained in 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 and the role of discounting in Section 3. Section 4 considers equilibria with binding credit constraints and establishes our main result on equilibrium multiplicity and robustness.