صورت پیش فرض و بازار بدهی کارآمد

We examine the nature of debt contracts when repayment of debt cannot be fully enforced. We study outcomes an infinite-horizon economy in which some individuals have access to a productive, intertemporal technology. Individuals without access to the technology must lend their savings to the rest. Borrowers can default on their debt at any time: lenders can capture a fraction of their investment incomes. Borrowers who default stand to lose the right to borrow in the future. These constitute the penalties of capture and exclusion. We evaluate debt and repayment paths that can be sustained in this these penalties. The set of allocations that can be supported by default-free debt is fully characterized; this set is non-empty, convex, and contains a subset that is fully efficient. We then evaluate the role of debt contracts in decentralizing constrained optima. Debt contracts that involve two-part pricing are shown to support efficient allocations subject to the no-default constraint. Efficiency is compatible with anonymous contracts.

We consider the extent of debt, and the nature of debt contracts, in a world where borrowers can default on debts. Our main interest lies in characterizing debt markets that support efficient investment and consumption paths. The economy, and all participants, have an infinite-horizon. Individuals differ in access to an intertemporal production technology. The need for borrowing and lending arises from this: those who do not have direct access to production lend their savings to those who do. Borrowers can default their debts, and lenders cannot enforce full repayment directly. We assume that partial repayment can be directly enforced: lenders can capture a proportion λ of investment income. In addition, a borrower in default can be excluded from debt markets: he is then unable to borrow again. We evaluate the properties of consumption, investment, debt and repayment paths that can be sustained by the twin penalties of λ-capture and exclusion; characterize the set of efficient allocations that can be so sustained; and deduce the structure of one-period debt contracts that can support these constrained efficient allocations. A debt plan, specifying a path of borrowing and repayments, can be sustained if borrowers do not default at any time and lenders do not capture their funds. For a debt plan to be default-free, the continued ability to borrow must generate a stream of rents for the borrower. For debt to be capture-free, lenders must earn enough from debt repayments. As default and capture are options available at every point of time, sustainable paths must promise sufficient future income to both sides at all times. Accordingly, sustainable debt plans must satisfy infinitely many inequality constraints. Theorem 1 characterizes debt plans that can be sustained. In Theorem 2, we evaluate the implied restrictions on consumption allocations. The sequence of constraints on debt plans are equivalent to a single constraint on the path of aggregate consumption. The set of sustainable allocations is non-empty and convex. Any sustainable consumption allocation can be supported by at least one feasible and sustainable debt plan. This characterization is particularly useful in analyzing efficiency, as well as decentralization. We show, in Theorem 3, that a subset of fully efficient, or first-best allocations, can be sustained; and that the set of efficient, sustainable allocations is non-empty for each λ, monotonically increasing in λ, and coincides with the set of fully efficient allocations when λ=1. Hence, any efficient allocation can be sustained for some λ. Turning to decentralization, we show, in Theorem 4, that efficient and sustainable allocations can be achieved by trading in one-period debt contracts. These contracts involve two-part pricing. Lenders pay a fixed fee every period in order to participate in debt markets, and then earn a common marginal rate of return on their loans. At the margin, this rate of return equals the marginal productivity of capital. This last is, of course, a familiar characteristic of first-best paths. The fixed fee is paid to borrowers, and generates the rents that are necessary to prevent default. The marginal price is common to all debt contracts; the fixed fee is typically personalized. This is necessary if we want to implement all of the efficient solutions; an anonymous debt-contract achieves one of these efficient allocations. The allocation achieved by a competitive equilibrium can be reached if λ is large enough relative to the distribution of endowments. The associated debt contract involves a two-part tariff whenever λ<1. Thus, in the absence of full enforcement, Walrasian allocations can be sustained only with non-Walrasian contracts. The possibility that repeated trade may achieve superior outcomes in environments of limited enforcement has been a persistent theme in several papers, starting from Allen, 1981, Allen, 1985, Green, 1987 and Bulow and Rogoff, 1989. Many recent approaches, such as Kimball, 1988, Atkeson and Lucas, 1992, Kehoe and Levine, 1993, Coate and Ravallion, 1993, Thomas and Worrall, 1994 and Kocherlakota, 1996, evaluate the role of exclusion as a threat in enforcing trade in exchange economies with individual endowment uncertainty. Typically, in these problems, individuals trade contracts, or securities for insurance purposes. These contracts pay positive amounts when their income is low, and negative when income is high. Individuals who renege on these payments, and suffer the penalty of exclusion. They will do so unless the right to continue trade is sufficiently valuable: in an exchange economy, this simply requires that equilibrium utility levels are large enough relative to autarky. This approach runs into some difficulties in situations where participants are able to save, independently of access to markets. An individual with access to storage can plan to default on their payments; excluded from asset markets, they can consume their savings for the rest of their lives. This possibility raises the incentive to default, and lowers the deterrent effect of exclusion. Typically, this reduces the set of outcomes which can be sustained by repeated trading with the threat of exclusion. Emphasized first by Allen (1984), this insight was used to derive a significant impossibility result by Bulow and Rogoff (1989). With complete, competitive markets, the threat of exclusion cannot deter default by sovereign countries: sovereignty implies λ=0 in our terminology. Storage, or investment, is central to our problem. Individuals who have access to storage are precisely the ones who are likely to default. The right to borrow is valuable only if it commands rents. The penalty of exclusion has a deterrent effect if these rents are sufficiently high. We simplify the problem in other respects by assuming that there is no uncertainty in production or endowments. The negative result of Bulow and Rogoff—that borrowing and lending cannot be sustained if λ=0—continues to be true. For positive capture rates, some amount of default-free debt can be sustained. Section 2 sets out the model. In Section 3, we demonstrate efficient allocations in a setting of full, and costless enforcement. The possibility of default, and the effect of penalties, are set out in Section 4: the two penalties impose incentive-compatibility constraints on the entire path of debt. Debt plans, and consumption allocations that can be sustained by the threat of exlusion are fully characterized in Section 5; in Section 6, we find constrained efficient allocations, and show that a subset of fully efficient paths are sustainable. In Section 7, we turn to decentralization of these constrained efficient allocations. Specifically, we propose debt contracts which require two-part pricing, as a participation fee plus return on loans, and show that every constrained efficient allocation path can be achieved as an equilibirum in an economy with two-part debt contracts, and redistribution of endowments. Section 7 concludes.

The debt contract: In Theorem 4, we show that two-part pricing, consisting of a participation fee and a marginal rate of return on loans, can support all efficient and sustainable allocations. A natural interpretation of this contract is that of “banking fees”. Depositors pay fees to banks, who have the option of declaring bank failure. Banks compete for funds, bidding up the deposits rate to ρ. Importantly, they take fees as given, and depositors are aware that a cut in fees can trigger bank failures. Typically, the fee is non-anonymous, i.e. depositor specific. • Anonymity and debt markets: debt contracts that support constrained optima typically involve lack of anonymity. As this provides natural difficulties of interpretation in decentralization, we evaluate the possibility of anonymous two-part contracts in Corollary 6. There, as in Theorem 4, lump-sum redistributions are necessary in the initial period. Thes redistributions are necessary for efficiency, and ensure participation. Otherwise, lenders with low endowments may choose not to save. We do not know, as yet, whether anonymous, non-linear contracts can support efficient allocations without redistributions. • Two-part pricing is routinely used to achieve efficiency in economies with non-convex technologies (e.g. Brown (1991)). It may appear that we use them for similar reasons. This is not true: the set of λ-sustainable allocations is convex. The need for a fixed fee is a direct consequence of the penalty of exclusion. Borrowers need to make rents every period in order not to default. These rents can be generated in more than one way. Fixed fees can generate rents for the borrower without doing violence to the marginal conditions for a lender’s optimum. It is likely, then, that a similar construction suffices in other problems involving moral hazard and the threat of termination, including “efficiency wages”, or risk-sharing with storage. • Optima and equilibria: We have looked for debt-contracts that support efficient allocations. Obviously, inefficient λ-sustainable allocations may be achieved by other contracts, including more standard debt contracts of the type In related work (Dutta and Kapur, 1998 and Dutta and Kapur, 1999), we evaluate the restrictions on lending rates rt that correspond to λ-sustainable debt-plans. • The two penalties: We note that niether penalty is redundant. In the absence of exclusion, effective debt-contracts correspond to capture at each t: which cannot support first-best paths if λ>1. Capture is quite definitely non-redundant, as the set of sustainable allocations increases monotonically with λ ( Corollary 3); so does the set of efficient sustainable allocations ( Theorem 4). From Corollary 4, non-trivial debt and consumption paths are impossible if λ=0. • Endowments and sustainability: Our model is special in many ways. While some of these simplify the problem, the endowment condition is critical in deducing (SC). We assume et=0 for t≥1. This condition is useful in focusing attention on the need for lending and borrowing; our characterization of the sustainability condition relies essentially on this property. The general condition, which restricts CL1−EL1 similarly, is valid for consumption paths that satisfy cLt≥eLt for t≥1. This is certainly true if endowments do not increase too fast; modified versions of our results hold if endowments growth is lower than θ, so that perpetual production is necessary to attain efficiency. Further, Corollary 4 may fail with some endowment distributions, as we show in Dutta and Kapur (1999); it is also possible that Corollary 2 fails for some endowment paths.