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I explore alternative central bank policies for liquidity provision in a model of payments. I use a mechanism design approach so that agents’ incentives to default are explicit and contingent on the credit policy designed. In the first policy, the central bank invests in costly enforcement and charges an interest rate to recover costs. I show that the second-best solution is not distortionary. In the second policy, the central bank requires collateral. If collateral does not bear an opportunity cost, then the solution is first best. Otherwise, the second best is distortionary because collateral serves as a binding credit constraint.

A primary role of a central bank is to facilitate a safe and efficient payments system. One source of inefficiency in payment systems is a potential shortage of liquidity. Central banks often respond by providing liquidity through the extension of credit. Because of this role, a central bank must manage its exposure to the risk that an agent does not repay. Some central banks, such as the European Central Bank, manage this risk by requiring borrowers to post collateral. Others, such as the Federal Reserve in the U.S., charge an explicit interest rate on credit and limit the amount any particular agent can borrow. In this paper, I explore these alternative credit policies in a theoretical model of payments and offer a rationale for why some central banks may choose one credit policy over another. I do this in a mechanism design framework, paying particular attention to the moral hazard issues associated with the repayment of debt that alternative credit policies aim to mitigate. The payment systems most relevant to this paper are large-value payment systems which are mainly intraday, interbank payment systems. Many large-value payment systems are operated by central banks and are often real-time gross settlement (RTGS) systems. In an RTGS system, payments are made one at a time with finality during the day. Examples of RTGS systems include Fedwire operated by the Federal Reserve in the U.S. and TARGET operated by the European Central Bank in the EMU.1 Because payments are made one at a time, liquidity is needed to complete each transaction. If participants do not have enough liquidity to make a payment at a particular point in time, they can typically borrow funds from the central bank by overdrawing on an account with the central bank, which they then pay back by the end of the day. The central bank faces a trade-off between supplying this intraday liquidity at little or no cost to enhance the efficiency of the system and accounting for moral hazard issues associated with the extension of credit. Of fundamental interest in this paper is how a central bank should design a credit policy for the provision of liquidity in an RTGS system to improve efficiency while dealing with moral hazard associated with debt repayment. The main contribution of this paper is a framework with which to study the alternative credit policies of central banks. The key features of the framework are (i) default decisions of agents are endogenous, and (ii) mechanism design. The first is important to rigorously introduce a moral hazard problem that arises when debt is extended. The second is a useful approach to evaluate what good outcomes are achievable under alternative credit policies taking into account agents’ incentives to default. This framework is applied to a model of payments that is similar to that of Freeman (1996). Such a model captures some key features of large-value payment systems. These features are (i) fiat money is necessary as a means of payment, (ii) there is a need to acquire liquidity (in the form of fiat money) during the day to make such payments, and (iii) money is also necessary to repay debts by the end of the day. These three features provide an endogenous role for an institution such as a central bank to provide liquidity to facilitate payments. An important abstraction in Freeman's original model, however, is that there is costless enforcement that exogenously guarantees that debts are repaid. Such an abstraction has led to conclusions by Freeman (1996), Green (1997), Zhou (2000), Kahn and Roberds (2001) and Martin (2004) that a credit policy of free liquidity provision is optimal. These conclusions are immediate given that there is no explicit moral hazard problem in most of these models.2 As a result, these models do not fully capture the trade-off between providing liquidity to facilitate payments and minimizing the exposure of credit risk associated with that provision. Moreover, Mills (2004) endogenizes the repayment decision of agents under costless enforcement in Freeman's model and shows that money is not necessary to repay debts if enforcement is too strong and so the need for liquidity in his model is questioned. As in Mills (2004), I shall depart from this abstraction so that the default decision of agents is not trivial. In the context of the background environment, I look at two alternative credit policies that resemble some of the features of such policies in actual large-value payment systems. The first such policy is that of costly enforcement and pricing. The central bank invests in a costly enforcement technology that allows it to punish defaulters by confiscating some consumption goods. The second policy is that of requiring those who borrow from the central bank to post collateral. Under this policy, the central bank does not charge an explicit interest rate on debt. Collateral, however, may have an opportunity cost in that it cannot earn a return that it otherwise would have. I use a mechanism design approach to see if the credit policies can achieve good allocations, which I define to be Pareto-optimal allocations. It is possible for both types of credit policies to implement these good allocations. In the case of the pricing policy, I find an example of where the optimal intraday interest rate is positive because of a requirement for the central bank to recover its costs of enforcement. This differs from the aforementioned literature and supports a suggestion made by Rochet and Tirole (1996) that the intraday interest rate be positive because monitoring and enforcement is costly. In the case of collateral, if it does not have an opportunity cost, such a policy can implement a good allocation that is first-best. If, on the other hand, there is a positive opportunity cost of collateral, requiring collateral adds binding incentive constraints that distort the allocation away from Pareto-optimality. Collateral serves as an endogenous credit constraint. This paper is most closely related to Martin (2004). Both papers are interested in evaluating how alternative credit policies address participants’ moral hazard in a general equilibrium model where money is necessary. Martin (2004) models moral hazard by endogenizing some agents’ choice of risk arising from a central bank's free provision of liquidity. Agents can choose a safe production technology or a risky one that exogenously leads to some default and central banks cannot enforce a choice of the safe asset. In his model, agents cannot strategically default. In this paper, agents do not have an opportunity to engage in risky behavior, but rather have the choice to strategically default. The central bank can enforce some repayment only after investing in a costly enforcement technology. Martin (2004) compares alternative central bank credit policies and concludes that a collateral policy with a zero intraday interest rate is preferred to debt limits in mitigating the credit risk. The collateral in his model is debt issued by private agents who exogenously commit to repayment (i.e., there is no choice to strategically default) and does not bear an opportunity cost. In this paper, the issuers of collateral do have the opportunity to strategically default and collateral does bear an opportunity cost. Moreover, Martin (2004) does not consider costly monitoring of agents receiving central bank liquidity and how that might compare to a collateral policy. Finally, in this paper the default decision of agents is endogenous, but the liquidity shortage is exogenous. This is complementary to an area in the literature by Bech and Garratt (2003), Angelini (1998) and Kobayakawa (1997). These papers endogenize the liquidity shortage by focusing on the incentives agents have to coordinate the timing of payments given alternative credit policies, but do not endogenize the need for such credit policies. The paper is organized as follows. Section 2 presents the environment while Section 3 provides a benchmark of optimal allocations. Sections 4 and 5 contain the main results as pertains to the credit policy with pricing and collateral, respectively. Section 6 extends the analysis to include exogenous default and central bank losses. Section 7 concludes.

The above analysis sheds some light on why different central banks may have different credit policies for RTGS systems. Collateral is preferred if there is no opportunity cost of collateral, such as may be the case when a wide range of assets are accepted as collateral. This is because it can achieve first-best allocations. If collateral does have an opportunity cost, comparison of the relative cost (in terms of good 2 in the model) is important. For example, the European Central Bank does not have monitoring authority over participating banks. Thus, it may be difficult to coordinate monitoring and enforcement authorities. In the context of the model, this is a high enough γγ so that collateral may be the preferred option. On the other hand, the Federal Reserve already has supervisory authority over depository institutions it serves over Fedwire, so that economies of scope are likely to yield a low γγ so that pricing may be the preferred option. In the case where the cost of both policies would be the same (γ=(R-1)σγ=(R-1)σ), the pricing policy would clearly be preferred due to the result that collateral adds a binding endogenous borrowing constraint that does not permit a Pareto-optimal allocation. Another credit policy tool that has not been modeled here is that of setting limits or caps to the amount a debtor can borrow. The Federal Reserve, for example, sets net debit caps that limit the amount that Fedwire participants can borrow to limit the Fed's exposure to credit risk. In the context of the model, such binding constraints could have a similar effect on the pricing policy as what takes place under exogenous default when the central bank held the intraday interest rate fixed at the risk-free rate. That is, it would reduce a debtor's consumption of good 1, but Pareto-optimal allocations may still be achievable. This would simply reduce the set of Pareto-optimal outcomes that would be achievable at the expense of debtors and for the gain of creditors. The results of the paper suggest that the existence of an opportunity cost of collateral is key to that type of credit policy leading to inefficient allocations. Thus, it is important to empirically understand whether or not there is an effective opportunity cost of intraday collateral. Collateral in this model is riskless to the central bank. An extension might involve the introduction of a range of collateral that varies according to riskiness. This complicates matters in that the central bank may have to decide what types of risky assets are acceptable as collateral. The conjecture here is that as a central bank accepts a wider range of assets, the opportunity cost to the participant of posting collateral is less, but collateral provides less protection to the central bank in the event of defaults unless the value of the collateral is discounted appropriately. Finally, this paper restricts itself only to two credit policies designed to replicate actual central bank policies. A more generalized study may reveal that a third policy may be more appropriate especially when some of the aforementioned complications are present in the model.