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Channel systems for conducting monetary policy are becoming increasingly popular. Despite its popularity, the consequences of implementing policy with a channel system are not well understood. We develop a general equilibrium framework of a channel system and study the optimal policy. A novel aspect of the channel system is that a central bank can “tighten” or “loosen” its policy without changing its policy rate. This policy instrument has so far been overlooked by a large body of the literature on the optimal design of interest-rate rules

Channel systems for conducting monetary policy are becoming increasingly popular.1 Several central banks already use a channel system, and others are using at least some features of the channel system.2 Despite its popularity, the consequences of implementing monetary policy with a channel system are not well understood. How does implementation of monetary policy in a channel system differ from plain-vanilla open market operations? Why do central banks choose different corridors? Most central banks choose an interest-corridor of 50 basis points (e.g., Australia, Canada, and New Zealand), while the European Central Bank (ECB) chooses one of 200 basis points. Why can some central banks control the overnight interest rate very tightly, while others cannot? For instance, the Euro repo rate fluctuates considerably around the minimum bid rate set by the ECB (Fig. 1), and it tends to be above the minimum bid rate. In contrast, the overnight interbank cash rate in New Zealand is almost always equal to the policy rate (Fig. 2).There are several stylized facts that a reasonable theoretical model of channel systems has to explain. First, all central banks set a strictly positive interest-rate spread—defined as the difference between the lending and the deposit rates. Second, central banks typically react to changing economic conditions by increasing or decreasing their interest-rate corridor without changing its spread. Third, the money market rate tends to be in the middle or slightly above the middle of the corridor. To study these stylized facts, we construct a dynamic general equilibrium model of a channel system with a money market and a welfare-optimizing central bank. Market participants are subject to idiosyncratic trading shocks that generate random liquidity needs. The shocks can be partially insured in a secured money market. To provide further insurance, the central bank operates facilities where market participants can borrow or deposit money at the specified rates. In accordance with central bank practice, there is no limit to the size of deposits on which interest is paid, and there is no limit to the size of a loan that a market participant can obtain provided that the loan is fully collateralized. Finally, the cost of pledging collateral is explicit and money is essential.3 Within this framework we answer the following three questions. First, what is the optimal interest-rate corridor? Second, what is the optimal collateral policy? Third, how does a change in the corridor affect the money market rate? The following results emerge from our model. First, it is optimal to have a positive spread if the opportunity cost of holding collateral is positive, and the optimal spread is decreasing in the rate of return of the collateral.4 Second, the money market rate is above the target rate if the opportunity cost of holding collateral is positive. This property of the model is consistent with the fact that the collateralized Eurepo rate tends to be above the minimum bid rate (Fig. 1). Third, a central bank has two equivalent options for implementing a given policy: it can either shift the corridor while keeping the spread constant or it can change the spread. For instance, to change its policy, it can keep the deposit rate constant and only change the borrowing rate, as done, for example, by the US Federal Reserve System, or it can shift the corridor without changing its spread as done by the ECB. An interesting aspect of the channel system is that a central bank can “tighten” or “loosen” its policy without changing its target rate. The reason is that by increasing the spread of the corridor symmetrically around the target rate, the central bank worsens the option for banks of accessing the standing facility. As a result, the policy regime is tighter.5 This suggests that a characterization of policy through an interest-rate rule, as is commonly done in a large body of the literature, is incomplete. Rather, in a channel system, any policy must be characterized through an interest-rate corridor rule. We provide more discussion on this result in the literature section below. 1.1. Literature There are very few theoretical studies of channel systems, and all of them are partial equilibrium models.6 An early contribution is the model of reserves management under uncertainty by Poole (1968). Woodford, 2000, Woodford, 2001 and Woodford, 2003 discusses and analyzes the channel system to address the question of how to conduct monetary policy in a world with a vanishing stock of money. Whitesell (2006) evaluates reserves regimes versus channel systems. Elements of channel systems have been previously discussed in Gaspar et al. (2004) and Guthrie and Wright (2000). It appears that there are two reasons why there is no other general equilibrium analysis of a channel system. First, money growth is endogenous in such a system. In contrast, most theoretical models of monetary policy characterize optimal policy in terms of a path for the money supply. In practice, however, monetary policy involves rules for setting nominal interest rates, and most central banks specify operating targets for overnight interest rates.7 This paper, therefore, is a further attempt to break the apparent dichotomy (Goodhart, 1989) between theoretical analysis and central bank practices. The second reason is related to the widespread belief that modeling the details of the framework used to implement a given interest-rate rule is unimportant when analyzing optimal monetary policy. That is, it is taken for granted that the economic consequences of interest-rate rules do not hinge on the specific details of monetary policy implementation. However, our analysis reveals that a characterization of optimal policy and its implementation cannot be separated. To see this, consider any interest-rate rule in a system with zero deposit rate as operated, for example, by the US Federal Reserve System. Such an interest-rate rule uniquely determines how “tight” or “loose” policy is. In contrast, the same rule or any other interest-rate rule has no meaning in a channel system, since it does not determine whether a policy is “tight” or “loose.” Consequently, in a channel system optimal policy must not only state an interest-rate rule, but it must also state an interest-rate corridor rule. This is a new insight, which goes beyond what we already know from the large and growing body of literature on the optimal design of interest-rate rules. The paper is structured as follows. Section 2 outlines the environment. The equilibrium is characterized in Section 3. Optimal monetary policy with an inactive money market is derived in Section 4, and Section 5 characterizes policy with an active money market. Finally, in Section 6, we discuss the policy implications that arise from the model, and Section 7 concludes. All proofs and a description of the Euro money markets and the ECB's operating procedures are available as supplementary material on-line (see Appendix).

We have analyzed the theoretical properties of a channel system of interest-rate control in a dynamic general equilibrium model with infinitely lived agents and a central bank. With this model, we could match several stylized facts regarding the use of channel systems by central banks. Moreover, we could derive several policy implications that we have summarized in Section 6. Perhaps the most important result is that interest-rate rules are meaningless in a channel system. In a channel system, any policy must be characterized through an interest-rate corridor rule. This is a new insight, which goes beyond what we already know from the large and growing body of literature on the optimal design of interest-rate rules. While our paper is a first step toward analyzing a channel system in a general equilibrium model, many aspects have remained unexplored. For example, why is there so little volatility in New Zealand's money market interest rate (see Fig. 2) and so much in the case of the European Central Bank (Fig. 1)? Moreover, we know little about optimal monetary policy in a channel system under stress due to aggregate shocks. Finally, a complementary modeling approach addresses monetary policy as a mechanism design problem (e.g., Wallace, 2005). Such an approach could potentially explain why central banks increasingly use channel systems. These are some of the issues left for future research.