%Paper: ewp-mac/9609002 %From: "Edward J. Green" %Date: Mon, 9 Sep 1996 21:46:36 -0500 %Date (revised): Mon, 9 Sep 1996 21:54:16 -0500 \documentclass[11pt]{article} \setlength{\textwidth}{6.4in} \setlength{\textheight}{21.5cm} \setlength{\topmargin}{0in} \setlength{\headheight}{0in} \setlength{\headsep}{0in} \setlength{\topskip}{0in} \setlength{\oddsidemargin}{0.1cm} \setlength{\parskip}{4pt} \def\Section#1#2{\section{#2 \label{sec:#1}}} \def\Subsection#1#2{\subsection{#2 \label{sec:#1}}} \def\sec#1{{s}ection \ref{sec:#1}} \def\display#1#2{\begin{equation} #2 \label{eqn:#1} \end{equation}} \def\disparray#1#2{\parbox{11cm}{\begin{eqnarray*} #2 \end{eqnarray*}} \hfill \parbox{.6cm}{\begin{equation} \label{eqn:#1} \end{equation}}} \def\eqn#1{(\ref{eqn:#1})} \def\weight{\pi} \def\bib{\relax} \begin{document} \title{Money and Debt in the \\ Structure of Payments} \author{Edward J.~Green\thanks{This paper is based on research conducted when the author was a Visiting Scholar in the Institute for Monetary and Economic Studies of the Bank of Japan. He would like to thank members of the Institute's Division I, including especially Dr.~Hiroshi Fujiki, for comments and suggestions. However, views expressed in the paper are solely those of the author, and do not necessarily represent those of the Bank of Japan, the Federal Reserve Bank of Minneapolis, or the Federal Reserve System.} \\ \strut \\ Federal Reserve Bank of Minneapolis \\ ejg@res.mpls.frb.fed.us} \date{August, 1996 \\ ewp-mac/9609002 \\ http://econwpa.wustl.edu} \maketitle \begin{abstract} Freeman (1996) formulates a model in which payment arrangements based on intermediated debt that is settled using money can achieve higher welfare than direct money payment achieves. Freeman finds that a monetary authority can sometimes further improve welfare, and achieve efficiency, by participating in a secondary market for debt. The main result of this paper is that a private intermediary can also achieve efficiency by means of novation and substitution, a contractual device widely used by clearinghouses. The features of institutional governance required for either a central bank or a clearinghouse to achieve efficiency, particularly features related to ``central-bank independence,'' are discussed informally. \end{abstract} \setlength{\parskip}{4pt} \Section a{Introduction} A famous aphorism in economics is that money exchanges for goods, and goods for money, but goods do not exchange for goods. However, if one interprets `money' to mean base money or other outside money (such as balances held at a central bank), then the aphorism's simple pattern of money-for-goods exchange hardly captures the structure of actual transactions. The goal of this paper is to understand the structure of transactions more closely, and to begin to address two major issues regarding it. Notwithstanding the dissimilarity among various payment arrangements at a fine-grained level, most such arrangements have two main structural features in common. First, with few exceptions (such as cashier's checks and some wire-transfer networks based on real-time gross settlement), payment arrangements involve the creation of short-term debt of the payor to the payee that is settled through intermediaries. Second, although incurring short-term indebtedness is a substitute for using money for the purchase of a good, these debt-based arrangements do not wholly replace money because money is used to settle the debt.\footnote{Throughout this paper, the term `money' refers to outside money.} Specifically, then, this paper concerns payment arrangements based on intermediated debt that is settled using money. These arrangements include checks, wire-transfer systems with netting arrangements, credit cards, and the like. These two features lie at the root of current discussions regarding welfare and policy aspects of the ``payments system.'' To begin, regarding large-value payments especially, there is controversy over whether or not the creation of debt is a desirable feature of a payment system. Given that there is a feasible way to make a cash transaction or to achieve gross settlement of an electronic transaction in real time, it is not obvious what is the gain from making payments in a way that involves creation of debt at an interim stage. In practice the creation of debt carries at least a small risk of inability to settle, so one would not choose arrangements involving netting or other forms of debt creation if cash or gross-settlement arrangements were equally good in other respects. To the extent that the concentration of this debt in the possession of an intermediary should be cause for additional concern, this argument becomes even more persuasive. In order to make any case for payment-system arrangements involving intermediated debt, therefore, some specific benefit must be found. Particularly in the case of electronic payments where the real cost of making a transaction is extremely small, the mere fact that netting economizes on the number of transactions is unlikely to be a sufficient consideration. Thus it is important to understand whether or not there is some additional benefit from using intermediated debt as a means of payment. The theoretical basis for such understanding is provided by Scott Freeman (1996), who shows that such a benefit does exist in some model environments.\footnote{Although I do not explicitly consider risk of the payor's inability to settle in this paper, Freeman does consider it. He finds that the benefit to using intermediated debt is robust to the existence of some level of settlement risk.} The use of cash settlement for the debt created in the payment system raises a further issue regarding the appropriate role of the public sector, and especially of a central bank. As of today, different countries are taking various stands on this issue. In some countries the government is solely a regulator of the payment system, while in others the government is an active participant. In either case, there is a subordinate issue of how to apportion the responsibility for public-sector involvement among the treasury, the bank-supervisory agency, and the central bank; and countries differ in their approach to this as well.\footnote{An issue that is related, although beyond the scope of this paper, concerns the scope of private-sector participation. By their regulatory policies, some governments are encouraging non-bank firms to enter the payments industry, while others are inclined to erect legal barriers to such entry.} Most current discussion of these issues considers the extent to which profit-maximizing operation of the payment system might potentially interfere with the conduct of monetary policy. There is consensus, although not unanimity, that this is not an urgent problem. However, there is another relevant issue that has not been much discussed: whether participation by the monetary authority can potentially enhance the economic efficiency of the payment system.\footnote{It is sometimes suggested that the central bank can enhance payment-system efficiency due to its ability to guarantee immediate and final payment, which private-sector intermediary cannot do. This suggestion seems to reflect a view that a private intermediary would face potential liquidity crises analogous to bank runs, which the central bank would not face because of its ability to issue new fiat money. However, if a central bank is empowered to serve as a lender of last resort to a private payment-system intermediary, then this observation is not sufficient to show that it must also participate in the payment system on a day-to-day basis, any more than the possibility of bank runs shows that the central bank must do a day-to-day business as a commercial bank.} In this paper, I adress this efficiency issue the context of Freeman's model.\footnote{As a model of a central bank, Freeman's model is clearly a partial-equilibrium model. An overall judgment about whether a central bank should participate in the payment system should take into account the opportunity cost of such participation with respect to its other objectives. However, if the participation of the monetary authority in the payment system can enhance its economic efficiency, then there is at least a prima facie case for that participation.} Freeman shows that the potential of a central bank to enhance payment-system efficiency can only be evlauated by close study of the economy concerned. For some parametrizations of the model economy, a laissez-faire market in intermediated debt is efficient. For others, restrictions on private agents' market access entail that the monetary authority can improve welfare relative to some baseline by participating in a secondary market for debt that has not yet settled. The baseline to which I refer is the payment system that would be efficient if only a subset of the restrictions on market access were in force. Of course, to make a strong case for the need for the central bank to be a payment-system operator, it would have to be shown that its participation can improve welfare relative to the best payment system that a purely private system could implement in precisely the economy where its participation is being envisioned. Freeman's model is not formulated at a sufficiently fundamental level to answer this question in a fully convincing way, but it comes close to doing so. I will show that efficiency requires an asset that is a perfect substitute for currency, in a sense that I will make precise. I extend the model economy to permit a private-sector intermediary to trade its own debt obligation for the debt issued by the initial payor, thus providing such a perfect-substitute asset in the model environment. Since the original debt claim is transferred from the payee to the intermediary, this trade of debt claims is tantamount to novation and substitution, a contractual device widely used by clearinghouses. Direct participation of the monetary authority is not essential to achieve efficiency in this model. This result can even hold in the extended version of a model environment that Freeman studies where intermediaries are unable to settle some of the debt that they issue. Both the version of the model with central-bank participation and the version with novation and substitution implicitly prejudge the issue of asset substitutability, since they abstract from aspects of the economy such as privacy of information and limited or costly enforceability of commitments, which might or might not give agents reason to regard a central bank as a more (or possibly less) trustworthy institution than a private clearinghouse. Although such issues related to ``credibility'' and institutional governance lie beyond the scope of the formal model, it is clear that they are inseparable from the market-equilibrium issues that are formalized in the model. In particular, issues that determine the effectiveness of participation by a central bank in the payments system appear closely related to those that arise with respect to ``political independence'' of a central bank. \Section b{Modelling strategy} To address the welfare questions discussed in the introduction requires a model in which the following three means of payment, which are observed in actual economies, emerge endogenously in an equilibrium. \begin{itemize} \item Money is used directly as a medium of payment for goods. \item Some purchases of goods are also financed by the issuance of private debt, and money must be used to pay these off. The use of money for settling debt is conceptually distinct from its direct use as a medium of exchange. In the equilibrium, one should be able to identify separate transactions where the two types of use occur. \item Besides there being transactions in which money is exchanged for a good, there are also transactions in which money is exchanged for debt that has not yet been settled.\footnote{This secondary-market transaction can be structured in various ways. The debt can be in the form of a security payable to the bearer, or it can be assignable, or novation can occur.} \end{itemize} To formulate such a model, I follow the general strategy that was introduced by Sargent and Wallace (1982), who exhibited an equilibrium that has the first two attributes. The idea is to use an overlapping-generations model, so that money can have value in equilibrium and its use can be essential for efficiency, and to posit some heterogeneity among agents within each generational cohort in order to provide incentive and efficiency rationale for other types of transaction to occur. I proceed by first constructing two simpler model economies, in order to make clear how subsystems of the main model work. To begin, I specify the population and endowment structure that are common to all of the models. Before beginning the technical exposition, let me emphasize that the overlapping generations structure of the model is a technical convenience. The aim is to formulate the simplest possible model in which the various kinds of transaction observed in actual economies can all play a role, and in which welfare questions regarding those transactions can be framed and analyzed. The spirit of the modelling exercise is that this model is exemplary of models with lack of double coincidence of wants, and with restrictions on agents' access to markets. These fundamental economic features of the model are what lead to the results; consequently one would confidently expect parallel results from the analysis of more ``realistic'' models with the same features. From this perspective, the specific demographic structure of the model formulated here is a matter of convenience, although it might be of great significance in the case of other applications. \Section c{The model} \Subsection d{The population} At each date $1,2,3,\ldots$, a set $A_t = C_t \cup D_t$ of agents is born. $C_t$ and $D_t$ each consist of a continuum of agents, of measure 1. I will sometimes refer to the agents in $C_t$ and $D_t$ as {\it creditor} and {\it debtor} agents, respectively, since the debtors will borrow from the creditors in the equilibrium trading pattern of the model. Each agent lives for two periods (dates $t$ and $t+1$). Furthermore there is a set $C_0$ of agents, the ``initial old'' (also a continuum of measure 1) who live only at date 1. Define $C = C_1 \cup C_2 \cup \ldots$ and $D = D_1 \cup D_2 \cup \ldots$. Each agent in $A_t$ is endowed with one unit of a perishable good at date $t$, and with nothing at date $t+1$. Agents in $C$ and $D$ are endowed different goods. Each agent in $C_0$ is endowed with one unit of fiat money but with no consumption good. Let $x_{1t}$ (resp.~$x_{2t}$) be an agent's consumption of the endowment good of agents in $C$ (resp.~$D$) at date $t$. An agent must consume a nonnegative quantity of each good at each date. Let the utility function of an agent be % \display a{w_i(x_{1t}, x_{2t}, x_{1(t+1)}, x_{2(t+1)}) = \cases{u(x_{1t}) + v(x_{2(t+1)}) & if agent $i$ is in $C$;\cr &\cr u_*(x_{1t}) + v_*(x_{2t}) & if agent $i$ is in $D$;\cr &\cr v(x_{21}) & if agent $i$ is in $C_0$.\cr }} % Assume that all of the functions on the right side are strictly increasing and strictly concave, and satisfy the Inada condition that the limit of the derivative as the argument tends to 0 from the right is infinite. Given this specification of utility functions, and given the focus on stationary allocations in this paper, the following notation that supresses time subscripts will be convenient. % \begin{eqnarray*} x_1 && \hbox{consumption of $x_{1t}$ by an agent in $C_t$;} \\ \strut \\ x'_2 && \hbox{consumption of $x_{2(t+1)}$ by an agent in $C_t$;} \\ \strut \\ x^*_1 && \hbox{consumption of $x_{1t}$ by an agent in $D_t$;} \\ \strut \\ x^*_2 && \hbox{consumption of $x_{2t}$ by an agent in $D_t$.} \\ % \end{eqnarray*} Note that agents in $D$ wish to trade with members of their own age cohort in $C$, while agents in $C$ wish to trade with members of the next age cohort in $D$. Thus it will be seen that, as in the standard overlapping-generations model of money (as well as most other models in which fiat money is endogenously valued in equilibrium), there can be no mutually advantageous trades unless fiat money has value. \Subsection e{Efficiency} I concentrate on stationary allocations, that is, those in which corresponding agents in distinct age cohorts receive identical lifetime-consumption bundles, except for the dating of their goods. (The consumption of an agent in $C_0$ is identical to the consumption of an agent in $C_t$ at date $t+1$.) An {\it efficient stationary allocation} is a stationary allocation problem that solves the problem of maximizing a weighted sum of utilities of the members of $C$ and $D$ in each age cohort. That is, $(\hat x_1, \hat x'_2, \hat x^*_1, \hat x^*_2)$ is efficient if, for some $\weight > 0$, it solves the problem of maximizing % \display c{\hbox{Maximize} \left[ u(x_1) + v(x_2') \right] + \weight \left[ u_*(x^*_1) + v_*(x^*_2) \right] } % subject to the feasibility constraints that % \display d{x_1+x^*_1=1 \hbox{\ and\ } x_2'+x^*_2=1.} A necessary and sufficient condition for a feasible stationary allocation to be efficient is that % \display e{{v'(x'_2) \over u'(x_1)} = {v_*'(x^*_2) \over u_*'(x^*_1)}.} I study this criterion of efficiency because of its technical simplicity, and because it implies the standard Pareto-efficiency criterion. An efficient stationary allocation is Pareto efficient in the set of all feasible allocations of the infinite-horizon economy, by a result of Okuno and Zilcha (1980). There is a specific allocation that I will be concerned with implementing under various constraints on market access. To define it, consider a two-agent exchange economy. The first agent is endowed with one unit of good 1, and has utility function $w(x) = u(x_1) + v(x'_2)$. The second agent is endowed with one unit of good 2, and has utility function $w_*(x^*) = u_*(x^*_1) + v_*(x^*_2)$. Define the stationary allocation $(\tilde x_1, \tilde x'_2, \tilde x^*_1, \tilde x^*_2)$ by stipulating $(\tilde x_1, \tilde x'_2)$ and $(\tilde x^*_1, \tilde x^*_2)$ to be the Walras consumption bundles of these two agents. Note that equation \eqn e is a necessary condition for a Walras equilibrium of the two-agent economy, so the corresponding stationary equilibrium of the infinite-horizon economy is efficient. Clearly the Walrasian price that supports this equibrium is \display f{\tilde p = \left( {1 \over \tilde x^*_1}, {1 \over \tilde x'_2} \right).} \Subsection f{Market access, securities, and equilibrium} I complete the specification of the economy by imposing explicit constraints on agents' access to markets in each periods.\footnote{This access is called `market participation' elsewhere, but I have already used `participation' in a different sense in the introduction. In a formal sense, of course, the fact that each agent has access to markets in only two periods is already a constraint. The constraints to be introduced here will impede trade within an age cohort.} In each period, there will be a sequence of sub-periods. In each sub-period, only a subset of the agents currently alive will be able to trade or settle debts. In order for trade or debt settlement to be transacted between agents who do not have direct access to one another, money or another security must be accepted by a third agent or even by several intermediate agents. Equilibrium is defined in terms of two features: that agents are price takers who make optimal trading plans, given prices in the markets to which they have access (including correctly anticipated prices in markets to which they will have future access); and that markets clear.\footnote{That is, the definition of equilibrium is in the spirit of Radner (1972). A fully adequate equilibrium concept for this environment would allow for the endogenous introduction of securities, as in Allen and Gale (1988) Instead, for each market, I specify an exogenous set of securities to be traded. In principle this is a shortcoming but, particularly since the equilibria to be studied here support efficient stationary allocations, apparently there would be no scope for the introduction of further securities. That is, I believe that these equilibria would continue to be equilibria if a robustness-to-innovation requirement were explicitly imposed.} For clarity, I will consider three different access-constraint specifications below. In the next section, I will specify the constraints in such a way that only the use of fiat money is required to support an efficient equilibrium. Following that, I will specify them in such a way that debt needs to be used, as well as fiat money. Finally I will specify the constraints in such a way that the debt must be intermediated in order to be settled. Also in this final specification, either the stock of money must fluctuate within each period, or else the debt must be exchanged for debt issued by the intermediary (that is, novation must occur), in order for an efficient stationary equilibrium to be supported. \Section g{Modelling money, debt, and intermediation} \Subsection h{A basic overlapping-generations structure: valued fiat money} Suppose that, at each date $t = 1,2,\ldots$, all of the traders currently alive are able to trade among themselves in the following pattern. First, the agents in $C_{t-1}$ trade with those in $D_t$. Subsequently the agents in $D_t$ trade with those in $C_t$. I will show that, because each agent in $C_0$ holds a unit of money, there is a trading pattern for goods that can achieve efficiency in this market structure. Young $D$ agents give some of their endowment to old $C$ agents, and subsequently they receive some of the endowment of the young $C$ agents. The entire money stock is passed in the opposite direction to goods at each stage, so that the old $C$ agents continue to be the money holders at the beginning of each period. If prices are set appropriately, markets clear and all agents have incentive to make the efficient trades. To formalize this idea, let each period $t$ be divided into two sub-periods, $t.1$ and $t.2$. Market participation is described by the following table, which lists the traders who have access and the goods that are traded within each sub-period. Money is also traded in each sub-period, and it is the numeraire.\footnote{The only equilibrium in which the price of money is zero is autarky.} It will be represented as the last coordinate of a price vector. \display g{\begin{array}{l c c c c} \hbox{sub-period} & \qquad & t.1 & \quad & t.2 \\ \strut \\ \hbox{access} && C_{t-1}, D_t && C_t, D_t \\ \strut \\ \hbox{traded} && 2, m && 1, 2, m \end{array}} That is, in the market at $t.1$, there is a price $p^1 = (p^1_2, 1)$, which has only two coordinates since good 2 (that is, the debtors' endowment good) is the only good available to be traded. In the market at $t.2$, there is a price vector $p^2 = (p^2_1, p^2_2, 1)$, since both goods 1 and 2 are available in the market. (By the Inada condition on $v_*$, debtors will not trade away their entire endowments at $t.1$.) I adopt the following notation to represent net trades. A net trade is always represented by the variable $z$, which can have the following superscripts and subscripts. \begin{itemize} % \item[-] An asterisk superscript immediately following $z$ indicates that the net trade belongs to an agent in $D$. % \item[-] A numerical superscript indicates the subperiod in which the net trade is made. % \item[-] If the numerical superscript is primed, it indicates that the net trade is made by an agent in the second period of life (that is, by an agent in $A_{t-1}$ in period $t$). % \item[-] A subscript indicates a coordinate of $z$. A numerical subscript 1 or 2 refers to one of the two goods available in the period of the market, and a letter subscript $m$ (money), $d$ (debt issued in the current period), $d'$ (debt issued in the preceding period). or $n$ (debt arising from novation, which will be introduced later in the paper) may also occur. % \item[-] The letter $p$ denotes a price vector. A numerical superscript indicates the sub-period of the market to which this price corresponds. A subscript, which can take the values just defined, indicates a coordinate. % \end{itemize} An agent in $C_t$ has access at $t.2$ (for $t>0$) and at $(t+1).1$. At $t.2$, the agent makes a net trade $z^2 = (z^2_1, z^2_2, z_m^2)$ and at $(t+1).1$ he makes a net trade $z^{1'} = (z^{1'}_2, z_m^{1'})$. Thus, the market-constrained optimization problem of an agent in $C_t$ is to maximize % \display h{u(x_1) + v(x'_2)} % subject to % \begin{displaymath} \begin{array}{r c l c r c l} (x_1, x'_2) & \in & \Re^2_+; & \qquad & z_m^2 & \ge & 0; \\ \strut \\ x_1 & = & 1 + z^2_1; && z_m^{1'} & \ge & -z_m^2; \\ \strut \\ x'_2 & = & z^{1'}_2; && p^2 \cdot z^2 & \le & 0; \\ \strut \\ z^2_2 & \ge & 0; && p^1 \cdot z^{1'} & \le & 0. \end{array} \end{displaymath} % (Note that, by the specification of the trader's endowment and utility function, utility maximization will clearly imply that $z^2_2 = z^{1'}_1 = 0$ and $z_m^{1'} = -z_m^2$. A trader in $C_0$ only makes net trade $z'$, and utility maximization clearly implies that $z_m^{1'}=-1$, that is, an old creditor disposes of his entire money stock.) An agent in $D_t$ has access at $t.1$ and $t.2$, and makes net trades $z^{*1} = (z^{*1}_2, z_m^{*1})$ and $z^{*2} = (z^{*2}_1, z^{*2}_2, z_m^{*2})$ at these dates respectively. His market-constrained optimization problem is to maximize % \display i{u_*(x^*_1) + v_*(x^*_2)} % subject to % \begin{displaymath} \begin{array}{r c l c r c l} (x^*_1,x^*_2) & \in & \Re^2_+; & \qquad & z_m^{*1} & \ge & 0; \\ \strut \\ x^*_1 & = & z^{*2}_1; && z_m^{*2} & \ge & -z_m^{*1}; \\ \strut \\ x^*_2 & = & 1 + z^{*1}_2 + z^{*2}_2; && p^1 \cdot z^{*1} & \le & 0; \\ \strut \\ z^{*1}_2 & \ge & -1; && p^2 \cdot z^{*2} & \le & 0. \end{array} \end{displaymath} Since $C_{t-1}$, $C_t$, and $D_t$ all have the same number of agents, the market-clearing conditions for this economy are that % \display j{z^{1'} = -z^{*1} \hbox{\ and\ } z^2 = -z^{*2}.} Now it is straightforward to verify, using equation \eqn e, that the Walrasian stationary allocation $(\tilde x_1, \tilde x'_2, \tilde x^*_1, \tilde x^*_2)$ is an equilibrium allocation of this market structure. Equilibrium is supported by the following net trades and prices. % \display k{\begin{array}{r c l c r c c c l} p^1 & = & \left( {1 \over \tilde x'_2}, 1 \right); & \qquad & z^{1'} & = & -z^{*1} & = & (\tilde x'_2, -1); \\ \strut \\ p^2 & = & \left( {1 \over \tilde x^*_1}, {1 \over \tilde x'_2}, 1 \right); && z^2 & = & -z^{*2} & = & (-\tilde x^*_1, 0, 1). \end{array}} Because the $C$ agents closely resemble the agents in the standard overlapping-generations model, and the $D$ agents want only to trade their endowment good for a contemporaneous good, it is not surprising that the efficient equilibrium here bears very close resemblance to the efficient overlapping-generations equilibrium. In particular, money has value but there is no credit and there is no role for a monetary authority. \Subsection i{Reversing the order of transactions within a period: debt securities} Now consider the opposite order of transactions. That is, suppose that first the agents in $D_t$ trade with those in $C_t$ and subsequently the agents in $C_{t-1}$ trade with those in $D_t$. For fiat money to be passed from the old $C$ agents to the young ones, it would have to pass through the hands of the young $D$ agents. But since those agents do not meet the old $C$ agents until it is too late to deal with the young ones, that cannot happen. If it is possible for young agents to issue debt securities that they pay in money when they are old, then there is a solution. The young $D$ agents can use these securities to finance their consumption of goods purchased from young $C$ agents, then give some of their endowments to old $C$ agents in return for their money, and finally carry the money into the next period and then use it to repay the holders (who will still be alive since they are young when the debt securities are issued). This repayment of debt requires an additional sub-period in each period, which I will assume to occur between the two sub-periods where markets occur. Although from an ex-post perspective repayment of debt is a mandatory transfer, not a voluntary exchange, it will be treated formally as an exchange. That is, after repaying his debt, a debtor holds a zero quantity of debt in his portfolio. The debt security traded in this economy is a commitment to pay one unit of money to the bearer, at some time during the period following the period in which it is issued. The quantity of this security that an agent acquires will be denoted by $d$. That is, issuing a unit of debt corresponds to choosing $d=-1$. The following table shows the order of transactions within each period $t$. The bottom row shows, for each sub-period, which goods (1 and 2) and assets ($d$ and $m$) are traded. These are listed in the order that they appear in the price vector. The numeraire is last. % \display l{\begin{array}{l c c c c c c} \hbox{sub-period} & \qquad & t.1 & \quad & t.2 & \quad & t.3 \\ \strut \\ \hbox{access} && C_t, D_t && C_{t-1}, D_{t-1} && C_{t-1}, D_t \\ \strut \\ \hbox{traded} && 1, 2, d && d, m && 2, m \end{array}} The market-constrained optimization problem of an agent in $C_t$ is to make net trades $z^1$, $z^{2'}$, and $z^{3'}$ that maximize % \display m{u(x_1) + v(x'_2)} % subject to % \begin{displaymath} \begin{array}{r c l c r c l} (x_1, x'_2) & \in & \Re^2_+; & \qquad & \\ \strut \\ x_1 & = & 1 + z^1_1; && p^1 \cdot z^1 & \le & 0; \\ \strut \\ x'_2 & = & z^{3'}_2; && p^3 \cdot z^{3'} & \le & 0; \\ \strut \\ z^1_2 & \ge & 0; && z_m^{3'} & \ge & -z_m^{2'}; \\ \strut \\ z^{2'}_m & \ge & 0 && z^{2'}_m & = & z^1_d. \end{array} \end{displaymath} The market-constrained optimization problem of an agent in $D_t$ is to make net trades $z^{*1}$, $z^{*3}$, and $z^{*2'}$ that maximize % \display n{u_*(x^*_1) + v_*(x^*_2)} % subject to % \begin{displaymath} \begin{array}{r c l c r c l} (x^*_1, x^*_2) & \in & \Re^2_+; & \qquad & \\ \strut \\ x^*_1 & = & z^{*1}_1; && p^1 \cdot z^{*1} & \le & 0; \\ \strut \\ x^*_2 & = & 1 + z^{*1}_2 + z^{*3}_2; && p^3 \cdot z^{*3} & \le & 0; \\ \strut \\ z^{*1}_2 & \ge & -1; && z^{*2'}_m & \ge & -z^{*3}_m; \\ \strut \\ z^{*3}_m & \ge & 0 && z^{*2'}_m & = & z^1_d. \end{array} \end{displaymath} The market-clearing conditions for this economy are that % \display o{z^1 = -z^{*1}; \hbox{\ } z^{2'} = -z^{*2'}; \hbox{\ and\ } z^{3'} = -z^{*3}.} Again, it is straightforward to verify that the Walrasian stationary allocation $(\tilde x_1, \tilde x'_2, \tilde x^*_1, \tilde x^*_2)$ is an equilibrium allocation of this market structure. Equilibrium is supported by the following net trades and prices. % \display p{\begin{array}{r c l c r c c c l} p^1 & = & \left( {1 \over \tilde x^*_1}, {1 \over \tilde x'_2}, 1 \right); & \qquad & z^1 & = & -z^{*1} & = & (-\tilde x^*_1, 0, 1); \\ \strut \\ & & && z^{2'} & = & -z^{*2'} & = & (-1, 1); \\ \strut \\ p^3 & = & \left( {1 \over \tilde x'_2}, 1 \right); && z^{3'} & = & -z^{*3} & = & (\tilde x'_2, -1). \end{array}} The efficient equilibrium in this transactions structure involves use of both valued fiat money and debt securities, but the debt securities are not intermediated and there is no role for a monetary authority. \Subsection j{Separation within a cohort: intermediated debt securities} Now I come to one of the two main market structures to be studied in this paper. In this structure, not all agents of the same cohort can communicate directly with one another in the second period of their lives. Specifically, some debtors are not able to repay creditors to whom they have issued debt. Those creditors therefore need to sell their debt to other agents with whom the debtors can communicate. These purchasers of debt thus serve as intermediaries in the settlement of the original transactions. To formalize this environment, define the partitions $C_t = C_t' \cup C_t''$ and $D_t = D_t' \cup D_t''$, for each $t \ge 1$. Define $C_0'' = C_0$. For each $t \ge 1$, let there be $\gamma \in (0, 1)$ traders in $C_t'$ and $\delta \in (0, 1)$ traders in $D_t'$. The market structure will be specified in such a way that creditors in $C_t'$ cannot be repaid at $t+1$ by debtors in $D_t''$. To do so, consider the following sequence of trading-opportunity stages within each period $t > 1$. (Only the first and last stages occur for $t=1$.) \begin{enumerate} % \item All agents in $A_t$ trade with one another. % \item All agents in $C_{t-1}$ enter the market. Agents in $D_{t-1}'$ also enter the market, and have the opportunity to pay the debt securities to their creditors. % \item All agents in $C_{t-1}$ can trade money for outstanding debt securities that have not been settled. For now, assume that no new debt can be issued in this sub-period. % \item Agents in $C_{t-1}'$ trade with agents in $D_t$, and then leave the market.\footnote{Alternatively it could be specified that all agents in $C_{t-1}$ trade with agents in $D_t$ in this sub-period. In equilibrium, every agent in $C_{t-1}''$ would make a zero net trade in this market.} % \item Agents in $D_{t-1}''$ enter and have the opportunity to pay their debt securities to anyone in $C_{t-1}''$ who is holding them. % \item Agents in $C_{t-1}''$ trade with agents in $D_t$. % \end{enumerate} This structure can be represented in tabular form as follows. % \display q{\begin{array}{l c c c c c c c c c c c c} \hbox{sub-period} & \quad & t.1 & \enspace & t.2 & \enspace & t.3 & \enspace & t.4 & \enspace & t.5 & \enspace & t.6 \\ \strut \\ \hbox{access} && C_t && C_{t-1} && C_{t-1} && C_{t-1}' && C_{t-1}'' && C_{t-1}'' \\ && D_t && D_{t-1}' && && D_t && D_{t-1}'' && D_t \\ \strut \\ \hbox{traded} && 1, 2, d && d', m && d', m && 2, m && d', m && 2, m \end{array}} There is an important distinction between sub-periods $t.2$ and $t.5$, on the one hand, and sub-period $t.3$, on the other. In $t.2$ and $t.5$, debt is being settled at face value. In contrast, in $t.3$, debt is being purchased at market terms prior to settlement. As in the other markets where voluntary exchange occurs, the price must be determined endogenously by agents' optimization together with market-clearing. When he is young, an agent's incentive to trade with another member of his cohort is evidently affected by what he knows or believes about both his own subgroup and his trading partner's subgroup in the market structure when they are old. I will assume that no information about these matters is available until the second period of agents' lives. Later I will discuss an implication of this assumption for welfare analysis. Another question concerns the structure of debt security issuance. Is trade bilateral, so that each young $D$ agent issues one debt security to a single young $C$ agent, or does each young $D$ agent make small purchases from many young $C$ agents, so that each $C$ agent holds a diversified portfolio of small-denomination debt securities afterwards? Risk-diversification considerations would seemingly lead the $C$ agents to prefer the latter arrangement, if it is feasible.\footnote{Moreover, if a bilateral arrangement is what one intends to have emerge as an equilibrium trading pattern, there must be some constraint on (or cost of) debt security issuance to induce it. In that case, the terms of trade would be negotiated by bargaining within each two-member trading coalition, rather than taken by agents as parametrically determined by an economy-wide price.} The diversified, non-strategic trading arrangement will be modelled here. This arrangement implies an asymmetry in the interpretation of the quantity of debt securities held by an agent. If an agent holds a positive quantity of these, then that quantity represents a diversified portfolio of securities payable by all issuers in the economy, in proportion to those issuers' amounts of debt outstanding. If the quantity of debt is negative (that is, if the agent is an issuer of debt), then it represents debt issued by the agent himself. As in the market structures studied above, equilibrium is defined in terms of agents' optimization together with market clearing. The objective function of an agent in $C_t$ is slightly different here than above, since his consumption can depend on whether he is in $C_t'$ or $C_t''$. I assume that such an agent maximizes expected utility, assigning probability $\gamma$ to the event that he is in $C_t'$ and consumes bundle $x'$, and $1 - \gamma$ to the event that he is in $C_t''$ and consumes bundle $x''$, in period $t+1$. The optimization problem of an agent in $C$, then, is to choose net trades $z^1$, $z^{2'}$, $z^{2''}$, $z^{3'}$, $z^{3''}$, $z^{4'}$, $z^{5''}$, and $z^{6''}$, to maximize % \display r{u(x_1) + \gamma v(x_2') + (1 - \gamma) v(x_2'')} % subject to constraints. The constraints and market conditions are conceptually straightforward but they are numerous, because the environment is so complex. They are presented in the appendix. The structure of trading in this environment is indicated in Figure 1. Time is on the horizontal axis. A trader's lifespan is depicted by a horizontal bar of two periods' length. Within each period, the sub-periods in which a trader has market access are shown by a thickening of the bar. The top bar (extending only through period 1) is $C_0$. After that, there are three generations having four bars each, representing $D_t'$, $D_t''$, $C_t'$, and $C_t''$ in descending order. $D_4$ is also shown, since those agents have transactions with $A_3$. 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\put(35.00,14.00){\makebox(0,0)[cc]{2}} \put(65.00,14.00){\makebox(0,0)[cc]{3}} \put(95.00,14.00){\makebox(0,0)[cc]{4}} \put(125.00,14.00){\makebox(0,0)[cc]{5}} \put(75.00,0.00){\makebox(0,0)[cb]{{\Large Figure 1}}} \put(4.00,140.00){\makebox(0,0)[lc]{$C_0$}} \put(4.00,132.00){\makebox(0,0)[lc]{$D_1'$}} \put(4.00,124.00){\makebox(0,0)[lc]{$D_1''$}} \put(4.00,116.00){\makebox(0,0)[lc]{$C_1'$}} \put(4.00,108.00){\makebox(0,0)[lc]{$C_1''$}} \put(14.00,100.00){\makebox(0,0)[lc]{$D_2'$}} \put(14.00,92.00){\makebox(0,0)[lc]{$D_2''$}} \put(14.00,84.00){\makebox(0,0)[lc]{$C_2'$}} \put(14.00,76.00){\makebox(0,0)[lc]{$C_2''$}} \put(44.00,68.00){\makebox(0,0)[lc]{$D_3'$}} \put(44.00,60.00){\makebox(0,0)[lc]{$D_3''$}} \put(44.00,52.00){\makebox(0,0)[lc]{$C_3'$}} \put(44.00,44.00){\makebox(0,0)[lc]{$C_3''$}} \put(74.00,36.00){\makebox(0,0)[lc]{$D_4'$}} \put(74.00,28.00){\makebox(0,0)[lc]{$D_4''$}} \end{picture} } \vfil \break \Section k{Inefficiency of equilibrium} The market structure just described permits trading of goods and three financial assets: money ($m\/$), new debt ($d\/$), and seasoned debt ($d'\/$). It is clear that there exists a pattern of trade, involving goods-for-new-debt, goods-for-money, and seasoned-debt-for-money market transactions, as well as settlement of seasoned debt, that achieves the stationary efficient allocation. That pattern of trade requires goods and assets to be exchanged in particular ratios. If those ratios are not the same as the price ratios in a competitive equilibrium, though, then the stationary efficient allocation will not be a competitive equilibrium allocation of the economy. Following Freeman, I show that equilibrium is inefficient in an economy where $\gamma > \delta$. The argument begins by supposing that, in sub-period 1 at date $t-1$, each agent in $C_{t-1}$ has acquired debt securities for 1 unit of money to be delivered at date $t$. (It is easy to see that, except in autarky equilibrium, the entire money stock of 1 unit must be passed from cohort to cohort in a stationary equilibrium.) Note that market clearing in that sub-period implies that each agent in $D_{t-1}$ owes 1 unit of money at date $t$. By diversification, in sub-period 2 at date $t$, each agent in $C_{t-1}$ receives a total of $\delta$ units of fiat money from the traders in $D_{t-1}'$, and is still owed $(1-\delta)$ from the remaining traders in $D_{t-1}$. Traders in $C_{t-1}'$ will not be able to collect their payments from those debtors in sub-period 4, though, so in sub-period 3 they will sell the debt securities still in their possession to other creditors who will participate in sub-period 4. Agents in $C_{t-1}'$ regard debt as worthless except in trade at Stage 3. They will trade away their full inventories at any positive price. Debt is certain to be paid by Stage 5, and agents in $C_{t-1}''$ do not need to use fiat money until Stage 6, so these agents will be willing to pay up to the face value of debt to obtain it at Stage 3. Thus all money held by agents in $C_{t-1}''$, up to the face value of the debt held by agents in $D_{t-1}''$, will be exchanged for that debt. This determines the equilibrium price in the secondary market. At the beginning of Stage 3, the aggregate amount of money that will be provided in settlement of the debt in the possession of agents in $C_{t-1}'$ is $\gamma (1-\delta)$. The total amount of money in the possession of agents in $C_{t-1}''$ is $(1-\gamma) \delta$. Thus the competitive price at Stage 3 of a debt claim for one unit of money is \display b{p^3_{d'} = \min \left[ 1, {(1-\gamma) \delta \over \gamma (1-\delta)} \right] .} If $\delta < \gamma$, then $p < 1$. Thus, if $\delta < \gamma$, then availability of money to intermediaries is a bottleneck in some sense. It remains to be shown that this bottleneck causes Pareto inefficiency. Freeman's argument continues by comparing the amount of consumption enjoyed by an agent in $C'$ with the amount enjoyed by an agent in $C''$ in equilibrium. The following allocation shows that the consumption of an agent in $C'$ is lower, so the fact that ``too few'' debtors have market access in sub-period 2 induces consumption inequality among agents who are identical except for market access. This inequality is risk from an ex-ante perspective, so from that perspective it is a Pareto-inefficient allocation among risk-averse agents.\footnote{The specification that all agents in $C$ are identical ex ante is inessential to producing consumption inequality, although it simplifies the calculation of equilibrium by making all young creditors' decisions identical. Its significance is to make an allocation with consumption inequality, which would be Pareto-incomparable to the equal-consumption allocation if agents were distinguishable ex ante, into a Pareto-inefficient allocation.} Specifically, an agent in $C_{t-1}'$ receives $\delta$ units of money in settlement of debt in Stage 2, and $p^3_{d'}(1-\delta)$ units of money from sale in Stage 3 of debt not yet settled. Thus an agent in $C_{t-1}'$ holds less than 1 unit of fiat money to trade in Stage 4. At Stage 3, an agent in $C_{t-1}''$ spends all of his money received in settlement of debt in Stage 2 to purchase debt at price $p < 1$, which will be settled at par at Stage 5. Thus he will hold more fiat money in Stage 6 than if he had not traded in the secondary market. That is, he will hold more than 1 unit of fiat money to trade in Stage 6. In equilibrium, agents in $D_t$ must sell their endowment good for the same price in Stage 4 as in Stage 6. Therefore an agent in $C_{t-1}''$ consumes more of that good than does an agent in $C_{t-1}'$, since he has more money to spend at the identical price for goods. \Section l{Chartering a monetary authority to achieve efficiency} \Subsection m{Representing a monetary authority within the model} Before presenting a result of Freeman regarding the potential role of a monetary authority in achieving efficiency, it is worthwhile to reflect on what a monetary authority is, and on how it ought to be modelled in this formal environment. First, consider what Freeman (1996, pp.~6, 14) assumes about the monetary authority, and how he characterizes its optimal policy. {\narrower \noindent There exists\dots a monetary authority able to issue fiat money\dots . This authority issues an initial stock of [money] to each initial old creditor. \dots\ Suppose that the\dots monetary authority (or ``central bank'') is now authorized to issue and lend fiat money equal to the nominal amount of debt presented by any of the late-leaving creditors. This central bank loan must be repaid with fiat money upon the arrival\dots of the late-arriving borrowers.\par } Because the monetary authority is described as dealing with the creditors in every cohort, superficially it might seem that the authority must be an infinite-lived agent. In that case, it would be in a position to provide intermediation services that no private agent could provide. There is a convincing argument that this is an inadvisable way to think about the role of a monetary authority or, in general, an agent that carries out public policy.\footnote{A very clear development of this argument is by Neil Wallace (1988), in a discussion of an analogous issue regarding the Diamond-Dybvig model of intermediation.} The criticism has to do with a dilemma regarding how to interpret the restrictions on market access in the model economy. These restrictions could be interpreted as reflecting technological restrictions, but then it would be inexplicable why the monetary authority is not bound by the same constraints that private agents face. Alternatively the restrictions could be interpreted as reflecting institutional or legal constraints from which the monetary authority is exempt, but then the most natural welfare conclusion to draw from the inefficency of competitive equilbrium would be that those constraints on private agents ought to be relaxed in general, not that there is a rationale for a distinguished agent to be granted a special exemption. These seem to be the only tenable interpretations of the market-access restrictions, and neither provides a good basis for understanding the role of a monetary authority. On closer inspection, though, the monetary authority does not intermediate between agents who do not meet one another. At every date, it issues money in sub-period 3, which it uses to purchase seasoned debt. Then, in sub-period 5 at the same date, it absorbs the money that it receives in settlement of this debt. Thus, rather than specifying that there is a special, infinite-lived, agent in the model, one can equally well specify that, in sub-period 2 at each date $t$, one of the agents in $C_{t-1}''$ is designated to be the monetary authority. \Subsection n{How a monetary authority can achieve efficiency} Consider what can be accomplished by such a monetary authority, consisting of one agent in each cohort (specifically in $C_{t-1}''$, at each date $t$) who is authorized to behave differently in one respect, and constrained to behave differently in another respect, from the other agents. This distinguished agent is authorized to create money in sub-period 3, and is required to destroy in sub-period 5 an amount of money equal to what he has created. Specifically the agent is authorized to create $\gamma(1-\delta) - (1-\gamma)\delta)$ units of money for purchase of seasoned debt in sub-period 2, so that (by the argument leading to \eqn b in the laissez-faire case) $p^3_{d'} = 1$. This intervention eliminates the inequality of consumption between agents in $C_{t-1}'$ and those in $C_{t-1}''$ Thus it attains efficiency from the ex-ante perspective. To interpret the monetary authority in this way, as being one of the private agents in the population who is selected to carry out a special responsibility, avoids making the suspect assumption that it has a mysterious technological superiority over the private agents. This interpretion also has a clear implication regarding the nature of the contract to which the monetary authority is subject. It is exempt from the prohibition that other agents face against creating money (that is, against counterfeiting). However, it is expected to absorb the money received in settlement in sub-period 5 (with the exception of money received in settlement of debt in its private portfolio, as opposed to the debt initially purchased with newly created money), rather than to spend that money in sub-period 6 to finance consumption for itself. For such an expectation to be fulfilled, the monetary authority must be constrained in some way, or its incentives must be modified in some way, that is not represented explicitly in the model. This implicit assumption is analogous the implicit assumption of some enforcement technology to compel repayment of debt. Subject to this assumption, the present analysis shows that the difference between a monetary authority and an ordinary private agent is simply one of incentives, and not of intrinsic opportunities or capabilities. (The one obvious advantage that a monetary authority typically enjoys with respect to private banks---a monopoly or at least a competitive advantage in note issuance---is an artifact of government policy rather than being intrinsic.) Nothing in the formal model requires that this special incentive arrangement should be offered only to a single agent. It could be supposed instead that all agents in $C_{t-1}''$ would be subject to the arrangement. However, the implicitly assumed monitoring and enforcement functions are presumably costly to carry out. It would be inefficient to exercise them over all agents in $C_{t-1}''$, or even over several of them, if one agent can make all of the transactions that are required for efficiency. This consideration suggests that the activity of central banking is probably a natural monopoly. \Subsection p{Relationship to central-bank independence} This interpretation of the nature of a monetary authority is different from the social-planner interpretation that economists often make. Nevertheless, it is consonant with the views expressed by distinguished scholars of central banking, such as Cairncross (1988), Cuikerman (1995), Goodhart (1988), and Sayers (1967). Numerous central banks, including the Bank of England, were initially chartered as private joint-stock companies and continued to operate under that form of ownership long after their public-policy roles were firmly established. In many countries today, including the United States, payment-system activities of the central bank continue to be conducted under a corporate charter, and the government is at most a minority owner. Thus it very appropriate to model the monetary authority as being identical to a private agent in most respects. However, despite their corporate form, central banks are organized in a way that induces a markedly different outcome from the operation of an ordinary corporation. ``Ownership'' of a central bank is typically an entitlement to a fixed income stream (analogous to ownership of preferred stock, rather than common stock), with residual profits actually accruing to the government. From a perspective such as that taken by Jensen and Meckling (1976), the government is the true owner of the central bank (as the residual claimant of its profit stream), and thus control of it by the nominal owners is really a means of separating ownership and control in economic terms. To the extent that the nominal owners of the central bank have the primary influence in the appointment and retention of its governor and other senior executives, it is foreseeable that the executives will have relatively small incentive to maximize profit. Other charter provisions, such as restrictions on the types of asset that can be held in the portfolio, complement the ownership structure by constraining the central bank from emulating the decisions that private agents would take to maximizing profits. The fact that central-bank charters have such striking and idiosyncratic provisions, which are recognized to safeguard ``central-bank independence'' from the residual claimant of its profit, constitutes evidence in favor of the modelling approach taken here: to represent a monetary authority as an agent with the same intrinsic opportunities and capabilities as other agents, but with different induced incentives or legal constraints. Conversely, if the market structure specified in \sec j is the one that would exist under laissez-faire, then the fact that an efficient allocation can be achieved by a departure from profit maximization on the part of the monetary authority provides a normative argument in favor of central-bank independence. \Section o{Institutional and contractual alternatives to central-bank participation} A careful statement of the conclusion reached in \sec n is that, if the market structure defined in \sec j would be in effect were there no participation by a monetary authority, then the participation described in \sec m (that is, open-market operations or equivalent intervention to support the secondary-market price of debt in sub-period 3) will support an efficient allocation that Pareto-dominates the laissez-faire equilibrium allocation from an ex-ante perspective. The applicability of this analysis to actual markets is an open question, because it is not certain that the market structure of \sec j is the one that would emerge under laissez-faire. That market structure abstracts from private-sector agents that provide payment services, such as escrow agents and clearinghouses. It also abstracts from contractual features of payment, such as contract netting and novation. In this section, I discuss one such private-sector arrangement that can achieve efficiency in the environment described in \sec j. This arrangment resembles a clearinghouse that uses \textit{novation and substitution} (that is, substitution of debt payable by itself for debt payable by the original issuer) to settle contracts. \Subsection q{A market structure with novation securities} An alternative to having a monetary authority is for traders in $C_{t-1}''$ to issue debt securities---call them \textit{novation securities} at sub-period $t.3$ in return for the debt securities of traders in $C_{t-1}'$ that have not yet been settled. The traders in $C_{t-1}'$ will exchange these novation securites for good 1 in sub-period $t.4$. The novation securities will be paid in sub-period $t.6$, when the agents in $D_t$ who have acquired them will meet the agents in $C_{t-1}''$ who issued them. In equilibrium, both the initial securities and the novation securities will trade at face value. Thus, again, the risk induced by trading-opportunity uncertainty will be fully insured, and efficiency will be attained. The asset structure of this economy is described by adding novation debt (denoted by $n\/$) to the trading structure described in table \eqn q as follows. % \display s{\begin{array}{l c c c c c c c c c c c c} \hbox{sub-period} & \quad & t.1 & \enspace & t.2 & \enspace & t.3 & \enspace & t.4 & \enspace & t.5 & \enspace & t.6 \\ \strut \\ \hbox{access} && C_t && C_{t-1} && C_{t-1} && C_{t-1}' && C_{t-1}'' && C_{t-1}'' \\ && D_t && D_{t-1}' && && D_t && D_{t-1}'' && D_t \\ \strut \\ \hbox{traded} && 1, 2, d && d', m && d', n, m && 2, n, m && d', m && 2, n, m \end{array}} % The budget constraints and market-clearing conditions for this market structure are straightforward modifications of those for the market structure specified in \sec j. With respect to the characteristics of securities that are represented explicitly in this model, there is hardly any difference between this novation security and the money issued and reabsorbed by the central bank in \sec n. Both money and the novation security are issued by agents in $C_{t-1}''$ in sub-period $t.3$ to agents in $C_{t-1}'$ in return for the debt held by those agents. The agents in $C_{t-1}'$ trade the newly-issued security (money or the novation security, depending on the payment arrangement) in sub-period $t.4$ to agents in $D_t$ for those agents' consumption good. The security, or another security of the same type, is thereafter removed from circulation by the issuer. In the case of money, this happens at in sub-period $t.5$ when the seasoned debt that was purchased with newly issued money is settled. In the case of novation debt, the money received settlement of seasoned debt in sub-period $t.5$ is used to settle the novation debt in sub-period $t.6$. Only with respect to the specifics of how removal from circulation is accomplished, does novation debt differ from money in more than name. Implicitly, though, money and novation securities differ in much more than name. What differs between the two asset structures is the institutional framework of ownership, monitoring, and enforcement that must exist to support them. In contrast to the distinctive features of a central bank that have been mentioned in \sec p, a clearinghouse that operates by novation and substitution is subject to roughly the same framework of contract and enforcement as is a private debtor. Although it would be an exaggeration to claim that a central bank is totally unlike a clearinghouse (especially since a clearinghouse is typically chartered as a nonprofit corporation, jointly owned by a group of the banks that it serves, and with restricted powers that prevent it from competing directly with them), in practice the distinction between them is substantial and easy to recognize. Historically, clearinghouses preceded central banks in most industrialized countries, and central banks were chartered in part to address perceived inefficiencies in the payment systems where those clearinghouses were already operating. Despite the presence of central banks, which have tended to be advantaged relative to clearinghouses in point of their legal powers, clearinghouses continue to exist and to play a major role. These facts suggest that probably neither institutional form has an absolute advantage over the other. The basic model of intermediated debt and its extension studied in this section can perhaps provide a basis for thinking systematically about the relative advantages of each type of institution in various circumstances. \Subsection r{An economic definition of \textit{novation and substitution}} A noteworthy feature of the extended model just discussed is that it permits an economic definition of novation and substitution. This operating procedure of a clearinghouse is typically described in institutional terms related to contract law, as in the following quotation from the Group of Experts on Payment Systems of the Central Banks of the Group of Ten Countries (1989).\footnote{This document is widely known as the ``Angell Report.''} {\narrower \noindent ``One type of arrangement would establish a clearing house that would be substituted as the central counterparty in deals submitted for netting by participants in the arrangement, in order to effect a binding multilateral netting among those participants (``multilateral netting by novation and substitution'').\par } Such substitution is exactly what takes place, in the equilibrium of the asset structure discussed in \sec p, when agents in $C_{t-1}'$ swap debt issued by agents in $D_{t-1}$ for novation securities (also debt) issued by agents in $C_{t-1}''$. Each agent in $C_{t-1}$ has a different portfolio of specific debt securities after this swap than beforehand. However, each of these agents has the same net credit position afterwards as beforehand. Agents in $C_{t-1}'$ hold debt securities both before and after the swap, and in equilibrium the face value of the securities (as well as the market value) is the same. Agents in $C_{t-1}''$ change from being only holders of debt before the swap to being both holders and also issuers afterwards, but again there is no change in their net credit position. Thus it is clear that novation and substitution can be defined in economic terms to be \textit{an issuance and exchange of debt that leaves the net credit position of all agents unaffected.} The economic role of novation and substition is to transfer debt from agents who do not have an opportunity to receive settlement of it to other agents who do have that opportunity, without affecting anyone's wealth position, and in such a way that the initial debt-holders have equivalent trading opportunities (that is, ``liquidity'') to what they would have had if their initial debt holdings had been settled rather than being traded. \Section s{Failure of a clearinghouse to settle} There is a consensus among payment-system experts that the failure of a clearinghouse to settle its obligations created by novation and substitution is an especially worrisome systemic risk. This view is clearly expressed by the Group of Experts on Payment Systems of the Central Banks of the Group of Ten Countries (1989). {\narrower \noindent [M]ultilateral netting by novation and substitution has the potential to reduce liquidity risks more than any other institutional form, but this depends critically on the financial condition of any central counterparty to the netting; if the liquidity of a central counterparty is weak, the liquidity risks of this institutional form may be greater than in the case of bilateral netting by novation; the credit risks of this institutional form are generally less than in other forms that have been considered, subject again to the identity and condition of any central counterparty. \par } Although Freeman does not make such a claim, one tempting way to interpret his result is that the inability of agents in $C''$ to settle novation securities makes the involvement of a monetary authority indispensible to attain efficiency in his model economy. Such an interpretation would be mistaken for two reasons. Before I discuss these reasons, let me mention that Freeman's model has a feature that I have omitted from the version developed in \sec n. Freeman posits that, before the beginning of sub-period $t.6$, the agents in $C_{t-1}$ and in $D_t$ are exogenously and randomly dispersed among several \textit{islands}. (This sequestration lasts only for the duration of the sub-period, so the debtor agents are able to trade in period $t+1$ exactly as specified in \sec n, or in \sec q if novation securities are traded.) If agent $\alpha \in D_t$ has accepted a novation security issued by agent $\alpha'' \in C_{t-1}''$, and $\alpha$ is on island $\iota$ in sub-period $t.6$, and $\alpha''$ is on island $\iota'' \neq \iota$ in sub-period $t.6$, then $\alpha''$ cannot settle the novation security that $\alpha$ holds. Despite this inability of prospective intermediaries in Freeman's model economy to settle all (or even most) of the novation securities that they issue, the market structure involving those securities will still be efficient. To see this, suppose that there are $I$ distinct islands. If the face value of novation securities issued by an agent in $\alpha'' \in C_{t-1}''$ is $\phi$, and if those securities are traded to agents in $D_t$ who are dispersed equally among the islands, then only a subset of the securities having value $\phi / I$ will be able to be settled. In sharp contrast, $\alpha''$ will receive settlement on all of the seasoned debt $d'$ for which he trades novation securities that he issues. Consequently traders in $C_{t-1}''$ will bid the novation-security price of seasoned debt (that is, $p^3_{d'} / p^3_n\/$) up to $I$, rather than only up to par. Subsequently, in sub-period $t.4$, agents in $D_t$ will recognize that only $1/I$ of the novation debt will be settled, so as a result of their optimization, the money price $p^4_n$ of a a unit of the novation security (specified to be settled in sub-period $t.6$ for one unit of money) in that sub-period will be only $1/I$. Thus, the amount of good 2 that an agent in $C_{t-1}'$ can obtain by exchanging a unit of seasoned debt for novation securities and then exchanging those for consumption is $i \cdot (p^4_n / p^4_2) = 1/p^4_2$, which is the same amount that the agent could obtain in the model economy studied in \sec q. That is, equilibrium in a version of that model economy with islands would still be efficient, because agents with rational expectations would fully adjust in market equilibrium for the occurrence of settlement failure on the part of intermediaries. The efficiency of this equilibrium is the first reason why it would be mistaken to suppose that participation of a monetary authority is necessary to attain efficiency in Freeman's model. Of course, the argument in the preceding paragraph makes it clear that the intermediary's inability to settle in the model economy differs radically in its foreseeability from the type of settlement failure on the part of an actual intermediary that concerns policymakers so much. This is not to say that policymakers' concerns are necessarily warranted, but rather that models of settlement do not yet reflect some of the features of the actual economy that are crucial to reasoning conclusively about those concerns. The other reason why it would be mistaken to interpret Freeman's model as justifying a necessary role for a monetary authority is directly related to the considerations in \sec m and \sec q, regarding the constraints facing a central bank and their relationship to the constraints that face a clearinghouse. The import of my arguments in those sections is that a central bank cannot be regarded as being intrinsically a better type of institution than a clearinghouse. Certainly, given the potential for the payment system to be abused for political ends, few people would be enthusiastic about transferring the main settlement responsibilities from a smoothly functioning clearinghouse to a central bank that lacked independence. On the other hand, as policymakers recognize, if the structure of a clearinghouse raises prudential concerns, one needs to examine whether the structure can be strengthened before concluding that the only solution is for the central bank to take over its function. \Section t{Conclusions} This paper has been concerned with the welfare analysis of central-bank and clearinghouse intervention in payment arrangements. At a formal level, this is done by extending a model of the use of intermediated debt for payment, so that private-sector intermediaries can issue debt that corresponds to the clearinghouse practice of novation and substitution. If such debt can be issued, then the resulting market equilibrium under laissez-faire is efficient, so there is no need for direct participation by a monetary authority. This result can even hold in the extended version of a model environment (which is seen to be very special, however) where intermediaries are unable to settle some of the debt that they issue. Although issues of institutional governance lie beyond the scope of the formal model, the analysis makes it clear that they are inseparable from the market-equilibrium issues that are treated explicitly. Whether or not efficiency might require a central bank to participate in the payments system depends on the degree to which a central bank can promise reliably and credibly to reabsorb money that it issues to facilitate payments, and also on whether the commercial-law framework governing the operation of a private-sector payments intermediary is sufficient to warrant agents' use of debt issued by the intermediary as a money-like medium of exchange. The credibility of a central bank's promise about reabsorption evidently depends, in turn, on its governance structure. It is likely that the institutions of central-bank governance necessary for credible participation in the payments system are essentially identical to those that are necessary for effective conduct of monetary policy in a narrow sense. Thus, to whatever extent that there is a need for a central bank to participate directly in the payments system, this need reinforces the considerations in favor of chartering a ``politically independent'' central bank. Moreover, the need for political independence suggests that the central bank would typically be a more appropriate public-sector participant in the payments system than would the treasury or another agency under the immediate control of the government. \vfill \eject \begin{center} {\Large Appendix: Optimization and Market Clearing} \end{center} The optimization problem of an agent in $C$ is to choose net trades $z^1$, $z^{2'}$, $z^{2''}$, $z^{3'}$, $z^{3''}$, $z^{4'}$, $z^{5''}$, and $z^{6''}$, to maximize % \begin{displaymath} u(x_1) + \gamma v(x_2') + (1 - \gamma) v(x_2'') \end{displaymath} % subject to % \begin{displaymath} \begin{array}{r c l c r c l} (x_1, x_2', x_2'') & \in & \Re^3_+; & \qquad & \\ \strut \\ x_1 & = & 1 + z^1_1; && p^1 \cdot z^1 & \le & 0; \\ \strut \\ x_2' & = & z^{4'}_2; && p^4 \cdot z^{4'} & \le & 0; \\ \strut \\ x_2'' & = & z^{6''}_2; && p^6 \cdot z^{6''} & \le & 0; \\ \strut \\ z^{2'}_m & = & \delta z^1_d; && z^{2'}_m & \ge & 0; \\ \strut \\ z^{2''}_m & = & \delta z^1_d; && z^{2''}_m & \ge & 0; \\ \strut \\ z_d^{3'} & \ge & (1-\delta) z^1_d && z_d^{3''} & \ge & (1-\delta) z^1_d \\ \strut \\ z_m^{3'} & \ge & -z_m^{2'}; && p^3 \cdot z^{3'} & \le & 0; \\ \strut \\ z_m^{3''} & \ge & -z_m^{2''}; && p^3 \cdot z^{3''} & \le & 0; \\ \strut \\ z_m^{4'} & \ge & -(z_m^{2'} + z_m^{3'}); && p^4 \cdot\ z^{4'} & \le & 0; \\ \strut \\ z^{5''}_m & = & (1 - \delta) z^1_d + z_d^{3''}; && z^{5''}_m & \ge & -(z_m^{2''} + z_m^{3''}); \\ \strut \\ z^1_2 & \ge & 0; && z^{6''}_m & \ge & -(z_m^{5''} + z_m^{2''} + z_m^{3''}); \\ \end{array} \end{displaymath} The optimization problem of an agent in $D$, is to choose net trades $z^{*1}$, $z^{*4}$, $z^{*6}$, $z^{*2'}$, and $z^{*5''}$, to maximize % \begin{displaymath} u_*(x^*_1) + v_*(x^*_2) \end{displaymath} % subject to % \begin{displaymath} \begin{array}{r c l c r c l} (x^*_1, x^*_2) & \in & \Re^2_+; & \qquad & \\ \strut \\ x^*_1 & = & z^{*1}_1; && x^*_2 & = & 1 + z^{*1}_2 + z^{*4}_2 + z^{*6}_2; \\ \strut \\ p^1 \cdot z^{*1} & \le & 0; \\ \strut \\ z^{*4}_m & \ge & 0; && z^{*6}_m & \ge & -z^{*4}_m; \\ \strut \\ z^{*2'}_m & = & z^1_d; && z^{*2'}_m & \ge & -(z^{*4}_m + z^{*6}_m); \\ \strut \\ z^{*5''}_m & = & z^1_d; && z^{*5''}_m & \ge & -(z^{*4}_m + z^{*6}_m). \end{array} \end{displaymath} The market-clearing conditions in this economy are % \begin{displaymath} \begin{array}{r c l c r c l} z^1 & = & -z^{*1}; & \quad & \gamma z^{2'} + (1-\gamma) z^{2''} & = & -\delta z^{*2'}; \\ \strut \\ \gamma z^{3'} & = & -(1-\gamma) z^{3''}; && \gamma z^{4'} & = & -z^{*4}; \\ \strut \\ (1-\gamma) z^{5''} & = & -(1-\delta) z^{*5''}; && (1-\gamma) z^{6''} & = & -z^{*6}. \end{array} \end{displaymath} \vfill\eject \begin{center} {\Large \bf References} \end{center} \parindent=0pt \bigskip \bib Allen, Franklin and Douglas Gale, ``Optimal Security Design,'' {\sl The Review of Financial Studies}, 1, 1988, pp.~229--263. \bib Cairncross, Alec, ``The Bank of England: Relationships with Government, the Civil Service, and Parliament,'' in G.~Toniolo, ed., {\sl Central Banks' Independence in Historical Perspective}, Berlin: Walter de Gruyter, 1988. \bib Cukierman, Alex, {\sl Central Bank Strategy, Credibility, and Independence: Theory and Evidence}, Cambridge, MIT Press, 1995. \bib Freeman, Scott, ``The Payments System, Liquidity, and Rediscounting'' University of Texas working paper, 1996 (forthcoming in {\sl American Economic Review\/}). \bib Goodhart, Charles A.~E., {\sl The Evolution of Central Banks}, Cambridge, MIT Press, 1988. \bib Group of Experts on Payment Systems of the Central Banks of the Group of Ten Countries, ``Report on Netting Schemes,'' Bank for International Settlements, Basel, 1989. \bib Jensen, Michael C.~and William H.~Meckling, ``Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure, {\sl Journal of Financial Economics,} 3, 1976, pp.~305--360. \bib Okuno, Masahiro and Itzhak Zilcha, ``On the Efficiency of a Competitive Equilibrium in Infinite Horizon Monetary Economies,'' {\sl The Review of Economic Studies}, 47, 1980, pp.~797--807. \bib Radner, Roy, ``Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets,'' {\sl Econometrica}, 40, 1972, pp.~289--303. \bib Sargent, Thomas and Neil Wallace, ``The Real-Bills Doctrine Versus the Quantity Theory: A Reconsideration,'' {\sl Journal of Political Economy,} 90, 1982, 1212--1236. \bib Sayers, Richard S., {\sl Modern Banking}, 7th ed., Oxford, Clarendon Press, 1967. \bib Wallace, Neil, ``Another Attempt to Explain an Illiquid Banking System: The Diamond-Dybvig Model with Sequential Service Taken Seriously,'' {\sl Quarterly Review of the Federal Reserve Bank of Minneapolis}, 12, 1988, pp.~3--16. \end{document}