Modelling Money As Tokens

Macquarie Graduate School of Management

MGSM WORKING PAPERS IN MANAGEMENT

Modelling Money as Tokens

Andreas Furche, Capital Markets CRC, Sydney, Australia

Ernestine M. A. Gross, Macquarie Graduate School of Management

Graham Wrightson University of Newcastle, Australia

MGSM WP 2003-24 November 2003

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MGSM WP 2003-24

Modelling Money as Tokens

Correspondence to:

Ernestine M. A. Gross Associate Professor in Management Macquarie Graduate School of Management Macquarie University Sydney NSW 2109 Australia

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Modelling Money as Tokens

Abstract

The model presented in this paper provides a formalisation of the concept of money and the mechanics of its circulation in an economy. Any instance of money is modelled as a Money Token. The mechanics of the creation, transfer and redemption of money are modelled using a limited set of four defined Basic Transactions. In this model, money is any contract, which can be represented by a Money Token. This is shown to include, but is not limited to, various types of securities, fiat money, cash, and commodities. The definition of a Money Token builds upon Roy Radner’s (1972) formalisation of securities contracts. The concept of the defined set of Basic Transactions originates in computer based electronic money technology. In both origin and applications the model provides a bridge between theoretical models of economies, the applied economics areas of monetary economics, finance, and banking and computer based systems for storage and circulation of financial instruments. It has been developed as a tool for research or practical implementation. This paper discusses the model, developed as part of a PhD thesis (Furche, 2001), in the context of ongoing research work.

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Modelling Money as Tokens

Introduction

When the term ‘money’ is mentioned, everybody immediately seems to understand what is meant. Yet amongst experts on the subject, for example economists or bankers, the question ‘What is money?’ draws a variety of different answers that often contradict each other. When asked for a definition of the term, neither these experts nor the textbooks on the subject are able to provide anything more than a loose description of the roles that money may perform in society. However, there is no shortage of concerns and opinions about the stability of the international monetary and financial system, about inflation, and about monetary policy, all of which seem to presuppose a definition of ‘money’, which is precise enough to allow measurements and the description of money creation, circulation, and destruction.

The lack of a precise, or mathematical, definition of money makes it difficult to deal with the subject in a structured and formalised way. This is a problem in a number of research areas dealing with the meaning and usage of money, as well as in applications in practice.

The aim of the work presented here is to develop a definition of a concept of money, which is precise enough to be useful for two specific areas of research. The first area is electronic money research and the implementation of IT based financial systems. The second research area is economics; economic theory and the applied areas of monetary economics, banking, and finance. The model presented here draws on the methodology of both general equilibrium theory in economics and electronic money research, in order to provide an improved conceptualisation of money and its circulation.

The approach taken in the development of the model deals with the history of descriptions of various forms of money and with the lack of a formal definition of money by providing a definition, which allows the characterisation of every ‘instance of money’. Each instance of money is modelled as a Money Token, a unique representation of a contractual arrangement between economic agents, which is shown to formally describe financial instruments that developed in the course of history, including debt contracts, equity shares, derivatives, fiat money (cash in today’s form), bank money and commodity money. A Money Token describes all distinct properties of each financial instrument in terms of a limited set of variables and a redemption rules function. Furthermore, the circulation of financial instruments within an economy is modelled, using a limited set of four Basic Transactions, which allow the precise description of the creation, transfer, and redemption of every financial instrument.

The definition of a Money Token involves a generalisation of the concept of a security as found in general equilibrium models of sequence economies, particularly Radner (1972). It incorporates and makes precise parameters suggested in Douglas Gale’s (1982) discussions of fiat money as a special type of ‘paper asset’ in the context of sequence economies. It allows for an extension of Gale’s arguments on intertemporally incomplete markets to spacially incomplete markets (partially segmented markets;

Gross, 1988) where each nation state issue its own currency. Furthermore, types of security contracts are distinguishable by their respective redemption rules function.

The structure of the model is directly linked to existing electronic money technology, so that the description of a financial system in the Model of Token Money can also serve as the basis for a computer-based implementation. This allows the model to be used as a tool in the design and implementation of computer based systems for financial transactions, as well as in the development of computer-based numerical methods of theoretical and applied research in economics.

This paper contains some applications of the model in the specialist field within information technology (IT), which deals with the development and implementation of computerised banking and trading technology. We will refer to this specialist area in IT as ‘financial IT’. In this area the model can serve as a simple and effective basis for the design, implementation, and maintenance of computer-based systems for storage and trade of financial instruments, and the interconnection of such systems into networks. Here, the model provides a uniform and formalised description for the building blocks of any computer based banking or trading system, as well as the exact system properties. In an area where system development is very security sensitive, currently extremely expensive, and interoperability of heterogeneous systems is the recognised problem, a uniform, formalised approach, offered by the model, allows significant improvements in efficiency of development, and system security. This application of the model has the potential for substantial improvements in the development of financial IT systems, and it will be discussed in detail in a forthcoming paper.

The model described in the present paper has been developed as part of a PhD thesis, titled The Model of Token Money (Furche, 2001). This paper provides a summary of this work. For more detail the reader is referred to the complete publication. Section 2 of this paper discusses briefly the difficulties in formalising a concept of money and the approach chosen here. In section 3 the Model of Token Money is introduced in a concise fashion. Section 4 contains some applications of the model, and section 5 contains the conclusion and discusses possible directions of further work based on the model. Both sections 4 and 5 are kept brief in the interest of limiting the size of this paper, and results of the application of the model presented here will be published separately in more detail. Formatted: Bullets and Numbering What is Money?

When attempting to develop a formalised methodology for the description of money, one immediately faces the problem that the term ‘money’ itself is not clearly defined. On close inspection, the views on whether a particular item is money or not vary significantly between people considered to be experts in money related matters, as well as practitioners, which, on the subject of ‘money’, includes just about everybody.

Textbooks on monetary economics generally deal with the matter by providing the so- called tripartite definition of money, which defines money as something that serves as

a unit of account, a store of value, and a medium of exchange (Jevons, 1875; Hicks, 1967; Issing, 1993; Jarchow, 1993; Dornbusch 1995). This definition is stated and the three functions of money described, usually in the earliest chapter, and it is then never used again for the remainder of the book. The main reason for this lack of later applications of this ‘definition’ is probably that in practice it is of little use. If it is in question whether a particular item constitutes money, the tripartite definition of money provides neither a necessary, nor a sufficient condition that could not be easily contested by questioning the ‘definitions’ of one of the three included functions of money.

Finding a clear-cut definition of money is difficult because what money is, is to a good extent a subjective decision, driven by beliefs and opinions. Money is essentially what passes as money, i.e. ‘what is commonly accepted as payment for goods and services’ (Galbraith, 1995) and the discharge of debt contracts (Keynes, 1930). What is accepted as money has changed throughout history together with the opinions and beliefs of people about what constituted money. Keynes (1930) referred to this process as the ‘evolution of money’.

The term evolution suggests an ongoing process of change, and money and monetary systems have surely continued to change since Keynes used the term in 1930. Today’s predominant fiat money system only came into being with the final collapse of the Bretton-Woods system in 1972-1973. Current developments, which could lead to further substantial change, include the development of advanced electronic money systems, and the strong increase in securities trading. New Monetary Economics (NME), a term introduced by Hall (1982), now represents a school of economists who argue that in the future national currencies will even completely lose their role as medium of exchange to securities.

The term security is well defined in the economics literature, known as general equilibrium theory or mathematical economics. Since the work by Arrow (1953), a formalised concept of securities has been used in theoretical models of economies with intertemporally incomplete Arrow-Debreu markets (sequence economies). These formalised concepts of securities, specifically the work by Radner (1972), form the basis of the model presented here. However, we note that none of the existing models of economies with securities markets treats the transaction mechanics of the circulation of such securities. Furthermore, the concept of securities in these models does not work very well to describe cash in a fiat money system.

In his discussions of money in a general equilibrium theory context, Douglas Gale (1982, chapter 5) proposed that the absence of trust among economic agents explains both, the need for a sequence of budget constraints (eg as in Radner, 1972) and the difference between money and other “paper assets” (i.e. other securities). He suggests money is that asset which imposes the least cost of gathering information to determine the trustworthiness (in the “broadest sense”) of the issues of the asset. As such the ‘money asset’ is accepted in all sub-markets in a sequence economy. In a model of a spacially incomplete global market (partially segmented economy; Gross, 1988), Gale’s argument about the property, which distinguishes money from other “paper assets” becomes weaker. There may be many national currencies, each of which might have

Gale’s distinguishing property locally but not globally. While some national currencies are more readily accepted in geographical sub-markets, it is not the case that there is only one national currency accepted in all spacial sub-markets.

The idea that the determination of the ‘trustworthiness’ of economic agents is important and costly is reflected in the activities of individuals, business enterprises, and institutions concerned with ‘credit risk’, ‘debt rating‘, financial reporting, ‘country risk’ and, at times, liquidation and litigation. The definition of a Money Token allows relevant information to be collected in a unifying framework. For example, the definition includes an identification code for the economic agent, who issues a Money Token, including national governments, which issue national currencies, which serves as a local unit of account. The anonymity of money is a choice variable. Furthermore, it includes codes for other economic agents, who may act as guarantors or certifying agents for a Money Token. In this regard, the definition could be modified, by suitable interpretations or additions of subindices, to allow for future institutional features or it could be applied on a micro-economic level such as data on credit sales and purchases among enterprises. The definition of a Money Token does not exclude the prognosis of the NME about the fate of national currencies as possible future empirical observations, but it does not presume it.

The predominant contemporary approach of dealing with the creation (‘supply’) and circulation of money is the ‘money multiplier model’ (eg Brunner, 1961; Brunner and Meltzer, 1964), the related discussions on ‘inside and outside money’ (eg Gurley and Shaw, 1960; Grandmont, 1985, chapter 2; Chari et al, 1995; Bullard and Smith, 2000), and hierarchies of money (Minsky, 1986). This approach involves the classification of balance sheet items of various financial enterprises or institutions into ‘monetary aggregates’ such as ‘base money’ (‘high powered money’), M1, M2, M3. A ‘money multiplier’ is a coefficient, which equates one monetary aggregate with another one. However, this approach to the creation and circulation of money is not satisfactory.

Firstly, financial accounting, hence balance sheets, presuppose the existence of ‘money’ because the entries – real numbers – represent monetary values of past transactions, denominated in a ‘national currency unit’. This is so whether or not a reporting entity is classified as a ‘financial institution’. To be sure, without the monetary valuation of the transactions, the items in balance sheets or across balance sheets could not be aggregated by addition. Moreover, since all balance sheet items, which enter monetary aggregates, are denominated in the same ‘national currency unit’ (‘the unit of account’), it is not clear why more than one ‘monetary aggregate’ should result in any one ‘national economy’ and it is not clear why the term ‘monetary aggregate’ should be used rather than total wealth (Debreu, 1959), using a ‘unit of account’ (Walrasian numeraire). Second, the distinction between ‘outside’ and ‘inside’ money is not obviously useful for monetary policy discussions in a ‘global economy’ where each sovereign nation state has the right to issue its own currency (and this right is typically being taken up) and economic agents (including banks or other ‘financial institutions’) are free to issue and trade debt, equity and derivative securities internationally. Third, as illustrated in the empirical research reported in Chari et al (1995), the monetary aggregates give conflicting signals (‘sign switch’) regarding the relationship between

‘money supply’ and interest rates. Since interest rates feature in traditional macroeconomics based policy discussion, the empirical data on ‘money supply’ does not seem to be very helpful for macroeconomic policy formation.

Our methodology for modelling the creation, the circulation and redemption of money, is drawn from the area of electronic money. This area of research consists mostly of the investigation of specific cryptography problems within computer science, but it also effectively deals with the transaction mechanics involved in the creation and circulation of electronic money. Advanced electronic money systems, such as those devised by Chaum (1982), allow the generation of electronic money with cash-like characteristics, including the anonymous transfer of funds.

In addition to the theoretical considerations, a more detailed classification of properties of ‘money’ was seen as useful for the development of a structured description of a concept of money that accounts for differences and similarities in numerous financial instruments that can be seen as ‘money’. This was arrived at by a classifying survey of objects, which at some time in history have been functionally used as money. This survey of the history of forms of ‘money’ included many financial instruments with different properties, such as commodity money, commodity backed money, fiat money, various forms of cheques, bank account balances with varying properties, credit cards, debit cards, private currencies. The survey yielded a classification of properties of money used in the model subsequently developed. The details of the relationship between the history of ‘money’ and the development of the Model of Token Money will appear in a separate paper.

In the Model of Token Money, money is any contract that can be represented as a Money Token. This is an intentionally non-exclusive definition of money for the framework of the model. In applications of the Model of Token Money, the definition of money can then be narrowed down to any desired level by considering defined sets of Money Tokens. Formatted: Bullets and Numbering The Model of Token Money

In this section, we introduce the Model of Token Money in a descriptive fashion. This is to introduce and illustrate the idea of the model. For the complete formal construction of the model the reader is referred to Furche (2001).

In the Model of Token Money, every instance of money is represented as a Money Token. The circulation of money is modelled by using a set of four operations defined on Money Tokens, which are called Basic Transactions. Formatted: Bullets and Numbering

1.1 Money Token

A Money Token is a representation of the contractual agreement that underlies any instance of money. It is built based on the formalisation of an elementary contract in Radner (1972), which is extended to represent a number of additional properties. An

elementary contract, as defined by Radner, is a contract between two economic agents, made at time t, with regard to the supply of objects at a future time u.

We call the economic agent, who is to supply the objects in the future, the Issuer (I), and the economic agent, who accepts the contract at time t, the Owner (O).

The contract obliging I to deliver a set of objects at time u is uniquely represented as a Money Token, T, which cannot be altered or copied. This Money Token specifies that I will supply objects in exchange for T. That is, I will supply the objects upon receipt of the Money Token T. We note that a delivery contract represented by T does not need to specify the economic agent receiving the objects, while it does need to specify the economic agent obliged to supply the objects, namely the Issuer I.

As a generalisation of the elementary contract used by Radner, we do not require the contractual delivery time u to be a fixed time. Optionally, the contract can oblige the Issuer I to deliver the objects at any time u ≥ t, or within any time frame v ≤ u ≤ w, with t ≤ v and v ≤ w ≤ ∞, when called upon to do so by the return of the Money Token to the Issuer. We call this a redemption of a Money Token.

Additionally, we allow more specific rules, or terms and conditions, than the elementary contract in Radner (1972). The complete specifications of the objects that are to be supplied in exchange for a Money Token T are dependent on variables specified in the terms and conditions of the contract. These variables can include the outcome of uncertain events or time, as in Radner, as well as any other conditions of the contract, such as the compliance with rules set out in the contract.

We model the terms and conditions of the contract as a function that returns the complete specifications of the objects to be supplied in return for T, depending on the value of variables set out in the terms and conditions, and depending on a specified amount for the contract, given as a positive real number. We refer to this function as the redemption rules function.

Finally, the token generation process, which is part of the transaction mechanics to be modelled here, is also represented in a Money Token T, as will be shown below.

A basic Money Token representing a delivery contract entered into by the Issuer I is denoted by

TI = [tok, cid, a, fkI(a, •), O]I , where tok is a number, which we call the token ID, and cid is a combination of characters (name), which we call the currency ID. tok and cid are chosen by the Issuer I such that together they uniquely identify the Money Token TI, amongst all Money Tokens that I may issue over time. a is a positive real number signifying the amount of the Money Token, TI.

O is an optional unique identifier for the Owner, that is the economic agent who accepts the Money Token from the Issuer, and is denoted by λ if it is not specified as part of the Money Token. fkI(a, •) is the redemption rules function, representing the terms and conditions of the contract determined by the Issuer I for Money Token TI. This contract can be described as a function f, which returns the specifications of the set of objects to be delivered in exchange for the Money Token upon redemption, depending on the terms and conditions of the contract. The type of the contract is considered to be its set of terms and conditions, which are represented by the complete definition of function f and its arguments.

We assume that there is a finite number of distinct types of contracts, denoted by K. Let the subscript kI denote the type of contract chosen by Issuer I for Money Token TI. fkI(a, •) is the function representing this contract. The arguments in fkI(a, •) denote that the function always takes the amount a as an argument. However, depending on the type of contract kI, the function may take additional arguments.

The notation [...]I is used to denote that economic agent I, in this case the Issuer of the Money Token, commits to the contract by signing the content within square brackets. This notation signifies that as part of the transaction mechanics of handling Money Tokens, which will be described in detail in section 3.3, a specific action (signing) is required by the Issuer in order to create a valid Money Token. Formatted: Bullets and Numbering

1.2 Guarantor and Certifying Agents

As an extension to the basic Money Token, we allow economic agents other than the Issuer to optionally contribute properties to a contract represented by a Money Token T. This extension is used to describe more complex contractual relationships that money may represent. Two kinds of additional properties of money were encountered in the review of payment instruments presented in (Furche, 2001). Firstly, money could be insured. In practice, an example for this is a guaranteed bank deposit. Secondly, properties of money or its Issuer could be certified by institutions, and this certification could be included in the representation of money. In practice, this is the case with personal cheques, which are bank branded, certifying the compliance of the Issuer with rules for ‘creditworthiness’ set by the bank.

We first consider the case of ‘insurance’ of a Money Token against default by the Issuer. A Guarantor, G, is an economic agent, other than the Issuer of Money Token, T, who promises to supply a set of objects in exchange for T, if the Issuer fails to do so. The specification of the set of objects that G will supply in return for T is again determined by a redemption rules function, which represents the terms and condition of the insurance contract, determined by G. This function is denoted by fk’G(a, •). The subscript k’G denotes the type of contract chosen by G for the insurance of the Money Token T. Contract k’, chosen by G, may or may not be the same type as contract k,

chosen by Issuer I. The insurance provided by G may hence be limited by the contract k’ and the ‘creditworthiness’ of the G.

The Guarantor, G, commits to his contractual obligation by signing the Money Token T. A Money Token, TI , with an insurance contract, k’, signed by Guarantor G is denoted by TIG = [TI , fk’G(a, •)]G.

Further extending the Money Token to include certifications is achieved in a similar way. A Certifying Agent is an economic agent who registers a Money Token T and, in doing so, certifies T.

For each token T, we define the set of all certifying agents contributing certification to T as C, C ⊂ A\I , C ≠ ∅, where A = 1, …, n is the set of all economic agents. For each c ∈ C , there is a set of certificates that c can provide to a Money Token, R(c):={r1(c),..., rp(c)}, p≥1. Each certificate r(c) ∈ R(c) is a statement, made by c, regarding one aspect of the Money Token. The Issuer of the Money Token selects a set of certificates for the Money Token. This set is denoted by DI ⊂ ΥR(c) . c∈C

An insured Money Token with certifications is denoted by TIGD=[TIG]DI. Formatted: Bullets and Numbering

1.3 Basic Transactions

The circulation of Money Tokens is modelled through a set of four Basic Transactions defined on Money Tokens, indexed by TR1, … ,TR4. These transactions define the lifespan of a Money Token by defining how it is created, transferred, and destroyed.

The transactions mechanism is presented here in diagramatic form. The relationship between the unique identifier, tok, and electronic money systems (Chaum, 1982) is outlined later in the paper. In the following, it is convenient to denote the unique identifying numbers of a sequence of Money Tokens by tok1, tok2, tok3, …

A Money Token, TI, is created by the Issuer I1. At the time of generating the Money Token, the contents of the token, tok , cid, a, fkI(a, •), are fixed, signifying the complete specification of the contract by the Issuer, who signs the Money Token to yield TI =

[tok1, cid, a, fkI(a, •), O]I1. The Issuer then sends the Money Token to an economic agent, say X1, who is to receive the Money Token. This operation is called the Token Issue Transaction (TR1). Once created, the Money Token, TI , can be transferred by its current holder, X1, to another economic agent, X2, at a later time through a Token Transfer Transaction (TR2).

T[tok1,cid,a,fkI(a, •), X1]I1 X1 I1

[tok1,cid,a,fkI(a, •), X1]I1

[tok2,cid’,a’,fkI(a’, •), X2]I1 X2

Figure 1: The lifecycle of a Money Token as transactions TR1, TR2, and TR3

An economic agent X2 who is in possession of a Money Token issued by an Issuer I1 can, at any time allowed in the terms and conditions, return the Money Token, TI , to the Issuer I1 in exchange for the objects specified in the Money Token. This is called Token Redemption Transaction.

As part of the Money Token redemption transaction, I1 verifies the validity of the Money Token by applying the redemption rules function, fkI, and the Money Token is invalidated (destroyed). I1. The object supplied in exchange for the redemption of the Money Token TI can in turn be Money Tokens (eg tok2 above). We differentiate between two Money Token Redemption Transactions, depending on whether the object supplied in exchange for a TI is another Money Token issued by I1 (TR3), or not (TR4).

[tok1,cid,a,f (a, •), X ] kI 1 I1 X I1 [tok2,cid’,a’,fkI(a’, •), X2]I2

I 2

Figure 2: Redemption of a Money Token issued by I1, held by X and a Money Token, issued by I2, held by I1

The four operations TR1 to TR4 are the only operations permitted on Money Tokens. All circulation of Money Tokens is modelled as a combination of these basic transactions. Formatted: Bullets and Numbering Applying the Model of Token Money

Some applications of the model in the areas of monetary economics, finance, banking and financial IT have been investigated as part of the development of the model (Furche, 2001). For the purposes of this paper, we limit the description of applications

of the model to several examples, and include a brief discussion only. Detailed results of some applications of the model, in development at the time of writing, will be published separately.

In section 4.1, we demonstrate how a financial security can be represented as a Money Token. This is done by describing a standard securities contract, and a standard share contract, and cash (fiat money) as a Money Token1. Section 4.2 uses the example of a cheque payment to demonstrate how the circulation of financial instruments is modelled. Section 4.3 briefly discusses the use of the model in systems design in financial IT. Formatted: Bullets and Numbering

1.4 Describing financial securities and fiat money as Money Tokens

The purpose of this section is to demonstrate how financial instruments can be expressed as Money Tokens. For this demonstration, we have chosen as examples the description of commodity securities, shares, and cash (fiat money) as Money Tokens. We use the formalisations of commodity securities and shares given by Radner (1972) as a basis.

An elementary contract for the future supply of commodities, entered into at event A at date t, is formalised in the Radner model as zh,t,u(A,B), representing the number of units of commodity h that an economic agent will deliver if event B occurs at date u.

Let this elementary contract be a contract between two economic agents I and O, such that I enters into the contractual obligation to deliver the specified commodities in future. This contract is described by the following Money Token.

zh if (event B) and (time = u) TI = [tok, cid, z, fkI(z, B, u), O]I ; fkI(z, B, u)=  Ø otherwise

Money Token TI specifies that Issuer I agrees to redeem the token for z units of commodity h if event B occurs at time u. Otherwise, Issuer I will not redeem the token for anything.

A equity share contract in the Radner model represents the ownership of a fraction of a producer in a production-exchange economy2. A share pays a dividend of the same fraction of the profits of the producer at date t+1 to the owner of the share at date t. Share contracts can be traded between economic agents.

1 Note that (Furche, 2001) contains a more extensive set of examples, including the description of various forms of cash, cheques, bank balances, etc. as Money Tokens.

2 The concept of a producer is defined in Debreu (1959)

Let a be the fraction 0 ≤ a ≤ 1 of ownership of a producer P that is represented by a share. In the Radner model, ownership rights are defined on profits and all profits are distributed. Let the total profits of P at time t be denoted by pr(t), with pr(t) ≥ 0 all t (limited liability). Let O be the economic agent owning the share a* of P at time t. Such a share, issued by producer P at date t, and accepted by O (in exchange for say, a ‘fiat money token’ or a ‘bank cheque token’) is represented by the following Money Token.

TP = [tok, cid, a*, fs(a*, t, •), O]P ; fs(a*, t, •) = {[tok, cid, a, fs(a, t+1), O]P, ([tok, cid, a*, fd(a*, t+1), O]P ; fd(a*, t+1) = a*(pr(t+1))}

Money Token, TP, is issued at date t, and specifies that at date t+1, the Issuer, P, will redeem the Money Token, TP, for two new Money Tokens. The first of these two tokens represents the new share of ownership, a, in P issued at date t+1 (a = a* if O does not transfer ownership on the stock exchange). The second token is the dividend paid out at date t+1. The transaction, which will result in the issuing of the new Money Tokens in exchange for TP involve the redemption transaction (TR3) at date t.

This approach transfers well to equity shares in publicly listed companies, issued and traded on stock exchanges in practice. An important difference between ordinary equity shares, commonly traded on the stock exchange, and equity shares in the Radner model is that the legal rights of shareholders are weaker than what is assumed in the Radner model. That is, in contrast to the assumption in the Radner model, a publicly listed company does not have to pay out all profits as dividends to ordinary shareholders (after all debt obligations have been met). This property of the legal aspects of the institutional framework can be modelled through an additional argument in the redemption rules function. Given current corporate law in Australia, the amount of the dividend payment is additionally depending on the outcome of an event, namely the decision at the annual general meeting for shareholders to accept (or reject) the directors’ recommended dividend payout. Shareholders cannot force the directors to increase the payout ratio.

An alternative way to model an equity share is to define the amount of a share equity money token as one share rather than the ownership fraction and making the dividend payment directly proportional to the share. This would allow for changes in the ownership fraction due to either sharemarket transactions made by a shareholder or changes in the total number of shares issued by a publicly listed company or both.

Cash in today’s form is in most countries fiat money. That is, it does not represent a contractual obligation by the Issuer (usually a central bank) to provide any objects in return for cash, other than the same amount of the same form of cash. In the Token Model of Money, we model cash as a contract of exactly this form. An Australian 100 dollar bill, issued by the Reserve Bank of Australia (RBA), is represented by the following Money Token Tc.

Tc = [tok, AUD, 100, fkI(100), λ]RBA ; fkI(a) = [tok, AUD, a, fkI(a), λ]RBA

Formatted: Bullets and 1.5 Modelling circulation of Money Tokens Numbering

The circulation of Money Tokens is modelled by describing exactly the transaction mechanics involved in the trade and exchange of Money Tokens between economic agents within an economy, based on the four basic transactions for Money Tokens.

For the purposes of this paper, we use as an example the processing of a cheque. In our example, the cheque is written out by Alice, a customer of bank ANZ, as a payment to Bob, a customer of Bank CBA. ANZ is a certifying agent for the personal cheque written by Alice. Settlement between the two banks is done through reserve bank accounts with RBA. The resulting transaction flow is described in figure 3.

6 (TR3) 4 (TR4) tok1 tok4 ANZ CBA RBA tok3 tok3 5 (TR4) 2 (TR2) tok1 tok 5 3 (TR1)

tok1 tok2

Alice Bob 1 (TR1) tok1

Step 1: [[tok1, AUD, 100, f1(100, •), Bob]Alice]ANZ; f1(a) = [tok, AUD, a, f5(a, •), Bob]ANZ Step 2: [tok2, AUD, 100, f2(100, •), Bob]CBA; (f2(a, •) of CBA bank account) Step 3: [tok3, AUD, 100, f3(100, •), ANZ]RBA; (f3(a, •) of Reserve Bank account) Step 4: [tok4, AUD, 100, f4(100, •), CBA]RBA; (f4(a, •) of Reserve Bank account) Step 5: [tok5, AUD, 100, f5(100, •), Alice]ANZ; (f5(a, •) of ANZ bank account)

Figure 3: Transaction flow resulting from cheque payment

Steps 1-6 indicate the different basic transactions involved in processing the cheque. In step 1, Alice writes out (issues) the cheque and gives it to Bob. In steps 2 and 3, Bob trades the cheque with his bank, in return for an increase in his account balance. Step 4 is the settlement between the banks ANZ and CBA, in which ANZ provides a Money Token representing part of its account balance in its clearing account with RBA, in return for the cheque. Step 5 represents Alice settling with ANZ, by providing part of Alice’s account balance in return for the invalidation of the cheque. Step 6 represents the transfer of RBA account balances from ANZ to CBA.

The numbering of steps 1 to 6 is not meant to imply an order of processing, which could occur in a different order. By analysing the order of processing, and the elapsed time between processing of individual basic transactions, it is possible to make

observations about the risk properties of a payment mechanism, and about the effect of processing of payments on the monetary aggregates (Furche, 2001). If desired, the level of detail used in describing the processing of our example cheque in the Model of 3 Token Money could be reduced, or further extended . Formatted: Bullets and Numbering

1.6 Applying the Model in Financial IT

The Model of Token Money provides a uniform description tool for financial instruments and operations on such financial instruments. This is of potential benefit in a number of areas in financial IT, including system security of financial IT systems and networks of such systems (Furche, 2001). These properties of the model can also be exploited by using the model as the basis for the design and implementation of computer based financial IT systems, which is one example of an application we will briefly discuss here.

The general approach is to use the model as a tool for a high level description of the financial instruments occurring in a financial IT system as Money Tokens. The operations made with these financial instruments in the financial IT system can then be described as transactions in the Model of Token Money. More specifically, this approach is implemented by using the Model of Token Money as the basis for a layered approach to the design and implementation of any financial IT system, as depicted in figure 4. A layered approach is used with important benefits in various specialised areas within IT, for example in computer networks. It allows the clear distinction between different interdependent components of an overall system.

In financial IT, a clear distinction between interdependent, yet very different components, is today generally not made during the design of computer based systems. This usually puts the emphasis in such system development on software design and implementation, which is not really necessary. It is the design of the financial properties of such IT systems that is usually the most complex. Yet, this task is usually not performed by financial experts but by IT experts attempting to extract requirements without a clear understanding of the systemic financial issues involved. The result is commonly an inefficient design and development process, occurring in a similar way across many organisations, and leading to similar, expensive problems across organisations.

Using a layered approach that allows the compilation of a complete set of specifications of the financial properties of a computer based system into a form that can directly be converted into computer systems design and implementation could be greatly beneficial here. The Model of Token Money could serve as a tool for such a layered approach.

3 The cheque from our example would in reality be processed as part of a large scale cheque processing system, in Australia the Australian Paper Clearing System (APCS). This involves the electronic exchange of an image of the cheque, and settlement with the RBA based on a multilateral netting process. This additional level of detail could also be modelled in the Token Model of Money, if desired.

On the top layer of the process, the Money Tokens are described. This step represents the design of the financial instruments within a financial IT system, including all their contractual properties. With the Money Tokens defined, the next layer is the description of the transaction flow based on the set of basic transactions for Money Tokens. In this way, the transaction mechanics within a system can be described by financial experts, and system properties can be analysed by financial experts, before any involvement from IT experts is required.

Tokens

Transactions

Cryptographic Protocols

Software Implementation

Figure 4: Layered approach to financial IT systems development

Only after the Money Tokens and the Transactions of the system are described and finalised, would the system development actually become IT systems development. At this time, the system is already described in a way that is adequate for IT systems design, given the close relationship between the Model of Money Tokens and the technology used in financial IT systems4. From a software perspective, the third level of the process is the selection of the appropriate cryptograhic protocols to be used for the implementation of the financial IT system. The fourth layer is the actual implementation in software. This is now a very constrained and well-defined problem, because it is limited to the implementation of a set of clearly defined transactional protocols.

The complete process could be supported by the development of a standard set of work tools, including analytic tools, standard hardware architecture solutions, and software development (programming) tools. The potential impact could be a significantly more efficient process in the development and maintenance of financial IT systems, an area that currently accounts for substantial cost in the financial industry. Formatted: Bullets and Numbering Conclusion and Further Work

The Model of Token Money contains two new concepts; Money Token and Basic Transactions. The definition of a Money Token extends the concept of a security, as

4 The basic transactions from the model can be mapped directly to existing cryptographic protocols used in electronic money systems.

found in general equilibrium models of sequence economies, particularly Radner (1972), by defining additional properties. The definition of a Money Token, relative to the definition of a security, has benefited from both, insights from discussions on money found in the literature on general equilibrium models with incomplete markets and a review of the descriptive history of money and money-like financial instruments. The generality of the definition of a Money Token was illustrated by providing examples of how financial instruments, including fiat money, can be described as special cases of a Money Token. The circulation, or transaction mechanics, of Money Tokens is fully described by four Basic Transactions. The concept of the defined set of Basic Transactions originates in computer based electronic money technology. The Model of Money Tokens does not contain a new hypothesis as to why money or particular forms of money exist in economies; it was developed as a tool for research in financial IT and economic modelling.

For applications in financial IT, the Model of Token Money has two important properties. Firstly, it provides a uniform description of any financial instrument, based on concepts from economic theory. Secondly, the Model of Token Money provides a constrained set of transactions permitted on Money Tokens as a description of their circulation. Both properties together provide a small set of basic building blocks for the description of any financial IT system. This allows the model to be used as a tool in the planning, design and implementation of financial IT systems, and interconnected networks of such systems.

The formulation of the model as a systems development tool would be the first step in an implementation of this work. This could be done through the development of a set of implementation tools to support the system and software development process based on the Token Model. They could include a standard software library providing a platform of tokens, transactions, and protocols, and/or a compiler that could convert high level system definitions, formulated in the Token Model, into software.

An analysis with a view to measuring the effects of the application of the Model of Token Money in financial IT systems development would form the next step in further research, and provide verification of the effectiveness of the approach. The aim would be to compare a design and development methodology based on the Model of Token Money with the ‘traditional’ process of designing a functionally equivalent system without the tool. The speed of development, the resources required, and the quality of results could be measured and compared. This approach could be applied in the design of new systems as well as the interconnection of existing systems. It needs to be noted that such research is likely to require significant resources, given that the development of financial IT systems is very expensive. However, if it is found to be successful, the potential benefits in the form of savings in financial IT cost are substantial5.

5 It is estimated that in Australia alone, as much as three percent of the GDP (or $15bn annually) is spent on the facilitation of non-cash payments (Laker, 1999). A significant part of this sum can be attributed to financial IT cost. Further financial IT cost occurs in other areas, such as the maintenance of share registers, etc.

In the area of formal analysis of software systems, specifically security assessments, a next step in further research would be the description of a complete financial IT system using the Model of Token Money, and the analysis of system properties based on this description. A uniform description of a simple base system as a building block could be developed and the properties of a network consisting of a large number of such building blocks analysed. This could also be implemented as a software-based simulation. If it is possible to mathematically prove relevant properties of the overall network in this way, the model will provide a useful tool in this area.

In the area of economics, several applications of the Model of Money Tokens have been identified. The model provides conceptual tools to unify quite separate research programs in the applied areas of money, banking, finance and macroeconomics. A few examples may serve here to illustrate the point and to outline further work in these areas. The first example is taken from finance theory, which developed quite separately from money related research in other applied areas in economics. The example is the Sharpe-Lintner-Mossin Capital Asset Pricing Model (CAPM), first developed in the 1960s and extended to the International CAPM by Solnik (1974), and to a multi-period framework by Merton (1973) and Cox and Rubinstein (1985). The simplest model will suffice here.

The CAPM assumes the existence of a risk free asset. The risk free asset is characterised by zero variance of its rate of return. The model (or versions thereof) is widely applied in practice. This involves the calculation of rates of returns from empirically observed money prices of financial securities (usually equity shares) and some government bond yield (or money market interest rate) as a proxy variable for the rate of return on the risk free asset. Under the heading ‘the time value of money’, finance texts typically contain a hand-waiving explanation as to why an accompanying diagram of the capital market line shows a strictly positive rate of return for the risk free security. However, there is no money in this model, which corresponds to the money prices used in the empirical studies, namely fiat money, issued by governments, and there is no ‘banking sector’. The CAPM is a characterisation of a solution (equilibrium) of a model of an exchange economy with complete securities markets (Hart, 1974). The institutional environment is completely described by markets; there is no room for a government, or for ‘outside money’ or for ‘bank money’ or any type of ‘fiat money’. A monetary interpretation of such a model of a private ownership economy would at most yield ‘pure inside money’, characterised as a security, which is in zero net supply, pays 1 unit of account under all conceivable future events, and trades at a market price of 1 unit of account, i.e. a numeraire (Duffie, 1990). The rate of return on this ‘pure inside money’ is zero with zero variance. An application of the Model of Token Money would also yield a security with zero rate of return and zero variance. However, there are two important distinctions. Firstly, in the Model of Token Money, the risk free security would be ‘pure outside money’, issued by a monetary authority (the redemption rules function of, say, an Australian $100 bill is f(A$100) = A$100). Second, the ‘pure outside money’ token would be either in strictly positive net supply or would not exist empirically. That is, if there is a (monetary) unit of account, then the supply of the security, which serves as unit of account, must be in strictly positive net supply. This

is not the case with ‘pure inside money’, as defined by Duffie. While the ‘pure inside money’ interpretation of a private ownership securities market economy model allows for borrowing and lending of the risk free asset (and all others), it is not clear how this could result in a positive interest rate because the rate of return on this ‘pure inside money asset’ is zero by definition of the equilibrium price of the unit of account. This problem does not arise when the concept of a Money Token is applied. The step from the creation ‘outside money’, which serves as unit of account, to borrowing and lending, in terms of the unit of account, involves the creation of at least one new Money Token. A nominal interest rate (i.e. in terms of the monetary unit of account) can then be calculated from these transactions. To illustrate, suppose one exchanges a A$100 bill for a bill of exchange (money market transaction), then the redemption rules function for the bill of exchange may entail a positive nominal rate of return. That is, the redemption rules function for the bill of exchange-token may specify a currency-token with a value greater than A$100. However, the interest rate is the outcome not of borrowing and lending of the abstract object that serves as unit of account but from exchanging one form of money for another form of money, one being ‘outside money’, the other being a form of ‘inside money’. The latter would commonly be called a credit instrument and its Issuer would be called a debtor. A debtor may default and, in the case of a bill-of-exchange, the previous Owners may default. Hence the security ‘bill- of-exchange’ is not a risk free security. The Issuer of the ‘currency-token’ is a monetary authority. Setting aside the special case of a currency reform and considering one country only, there is only one unambiguously risk free asset, in terms of the monetary unit of account, namely the currency-token or ‘outside money’. The monetary rate of return from investing in (i.e. holding) this ‘paper asset’ is zero. To make the point in a slightly different way, it is not only conceivable but there are examples recorded in history where the issuer of government bonds has defaulted but the currency, issued by the same issuer remained in circulation, at least locally (and vice versa).

Clarity on the relationship between theoretical models in Finance and the data used in empirical studies is of practical importance, particularly regarding the estimation of the cost of capital in corporate finance. As part of the ongoing research, some further analytical work is planned to investigate the CAPM (and its extensions) in the context of a model of a monetary economy and applying the concepts of a Money Token and Basic Transactions. As indicated above, this would involve the description of an institutional environment, which integrates at least to some extent the areas of ‘banking’ and ‘finance’.

A related research question concerns the treatment of ‘defaultable debt’ (risky debt) in the CAPM. So far the difficulty of non-linear pay-off structures, of which defaultable debt is one example, have been treated in the theoretical literature by means of assuming continuous trading with an appropriate assumption on the price diffusion process (eg Merton 1975, 1990). The problem of non-linear pay-off structures of securities has been largely ignored in the vast number of empirical ‘anomalies’ studies, published primarily in the Accounting-Finance literature. It continues to be ignored in practice, which is of particular concern in the area of ‘leveraged buy-outs’, including some takeovers. The calibration errors, due to excluding risky debt from the construction of the market portfolio are significant, even if the continuous trading

assumption is maintained as an approximation for actual trading intervals (Ferguson and Shockley, 2003). The assumption of continuous trading is not always satisfactory, particularly when various markets have different trading intervals. We believe the Model of Token Money provides a useful framework for computational methods to build upon the work by Brown et al (1996) and Herings and Kubler (2000) to study the effect on asset prices of various types of securities, including defaultable debt, and non- synchronised trading intervals..

Another area of practical relevance, where the Model of Token Money may be applied, is ‘financial accountability’. The term financial accountability is used here, rather than financial accounting, to avoid issues arising from the regulatory and statutory requirements and the weight of the traditional relationship between accounting and commercial law, which could not possibly be discussed in the space available. The point is that the data summarised in the Accounting Statements (Balance Sheet, Profit and Loss, and Statement of Cashflows) can be obtained from an information system based on the Model of Token Money. The converse is not true. The financial accounting model (first developed by Paccioli, 1494) records only the amount, a, of a Money Token, but not the associated redemption rules function, fkI(a, •). However, this function conveys the contractual obligations, which link the past and present to the future. As such, this information would be useful for stakeholders (shareholders, creditors, employees, suppliers, customers, the government) to form expectations about the financial risk, including bankruptcy, of an enterprise. The intertemporal and state- contingent monetary contracts, described by the redemption rules functions, include employment contracts (including those of senior managers and directors, which seem to be of recurrent concern), options on physical assets or on equity shares, consumer loyalty schemes, convertibles, credit sales and purchases, future and futures contracts, including foreign exchange, individually negotiated financial securities (‘over the counter’ transactions) and other items which are often reported as ‘extraordinary’ or ‘abnormal’ in the traditional Accounting Statements or in footnotes to these statements, or are discovered by accounting experts at the stage of litigation. The inadequacy of the traditional financial accounting framework (and the impotence of credit rating agencies, who use this information), in providing ‘relevant’ and ‘timely’ information continues to be illustrated by apparently unanticipated corporate failures. (Unanticipated corporate failures are of particular concern when the corporations involved – eg HIH - claim to provide insurance for their clients.) Applications of the Model of Token Money in this area would to be experimental initially, involving the development of methods to allow a comparison of the output of the traditional financial accounting system with the proposed system under controlled conditions. This work would require the specification of all the arguments in the redemption rules functions of the Money Tokens by means of translating the terms and conditions of actual monetary contracts, enmeshed as they often are in legal writings, into variables and parameters, and it would involve the sorting of the resulting Money Tokens by the form of the redemption rules functions. It would be interesting to see whether the quantitative relationship of various types of Money Tokens would provide a better indicator of corporate failures than indicators obtained from traditional accounting information. (It would also be interesting to see whether there is support for Shubik’s 1975 suggestion that a minimal requirement for modelling the financial institutional environment are ‘eight units’.) We believe this

research project could benefit from industry participation, involving practising corporate accountants and practising corporate lawyers.

In the context of the methodology of general equilibrium theory, the definition of a Money Token provides a characterisation of ‘monetary objects’, which allows the simultaneous treatment of various means of payments, stores of value and units of account. As such, both the ‘supply of’ and the ‘demand for’ monetary objects is amenable to investigation regarding their relationship to the elements of models of economies, namely agents, objects of choice, endowments, preferences, technology, and institutional environment. To the best of our knowledge, none of the models of monetary economies uses a notion of money, which can deal with the tripartite functional definition of money. Duffie’s, 1990, characterises the means of payment role of money as a real number in his model of ‘pure outside money’ and he characterises the store of value role of money in his model of ‘pure inside money’ as a Radner security with a constant dividend, as described in the above discussion on the CAPM. However, having a separate model for the medium of exchange (means of payment) role of money and for the store of value (securities) function of money is not satisfactory. For example, there are ample examples where equity shares (securities) have served as medium of exchange in corporate takeovers and in situations of financial distress and restructuring, involving corporate or national debt. In the methodologically related area of game theory, recent work by Alonso (2001) contains a model of an economy with multiple decentralised equilibria, allowing for the coexistence of barter and fiat money in its role as medium of exchange. Alonso used a one-shot Shubik-type trading-post- game framework. There is no room for privately issued securities in this model and hence no room for private credit or risk sharing. Multiple decentralised equilibria is a feature of a model of a spatially partially segmented model of an economy with multinational producers in a general equilibrium framework (Gross, 1988) with intertemporally complete markets. In this model there is no role for any money other than a Walrasian numeraire. However, this model contains a technology, which appears most suitable as a starting point for formalising the Basic Transactions, which are described at present in diagrammatic form. Furthermore, the technology in this model makes precise the notion of ‘technological advantage’, as found in the empirically oriented literature on multinational firms (eg Hymer, 1976) and may hence be useful for modelling differences in transactions costs. Transactions costs feature in the earlier literature as a hypothesis for the existence of money, however defined (Hicks, 1935; Hahn, 1971, 1973; Ostroy and Starr, 1974; Duffie’s 1990 ‘outside money model’). The ‘bounded rationality’ assumption on agents’ information, which underlies the partially segmented market structure, might provide a rationale for having the identity of the Issuer matter in a general equilibrium framework. A formalisation of the ‘financial systems technology’, which preserves the structure of the Basic Transactions¸ is desirable to allow the application of computational methods for types of Money Tokens with redemption rules functions for which there are no analytical solutions.

Finally, it would be interesting to do further interdisciplinary work by learning and comparing the methods of proof of relevant properties of networks as used in computer science and in mathematical economics.

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