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Colin Rogers
School of Economics
University of Adelaide
Draft-August 20-2005
I Introduction
The emergence of electronic monetary systems, where payments are made by electronic transfer rather than by cash, has transformed the way central banks implement monetary policy. Monetary aggregates are out, interest rate rules are in and central banks apply explicit or implicit inflation targets. These electronic monetary systems have been in place for almost a decade in some economies and appear to be working well. For central bankers the world of e-money has arrived. The fears of those who worried that advances in electonics would undermine the ability of central banks to conduct monetary policy, (Friedman, 2000), have proven to be unfounded.
Academics, not satisfied that the system works in practice, ask the question: Does it work in theory? Leading theorists who answer in the affirmative are Woodford (2003) and Cochrane (2005). Both employ what they call a cashless, frictionless economy, as a model of the modern e-money economy to argue that interest rate rules or fiscal policy can control the price level (inflation) in such a world.
Woodfords book, titled Interest and Prices; Foundations of a theory of monetary policy, has received praise from several leading economists. For example, Kenneth Rogoff, the former Director of Research at the IMF, is of the opinion:
This is the most important book in monetary theory in at least the last two decades, illustrating all the major conceptual ideas in modern monetary economics, and then some.
And in a recent review of Interest and Prices in the Journal of Economic Literature Green (2005, p. 133) suggests that the analysis is of direct practical relevance to central bankers:
From the perspective of central bank economists, it is of great value to have a family of tractable models that yield intuitively appealing policy alternatives as optima.
Finally, in a recent paper titled Money as Stock, Cochrane (2005) endorses Woodfords analysis and presents a defence of the fiscal theory of the price level in the context of the cashless, frictionless model. Thus it is clear that both Woodford, Cochrane, and many others, treat the cashless, frictionless model is a good approximation to the world of electronic money and believe that the model therefore provides a sound foundation for the theory of the price level and monetary policy in such a world (the sub-title to Woodfords book).
In this paper I spell out the case for the negative. The cashless, frictionless model of Woodford and Cochrane does not provide a sound foundation for a theory of monetary policy. Central Bankers and their economists can rest easy. They have nothing to learn from Woodfords Interest and Prices that they dont already know. More significantly the concept of the cashless, frictionless economy espoused by Woodford and Cochrane exposes deep conceptual flaws in a branch of monetary theory that have been present since at least Patinkins Money, Interest and Prices: The integration of money and value theory. To make the case the paper proceeds as follows.
Section II applies the principles of monetary economics 101 to examine forms of e-money. It is known that the money has value because it overcomes the frictions of barter, expands the choice and production sets by enabling the capture of the gains from trade, specialization and any increasing returns to scale. It is also known that e-fiat money is simply a form of fiat money and that the principles of management of fiat money can be applied to e-fiat money. The current e-fiat money system based on clearance through the central bank using RTGS systems is such a management system using interest rate rules. Freedman (2000) provides a comprehensive overview of how those systems work. By contrast, forms of e-money that allow trading of assets in real time without clearance through the central bank as conjectured by King (1999)- even if technically feasible, encounter transactions frictions of the type familiar from barter. These systems are dominated by the existing e-money systems in terms of cost and risk. To create a frictionless e-money system something else is needed.
Section III turns to theory to outline the property of a model that would allow for frictionless trading. This is the world of Arrow-Debreu contingent securities and a Time-0 auction the frictionless world of financial economics and real general equilibrium models that Woodford and Cochrane explicitly recommend as the foundation for monetary theory and policy. The attraction for Woodford and Cochrane is twofold. First, the transactions frictions encountered by e- trading of assets in real time do not arise in a model with a Time-0 auction. Second, it allows them to avoid the fact the e-fiat money has no value in such a model by redefining money as an asset.
Section IV outlines the fundamental conceptual error at the heart of the concept of the cashless, frictionless economy employed by Woodford and Cochrane. Allowing frictionless trading under an implicit or explicit Time-0 auction is far too strong an assumption. It is so strong that it destroys any role for nominal magnitudes or any institutions other than the shadowy auctioneer or social planner. Concepts such as the nominal interest rate and price level have no meaning and serve no useful purpose in the cashless, frictionless world of Woodford and Cochrane. The difficulty arises because the Time-0 auction is a theoretical but non-operational substitute for money of any form be it e-money or cash.
Such a world has no place for nominal interest rates, the price level and a central bank. The cashless, frictionless world cannot then be employed to analyse interest rate rules or provide advice to central banks. Woodford therefore fails in his attempt to use the cashless, frictionless model as a rationalisation for the channel system currently employed by central banks. His model (in cash or cashless states) has no place for the channel system. For similar reasons Cochranes claim that he can present a fiscal theory of the price level in such a world should be rejected. Neither the price level nor government are concepts that have any meaning in the cashless, frictionless economy.
As Capie, Tsocomos and Wood (2003, p. 10) remind us, George Stigler (1972) observed that in a world without transactions frictions there would be no money and no institutions like banks. Yet this is the strange world that Woodford and Cochrane propose as a foundation for a theory of the price level.
Section V illustrates these arguments with reference to some specific properties of the cashless, frictionless models presented by Woodford and Cochrane. Section VI concludes.
Nothing in this paper is original. All the facts are well known in the literature. This paper attempts only to arrange them to produce a clear picture of the issues.
II Monetary economics 101 and forms of e-money
The major problem faced by monetary theorists seems to be that they are unsure what a monetary economy is. what are its essential properties? In monetary theory 101 we are told that money serves three functions unit of account, medium of exchange and store of value. Also, money removes the frictions of barter such as the double coincidence of wants and other transactions frictions. Examples of frictions that exist under barter would be the attempt to trade goods or services that differ significantly in absolute exchange value. Call it lumpiness. A practical example is the attempt to trade haircuts in Adelaide for a holiday in Bali. It would take an awful lot of the former to pay for the latter, even if it were a feasible barter trade which it obviously isnt. Without the intermediation of money it is hard to imagine how such a barter exchange could take place or why the individuals involved could specialise in those activities. With money the problem is solved, specialisation is possible and the gains from trade can be captured.
Thus as commentators since Adam Smith have observed, the invention or use of money has a remarkable effect- it stimulates trade, production, permits specialisation and promotes growth. It enables the economy to progress beyond the Yeoman farmer model. From this perspective it makes no sense to state that money is neutral. It is also apparent that in a monetary economy money can be borrowed and lent and a nominal rate of interest charged- quantity of money today vs the quantity tomorrow and so on. It also follows that to encourage its use it is desirable to maintain a relatively stable purchasing power of the monetary unit. And to get some idea of what is happening to purchasing power it is useful to have a measure of what is happening to the average price level are all goods and services rising in price or are we observing changes in the relative dollar prices of goods and services? The concept of a price index is both necessary and useful in a monetary economy. Also, use of a common unit of account dramatically reduces the number of prices that need to be quoted and improves efficiency relative to barter. In a world with n commodities the number is reduced from n(n-1)/2 to n Capie, Tsomocos and Wood (2003).
Fiat money therefore has value in a monetary economy because it provides access to goods, services and income streams that would otherwise not be achievable. It also provides insurance against uncertainty, panic and other disruption to the economy- although the scramble to acquire it may make the situation worse. Central banks have a role to ply here. Assets, as titles to income or consumption streams, cannot provide such insurance at the same cost as the values of those titles come into question in a panic. In this sense money has a liquidity premium that does not attach to other assets. In a modern economy the government and the central bank stand behind that liquidity premium in a way that private provision of money would be unable to replicate.
The world of electronic money is simply the latest stage in the evolution of money from commodity to fiat money. Electronic money is just a change in the physical form of fiat money from paper note to electronic book entry and nothing fundamental in monetary theory is at stake due to this change. For central bankers the world of e-fiat money is here and they have responded by refining their management of the system. Freedman (2000) provides an excellent overview. He stresses two factors that enable central bank control over the system; i) The monopoly supply of clearing balances (money) by the central bank; and, ii) The ability of the central bank to impose losses on the banks. This is essentially the channel system described by Woodford (2003 chapter 1). The central bank keeps the banks in the Bank using daily open market operations and can apply penalty rates to banks who habitually mismanaged their cash flows. Reference also the RBA system
Those monetary theorists who imagined that the evolution of electronic money would lead to a loss of control over monetary policy are therefore mistaken so long as the central bank retains its monopoly position. The evolution of electronic money does not mean that the world may come to resemble a pure exchange economy as King (1999) conjectured for reasons that will be outlined below. Nor does it mean that Microsoft stock can function as money as Cochrane (2005) now claims. To see why consider the world of e-asset trading based on the transfer of assets in real time by super computer outside the control of the central bank. King (1999) imagines such a world because of . the ability of computers to communicate in real time to permit instantaneous verification of the creditworthiness of counterparties, thereby enabling private sector real time gross settlement to occur with finality.
Unfortunately (fortunately?) it takes a lot more than real time computer power to get this system to work without frictions similar to those associated with barter. For example, recall the Adelaide hairdresser who holds Microsoft shares in her portfolio. What if the Bali tour operator will not accept them (Hes a Muslim!). The general point is that for the computer system to be a practical means of trading assets the portfolio must have assets that are acceptable to the counter party our old friend the double coincidence of wants applies also to trades in assets. All the timing problems associated with trading in real time will also arise in the e-asset trading. Other transactions frictions arise when using assets whose prices fluctuate on a daily basis. The Adelaide hairdresser may well pay for the holiday with her Microsoft shares but how will the Bali operator feel if Microsoft stock fell by 10 per cent the day after payment? He will be short if he was planning to pass them on as payment for the goods and services he needs. How would the Adelaide hairdresser feel if Microsoft stock rose by 10% the day after payment? The difficulty here is that the payment system requires short-term stability of value to complete a chain of payments in real time. Fluctuations in asset prices make this difficult and induce agents to seek assets with stable prices, Alternatively, a form of Greshams Law may eventuate where agents attempt to pass of assets they expect to fall in value and hold assets they expect to appreciate in value. In a world with perfect foresight this is ruled out but in real time it is a distinct possibility and would impair the efficiency of the system, super computer or no. What is needed to avoid these frictions is an asset that is generally acceptable namely money. The information requirements of e-asset trading are a lot higher than for e-money. In other words the super computer is still subject to transactions frictions unless there is a money-like asset. Transactions frictions are unavoidable in this system and money would help to resolve them.
Freedman (2000) also considers additional factors that would effectively increase the risk and cost of actual attempts to implement a system of e-asset trading in real time without a central bank. For example, a private institution operating the computer system would be subject to increased risk, bank risk, if it also made loans, i.e., if it acted like a bank. If it did not and could not act as a lender of last resort to smooth payments imbalances between transactors, transactors would need to hold large stocks of assets to eliminate the possibility of payments imbalance. For these reasons, even if the super computer system could be set up it would be a riskier and higher cost system than the e-money system currently in place. Thus, e-trading of assets even if it is technically feasible is not competitive in terms of risk and cost with the current electronic fiat money based on RTGS systems clearing through the central bank. Woodford (2003, chapter 1) accurately describes how the current e-fiat money system works in terms of what he calls the channel system monetary policy without control of monetary aggregates. But as we will see the difficulty he faces is accounting for the existence of this system in his cashless, frictionless world.
Hence, the central bank remains at the heart of the modern system of e-money and so long as it retains its monopoly control over clearing balances the situation is no different from Keyness (1930) discussion of Bank Rate. Freedman (2000) gives some compelling reasons why clearing through the central bank will remain the lowest cost and risk alternative for a world with e-fiat money as do Capie, Tsocomos and Wood (2003). In what follows I spell out the conceptual confusions that arise from conflating the e-trading of assets in real time (e-barter), the concept of the cashless economy proposed by Woodford and Cochrane, and the existing world of e-fiat money with central bank clearing. In particular, we must answer the question: how can the transactions frictions that would afflict e-trading of assets in real time be avoided? We need to answer this question to see what Woodford and Cochrane mean by their concept of a cashless, frictionless world. The latter is clearly not trading assets on a super computer in real time but neither is it the channel system of e-fiat money clearing by the central bank described in chapter 1 of Interest and Prices.
III Properties of a cashless, frictionless world
Although the e-trading of assets in real time does not approximate the cashless, frictionless world that Woodford-Cochrane have in mind there is one world that does. It is the Arrow-Debreu world. As many theorists are fond of claiming the best-developed model of the economy is the Arrow-Debreu model. The embarrassment for theorists is that Arrow-Debreu model had no role for money, Hahn (1982, p. 1) put it succinctly:
The most serious challenge that the existence of money poses to the theorist is this: the best developed model of the economy cannot find room for it. The best-developed model is, of course, the Arrow-Debreu version of a Walrasian general equilibrium. A world in which all conceivable contingent future contracts are possible neither needs nor wants intrinsically worthless money. . The point is obvious and has been made quite often. But it is doubtful that it has been fully taken on board.
As Sargent (1987, p. 133) makes the same point: In equilibrium, an inconvertible currency is valueless; this result generally obtains in Arrow-Debreu models.
The reason for the inability to show that money has positive value in the Arrow-Debreu model can be traced to the nature of the auction that is assumed to underpin the model. This form of auction arrangement may be suitable for some purposes but it turns out to be most unsuitable for monetary theory. To see why, consider the Ljungqvist and Sargent (2004, Ch 8, p. 208, p. 217) description of the Time-0 auction for a competitive Arrow-Debreu-Walrasian model:
In the competitive equilibrium, all trades occur at date t = 0 in one market. Deliveries occur after t = 0, but no more trades. A vast clearing or credit system operates at t = 0. It ensures that [the budget constraint] holds for each household i. A symptom of the once-and-for-all trading arrangement is that each household faces one budget constraint that accounts for all trades across dates and histories.
The difficulty for fiat money in a model based on this sort of auction is that it has no role to play. The vast clearing or credit system as Ljungqvist and Sargent describe it, has nothing to say about how trades would actually be executed so the model specifies no transactions technology. A model with a time = 0 auction is simply not capable of analysing transactions technology. As outlined in section II money can be thought of as a transactions technology that over comes real world barter and other transactions frictions. But under a time = 0 auction those frictions dont arise so no transactions technology need be specified in the model. Hence the medium of exchange function of money is not required, any commodity can act as numeraire, and the store of value function is dominated by assets with higher rates of return. Obviously there is also no possibility of a panic in an Arrow-Debreu economy.
McCallum (2003, pp. 1-2) describes trading under what we call the time =0 auction in the following terms. In his view:
..an accounting system of exchange[the time = 0 auction] is one in which there is no money but exchanges are conducted by means of signals to an accounting network, with debits and credits to the wealth accounts of buyers and sellers being effected with each exchange. In the present paper, as in McCallum (1985), I will classify the latter type of system as non-monetary. In effect, an accounting system of exchange is a highly efficient form of barter.
Indeed, we could go so far as to describe the time = 0 auction as a system of perfect barter because it eliminates all the frictions usually associated with barter of commodities or assets. Under a time = 0 auction all commodities and assets have equal exchange value. In our example, the Adelaide hairdresser would have no problem overcoming the transactions frictions imposed by cutting hair, or exchanging Microsoft shares for a Bali holiday. Real world transactions frictions do not exist in the frictionless world of a time = 0 auction.
The cashless, frictionless world can also be extended in a way that appeals to financial economists. This is the model of Arrow-Debreu contingent securities. But in this world unbacked e-fiat money, also has a zero value. Sargent (1987, p. 136) describes the problem for the case of a Lucas tree model:
In this economy, assets are valued according to the value of the stream of consumption that they support. An unbacked inconvertible currency promises to pay off nothing in the future. We have seen that introducing an asset with such a payoff stream into Lucass tree model leaves the equilibrium interest rates unaltered and causes the asset to receive a zero value.
Thus everyone has now taken on board (since Hahn 1982) that the Arrow-Debreu model has no role for e-fiat money. Sargent (1987, p. 137) explains how monetary theorists attempted to generate models in which money has value by developing models of decentralized trading. The latter attempts are important for monetary theorists but will not be considered any further as we are concerned only with the concept of the cashless, frictionless economy proposed by Woodford and Cochrane. We are concerned with how Woodford-Cochrane deal with Hahns challenge. Woodford and Cochrane respond to this challenge by abandoning the concept of fiat money and embracing the notion of money as an asset with an income stream money as stock as Cochrane (2005) puts it. On this definition money has value in an Arrow-Debreu economy and the frictions of e-asset trading in real time are eliminated by the time-0 auction.
So far so good-But how do we sell a non-monetary model to central bankers? Once their economists start looking at the model wont they begin to find some curious features?
The first difficulty with the concept of the cashless, frictionless world is that a super computer, conducting asset trading in real time is does not approach the properties of a time-0 auction. (Hoover, 1988, p. 97) makes the obvious, but often overlooked, point that the adoption of e-fiat money does not mean that the real economy is converging on the properties of a world with a time-0 auction:
The fact that computerization may allow us to dispense with notes and coins does not transform our economy from one in which transactions are made in a higgledy-piggledy uncontrolled manner into one in which they are coordinated by central auction.
It is simply impossible to construct a computer that would be capable of collecting the information and coordinating anything remotely resembling a time-0 auction- the time-0 auction is simply a non-operational thought experiment. It is a theoretical but non-operational substitute for money. I dont think anyone disagrees with this interpretation and suspends disbelief when they employ the model. But conceptual problems will emerge if the time = 0 auction is treated as if it were a reasonable approximation to the current US payments system as Cochrane (2005, p. 505) implicitly suggests.
When we make that step more fundamental conceptual problems arise once it is realised that the time = 0 auction not only eliminates any role for e-fiat money but also eliminates any role for money -of whatever type and therefore all nominal magnitudes. As McCallum (2003) correctly points out, the cashless, frictionless world, what he calls an accounting system of exchange, is a non-monetary system. But if it is a non-monetary system it can have no role for nominal magnitudes. By eliminating nominal magnitudes it also eliminates any scope for the central bank or fiscal policy to determine the price level. Recall Stiglers (1972) insight. It turns out that the frictionless world is far too strong an assumption on which to build monetary theory or a theory of monetary policy.
The fact that nominal magnitudes and the price level are concepts that take on new meanings in the frictionless world under a time = 0 auction has been recognised by a number of authors over the years. Hoover (1988, p. ) when discussing Famas (1980) earlier attempt to apply the theory of finance to monetary theory, notes that Fama uses the term price level to describe the numeraire relative price of commodities. For example, if oil is the numeraire then the numeraire price of all other commodities in terms of oil is a commodity relative exchange vector (so many grams of butter, jam etc per litre of oil with the litre of oil as numeraire). The nominal price, $s per litre of oil is only of interest if we can part with the $s to acquire the oil. Nominal magnitudes have meaning in a world where the purchasing power of money needs to be maintained so as to sustain the gains from trade that money makes possible. In other words, an economy with a medium of exchange needs to pay attention to its general purchasing power. But in a world where the super computer (time = 0 auction) can spit out the exchange value of an endowment in terms of any commodity as the numeraire, the notion of a price level from a monetary economy is transformed into something else - it also provides no useful additional information so is effectively redundant.
To see this consider McCallums (2000, p. 282) discussion of what the term price level means in a non-monetary accounting system of exchange with a very efficient computer (the time = 0 auction). He points out that in that world the price level cannot be the inverse of the purchasing power of money because no money exists. He conjectures that it could be defined as the inverse of the value of the medium of account (numeraire) relative to goods in general. And this could be justified on the grounds that it would make a great saving in transactions costs to have all prices quoted in terms of the numeraire; n instead of n(n 1 )/2. In reality that may well be the case. But in the cashless, frictionless world of the time = 0 auction such frictions or transactions cost do not exist. In the frictionless world of super computing power households could view the value of their endowment in terms of any commodity or asset at the press of a button. The auction generates all n(n 1)/2 exchange ratios and prices can be quoted in terms of any of the n commodities as numeraire. Consequently even if we accept this part of McCallums argument and attempt to construct indices of the purchasing power of jam, wheat, etc they are indices that do not convey any additional relevant information in a frictionless economy. The concept of a price-level simply has no role to play in a model with a time = 0 auction. The concept of price level as a measure of purchasing power is relevant to a monetary economy where its purchasing power may be eroded. But erosion of purchasing power cannot occur in a world of perfect barter. The concept simply serves no useful purpose in a frictionless world. It is also a property of this cashless, frictionless world that we could also introduce Arrow securities and price them in terms of the consumption goods, eg jam, to which they are title, even if they dont exist without changing anything of substance. (See Sargent 1987 for an accessible treatment of state-preference theory)
In similar vein McCallum (2000, p. 282) points out that the k period nominal interest rate the relative price for using money for k periods also does not exist in a non-monetary world. The nominal rate of interest is a pure number that expresses the return, measured in money, for parting with (lending) money for some purpose. If deposited with a bank, our Adelaide hairdresser has her account credited in $s periodically. The calculation is simply EMBED Equation.3 per $ deposited. If instead she buys a coupon bond issued by the government she will receive regular coupon payments in $s and the return on her investment can be calculated as a nominal yield as explained in financial economics 101. We take the $ value of her initial investment and compare it to the terminal $ value. We have the same relationship as with the deposit and the calculation is simply EMBED Equation.3 per $ invested. Now the condition EMBED Equation.3 usually applies because bonds are riskier than deposits as interest rates may change during the period of the loan. Both interest rates are obviously nominal rates because they are transactions made possible by the use of money. Both are loans that generate a yield from the calculation of money given up at date t in terms of money received at date t+1. If money were to vanish neither transaction could occur. Also for both cases we can convert the nominal interest rates or yields into real yields (means constant purchasing power) by adjusting them for any change in the purchasing power of the $ as a result of a change in the price level.
In the cashless, frictionless world without money nominal interest rates are simply not defined. Nevertheless, some interest rates do exist. They are commodity interest rates and there are as many of them as there are commodities. For example, in the inter-temporal Arrow-Debreu world of time-dated commodities we can compare the quantity of jam that must be given up at date t for the quantity of jam at date t+1. That calculation generates a pure number with the dimensions of an interest rate the jam rate of interest. This is a real rate of interest but not one that has been adjusted for inflation al la Fisher. It is a real rate in the sense that it is a commodity rate of interest. Such rates are generated automatically by the auctioneer in the time = 0 auction of the Arrow-Debreu time-dated economy. The auction also ensures that the cross rates rule out any arbitrage opportunities. (See Hahn 1983?).
To sum up, the cashless, frictionless economy is thus just too good to be true. It is an imaginary world in which all the issues of interest to monetary economists are eliminated by assumption. Nominal magnitudes do not exist, the concept of the price level is redundant and there is by implication then no scope for the central bank or government to determine it. The Arrow- Debreu model, which has these properties, is a theoretical construct that no doubt has its uses. And those, like Hahn (1982), who believed that it was (is) the best-developed model of the real economy, and can be adapted to incorporate money may be mistaken but we can debate the issue. Those like Wallace (2004) who simply attempt to incorporate a central bank as an agent in the Arrow-Debreu model are surely mistaken and will generate only counter intuitive results and puzzles (as Wallace does). Similarly, those like Woodford and Cochrane who apply the cashless, frictionless model as an approximation to existing e-money systems are also surely mistaken.
IV Properties of the WoodfordCochrane cashless, frictionless world
Prior to Woodford and Cochrane, monetary theorists attempted to introduce money into the cashless, frictionless world. Patinkin made the attempt with money in the utility function. Clower proposed the cash-in-advance constraint. From what we have said it is apparent that those attempts fail because they attempt to impose money on a model in which it is not required. Fiat money has zero value and if it is imposed via a cash-in-advance constraint it appears to be a welfare reducing innovation contrary to monetary economics 101 (Clower 1984). Woodford and Cochrane take different tack. They wish to retain the cashless, frictionless model as a benchmark into which realistic frictions may later be added. But at the same time they wish to use the cashless, frictionless model to determine the price level and examine nominal interest rate rules employed by central bankers. Both of these objectives are not achievable with their cashless, frictionless model.
Woodford and Cochrane face a conundrum: It is not possible to insert frictions into a frictionless model but when the frictions dont exist the model has nothing interesting to say about monetary theory and policy. It is my contention that they resolve conundrum by resorting to story telling rather like Patinkins explanation for unemployment in chapter 13 of Money, Interest and Prices.
Both Woodford and Cochrane are quite explicit about the strategy they adopt. Woodford (2003, pp. 61-62) outlines his objective as follows:
I first expound this approach in the context of a purely cashless economy one in which there are assumed to be no transactions frictions that can be reduced through the use of money balances, and that accordingly provide a reason for holding such balances even when they earn a rate of return that is dominated by that available on other assets. Such a setting one that is commonly assumed in financial economics and in purely real models of economic fluctuations alike..At the same time, neither the usefulness nor the validity of the approach proposed here depends on the claim that monetary frictions do not exist in actual present-day economies. After expounding the theory for the cashless case, I show how the framework can easily be generalized to allow for monetary frictions, that are common in monetarist models of inflation determination (by including real balances in the utility function or a cash-in-advance constraint).
Hence Woodford treats the cashless, frictionless model as a limiting state of an economy with monetary frictions. In similar vein, Cochrane (2005, p. ) argues that the cashless, frictionless fiscal model can provide a useful benchmark for more complex and realistic analysis with frictions.
Throughout economics, frictionless competitive models are the benchmark, the foundations upon which we add interesting frictions.
From what we have said so far it is apparent that any attempt to introduce frictions into the cashless, frictionless model will fail. It is not possible to introduce frictions as a basis for justifying the existence of money (of whatever sort) into a frictionless benchmark model where those frictions are eliminated by the time=0 auction. The time = 0 auction is essential for the frictionless property of the model and cannot be dropped when moving to a state with monetary frictions without the development of what Hahn (1974) called an essential sequence economy. The latter is a world in which all the transactions frictions removed by the time = 0 auction reside. So the time = 0 auction and the auctioneer must go to enter that world as many have realised. It is rather like the world of monetary economics 101 and the world of e-money inhabited by central bankers. Hence it makes no sense to claim, as Woodford and Cochrane do, that they can easily generalise their cashless, frictionless world to incorporate frictions. If they insist on introducing what they call monetary frictions then they suffer the same fate as Patinkin and Clower- the analysis is counter intuitive. At this point we can therefore predict that the Woodford-Cochrane frictions story will exhibit counter intuitive puzzles and properties. But we can go much further. The cashless, frictionless state of the model will have no role for nominal magnitudes, the price level, central banks of governments. It is therefore quite incapable of providing a theory of the price level, or advice to central bankers on nominal interest rate rules.
Over the past decade Woodford has offered two versions of the cashless, frictionless economy. The first, in Woodford (1998), employs the concept of a cashless limit. I have discussed this case in more detail elsewhere (Rogers 2005). The second version of a cashless economy is the cashless, frictionless world presented in Interest and Prices. From the description provided by Woodford the only world consistent with his vision is a model based on a Time-0 auction. In particular, Woodford (2003, p. 62, italics added) states that he is considering price-level determination in an economy in which both goods markets and financial markets are completely frictionless.Under the assumption of frictionless financial markets, it is natural to suppose that no monetary assets are needed to facilitate transactions. The latter statement is particularly revealing because it means that money is an asset but even that asset is not required to make transactions in the frictionless world. The only world in which those statements are true is the Arrow-Debreu economy and its time = 0 auction. Despite that Woodford (Woodford, p. 63) goes on to assert that:
As we shall see, the central banks policy rule is one of the key determinants of the equilibrium price level even in a cashless economy.
But as I will suggest, it is here that Woodfords disregard for the history of monetary theory and the properties of his model come home to roost.
First, from Woodfords description of the cashless, frictionless model it is apparent that even e-asset trading has no role no monetary assets are needed to facilitate transactions. If the goods markets are frictionless then they have the properties exhibited by the Time-0 auction and the model has nothing to say about how those exchanges will be executed. Commodities trade directly for commodities in that world so there is no need for e-asset money (as Woodford actually points out) let alone e-fiat money. Under a Time-0 auction there is also no need to distinguish the asset or commodity composition of the household endowment. All commodities and assets are on an equal footing and all can be traded directly under the Time-0 auction that is why it is a cashless, frictionless world. (See the description of the household budget constraint below). That world has no role for money of any sort, be it electronic or cash; money has no value and can serve no useful purpose.
Second, it follows from what has been said previously that there is then no role for nominal rates of interest, the price-level and that also eliminates any role for the central bank. Commodity and asset interest rates exist and are defined in terms of inter-temporal commodity prices expressed in the numeraire. Prices are expressed in terms of some arbitrary numeraire, it could be jam or it could be the non-existent $. But in this world the central bank has nothing to do. It certainly cannot interfere with the utility maximising decisions of households under the time-0 auction. Woodford actually attempts to give the central bank a role by arguing that sticky prices produce allocation inefficiencies. That may be true in reality but it cannot happen in Woodfords model without taking out the time-0 auction and he never proposes that.
What, then, is the central bank doing in Woodfords Interest and Prices controlling the nominal interest rate to maintain stability of the price level? In chapter 1 of Interest and Prices Woodford describes what he calls the channel system of interest rate control. This is consistent with the schemes outlined by Freedman (2000) and the RTGS systems as implemented by the central banks of Australia, New Zealand and Canada, among others. He also suggests that Kings (1999) conjecture may become a reality and eliminate the advantage of clearing through the central bank. We have already explained why this will not happen (e-asset trading in real time is dominated by the existing system in terms of cost and risk and e-money is not a replication of a time = 0 auction. The monetary system cannot converge on the pure exchange economy as conjectured by King).
He then turns to Wicksells notion of the pure credit economy to stress that in that economy money does not circulate, either in the form of notes or coins. All payments are made by book entry or in todays world by e-money. In a sense we could describe Wicksells model as cashless. For Wicksell cashless does not mean moneyless but for Woodford cashless does mean moneyless. Woodford does not appear to notice this and goes on to suggest that it is Wicksells vision that provides the basis for the cashless, frictionless model presented in chapter 2. After quoting Wicksell, Woodford states:
This is the approach that is taken in the chapters to follow. The basic model (developed beginning in Chapter 2) is one that abstracts from monetary frictions.
But the tragedy for Woodford is that Wicksells pure credit economy is a monetary economy not an imaginary frictionless world based on a time = 0 auction. The modern e-money economy does indeed approximate Wicksells pure credit economy. Both are monetary economies. The cashless, friction model that Woodford develops in chapter 2 is a non-monetary model of perfect barter that bears no relation to the questions of monetary theory and policy to which he attempts to apply it. The difficulties faced by Woodford are captured by Greens (2005, p. 124) description of Woodfords intentions:
In the cashless economy that Woodford models, the central bank can set the a nominal interest rate directly by standing ready either to lend or borrow unboundedly at its policy interest rate (analogous to the federal funds rate in the United States). However, the outside money that is borrowed or lent is a redundant asset in a complete system of markets for dated, state-contingent consumption, and plays no essential role in facilitating transactions.
It is not the case that the central bank could behave as described in the cashless, frictionless model (See also McCallum 2000, p. 282.)
The simple conclusion here is that there is no connection whatsoever between Wicksells pure credit economy, or the modern world of e-money in which central banks conduct monetary policy by interest rate rules, and Woodfords cashless, frictionless model. The channel system applies to the real world of e-fiat money in which exchange imbalances between banks clear through the central bank in a RTGS system. In Wicksells model of book entries, if inflation occurs the central bank must raise the nominal interest (and the inflation adjusted rate) to increase the cost of borrowing and contract economic activity. None of this can happen in Woodfords cashless, frictionless model. If we are trading commodities and assets in a time-0 auction as imagined in the frictionless world of financial economics then all we need is the auctioneer. The book entries made in the frictionless world are those of the vast credit system of the time = 0 auction run by the auctioneer. They are NOT the book entries imagined by Wicksell as an efficient form of monetary transaction in the higgledy-piggledy trading of the real world. The electronic money that may be imagined by Woodford in the cashless, frictionless world is NOT the electronic money of the channel system. From this perspective the assumptions underlying the frictionless, cashless world decimate the central bank and anything of interest to central bankers.
In conclusion, the frictionless, cashless world of Woodford and Cochrane is the world of Arrow-Debeu securities underpinned by the time = 0 auction. It is the failure to recognise the limitations of this property of their cashless, frictionless model that has led both Woodford and Cochrane into conceptual error. In this world they can apply the arbitrage relations familiar from financial economics to find the implicit price of cash that has been made to vanish is if money is an Arrow-Debreu security. Although this is a false description of a monetary economy they compound the confusion by retaining a role for cash (fiat money) in some states of the model. In these states their model exhibits the Patinkin-Clower conundrum money is a welfare reducing innovation contrary to the facts. As expected the frictions version of the frictionless model exhibits numerous counterintuitive and puzzling properties. But more damaging is the fact that the frictionless world has no role for nominal magnitudes -interest rates, prices and price levels and therefore no role for central banks. To see these features we examine the structure of the models in more detail.
V Conceptual puzzles in the Woodford-Cochrane models
As Woodford is advocating a cashless, frictionless world as a benchmark into which more realistic monetary frictions can later be added, he retains money (cash) and nominal interest rates in the households one-period budget constraint:
EMBED Equation.3 (1.7)
where EMBED Equation.3 . The budget constraint is derived under the assumption of compete financial markets, that is that available financial assets completely span the relevant uncertainty faced by households about future income, prices, taste shocks and so on so that each household faces a single budget constraint. This is the frictionless world familiar from financial economics. The variables are defined as follows: The variable EMBED Equation.3 is the end of period holding of money base, while EMBED Equation.3 is the stochastic present value of monetary and non-monetary wealth as EMBED Equation.3 where EMBED Equation.3 is the random value of non-monetary wealth. EMBED Equation.3 is the price of the consumption good in terms of money and EMBED Equation.3 is the possibly stochastic endowment of the single good. EMBED Equation.3 is net nominal tax collected by the government. Woodford then argues that the infinite sequence of budget constraints in (1.7) is equivalent to a single inter-temporal budget constraint (1.12).
EMBED Equation.3 (1.12)
The latter inter-temporal; budget constraint simply requires that the present value of the households planned consumption over the entire indefinite future plus the cost to it of its planned money holdings must not exceed its initial financial wealth plus the present value of its expected after-tax income from sources other than financial wealth.
The ability to construct a single budget constraint like 1.12 is, of course, a symptom of the time =0 auction that underpins Woodfords frictionless model. Recall L&S.
.
Woodford then argues that, in the cashless economy there is no non-pecuniary benefit from holding money balances so household optimization requires that:
Either, EMBED Equation.3 or EMBED Equation.3 ;
at each date and in each state (but which condition obtains may differ across dates and states).
But what exactly does this condition mean? Consider the variables EMBED Equation.3 and EMBED Equation.3 . The former is defined as the nominal rate of interest paid on money balances held at the end of the period, t. The variable EMBED Equation.3 is defined as the one-period (short term) nominal interest rate that solves the equation EMBED Equation.3 . The RHS expression here is the expected value of the stochastic discount factor EMBED Equation.3 . Presumably, if money balances are zero we are in the cashless, frictionless state and EMBED Equation.3 also, leaving only what Woodford calls the nominal interest rate, EMBED Equation.3 However, if there is no money (cash) how can the nominal interest rate EMBED Equation.3 exist when the nominal rate oh cash, EMBED Equation.3 does not? It cannot, as McCallum (2000) explained. In Woodfords model the nominal rate of interest, EMBED Equation.3 , is defined as the short tern nominal interest rate that could solve the equation EMBED Equation.3 where EMBED Equation.3 is the nominal value (in terms of numeraire) of household end-of-period portfolio of other financial wealth (excluding money).
In the model we thus have two nominal rates of interest one on money and one on other financial wealth denominated in money. In the cashless, frictionless state, the nominal rate of interest disappears along with the cash (money base). That leaves only the non-monetary financial assets expressed in terms of the numeraire, $s say. This is the world where money is not required to make transactions and the numeraire can be anything, even something that has disappeared and has no physical existence. But that does beg the question- what does nominal mean in this context? A nominal interest rate is nominal because it implies a calculation using an interest rate (a pure number) that produces a quantity of money for future use. When the $ is only a numeraire and has no physical existence the fact that the amount of interest earned on a non-monetary asset is calculated in $s does not mean that it is a nominal interest rate. In the cashless, frictionless world the choice of numeraire is entirely arbitrary-it could be jam. We would not describe the jam rate of interest on a bond as a nominal interest rate but this is implicitly what Woodford expects us to do.
The same logic also applies to Woodfords use of nominal to describe prices in his cashless, frictionless economy. Quoting prices in a numeraire called the $ does not mean that nominal magnitudes are being described. A similar conclusion applies to the numeraire $ price of the consumption good. In the cashless, frictionless world where only the numeraire function of money exists there are no nominal prices. The Time = 0 auction is precisely the situation under which base money is not required and all commodities and assets become money. There is no role for nominal magnitudes in Woodfords cashless, frictionless model.
Conceptual puzzles also arise (as predicted above) when we examine Woodfords model when transactions frictions supposedly exist. I say supposedly because if the Time =0 auction still applies the model cannot accommodate frictions. In the monetary frictions state Woodford writes EMBED Equation.3 as EMBED Equation.3 ( EMBED Equation.3 ) which as Woodford (2003, p. 63) explains, means that cash is a perfect substitute for other riskless nominal assets, whether of private or government origin (this is surely false in reality). But, although Woodford has not included money in the utility function, we are back with the Patinkin-Clower problem. Recall that for Woodford money is an asset with an income stream so he evades the problem of a zero value for fiat money by changing the definition of money- fiat money has been replaced by an income-earning asset. However, even if we accept that assets are money in the cashless, frictionless world any and all assets are money. Under a Time-0 auction the composition of the endowment is irrelevant (distinctions between types of assets is of no importance) -only its value counts. [See Woodford p, 65] For reasons outlined above, real time computer trading of assets cannot approximate this type of Time-0 auction.
Woodfords cashless, frictionless world is a world in which no form of money is required or for which there is any reason for its existence. It is not the world of monetary economics 101 or the modern world of electronic money. But more seriously the frictionless commodity and asset trading of the Arrow-Debreu economy with a complete array of securities under a Time-0 auction has no role for nominal magnitudes or a central bank. Woodford therefore fails in his attempt to develop a theoretical foundation for real world monetary policy in his cashless, frictionless competitive world. Advice to central bankers about interest rate rules derived from these models amounts to no more than storytelling. I leave the reader to judge what all the attempts at quantification may mean.
A similar conclusion applies to Cochranes model.
Cochrane (2005) has a different objective in mind when he argues that money is stock (equity). Cochrane and Woodford have been exponents of what has become known as the fiscal theory of the price level and Cochrane (2005) is a defence of this theory against attacks by Buiter (1999, 2002, 2004) and others. Part of Buiters (1999, p. 1) objection to the fiscal theory of the price level was his opinion that it required the governments inter-temporal budget constraint to hold only in equilibrium and not for all price vectors. Cochrane (2005) correctly rejects this criticism if it is applied to his Arrow-Debreu-Walrasian world. In such a world Walrass Law holds and all agents satisfy their budget constraints for all equilibrium or disequilibrium price vectors. However, not all macro models satisfy Walrass Law. Tobins models with a wealth constraint are a good example so there may be some misunderstanding here. Nevertheless, the fiscal theory of the price level as presented by Woodford and Cochrane is open to criticism on the grounds sketched above. The cashless, frictionless fiscal model employed by Cochrane (2005) has no role for the price level of the government. To see this consider Cochranes story.
Cochrane (2005) argues that we can understand the price level using the usual frictionless stock valuation equation:
Number of shares = Expected present value of future dividends or earnings. (1)
Price level
Where the price level is defined as shares per good. This is an interesting definition of the price level but we may get a clearer idea of what it means below. The fiscal theory of the price level is based on the idea that nominal debt is a residual claim to government primary surpluses. Hence it is possible to determine the price level via the valuation of government debt:
Nominal government debt = Expected present value of primary surplus (2)
Price level
Cochrane uses Microsoft shares in his discussion but recall that any and all shares are part of the money supply in this world and only the value of the endowment and not its composition is important. The conceptual difficulties raised by this vision of the world were noted by Hoovers (1988) review of an earlier attempt at the same idea by Fama (1980). In what follows I will examine the properties of Cochranes model to highlight the conceptual contortions needed to achieve his conclusions. I will argue that the Cochranes fiscal theory of the price level is false. There may well be some important relationships between real world fiscal deficits, their financing and the price level. But any relationship between them and Cochranes cashless, frictionless fiscal model is just wishful thinking.
Cochrane (2005, p. 505) proposes to use a simplified version of the familiar cash-in-advance framework in Sargents (1987) textbook. He explains that; I use this framework because it is a reasonable abstraction of the current U.S. payments system, and because it maintains a close connection to a familiar setup. He makes a small modification to the model by reopening the securities markets at the end of each day. This allows agents to transform their money holding into securities and hold no money overnight. His intention here is to study price level determination at the limit point in the context of Woodfords cashless limit (Cochrane 2005, p. 503). At the limit point there is no cash (fiat money)
In view of what was said in section III the intentions behind this setup are transparent. The cash-in-advance constraint gives cash value during each trading period. Cash has value that is imposed by the CIA constraint. Nevertheless, cash is a welfare reducing friction that disappears at the limit point at the end of each day when all cash is converted to equity. In Cochranes cashless, frictionless fiscal model, cash is converted into a title to an income stream at the end of each period and therefore has value. This is the cashless, frictionless point of Woodfords (1998) cashless limit. It is a non-monetary point and all the properties of Woodfords analysis apply to Cochrane mutatis mutdandis. To see these properties consider the characteristics of Cochranes (2005, p. 510) equilibrium solution in the frictionless model they mimic exactly Woodfords setup discussed above.
Cochrane presents 3 characteristics of equilibrium (cashless point) in his model:
EMBED Equation.3 (17)
The marginal rate of substitution is equal to the stochastic discount factor.
(2) Any equilibrium with positive nominal interest rates must have no money;
EMBED Equation.3 (18)
No equilibrium can have negative nominal interest rates.
(3) The government debt valuation equation holds.
EMBED Equation.3 (19)
Condition (17) is simply the utility maximising condition that applies to agents in the frictionless model. Condition (18) states that there is no M in the frictionless equilibrium and from the discussion of Woodford we saw that this implies that the nominal interest rate must be positive. That is when EMBED Equation.3 then EMBED Equation.3 and as EMBED Equation.3 when EMBED Equation.3 it follows that EMBED Equation.3 . Condition (19) is not a government budget constraint but a government bond valuation equation.
But as we now know, the cashless, frictionless, fiscal model at the cashless point of interest to Cochrane is not a monetary economy. The frictionless model is frictionless because it rests on a non-operational Time-0 auction at the cashless point at the end of each period. The CIA constraint during the trading period gives cash something to do but is subject to the Clower puzzle cash is a welfare reducing innovation. There is no good reason for introducing it. Cochrane justifies it only on the grounds of familiarity. It does however, illustrate the point that a monetary friction has been introduced when that friction is inconsistent with other features of the model. The existence of the auctioneer or social planner conducting the Time-0 auction is sufficient. But that means that, the cashless, frictionless fiscal model exhibits all the features of Woodfords model. Consequently it has no need for the price level so it cannot provide the foundations for a fiscal theory of the price level. All these features are revealed by Cochranes conditions (18) and (19).
With EMBED Equation.3 there can be no nominal rate of interest on money balances or on government bonds. As McCallum (2000) explained the interest rate on government bonds is not a nominal rate because it cannot be paid in money (cash) Buiter (1999, 2002) made the same point. Cash does not exist at the cashless limit. Interest must therefore be paid in terms of some other commodity even if it is expressed in terms of the numeraire. In the frictionless economy at the cashless point the numeraire can be anything. In reality the purchase of a government bond is like any other loan. The lender undertakes it on the basis of an assessment of risk and return expecting a payoff in money. That cannot happen in Cochranes cashless, frictionless point. For Cochrane government bonds are simply titles to the present value of the primary surplus like company dividends. In this respect governments are just like to firms. Cochrane (2005, p. 506) also explicitly makes the claim that these bonds can be used to make transactions (like money):
The economy (the US economy or the model economy?) can work just as well if transactions are mediated by claims to maturing government debt, and if old debt is exchanged directly for new debt and to pay taxes. I refer to this case as the cashless model.
But as we know, the frictionless world has no role for such transactions services. In real time such e-asset trades would be dominated by the current e-money system. A further question suggests itself. To have value in the frictionless equilibrium, government bonds must have a title to a future income stream. In Cochranes world that income stream is the primary surplus. Why such a surplus would exist is a moot point and in any event Cochrane (2005, p. ) states explicitly that he is presenting a: standard and well specified Walrasian model in which government has no special status. In the cashless, frictionless model that Cochrane employs we have seen that no only does the government have no special status -it has no raison detre.
The interpretation of expression (19) is the crux of Cochranes FTPL and the key to understanding it is the idea that in the cashless model the quantity equation has vanished as EMBED Equation.3 so that expression (19) can be applied to determine the price level, EMBED Equation.3 . He argues that expression (18) is still a money demand equation but that it can no longer pay a role in determining the price level. Ignoring our earlier questions about what the price level means in this context, it seems that Cochrane is simply presenting us with an argument that has the same structure as the old argument between liquidity preference and loanable funds theories of the rate of interest in the context of Patinkins real Walrasian general equilibrium system.
To see this, note that Cochrane (2005, p. 506) points out that in the simple monetary frictions state of the model, where EMBED Equation.3 the model produces two equations containing the price level, EMBED Equation.3 . These equations are:
EMBED Equation.3 (3)
and
EMBED Equation.3 (4)
He that remarks: We see a problem immediately: (3) and (4) are two equations in one unknown, EMBED Equation.3 . Clearly one of theses equations is redundant. Cochrane them argues that in the cashless state, when EMBED Equation.3 , equation (3) disappears. But as it is redundant anyway that is no problem -we simply use equation (4) to determine EMBED Equation.3 and call it the FTPL.
We can, of course, for those who remember, recognise this argument from Patinkins discussion of the loanable funds vs liquidity preference theory. The equivalent equations from Patinkins (1965, p. 229) Money, Interest and Prices are listed as equations (1) to (4). There Patinkin has the labour market, goods market, money market and bond market to determine three endogenous variables, the money wage, the interest rate and the price level. He notes that Walrass Law can be applied to eliminate one of the markets and then goes on to point out that:
We shall now show that the conclusions reached in the preceding chapters by an analysis of the commodity and bond markets can also be reached in a somewhat more familiar way by an analysis of the money market. The equivalence is, of course, a simple implication of Walrass Law. Patinkin (1965, p. 253).
We can drop either the money market or the bond market. Dropping the money market supposedly produced the loanable funs theory of the rate of interest while dropping the bond market meant that we had the liquidity preference theory of the rate of interest. None of that was true, of course. And Abba Lerner rather gave the game away when he asked: why not drop the market for peanuts?
Nevertheless, Cochrane effectively replicates Patinkins argument by eliminating the money market to produce the cashless model, and uses the bond market equation to determine the equilibrium price level, EMBED Equation.3 . In Cochranes world, money has been dropped from Patinkins title and redefined as an income-earning asset. The present value of the government primary surplus from equation (4) in Cochranes model is then a pseudo-quantity equation with bonds replacing cash (money in Patinkin) as in expression (2) above bonds are money to Cochrane and Woodford.
On reflection it seems that Patinkin beat Cochrane to the FTPL. In fact, it is implicit in what I have been saying that he also beat Woodford and Cochrane to the cashless economy money has no essential role to play in Patinkins model any more than it has in Woodford-Cochrane. Patinkin thought money was important so he attempted to include it in his model. Woodford and Cochrane think money has disappeared so the propose to leave it out. Neither strategy produces a usable monetary theory.
The unfortunate fact is we could just as easily follow Lerners suggestion and generate the peanut theory of the price level or the rate of interest in the Patinkin-Woodford-Cochrane model. We can construct an index of the purchasing power of peanuts or any other commodity in the endowment as McCallum (2000) explained. Whatever such an index measures in is not the CPI or the GDP deflator. There is, however, no need for such an index in the model using a time = 0 auction the frictionless world of Woodford and Cochrane.
Finally, as a matter of interest, it is also worth pointing out that Patinkin ran into the same sort of conceptual errors encountered by Woodford and Cochrane. Patinkin was concerned with unemployment but we all remember the notorious chapter 13 where households were forced off their labour supply curves. Such a move violates the assumptions underlying the model, as many were quick to point out, because the model is simply incapable to explaining unemployment as opposed to the inefficient allocation of labour- formally complete by the fixed-price extensions to Patinkins model. As Lucas was later to suggest, involuntary unemployment cannot be defined in a Yeoman farmer model.
IV Concluding remarks.
It is not often that we seen a respected macro-monetary economist make statements of the following sort:
It is not common for an entire scholarly literature to be based on a fallacy, that is, on faulty reasoning; misleading or unsound argument. (concise Oxford Dictionary). The recently revived fiscal theory of the price level is an example of a research programme that is fatally flawed, conceptually and logically. Buiter (1999, p. 1)
Buiter (2002) later toned down his rhetoric. But on reflection I now have much sympathy with his original sentiments. Especially because what so upset him about the fiscal theory of the price level is not restricted to that research programme. The counter intuitive and puzzling properties that attracted Buiters attention in the context of the FTPL debate are merely a symptom of deep-seated and fundamental conceptual flaws that lie at the heart of a major branch of post war monetary theory.
These flaws originated with attempts to incorporate money into real Walrasian general equilibrium systems of which Patinkin (1965) is the most well known example. Clowers (1967) attempt to address the problem head on with the CIA constraint led him ultimately to the realization that the attempt was counter intuitive money was a welfare reducing innovation in a real Walrasian general equilibrium model contra monetary economics 101 and 200 years of accepted wisdom. As outlined in the paper, the difficulty here was the attempt to incorporate money into a model where all the functions of money had been taken over by the auctioneer. This property of the model reaches its apogee in the time = 0 auction of the Arrow-Debreu model. And it is this model that Woodford and Cochrane take as the basis for their cashless, frictionless world.
Unlike Patinkin and Clower, Woodford and Cochrane do not seek to introduce money directly in the real general equilibrium system. But by so doing they make two mistakes. They claim that they can determine the price level in a real general equilibrium model the cashless, frictionless model and they also claim that that model is also easily generalised to incorporate what the call monetary frictions. Both claims are false.
The cashless, frictionless model that they employ is a moneyless real general equilibrium model (which they acknowledge) based on a time = 0 auction. But they overlook the power of the time = 0 auction. Not only does it eliminate the need for cash (money) but it also eliminates the need for any nominal magnitudes, the price level and the government or central bank. Logically, it could be claimed that such a model could form the basis for a model of the real business cycle. But it has nothing to say about monetary theory and monetary policy. It is most certainly not a model of the e-money payments systems currently operated by central banks. Attempting to generalise the model by incorporating monetary frictions, such as the CIA constraint, then leads only to the Patinkin-Clower puzzle why is money a welfare reducing innovation?
Attempting to forge ahead with the cashless, frictionless model as a basis for monetary theory only generates the array of counter intuitive conclusions and conceptual puzzles documented above. A stiff tutorial with Humpty-Dumpty or the White Queen is needed before any sense can be gleaned from the cashless, frictionless model presented by Woodford and Cochrane. They have, however, shown us clearly what happens when the logic of the Arrow-Debreu world is pushed beyond its limits. Monetary theorists can now get on with the job of developing the theoretical foundations of monetary policy in models that do capture the insights of monetary economics 101- as indeed many are.
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Woodford, M. 2003. Interest and Prices: Foundations of a theory of monetary policy, Princeton, Princeton University Press.
Friedman, (2000, p. 261) worried that: The prospect that electronics advances in banking practices may present complications for central banks, perhaps to the point of threatening the efficacy of monetary policy influence over inflation and economic activity, .
The debate between those who think that the central bank should control base money and not use interest rate rules continues. See Capie, Tsomocos and Wood (2003, pp. 23-26) Central banks have opted for interest rate rules because they doubt the stability of the demand for base money. Some argue that imposing a growth constraint of a Friedman sort would only result in disintermediation of the type that emerged when interest rates were controlled and quantitative controls were placed on some forms of loans by the banks.
Capie, Tsomocos and Wood (2003) present a model to show that fiat money is a superior transactions technology to e-barter because fiat money or e-fiat money has lower information requirements.
For example, Wallace (2004) claims that the Arrow-Debreu model is the developed part of economics while monetary theory is undeveloped.
There are sequence versions of this auction but as they are not relevant to the cashless, frictionless competitive model espoused by Woodford and Cochrane I will not consider them here The difficulty is to produce a essential sequence economy in the sense of Hahn (1974). Ljungqvist and Sargent (2004, chapter 8?) give an illustration of an inessential sequence economy.
For this reason Kings concern that, .. the world may come to resemble a pure exchange economy, is unfounded. To do so electronic money of some form would have to approximate the time-0 auction an impossibility.
Hence Kings (1999) fear that electronic money would evolve to a state similar to that of a pure exchange economy is unfounded.
Insert Buiters objection to Woodfords interpretation of the cashless limit.
Wallace (2004) attempts to prove the existence of a competitive equilibrium in an Arrow-Debreu model with a central bank. But as the central bank is supposed to act as a price setter rather than a price taker this raises some puzzles that Wallace leaves unresolved.
Definition of variables
In the case where money balances are zero the term EMBED Equation.3 , ie EMBED Equation.3 .
Note Hoovers (1988) explanation that this is an example of Famas sleight of hand. What is described is a relative price and not the price level. See also Rogers (2005).
The calim that his model is a reasonable approximation of the US payments system is false. Asset-trading under a Time-0 auction, i.e., in a cashless, frictionless economy does not require clearing through a central bank. Even proposals for real time asset trading systems make this clear. The auctioneers computer does the job. Introducing another agent called a central bank will only cause congestion and conceptual confusion.
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