Alexander Yakovlev, PhD in Economics, Associate Professor at the Department of Economic Theory of St. Petersburg State Electrotechnical University (LETI). Author of The Theory of Money: From Gold to the Cryptosystem of Exchange.
With the introduction of bitcoin into the realm of economic theory, there has already been a steady stream of publications about it. Thus, when evaluating bitcoin on the basis of the equation of exchange, a “simple economic model” is applied (cf.. Joseph C. Wang “Simple macroeconomic model of bitcoin”), although in fact both the analysis and the conclusions may be completely unrelated to the exchange and its patterns.
Fisher’s equation does not exhaust quantitative theory. Many economists consider the equation itself, and not without reason, as an identity, which fundamentally changes its economic and mathematical meaning. Nevertheless, Irving Fisher’s equation of exchange is the foundation of quantitative money theory, which in turn is the foundation of money theory in the twentieth century. It is the basis, by and large, the entire modern theory of money, which includes many versions and nuances, and the official monetary policy, in support and development of which created an extensive apparatus of mathematical modeling. In short, the so-called “mainstream” in money theory, which fits into the concept of general economic equilibrium, is based on the equation of exchange.
Irving Fisher’s famous equation of exchange is described in detail in his monograph The Purchasing Power of Money: Its Determination and Relation to Credit, Interest and Crises, first published in 1911 (the Russian version of the title “Purchasing Power/Capacity of Money” was established). Fisher’s equation, despite its apparent mathematical simplicity, is internally contradictory, and it is not for nothing that it has been the subject of debate for more than a century.
Fisher’s equation of exchange (traditionally, in economics literature it is assumed that it looks like MV = PQ) is an attempt to formalize mathematically the economic law of monetary circulation. Every word counts.. An equation is an attempt to express a law, but it is not a law in itself.. In other words, it cannot be regarded as some kind of Ohm’s or Newton’s law. Fisher’s equation is only a mathematical model, an abstraction, and a very simplified, if not primitive one. It reflects rather a trend in economics that economists and mathematicians do not understand (or rather, they understand, but “in their own way”).. This tendency is constantly violated and constantly reproduced, because Fisher’s equation of exchange is a perfect reflection of the law of value in circulation (I emphasize, in circulation).
Both quantitative theory itself and its model in the form of the equation of exchange have been and are subject to serious criticism. By the scientist’s own admission [I. Fisher]: “Quantitative theory has been one of the most passionately contested theories in economics …,” (referring here mainly to the famous discourse of the monetary and banking schools).
If, as some economists try to do, talk about applying Fisher’s equation to bitcoin analysis, then the first step, i.e.. the introduction of economic or qualitative conditions (parameters) of the model, usually becomes the last.
What is proposed? An apparently innocuous solution by analogy, the so-called “modification”. As an example, I quote: “Now we modify this equation to account for the unique characteristics of bitcoin. First we express all of our quantities in units of fiat currency. Expressing all our values/values in terms of fiat currency, we can set [value] P [equal to] 1. Since we express all values in units of fiat currency, the value of M is now the value of bitcoin measured in units of fiat currency” (??).. So decided to apply the equation of exchange MV = PQ in the analysis of bitcoin in one of the papers.
In fact, there is a substitution of one model, where bitcoin circulation takes place, with another, where fiat money circulation takes place. Instead of one macroeconomic model, an analysis of a completely, qualitatively different. Replacing the unit of account, shall we say, transforms the digital environment into an analog one, and bitcoin as “a digital, decentralized, partially anonymous currency, not backed by any government or other entity and not redeemable for gold or other commodity” becomes analog, centralized, government-guaranteed fiat money. Further analysis becomes meaningless, because the conclusions will be obviously wrong. The mathematical apparatus counts “not green, but salty.”
What are the problems of the exchange equation important to consider when analyzing bitcoin? Is it possible in principle to apply this equation to cryptocurrency?
1. The main problem, in my opinion, is this: the equation of exchange has a methodological, shall we say, duality. On the one hand, it is really a macroeconomic model, and on the other the equation of exchange has a microeconomic basis. This dialectic (it is quite appropriate to recall if not Georg Hegel, then Karl Marx) of the law of money circulation, the relationship between form (not even the abstract mathematical model itself, but the law in the sphere of exchange, which it reflects) and content (the real processes of reproduction, i.e.. The dynamics of the creation and movement of the totality of goods, including numerous feedbacks) is, in my opinion, the most difficult for economists to understand. In other words, money circulation (on the surface, in the phenomenon) has only relative independence, the theory of money is one of the consequences of the theory of value, which is formed not in the exchange, but in production. Goods enter into exchange already having prices, rather than receiving them in circulation, as one might think, and as Irving Fisher believed. At the same time, the scientist tried to build his version of the theory of money on the basis of only one equation of exchange, i.e.. on the basis of the formula itself, which is internally contradictory, dialectical, develops following the development of economic relations, its variables both left and right qualitatively change, their economic content becomes different, but proponents of quantitative theory for over a century have stood on the formal point of view and tried not to notice the changes.
2. General conditions for building a model and solving it as a mathematical problem, i.e.. time and place, Irving Fisher puts it this way: “The equation of exchange is the mathematical expression of all transactions occurring at a given time in a given society.. Place, i.e.. “in a given society,” as can be understood, is the national economy. Time is implicitly present in the exchange formula. Fisher believes that “the equation of exchange is simply the sum of the equations combining all individual exchange transactions during the year.. It is clear that this is an abstraction, an assumption, a formal parameter that is important only for statistics. It is also clear that during the year the situation may change, and more than once, in the most paradoxical and radical way.
3. The equation of exchange does not take into account (at least formally) time as an argument, it is always static. But the fact is that does not take into account such an important factor as the inertia of money circulation, which determines the dynamics of all the parameters of this economic process, for example, the same inflation. If in a macroeconomic model, the change in the parameters of the equation is mathematical, i.e.. “In the real economy, this change can last for days, months, or years.. One may object: yes, the formula itself does not take into account, but the quantitative theory of money as a whole does.. And present a package of graphs and charts unfolded in time. How so? Irving Fisher writes, “There are myriad … factors, standing outside the equation of exchange, which act on prices …” and this is true.
Irving Fisher, of course, sees this problem and defines it as “a violation of the equation of exchange and the purchasing power of money during periods of transition.”
This is an objective contradiction, linked, in my view, again to the methodological duality of monetary circulation. The scientist understands this, since he devoted an entire chapter to the problem. What is the conclusion? “Quantitative theory is not strictly fair during transitions.”. And this is the title of the paragraph. What happens in this case? Equality of exchange is violated, according to Fisher’s version, when the prices of goods and services do not rise in strict proportion to the growth of the money supply;
How, then, do we understand what “transitional times” are? There is no clear definition, but there is an interesting detail: “transitional periods can be characterized by either rising or falling prices.”. In other words, any price movement can be interpreted as a “transitional period” regardless of the reasons that gave rise to it. It turns out that the “transition period” can last all the time? Then the question arises: how does the equation MV = PQ behave during “transients”? What is equal or not equal to what? There is no answer. In my opinion, there can be no answer (or clear definition), because the formula describes only the process of reversal, and the real reasons for all its variables are external, not internal.
4. Quantitative theory of money as a theoretical reflection of the law of money circulation was originally built on the fact that money as a social relation is represented in the form of commodity money, where the monetary material is gold, which has the so-called “intrinsic value” of money, due to which the mechanism of self-regulation of exchange, based on the equivalence of each transaction or metamorphosis T – D – T in the form T = D = T. At the same time, all five functions of money (universal equivalent, universal means of exchange, means of preservation/savings, etc.) act as a peculiar “regulatory mechanism.. On the whole, this looks like some version of the law of conservation of matter. Irving Fisher, to his credit, as an outstanding statistician and strong mathematician of his time, understood this.
Irving Fisher’s equation of exchange is about money, only money.. The scholar’s analysis and conclusions come from a practice that was literally changing before his eyes. Since the only tool in his hands is the equation of exchange, Fisher often simply captures the practice, without any theoretical justification. Thus, in his opinion, “there are two kinds of genuine money: primary and fiduciary.. Money is called full money when the commodity from which it is made has the same value both in its use as money and in all other uses. … and the value of credit money depends partly or wholly on the certainty that its owner can either exchange it for other goods, such as full money in a bank … or at any rate pay debts with it or buy goods with it.”. The division into commodity and credit (fiat or fiduciary) forms of money undoubtedly lies outside the analysis of the equation of exchange. Within the framework of the quantitative theory of money there is no justification for this fact.
Credit money destroys the feedback mechanism that existed in the era of the gold standard, the system of monetary circulation loses its stability, as a consequence, the role of the regulator, essentially a non-economic or administrative body with the economic functions of the “issuer” of currency (the Central Bank) increases sharply. Self-regulation of the system is theoretically possible, of course, but within an association, not on the basis of free competition. This issue could be debated, since compliance with the equation of exchange requires constant regulation (intervention), which has no objective economic boundaries. Quantitative theory in Fisher’s version recognizes these changes … the regulator is the interest rate.
5. Not every economist knows that Irving Fisher “corrected,” as he writes, the exchange equation. More precisely, I analyzed it in two stages. The formula MV = PQ is valid for the scientist only at the first stage of analysis, at the second stage he adds the expression M’V’ and the left part of the formula turns into MV+M’V’. Thus, “the total value of all purchases for the year will therefore no longer be measured by MV, but by MV + M’V’.. His only argument for doing so is the practice of monetary circulation, which the monograph expresses in one phrase: “The analysis of bank balance sheets has prepared us to include bank deposits, or circulating credit, in the equation of exchange.”
What is M’V’ in the scholar’s understanding? It is the circulation (precisely the circulation) of checks for bank deposits as an element of monetary circulation in general. Why this conclusion? And again we get a wonderfully brief answer: “The study of banking operations reveals two kinds of means of circulation: one is banknotes, belonging to the category of money, and the other is deposits.
Irving Fisher was no doubt familiar with the innovations of the economic literature of the time, but in his work, which later became a classic, he is careful not to mention them. Say, a scholar does not recognize deposits as money, but includes them in the equation of exchange only on the grounds that deposits are a “fine substitute.
6. Circulation speed is the most mysterious parameter of the model. It is the determination of the velocity of AND. Fisher allows us to consider the exchange equation as an identity, i.e.. faithful always. It is the speed of circulation changes in one direction or another, becomes the “regulator of last resort” when there are no other arguments. This parameter is not statistically observed and makes the equation completely mnemonic. If cash in the era of the gold standard could be represented in dynamics, as a movement from hand to hand (according to Fisher’s definition – “the speed of circulation, or the speed of transition of money from hand to hand”), the speed of circulation of paper money, and even more so of non-cash circulation – the concept is more than conditional. Technical speed of transactions is clearly not the parameter that matters. The speed of circulation has formed, in my opinion, as an economic category, but then it should be defined in some other way. It is not the physical speed of movement of money, but the willingness or ability to carry out the transaction, i.e.. simply storing funds in monetary form for the time being, which gives the exchange equation a completely different economic meaning. This is already Cambridge.. Then what is left of Fisher’s exchange equation?
7. A theoretical problem Irving Fisher could not explain. Neither are his followers in a hurry to do so.. The bifurcation point is as follows: “Although a bank deposit transmitted by check is regarded as a medium of circulation, it is still not money, and the banknote is both a medium of circulation and money. Between the check and the banknote lies the last line of demarcation between what is money and what is not. It is true that it is very difficult to draw this line precisely…” So, the means of circulation is the deposit, but as money (for Fisher) it is not yet. But in the equation of exchange, where the first stage was only the circulation of cash, Irving Fisher includes the circulation of checks or simply the movement of entries in bank deposit accounts. Why? And where is the line between a deposit and a banknote? There is no answer.
The scholar’s decision not to consider a bank deposit as money contradicts his own definition of money, such as “we have defined money as all that is accepted by all in exchange for goods” or “every commodity generally recognized in exchange must be called money.”. This is inaccurate because, according to Fisher, “the banknote is both medium and money,” and the bank deposit is not money, but only a “substitute,” though it is accepted by all.. What the category “substitute” means is not explained in this paper.
Irving Fisher, as stated above, distinguishes between commodity money and credit money, but conflates credit (banknote) and commodity (gold coin) forms of cash (recall, the book was written in the era of the gold standard) as M, as opposed to deposits, i.e.. non-cash, but credit, means of payment or M’. Perhaps if the scholar had merged the means of credit, which is also true, the system of monetary aggregates would have been shaped differently today.
8. Another paradox of the macroeconomic model of the law of monetary circulation.
Despite dozens of pages of text in a monograph about gold, its production and its effect on prices, gold on the famous “Fisher Scale” is missing. So where to put it? It would seem to be on the left, where the money is, as Fisher himself repeatedly wrote? But then how to account for its extraction as a commodity, albeit a monetary one? Put it on both sides of the scale? Or how? After all, money is money, only confirming its status, shall we say, in the constant and infinite metamorphosis T – D – T (T = D = T). In other words, the law of circulation of money cannot take into account the processes of its creation and distribution (strange as it may seem, they also take place), money signs in the equation of exchange as if they do not exist, or rather, money is represented perfectly, since their carriers are not considered in any way.
9. As one of the conditions and assumptions of the macroeconomic model, it is assumed that the sale of goods and services occurs without difficulty, i.e.. instantly and without residue. Thereby it is a priori assumed that there is a stable aggregate demand, which is bound to absorb the entire stock of goods. The question of how such aggregate demand is formed remains unanswered. If we “remove” this assumption, then the exchange formula itself is in doubt.
The problems described above, in my opinion, unsolvable within the framework of the quantitative theory, as the latter is not a complete theory of money, but is only an abstract macroeconomic model or formula that reflects a particular stage in the development of both the theory and practice of money circulation. But Fisher’s equation of exchange in the form of MV = PQ is not only of historical value, it is the starting point for the construction of macroeconomic models that reflect the reality of monetary relations today. At the same time, the claim of quantitative theory to take center stage, to be the methodological basis of modern monetary theory, in my view, requires justification.
And so it happened.. Digital money” (the name is conditional) or Bitcoin appeared. It’s not money yet, it’s potential money at best.. I propose the definition of “cryptosystem of exchange,” since the main function of all forms of exchange value, or money, due to the conditions described above, it is not fulfilled. There is no exchange of equivalents in general or in particular.
“The money of the future is just being created.. And all the attention of private business, which is the creator and driver of this process, is turned to the process of production and distribution of the “money of the future,” while the academic community is still studying mainly the circulation process, but the laws of circulation at this stage of development of the “money of the future” are secondary by definition. The scientific world still does not know how to approach and evaluate the production (exactly the production) of “money of the future”. It turns out, as if it were outside the circle of his interests, a new phenomenon is often simply rejected under any, often obviously far-fetched pretext, because it does not fit into the mainstream. And when they do try to analyze this process, they use the wrong tools from the past, from analog economics, up to the already ridiculous attempts to “simply” (I quote) replace one concept with a completely different one, thus creating a “simple macroeconomic model of Bitcoin”.
A powerful impetus to the discussion of the role of quantitative money theory in bitcoin valuation has come from the practice of. The launch of bitcoin futures trading on major U.S. exchanges in December 2017 caused a stir in the market and in the business press, including the publication of Chris Burniske and Adam White’s bestseller “Cryptoassets: The Innovative Investor’s Guide to Bitcoin and Beyond,” which in turn sparked a wave of publications on the topic of bitcoin’s place and role in today’s (digital) economy.
The basic idea of this popular science work that a new class of financial assets, or cryptoassets, has emerged is an indisputable fact of economic theory. Cryptosystems of exchange are an extremely complex class of assets due to the lack of traditional valuation metrics, usually used when using the traditional method of valuation by discounting the cash flow. Unlike a company’s assets, crypto-assets have no income, cash flow, or profit in order to value a company’s business on their basis. The estimation [of the value (price)] of a crypto-asset is a critical theoretical and practical problem that has not yet been solved.
A serious methodological mistake made by cryptocurrency analysts is that they use Fisher’s exchange equation to build a model for valuing a crypto-asset. Why “serious” and why “methodological”? Fisher’s equation expresses the regularity of monetary circulation, i.e.. its field of application is the theory of money. Business valuation is, after all, a theory of capital, albeit in monetary form, but capital.
It must be said that in their White Paper, Burnisk and White did not dare to link the value of a crypto-asset with Fisher’s equation of exchange directly, but instead settled for an analogy, which is very revealing, with gold. But the answer to the question: how is “fundamentally” defined, i.e.. theoretically, the value of the crypto-asset, is not going anywhere. Therefore, in a separate article “How to Evaluate Cryptoassets? (Cryptoasset Valuations) the author of the idea Chris Burnisk still expresses the theory underlying cryptoasset valuation more definitely. Of course, this is the equation of exchange And. Fisher. Why? Because “in its own protocol, a crypto-asset serves as a medium of exchange, a store of value, and a unit of account/accounting,” i.e.. is, according to the modern interpretation, money. The problem is that this is how money is defined in modern economic theory, from Krugman to representatives of the Austrian theory of money, but in the classics of the genre the first function is still a measure of value or a universal equivalent, the consequence (only consequence) of which is the “unit of account/accounting” or, more precisely, the scale of prices (see. К. Marx, Capital).
Bitcoin has not become money yet; today it is just a cryptosystem of exchange, a specific means of payment that performs only some functions of money. But the crypto-analyst had his own logic, of course. In my opinion, the lesser of two evils was chosen. If there is no “revenue, margin and profit” within the system, you can use what you have (again, within the system or protocol). This is where Fisher’s equation of exchange comes in, because it is usually used by the mainstream to look for a “fair” or “fundamental” (in our case, a rational market price).
That’s why, according to Chris Burnisk, “the exchange equation … becomes the cornerstone for evaluating the value of a crypto-asset.”. There is no point in analyzing it further, it is beyond the scope of economic theory, and economics in general, let it remain on the conscience of Stanford graduate Chris Burnisk.
But the publication of cryptocurrency analysts was not the end of the matter. Also in 2017, Vitalik Buterin, the creator of the second-generation cryptosystem Ethereum (and an honorary doctorate at the University of Basel) gave his version of crypto-assessment. In a short and succinct – and generally very original – text, Buterin also uses a simple economic model, as he calls the equation of exchange And. Fisher;
So, according to Buterin’s version, “Traditional macroeconomics has a simple equation to try to value a medium of exchange: MV = PT”. Why not? But what are the elements that make up this “simple equation”? Just as traditional as the equation as a whole, except for T, which represents, in Buterin’s version, not the volume of commodity mass, but “the transaction volume: the economic value of transactions per day” (the transaction volume: the economic value of transactions per day).
Despite the author’s obvious giftedness and the “triviality” of the formula, he also makes the mistake of using Fisher’s exchange equation to get the market capitalization of one of his projects. In the course of “trivial” actions Buterin gets the equality M*C = T*H, where “the expression on the left term is quite simply the market capitalization” (the left term is quite simply the market cap), and on the right term is something unimaginable. “The definition on the right is the economic value of the transaction for the day multiplied by the amount of time the user owns the coin before using it to make a transaction.”
Why did the methodological error happen? Because the capitalization of a project, even expressed in money, is an estimate of the project’s cost of capital, and Fisher’s equation of exchange shows equality (or even identity) at the level of the Commodity-Money-Commodity metamorphosis.
It must be said that professional economists do not make such gross errors after all. But that does not mean that they do not make mistakes at all. The main problem of mainstream economists is the conscious, but more often subconscious, implicit transfer of the solution obtained in the analog economy to the digital economy, to the cryptosystem of exchange. For example, take, “Some simple Bitcoin Economics,” which is roughly how the work of scientists Linda Schilling and Harald Uhlig can be translated. Why hers? Well, the model is simple, but seriously, its authors postulate the following: “Traditional quantitative theory of money assumes that central banks can control the price level (inflation) of their fiat currencies by changing the total supply of currency. (Traditional quantity theory of money suggests that central banks can control the price level (inflation) of their fiat currencies through variation in the total currency supply). That is, they obviously rely on the equation And. Fisher.
Further, the main interest of economists in this famous paper focuses on answering all the same relevant questions: “What determines the price of cryptocurrencies, how can fluctuations occur, and what are the implications for monetary policy of central bank-controlled currencies in competition with cryptocurrencies?” and hope that their work “sheds light on these questions.”
Linda Schilling and Harald Uhlig s model compares two currencies, the dollar and bitcoin, or more precisely, the agent’s expectations for the dollar and bitcoin, while arguing that an equilibrium “in the market” for money is possible. And it is even suggested that “intuitively, by setting the number of dollars, the Central Bank can control the price of bitcoin.”
The economists claim that the result of their study “can be understood as an updated version of the famous Kareken-Wallace (1981) result.”. While welcoming any experiments at the boundary of two qualitatively different monetary systems: digital and analog, one should not forget that Bitcoin is in principle inapplicable to direct, direct participation (or “substitution”) in models where fiat money is studied, especially in laissez-faire mode, which, in fact, Larry White also points out. He explicitly writes that “the key assumption [of the Kareken-Wallace model] – that perfect substitutes [for fiat currency] are easy to create – is actually false with respect to real crypto-assets. Bitcoin and its real and potential competitors are not in fact perfect substitutes and therefore do not satisfy the Kareken-Wallace hypothesis.
The reason is that despite both the external proximity, the similarity of processes, and the common economic essence, which is not easy to recognize, the digital economy and crypto-assets as its basis are not identical, qualitatively different with the analog economy and fiat money as its component. The theory of money of the twenty-first century fundamentally does not integrate into the monetary models of the twentieth century, not because of legal or legislative features or interpretations, but because of the differences in economic systems arising from different qualities of technological platforms.
This is a key question, as we see it, of both practice and theory, not only of money, but of the digital economy as a whole. The foundation on which monetary theory was built in the 21st century – quantitative theory of money – does not satisfy the economic realities of the 21st century.