Economist Irving Fisher's equation of exchange is considered a mathematical model. Its interpretation and use in relation to bitcoin is a vivid example of how the mathematics of a macroeconomic model replaces not only logic, but also common economic sense. The author of the article is Alexander Yakovlev, Candidate of Economic Sciences, Associate Professor of the Department of Economic Theory, St. Petersburg Electrotechnical University (LETI). Author of the book “The Theory of Money: From Gold to the Cryptosystem of Exchange”. In connection with the introduction of the topic of bitcoin into the field of economic theory, steady turnovers have already appeared in publications about it. Thus, when evaluating bitcoin based on the equation of exchange, the “simple economic model” turnover is applied (See. Joseph C. Wang “Simple macroeconomic model of bitcoin”), although in fact both analysis and conclusions may be completely unrelated to the exchange and its patterns. Fisher's Equation Does Not Exhaust Quantity Theory. Many economists, and not without reason, consider the equation itself to be an identity, which fundamentally changes its economic and mathematical meaning.. Nevertheless, Irving Fisher's equation of exchange is the basis of the quantity theory of money, and it, in turn, is the foundation of the theory of money in the 20th century.. On its basis, by and large, the entire modern theory of money is built, including many versions and nuances, and the official monetary policy, in support and development of which an extensive apparatus of mathematical modeling has been created.. In short, the so-called “mainstream” in the theory of money is built on the basis of the equation of exchange, which fits into the concept of general economic equilibrium. 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. Fisher's equation, despite its apparent mathematical simplicity, is internally contradictory, and it is not for nothing that it has been the subject of discussion for more than a century. Fisher's equation of exchange (traditionally in the economic literature it is considered that it looks like MV = PQ) is an attempt to mathematically formalize the economic law of money circulation. Every word matters here.. An equation is an attempt to express a law, but in itself is not one.. In other words, it cannot be considered a kind of Ohm's or Newton's law. Fisher's equation is just a mathematical model, an abstraction, and very simplified, if not primitive.. It rather reflects a certain trend in the economy, which economists-mathematicians do not understand (more precisely, they understand, but “in their own way”). This trend is constantly violated and constantly reproduced, since Fisher's equation of exchange is an ideal reflection of the law of value in circulation (I emphasize, in circulation). Both the quantitative theory itself and its model in the form of an equation of exchange have been and are being seriously criticized.. According to the scientist himself [I. Fisher]: “Quantity theory has been one of the most passionately contested theories in economics …”, (here we mean mainly the famous discourse of the monetary and banking schools). If, as some economists try, to talk about the application of the Fisher equation in the analysis of bitcoin, then the first step, i.e.. the introduction of economic or qualitative conditions (parameters) of the model, usually becomes the last one. What is offered? Seemingly harmless solution by analogy, the so-called “modification”. As an example, I quote: “Now we modify this equation to take into account the unique characteristics of Bitcoin.. First, we express all the quantities of our fi phi fi fi pheres. Expressing all of our quantities/values in terms of fiat currency, we can set [value] P to [equal to] 1. Since we are expressing all quantities in terms of fiat currency, the value of M is now the value of bitcoin measured in terms of fiat currency” (??). So we decided to apply the equation of exchange MV = PQ in the analysis of bitcoin in one of the works. In fact, there is a substitution of one model, where the circulation of bitcoin takes place, another, where the circulation of fiat money takes place.. Instead of one macroeconomic model, an analysis is proposed that is completely, qualitatively different. Replacing the unit of account, so to speak, transforms the digital environment into an analog one, and bitcoin as a “digital, decentralized, partially anonymous currency, not backed by any government or other legal entity and not redeemable for gold or other commodity”, turns into analog. centralized, government-guaranteed fiat money. Further analysis becomes meaningless, since the conclusions will be obviously wrong.. The mathematical apparatus considers “not green, but salty.” What problems of the equation of exchange are important to consider when analyzing bitcoin? Is it possible in principle to apply this equation to cryptocurrency? one. The main problem, in my opinion, is this: the equation of exchange has a methodological, let's say, duality. On the one hand, this is indeed a macroeconomic model, and on the other hand, the equation of exchange has a microeconomic basis. This dialectic (it is quite appropriate to recall, if not Georg Hegel, then Karl Marx) the law of money circulation, the correlation of form (not even the most abstract mathematical model, but the regularity in the sphere of exchange that it reflects) and content (real processes of reproduction, i.e.. the dynamics of the creation and movement of the entire set of goods, including numerous feedbacks) is, in my opinion, the most difficult thing 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 exchange, but in production.. Commodities enter into exchange already having prices, and do not receive them in circulation, as it may seem 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 on the left and on the right change qualitatively, their economic content becomes different, but for more than a century, supporters of the quantitative theory have been on the formal point of view and try to ignore the changes. 2. General conditions for building a model and solving it as a mathematical problem, i.e.. time and place, by Irving Fisher are designated as follows: “The equation of exchange is the mathematical expression of all transactions made in a given period of time in a given society”. Place, that is. “in a given society”, as one can understand, there is a national economy. Time in the exchange formula is present implicitly, indirectly. Fisher believes that “the equation of exchange is simply the sum of the equations that combine all the 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 can 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 such an important factor as the inertia of money circulation, which determines the dynamics of all parameters of this economic process, for example, the same inflation, is not taken into account.. If in the macroeconomic model the change in the parameters of the equation occurs mathematically, i.e.. “instantly”, then in the real economy this change can last days, months, and years. It may be objected: yes, the formula itself does not take into account, but the quantity theory of money as a whole does take into account. And present a package of graphs and charts deployed over time. How so? Irving Fisher writes, “There are myriads of… factors outside the equation of exchange that act on prices…” and they are right. 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 transitional periods.” This is an objective contradiction, connected, in my opinion, again with the methodological duality of money circulation.. A scientist understands this, since he devoted an entire chapter to the problem. What is the conclusion? “Quantitative theory is not strictly valid during transitional periods”. And this is the title of the paragraph.. What then happens? Equality in exchange is violated, according to Fisher, when the prices of goods and services do not rise strictly in proportion to the growth of the money supply. How then to understand what “time of transitional periods” is? There is no clear definition, but there is such an interesting detail: “transitional periods can be characterized by either an increase or a fall in 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 “transitional period” can last all the time? Then the question arises: how does the equality MV = PQ behave during “transitional periods”? What is equal or not equal to what? No answer. In my opinion, there cannot be an answer (or a clear definition), since the formula describes only the process of circulation, and the real reasons for changing all its variables lie not inside, but outside. 4. The quantitative theory of money as a theoretical reflection of the law of money circulation was originally based on the fact that money as a social relation is presented in the form of commodity money, where the monetary material is gold, which has the so-called “intrinsic value” of money, due to which a mechanism for self-regulation of exchange is formed, based on the equivalence of each transaction or metamorphosis C – D – C in the form T = D = T. At the same time, all five functions of money act as a kind of “regulation mechanism” (universal equivalent, universal medium of exchange, means of conservation/accumulation, etc.). In general, it looks like some version of the law of conservation of matter. Irving Fisher, to his credit, as an outstanding statistician of his time and a strong mathematician, understood this. Irving Fisher's equation of exchange is about money, only money.. The scientist in his analysis and conclusions comes from practice that was changing literally before our eyes. Since the only tool in his hands is the equation of exchange, Fischer often simply fixes the practice, without any theoretical justification.. So, in his opinion, “there are two types of genuine money: full-fledged (primary) and credit (fiduciary). Money is called valuable when the commodity from which it is made has the same value both when used as money and in any other use.. … and the value of credit money partly or entirely depends on the confidence that the owner of this money will be able to either exchange it for other goods, for example, for full-fledged money in the bank … or in any case pay off debts with it or buy goods with it “. The division into commodity and credit (fiat or fiduciary) forms of money, no doubt, lies outside the analysis of the equation of exchange. There is no justification for this fact within the framework of the quantity theory of money. Credit money destroys the feedback mechanism that existed in the era of the gold standard, the monetary circulation system loses stability, as a result, the role of the regulator, in fact, a non-economic or administrative body with the economic functions of the “issuer” of banknotes (the Central Bank), increases sharply. Self-regulation of the system is theoretically possible, of course, but within the framework of association, and not on the basis of free competition. This issue could be discussed, since the observance of the equation of exchange requires constant regulation (intervention), which has no objective economic boundaries. Quantity theory in Fisher's version recognizes these changes… the rate of interest is the regulator. five. Not every economist knows that Irving Fisher “corrected”, as he writes, the equation of exchange. More precisely, he 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 side of the formula becomes 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'”. The only argument why he decided so is the practice of money circulation, which is expressed in the monograph in one phrase: “The analysis of bank balance sheets has prepared us to include bank deposits, or circulatory credit, in the equation of exchange.” What is M'V' in the understanding of the scientist? This is the circulation (precisely the circulation) of checks for bank deposits as an element of money circulation as a whole. Why such a conclusion? And again we get a remarkably brief answer: “The study of banking operations reveals two types of medium of circulation: one is banknotes belonging to the category of money, and the other is deposits.” Irving Fisher, no doubt, was familiar with the novelties of the economic literature of that time, but in his work, which later became a classic, he tries not to mention them.. For example, a scientist does not recognize deposits as money, but includes them in the equation of exchange only on the grounds that deposits are “an excellent substitute”. 6. Velocity is the most mysterious parameter of the model. It is the definition of speed and. Fisher allows us to consider the equation of exchange as an identity, i.e.. always true. It is the speed of circulation that 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 the transfer of money from hand to hand”), then the speed of circulation of paper money, and even more so of non-cash circulation – the concept is more than conditional. The technical speed of transactions is clearly not the parameter that is important. Velocity of circulation was formed, in my opinion, as an economic category, but then it must be defined somehow differently. This is not the physical speed of movement of banknotes, but the desire or ability to carry out a transaction, i.e.. just storing funds in cash for the time being, which gives the equation of exchange a completely different economic meaning. This is Cambridge. Then what remains of Fisher's equation of exchange? 7. The Theoretical Problem Irving Fisher Couldn't Explain. His followers are not in a hurry to do this either.. The bifurcation point is as follows: “Although a bank deposit transferred by check is considered a medium of exchange, it is still not money, and a banknote is both a medium of exchange and money.. Between a check and a banknote lies the last line of demarcation between what is money and what is not.. True, it is very difficult to draw this line exactly … ”So, the deposit is a means of circulation, but money (for Fisher) is not yet. But in the equation of exchange, where at the first stage there was only the circulation of cash, Irving Fisher includes the circulation of checks or simply the movement of records in bank deposit accounts.. Why? And where is the line between a deposit and a banknote? No answer. The scientist’s decision not to consider a bank deposit as money contradicts his own definition of money, for example, “we have defined money as everything that is accepted by everyone in exchange for benefits” or “any commodity generally recognized in exchange should be called money”. This is an inaccuracy, because, according to Fischer, “a banknote is both a medium of exchange and money”, and a bank deposit is not money, but only a “substitute”, although it is accepted by everyone.. What the category “substitute” means is not explained in this paper. Irving Fisher, as mentioned above, distinguishes between commodity and credit money, but combines credit (banknote) and commodity (gold coin) forms of cash (let me remind you, 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'. It is possible that if the scientist combined credit means of payment, which is also true, today the system of monetary aggregates would be formed differently. eight. Another paradox of the macroeconomic model of the law of money circulation. Despite dozens of pages of text in a monograph on gold, its production and the impact on prices, there is no gold on the famous “Fischer scales”. So where do you put it? It seems to be on the left, where is the money, as Fischer himself repeatedly wrote? But how then to take into account its production as a commodity, albeit a monetary one? Put on both scales? Or how? After all, money is money, only confirming its status, let's say, in a constant and endless metamorphosis T – M – T (T = D = T). In other words, the law of circulation of money cannot take into account the processes of their creation and distribution (oddly enough, they also take place), banknotes do not seem to exist in the equation of exchange, more precisely, money is represented ideally, since their carriers are not taken into account in any way. nine. As one of the conditions, assumptions of the macroeconomic model, it is assumed that the sale of goods and services occurs without difficulty, i.e.. instantly and without a trace. Thus, it is a priori assumed that there is a stable aggregate demand, which will necessarily absorb the entire mass of commodities.. The question of how such aggregate demand is formed remains unanswered.. If, however, this assumption is “removed”, then the very formula of exchange becomes doubtful. The problems described above are insoluble, in my opinion, within the framework of the quantitative theory, since the latter is not a complete theory of money, but is only an abstract macroeconomic model or formula that reflects a certain 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 building macroeconomic models that reflect the reality of monetary relations today. At the same time, the claim of the quantitative theory to occupy a central place, to be the methodological basis of modern monetary theory, in my opinion, requires substantiation. And so it happened. Appeared “digital money” (conditional name) or Bitcoin. 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, is not fulfilled by it. There is no exchange of equivalents either in general or in particular. “Money of the Future” is just being created. And all the attention of private business, and it is the creator and driver of this process, is drawn to the process of production and distribution of “money of the future”, while the academic community is still studying, mainly, the circulation process, but the patterns of circulation at this stage of development ” money of the future” are, by definition, secondary. The scientific world still does not know how to approach and how to evaluate the production (precisely the production) of “money of the future”. It turns out that it is, as 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 nevertheless undertake to analyze this process, they use unsuitable tools from the past, from the analog economy, up to attempts already ridiculous in practice to “simply” (this is a quote) replace one concept with a completely different one, thereby creating a “simple macroeconomic model for Bitcoin (simple macroeconomic model of Bitcoin). A powerful impetus to discuss the role of the quantity theory of money in the evaluation of bitcoin was given by. The launch of bitcoin futures trading on the largest US exchanges in December 2017 caused a stir in the market and in the business press, including the publication of a bestseller by Chris Burniske and Adam White, a former top manager of the Coinbase platform , now CEO of Bakkt) “Cryptoassets: The Innovative Investor's Guide to Bitcoin and Beyond”, which, in turn, caused a wave of publications on the place and role of bitcoin in the modern (digital) economy. The main idea of this popular science work that a new class of financial assets has appeared, or crypto assets (cryptoassets), is undoubtedly a fact of economic theory.. Exchange cryptosystems are an extremely complex asset class due to the lack of traditional valuation metrics commonly used when using the traditional discounted cash flow valuation method.. Unlike company assets, cryptoassets do not have income, cash flow or profit in order to evaluate the value of the company's business based on them.. Estimation [of the value (price)] of a crypto asset is the most acute both theoretical and practical problem that has not been solved so far. A serious methodological mistake of cryptocurrency analysts is that they use Fisher's equation of exchange to build a cryptoasset valuation model. Why “serious” and why “methodological”? Fisher's equation expresses the pattern of money circulation, i.e.. its scope is the theory of money. Business valuation is still 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 the Fisher equation of exchange directly, they managed by analogy, which is very significant, with gold. But the answer to the question: how is “fundamentally” defined, i.e.. theoretically, the value of a crypto asset has not gone away. Therefore, in a separate article “How to evaluate crypto assets?” (Cryptoasset Valuations) the author of the idea, Chris Burnisk, nevertheless expresses the theory underlying the valuation of a cryptoasset, more specifically. Of course, this is the equation of exchange. Fisher. Why? After all, “in its own protocol, a cryptoasset serves as a medium of exchange, a store of value, and a unit of account / accounting”, i.e.. is, according to 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 of the functions 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. To. Marx, Capital). Bitcoin has not yet become money, today it is just a cryptosystem of exchange, a specific means of payment that performs only certain functions of money. But the cryptanalyst had his own logic, of course.. In my opinion, the lesser of the evils was chosen. If there is no “revenue, margin and profit” inside the system, then you can use what is (again, inside the system or protocol). This is where the Fisher equation of exchange comes in, because with its help, representatives of the mainstream usually look for a “fair” or “fundamental” (in our case, rational) (rational market price) price. That is why, according to Chris Burnisk, “the equation of exchange … becomes the cornerstone for estimating the value of a crypto asset”. It makes no sense to analyze further, this is outside the framework of economic theory, and economics in general, let it remain on the conscience of Stanford graduate Chris Burnisk. But the matter did not end with the publication of cryptocurrency analysts. In the same 2017, Vitalik Buterin, the creator of the second-generation cryptosystem Ethereum (and an honorary doctorate at the University of Basel) presented his version of the cryptoasset evaluation.. In a short and concise – and overall very original text – Buterin also uses a simple economic model, as he calls the equation of exchange AND. Fisher. So, according to Buterin, “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”? As traditional as the equation as a whole, with the exception of T, which, according to Buterin, is not the volume of the 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 obvious giftedness of the author and the “triviality” of the formula, he also makes a mistake, as a result of which, using the Fisher equation of exchange, he receives the market capitalization of one of his projects. In the course of “trivial” actions, Buterin obtains the equality M*C = T*H, where “the expression on the left is just market capitalization” (the left term is quite simply the market cap), well, on the right – something unimaginable. “The definition on the right is the economic cost of a transaction per day times the amount of time a user owns a coin before using it to make a transaction.” Why did the methodological error occur? Because the capitalization of the project, even expressed in money, is an estimate of the cost of the project's capital, and the Fisher equation of exchange shows equality (or even identity) at the level of the metamorphosis Commodity – Money – Commodity. I must say that professional economists still do not make such gross mistakes.. But that doesn't mean they don't 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, let's take, “Some simple Bitcoin Economics”, something like the translation of the work of scientists Linda Schilling and Harald Uhlig. Why her? Well, the model is simple, but seriously, its authors postulate the following: “The traditional quantity theory of money assumes that central banks can control the price level (inflation) of their fiat currencies by changing the general 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, obviously, based on the equation AND. Fisher. Further, the main interest of economists in this well-known work is focused on answering the same pressing questions: “What determines the price of cryptocurrencies, how fluctuations can occur, and what are the consequences for the monetary policy of central bank-controlled currencies in the face of competition with cryptocurrencies?” and hope that their work “sheds light on these questions.” In the model of Linda Schilling and Harald Uhlig, two currencies are compared: the dollar and bitcoin, more precisely, the agent's expectations for the dollar and bitcoin, while it is argued that an equilibrium “on the market” of 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 result of Kareken-Wallace (1981)”. Welcoming any experiments on the border of two qualitatively different monetary systems: digital and analog, one should not forget that for Bitcoin, in principle, direct, direct participation (or “substitution”) in models where fiat money is studied, especially in the laissez-faire mode, is not applicable. , which, in fact, is also indicated by Larry White. He bluntly writes that “the key assumption [of the Kareken-Wallace model] – ideal substitutes [for fiat currency] are easy to create – is in fact false in relation to real crypto assets.. Bitcoin and its actual and potential competitors are in fact not perfect substitutes and therefore do not satisfy the Kareken-Wallace hypothesis.” The reason is that despite both the external proximity, similarity of processes, and a single economic entity, which is not so easy to admit, the digital economy and crypto assets as its basis are not identical, they are qualitatively different from the economy of analog and fiat money as its integral part.. The theory of money of the 21st century is fundamentally not integrated into the monetary models of the 20th century, not due to legal or legislative features or interpretations, but due to differences in economic systems that arise on the basis of technological platforms of different quality. This is a key issue, as we can see, both in practice and in the theory of not only money, but also the digital economy as a whole. The foundation on which monetary theory was built in the 21st century – the quantity theory of money – does not satisfy the economic realities of the 21st century.

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