Diversification and evolution of post-modern money as "ideational money": from MMT to PMMT

Abstract

The current post-modern private currencies including cryptocurrencies and community currencies are becoming extremely diverse. We need a clear-cut framework to put our present situation in perspective to understand the diversity and evolution of money in human history and consider the status quo and the future of money. The purpose of this paper is to place such diversified post-modern currencies as well as previous forms of money in the evolutionary tree diagram of money, grasp the essential nature of post-modern money represented by the fiat central banknotes as "ideational money" or "symbolic money", neither material money nor credit money, and analyze the dynamics of stability and instability of the value of such ideational money as "legal tender" or "cash currency", and gain a clear vision on how the money will evolve in the future, so that we can finally make a critical evaluation on Modern Money Theory (hereinafter MMT) from the viewpoint of our money theory, Post-modern Money Theory (hereinafter PMMT), as an alternative to it.

1. Introduction 1

In 1844, Bank of England's convertible notes were issued as the central banknotes (3.17 pounds per ounce of gold), and the pound system was established based on the international gold standard by the end of the nineteenth century. After WWII, the dollar system was newly organized internationally by the gold exchange standard (35 dollars per ounce of gold) and the fixed exchange rate system (360 yen per dollar, etc.), while a managed currency system and a fiat central banknote were institutionalized domestically. However, the dollar system collapsed in 1971, and the floating exchange rate system was introduced in 1973. Afterwards, regardless of some exceptions including the Euro, two major international financial institutions of "one country, one currency", and "floating exchange rates" have maintained for 50 years till now, and it is widely believed that they will remain unchanged in the future.

The current post-modern private currencies are extremely diverse. They include cryptocurrencies (Bitcoin, Ethereum, Litecoin, etc.) , various payment systems (***Pay, ***Coin, etc.), electronic money (Suica, nanaco, WAON, etc. using Felica) , corporate currencies (various points and mileages), regional gift certificates (with or without premium), and community currencies (banknote-type, bank account-type, digital local currencies, etc.). The issuing entities are a wide variety of local and private organizations such as municipal governments, chambers of commerce and industry, commercial enterprises, NPOs, cooperatives, and voluntary associations, other than the national government (central banks and central governments).

In Bitcoin, there is no issuing entity because money is issued in a decentralized manner on the internet when many servers called "miners" keep on updating the blockchain every 10 min. Such financial innovations brought up a fundamental turn in the concept of money. Therefore, simply classifying the various types of money in detail according to their superficial conditions and characteristics does not answer the core question of what they are and why such diversification is occurring. It may seem that such diverse private and national currencies are completely dissimilar. However, once we understand that "ideational money" or "symbolic money" is a common characteristic of post-modern currencies, we can see that they are in fact the same kind of money, and the challenges facing the whole money system in the twenty-first century will emerge.

The purpose of this paper is to place such diversified post-modern currencies in the evolutionary tree of money, understand the essence of modern money as "ideational" or "symbolic", and gain a clear perspective on how money will evolve in the future so that we can critically evaluate Modern Money Theory (hereinafter MMT) and present our theory, Post-Modern Money Theory (hereinafter PMMT), as an alternative to it.

2.1 Evolutionary Tree Diagram Of Money

In this section, we will briefly review how money has evolved over the course of human history and consider what the properties of post-modern money are. As a rough outline, a tree diagram of monetary evolution is shown in Fig. 1 .

This tree diagram depicts the evolution of money on the following four eras: (1) Primitive: the emergence of primitive money as "internal money" used for a medium of gift-giving and reciprocity in primitive communities; (2) Ancient to medieval: the parallel emergence and coevolution of two types of independent "external money," which is used for a medium for equivalent exchange, as both "material money" represented by gold and silver and "credit money" represented by such drafts and bills as certificate of obligations and IOUs; (3) Modern: the coexistence of two kinds of currencies, cash currency and deposit currency, with the central banknote functioning as the core for integrating both material money as cash currency and credit money as deposit currency in the period of capitalism's establishment; and (4) Postmodern: the emergence of ideational/symbolic money as fiat central banknotes in all national currencies with the floating exchange rate system after 1973 and the ongoing diversification of private-sector currencies such as virtual currencies, corporate currencies, commodity tokens, and local currencies.

Primitive money was variously made of grain, livestock, cloth, woolen thread, whale teeth, and conch shells. However, the oldest primitive money that cannot be directly consumed is the ancient Chinese shell coin, and the world's oldest cast coin has been discovered that is a bronze imitation of this coin.

The most famous surviving primitive money is "Fei", a large stone money with a hole in it, used on Yap Island (Fig. 2) . Its diameter ranges from 0.6 to 3 m. The larger ones cannot be moved by even a few adults, so they are often left on roadsides or in collection sites, where only their ownership has been transferred. They were used mainly as expensive ceremonial gifts at weddings and funerals, for example, as tribute money at the time of marriage (like a betrothal gift in Japan), with social and cultural significance. Thus, its possession represented not only economic wealth but also social honor and cultural pride.

It is known that Fei was carried by canoe from Palau, about 500 km away. Often, rafts were wrecked and sank into the sea while canoes were transporting stone cargo from Palau. They say that if many islanders believed the canoeists' story about the largest stone cargo ever brought by canoe, then Fei sunk in the sea was officially approved as their property. Since Fei is rare and rather symbolic without intrinsic use value, it can be accepted as we have just said, though no one has ever seen it in the sea. Therefore, it is neither material money, nor is it credit money as a negotiable certificate of debt, even though it is based on faith in the veracity of the stories of those who produced and transported it. Fei cannot be understood from the external money that presupposes equivalent exchange in the market. However, it has something in common with the ideational and symbolic characteristics of post-modern fiat central banknotes, which we will see later.

The most striking feature of such primitive money is that it was used to realize ritualistic and customary bilateral gift-giving and gift-returning within a certain community, or reciprocal exchange as a chain of three-party gift-giving. Moreover, primitive money, like Fei, contains both economic/commercial and non-economic/ non-commercial social and cultural purposes, the latter often being more important. In other words, when goods and services are exchanged in a community in a bilateral gift/return or three-way or more reciprocal exchange, we are not only conducting an economic transaction of goods and services between constituent members or tribes. The primary purpose is to enhance communication and maintain cooperative relations based on a sense of trust and fairness, as well as to mutually confirm and reinforce social status. The transfer of goods and money between two or more parties is a means to these ends (Polanyi K 1957) .

Primitive money is a medium for "reciprocal exchange" that aims to sustainably reproduce the entire community by a chain of transactions without considering the equivalence or inequality (gain or loss) of each transaction. It is "internal money" in which economic objectives are embedded in socio-cultural objectives, and the two become one and the same. In contrast, "external money" is a medium for realizing "equivalent exchange" between money and goods of the same value in individual transactions in markets outside the community, which for the first time made it possible to pursue only economic objectives separate from social and cultural objectives.

Modern national currency, which has made possible globalization of capitalism, inherits the characteristics of this "external money". Local currencies or community currencies, on the other hand, inherit the "internal money" characteristics of primitive money and are hybrid communication media that have both "economic media" aspects for stimulating local economies and "social and cultural media" aspects for revitalizing local communities. 2 By taking advantage of these characteristics, it aims to correct and solve economic problems such as long-term recession, unemployment, stagnation of local economies, and disparities in income and assets, as well as socio-cultural problems such as the decline of nations and the disintegration of communities such as families, schools, and neighborhoods, caused by globalization.

2.2 Material Money And Credit Money As External Money

Primitive money was "internal money" and special-purpose money that could be used for only some of the various functions such as a means of exchange, a measure of value, and a means of the hoard. On the other hand, "external money", which forms a competitive market outside the community, is an all-purpose money with all of three functions, and two types of external money have independently emerged and coevolved: material money and credit money.

First, let us examine the meaning of "material money". It is a physical and tangible entity such as ore and metal. This is often called "commodity money" in economics, but we claim that this is not a correct concept. Since the category of commodities as objects to be bought and sold in money arises simultaneously with the emergence of money and transactions in money, there existed "goods" (objects of use value) as objects of barter but no "commodities" (objects of value) as objects of monetary exchange before the emergence of money and transactions in money. At the same time when a certain good becomes money, other goods become commodities that are to be bought and sold in money. Therefore, the designation "commodity money", which is based on the idea that a certain commodity becomes money, is conceptually erroneous.

Next, we examine how material money spontaneously emerges. In the theory of material money, the goods that most people are willing to accept in exchange for their own goods, specifically gold and silver, from among many goods in terms of their use value based on their physical and chemical properties, become money. If the owner of good A wants to obtain good B, but the owner of good B does not want to obtain good A, then direct exchange or barter between A and B is impossible.

In the case, even if the owner of A does not want to consume good X such as gold and silver but if many people want it, in other words, if the popularity of good X is very high, the owner of good A can expect that the probability of bartering (direct exchange) of good X for good B will increase if he or she has good X. If the owner of good A expected such a future situation, then good X would be the object of wants as a means of exchange to obtain good B. The probability of barter (direct exchange) is called "direct exchangeability" (Marx 1965) or "saleableness" (Menger 1892).

Once people begin to want good X that has a slightly higher direct exchangeability than other goods, good X becomes more and more popular, and the direct exchangeability of good X will rapidly increase. Thus, as the number of owners who wants good X as a medium of exchange rather than an object of consumption increases, the direct exchangeability of good X for other goods increases cumulatively. Eventually, good X becomes material money for all goods owners to obtain and use as a medium of exchange. Simultaneously, all goods other than good X (say, gold) that has become material money become commodities that are the object of money transactions, buying and selling. This is called "material money" because particular goods become money and all other goods become commodities at the same time.

The direct exchange (barter) between good A that one owns and good B that one wants becomes possible only when the "double coincidence of wants" (Jevons 1875) is realized, where the owner of good A wants good B and the owner of good B wants good A, and when an agreement on the exchange ratio is reached between the two parties. But, as the number of goods increases, the probability of the realization of the double coincidence of wants decreases. As a result, the direct exchange of one's good A for good B < Good A → Good B > becomes increasingly difficult. However, if money M comes into being as the medium of exchange, an indirect exchange mediated by money M < Commodity A → Money M → Commodity B > (sale of commodity A to money M and purchase of commodity B by money M), i.e., buying and selling by money M, becomes possible. Thus, since goods are not commodities before the emergence of money, such a situation should be expressed as not "a commodity becomes money" but "a good becomes money". 3 In economics in most cases, after the initial emergence of material money as explained earlier, credit money is introduced as a means of forming a credit relation (credit-debt relation) in terms of material money. Credit money is money issued based on a credit relationship (loan relationship) between a lender and a borrower, such as bills and banknotes. A bill is an instrument in which the borrower promises to repay the principal plus interest after a specified borrowing period (such as three months or one year) when he borrows money from the lender (margin purchase). A convertible banknote is an instrument in which a bank accepts gold coins or other specie as a deposit and promises to refund it upon presentation of the certificate.

If these certificates of indebtedness are transferable to third parties, they are passed from one person to another. The certificates of indebtedness are called "IOUs" because of the expression "I Owe You" in English, and convertible banknotes as IOUs can be redeemed for the same amount of gold or silver coins when taken to a bank teller. In fact, Bank of Japan's old convertible banknote, a ten yen note, stated, "In exchange for this note, you may have in hand ten yen in gold coins". In the case of a bill, if the lender needs cash immediately, the bill (certificate of obligation) can be discounted at a bank, i.e., by having the bank deduct interest and fees for the remaining days from the face value of the note.

Under the gold standard, credit money as convertible central banknotes circulated widely as a proxy for standard money (specie) such as gold and silver coins. Therefore, in modern capitalism, the prevailing view was that the primary money was material money such as gold bullion or minted gold coins and that credit money such as commercial bills or convertible banknotes emerged derivatively from the credit relation of material money such as cash and gold coins. In this case, the primary currency (specie) would be a means of payment used to repay debts and settle credit-debt relations.

Thus, the dominant view in economics has been that credit money is generated as a derivative of material money. However, in recent years, due to the spreading influence of bitcoin's blockchain (distributed ledger technology), some economists have contended that the origin of money in human history lies in the ledger system. This is connected with the view that the origin of money or the essence of money does not lie in the use value or value inherent in the physical material of money, but in the credit relations with the counterparty with whom one trades the physical goods, and that credit money is the original form of money. In contrast to the theory of the origin of material money as explained earlier, this view can be called the theory of the origin of credit money.

2.3 Theory Of The Origin Of Material Money Vs. Theory Of The Origin Of Credit Money

As we have just seen, the theory of the origin of material money is based on the idea that, because direct exchange (barter) is difficult, money is the primary currency, which appears spontaneously as a means of exchange mediating indirect exchange, and that credit money arises derivatively as a negotiable debt instrument that certifies the credit-debt relation of money. On the other hand, the theory of the origin of credit money argues that the credit settlement system is money because the numbers in the ledgers that record transactions play the role of money as long as there is a monetary unit for recording, even if there is no real money such as material money in the first place. It explains that credit money can stand alone without standard money (specie) such as material money. According to this view, money is not a thing that is a means of exchange, but a negotiable credit (debt). It is a transaction clearing system consisting of three basic elements: (1) units of value, (2) an accounting system, and (3) negotiability or transferability, and the social technology of credit and settlement is the basic source of money (Felix 2014) .

In ancient Mesopotamia, the highly developed bureaucratic command economy of the state gave rise to the three major social technologies of human civilization: letters (cuneiform), numbers, and accounting. Although the command economy based on the principle of redistribution prevailed there, trade and specialization led to the rise of urban civilization, resulting in frequent buying and selling near trading ports, trading posts, city gates, streets, and warehouses on the outskirts of the city-state. In other words, many markets for exchange were formed outside the cities as a complement to state redistribution, where transactions were conducted not with physical money but with written ledgers. Thus, material money and credit money were not necessarily a product of modern capitalism but already existed in the ancient world.

In medieval Europe, split tallies ( Fig. 3 ) were widely used, in which a creditor and a debtor recorded debt information, which was then split in two and kept as a certificate by both parties. Single tallies, in which debt information was recorded on animal bones, can be traced back to the Paleolithic period. These credit moneys were used not only among private merchants and artisans but also between them and the official state. Thus, it is becoming increasingly clear that credit money has a history as long as that of material money.

The question we should ask here is whether the question of "which" is the essence of money, material money or credit money, and "which" is the historical origin of money, is correct. This is because such a question itself may be misleading. The reason why we tend to think that the money that forms the market economy is "either" material money or credit money might be that we unconsciously assume that the evolution of money up to now has always been in a straight line since there is only one type of modern money that we experience every day under the current "one country, one currency" system. However, if the evolution of money was not monolithic but multilinear, and if the nature of monetary exchange was diverse, then no single theory or position can explain the actual history.

In human history, internal and special-purpose money for the reciprocity and redistribution of the community has preceded to external and all-purpose money that developed the market economy outside and between communities. As shown in Fig. 1 , when external money emerged to provide the equivalent exchange principle of the market, primitive money as internal money within the community diverged into material money and credit money, and they have continued to expand in parallel until the birth of the capitalist market economy.

2.4 Diversity Of Monetary Exchange And The Evolution Of Money

According to Kuroda (2020), a monetary historian, there were a variety of ways of monetary exchange, not a single way from a global historical perspective. The horizontal axis in Fig. 4 indicates whether transactions were anonymous or nominal, and the vertical axis indicates whether they were interregional or local. By using these two axes, a monetary exchange can be classified into four different domains.

First, let us look at the first quadrant, which is anonymous and interregional. When merchants did not know each other and conduct high-value transactions in the international market, payment was made in gold and silver coins as material money. Next, in the second quadrant which is both nominal and interregional, when merchants engage in remote trade as business acquaintances and they could use a draft or bill of exchange, which are credit money intermediated by a trusted third party because they could trust their counterparts with whom they had maintained a longterm relative trading relation. Furthermore, the third quadrant, which is both nominal and local, corresponds to the case where local produces or consumers make continuous transactions at neighborhood stores or artisan workshops. Since both parties were already acquainted with each other and conducted small transactions, book transactions were carried out using credit money as book-keeping and split tallies that recorded credits and debts. Finally, the fourth quadrant, which is anonymous and local, refers to transactions in nonpermanent markets such as regular markets and bazaars around cities. In small transactions at fish and vegetable markets, where strangers acted as buyers or sellers, payment was made in copper and tin coins as material money.

Thus, anonymous business relations use material money, while acquainted business relations use credit money, and the specific type of money is determined by whether the transaction is interregional or local. At least until the late eighteenth century, when capitalism was established, such diversity in money transactions was widespread. However, after the nineteenth century, with the development of the capitalist market economy and the establishment of the central bank, the "one country, one currency" system was established, the diversity of monetary exchange was lost, and material money was fixed into cash currency and credit money into deposit currency, both of which formed the national currency. This monetary diversity once disappeared but is emerging again as the diversity of private currencies at present.

Money, like language, was not deliberately invented or created by a specific person but was spontaneously generated through repeated interactions among people. The rules differ slightly from region to region, and local rules change little by little through the passage of time, and the system that is accepted by the people of each space and time is inherited, while the system that is not so is discontinued. Currency is thus self-organized, propagating and spreading, and new types and characteristics are created through innovations in which people intentionally change the rules concerning new materials, technologies, and the scope of circulation, etc. Sometimes those that adapt well to the rapidly changing environment survive, while others perish. In other words, the evolution of money can be understood as dynamic and complex phenomena consisting of the following four different processes: (1) selforganization (emergence), (2) replication (propagation and spread), (3) mutation (innovation), and (4) selection and elimination (persistence and extinction). 4

3 The nature of postmodern money: a third type of money, "ideational money," different from "material money" and "credit money"

3.1 "One country, one currency" system with a national currency

Modern legal tender consists of central banknotes and central government subsidiary coins although the former plays a central role. The central bank exclusively issues central banknotes as cash currency, from which deposit currency created by private banks are derived, and a type of currency with a monetary unit called "yen" circulates in Japan. Bank of Japan (BOJ hereafter) is a licensed corporation under the jurisdiction of the Ministry of Finance (MOF hereafter) in accordance with BOJ Law, and is a semi-private, semi-governmental institution with 55% of its 100-million-yen capital funded by the government and the remaining 45% of its equity securities listed on Tokyo Stock Exchange. Although legally independent of the government, it is in effect a quasi-public organization controlled by the government, with particularly strong ties to MOF. Thus, since the central bank is the only institution that issues central banknotes on behalf of the nation, the modern currency takes the form of a "national currency", creating a "one country, one currency" system in which there is only one national currency. There are a few exceptions for it as in "one country/ region, multi-currencies" system in the UK and Hong Kong, where multiple currencies coexist within a country/region, and as in "one union of nations, one currency" system, where a unified currency Euro circulates mostly in EU.

When the Peel Act of 1844 abolished private banknotes and established the monopoly of central banknotes issued by Bank of England, a national currency characterized by the "one country, one currency" system was introduced. Subsequently, the central bank system was propagated as a replica to other advanced capitalist countries. BOJ was founded in 1882 when Japan was trying to modernize itself through introducing Western culture and civilization for strengthening national wealth and military power after Meiji Restoration. From the perspective of hundreds of thousands of years of human history and thousands of years of monetary history, the 180 years of the central banking system and the 140 years of BOJ's history should be seen as very short.

3.2 The Central Bank'S Balance Sheet

We now turn to the controversial issue of central banknotes which make up the bulk of legal tender and the core of the national monetary system. Let us take the BOJ note as an example to find out what exactly a central banknote is, whether it is a liability or an asset, and why it circulates from person to person.

When BOJ notes are held by all economic agents other than BOJ, such as governments, private financial institutions, corporations, and citizens, they are recorded as "cash" in the assets section of their balance sheets. On BOJ's own balance sheet, however, BOJ notes in issue, i.e., the total amount of BOJ notes held by all entities other than BOJ at a given point in time are recorded as "banknotes" in the liabilities section of the balance sheet. Also, the total deposits held by all private financial institutions with BOJ are recorded as "deposits" in the liabilities section.

When BOJ conducts a "buying operation" in which it purchases previously issued government bonds from financial institutions, the proceeds are transferred to the BOJ current account at the counterparty financial institution, thereby increasing the BOJ current account deposits. BOJ supplies BOJ notes to the market when private financial institutions withdraw them as cash from their BOJ current accounts. When this happens, BOJ notes issued increase and its current account deposits decrease by the same amount. Conversely, when financial institutions deposit unnecessary cash into BOJ current accounts, the amount of banknotes issued decreases and BOJ current deposits increase by the same amount. This is called the reflux of BOJ notes.

On the other hand, the Mint, an independent administrative agency, produces supplementary coins on behalf of the government and delivers them to BOJ, and they are recorded as "cash" in the assets section of the balance sheet. In other words, "cash" doesn't refer to BOJ notes, but to the subsidiary currency issued by the government and held by BOJ.

Thus, the central banknotes issued by the central bank are debt instruments and represent liabilities of BOJ to other entities, and only government money (subsidiary currency) held by BOJ itself is an asset as "cash". According to BOJ's financial statements as of March 31, 2020 (Table 1) , total assets were 604,484.6 billion yen, total liabilities were 599,937.2 billion yen, and net assets were 4,547.3 billion yen. The government supplementary coins in assets as "cash" is 205.0 billion yen, and BOJ notes issued in liabilities are 109,616.5 billion yen.

The following points should be noted here. If the government produces 200 billion yen of money (supplementary coins) at a cost of 40 billion yen and delivers it Table 1 Balance Sheet of Bank of Japan (March 31, 2020) Source: Financial Statements for the 135th Fiscal Year/Fiscal 2019 (https:// www. boj. or. jp/ en/ about/ accou nt/ zai20 05a. pdf) to BOJ, it is recorded as "cash" of 200 billion yen in BOJ's assets section, but no government liability arises. Thus, the difference between the two, 160 billion yen, is the profit. Such a gain on money issuance is "seigniorage". Similarly, it would be tempting to think that seigniorage is generated by BOJ notes, but the official view is that seigniorage is not generated by BOJ notes because they are recorded as debt obligations in the liabilities section. Is this true on earth?

BOJ used to issue convertible banknotes that were obligated to be exchanged for specie, the standard currency of the country. A convertible banknote is a certificate of deposit in specie, a deed of obligation that guarantees the handing over of specie to the person who brings it to the bank. Here, a specie was a gold or silver coin which under the gold or silver standard contains a certain amount of precious metals at par and was supposed to have no difference between the real value and the face value of the specie. In Japan, the gold par value was 1.5 g of pure gold per 1 yen under the New Currency Ordinance of 1871 but was halved to 0.75 g of pure gold per 1 yen under the Currency Act of 1897.

When BOJ issued convertible banknotes, it recorded the gold and silver, or the gold and silver coins as a reserve asset on its balance sheet and the banknotes issued as liabilities. At the time, BOJ convertible notes were credit money as negotiable certificates of obligation (IOUs). However, since the shift to a floating exchange rate system in 1973, all national currencies, including the U.S. dollar, are no longer guaranteed to be convertible to gold. Central banks of all nations now issue fiat banknotes, which are not convertible into material money, and since these are legal tender or cash, there is no longer any material money except government supplementary coins. The exchange rate, which fluctuates all the time in the foreign exchange market, represents merely the relative exchange ratio of the two national currencies and does not represent any physical entities of absolute real value. In postmodern terms, modern money is merely information that displays only "difference" without any substance. However, BOJ continues to list the balance of BOJ notes issued as "banknotes" in the liabilities section of its balance sheet, just as it did in the days when it issued convertible notes. In the assets section, instead of gold and silver, gold and silver coins for redemption reserves, BOJ listed Japanese Government Bonds (JGBs), loans, Exchange Traded Funds (ETFs), Real Estate Investment Funds (REITs), and equities. Table 1 shows that JGBs accounted for about 80% of the total assets at 485,918.1 billion yen, followed by loans of 54,328.6 billion yen, ETFs of 29,718.9 billion yen, foreign exchange of 25,966.2 billion yen, stocks of 727.7 billion yen, REITs of 575.3 billion yen, gold bullion of 441.3 billion yen, and cash of 205.1 billion yen. It should be noted here that JGBs, ETFs, and REITs grew significantly. In contrast, in the liabilities section, banknotes and deposits increased up to 109,616.5 billion yen and 447,776.2 billion yen, respectively, while government deposits decreased by 12,633.8 billion yen, probably due to an increase in temporary expenditures for corona measures.

ETFs and REITs, assets other than government bonds, have been rapidly increasing in assets since BOJ started purchasing them in 2010 after the subprime financial crisis with the aim of bringing the Japanese economy out of crisis and promoting stable growth. They are not stocks of specific industries or companies, or specific buildings or land, but rather indices that represent weighted averages of the market value of Japanese stocks and Japanese real estate listed and traded on the stock market, and BOJ can be regarded as a sort of sovereign fund that anonymously holds real estate and stocks throughout Japan. Looking at the composition of ETFs owned by the BOJ, there are more than 200 companies in which the BOJ owns more than 5% of the shares, and about 50 companies in which the BOJ owns more than 10%. Although it is the investment management companies that exercise voting rights, the BOJ not only influences the stock market but also exerts significant influence over these private companies as major indirect shareholder, so to speak. 5

3.3 Why Are Central Banknotes In Issue Listed As Liabilities On The Balance Sheet?

Why does the central bank record the banknotes in issue in the liabilities section of the balance sheet? According to BOJ's view, it is because the value stability of BOJ notes is due to the Bank's appropriate monetary policy, and BOJ notes are "like" certificates of indebtedness. But the logic is not understandable because whether fiat central banknotes are debt obligations or not has nothing to do with the appropriateness of BOJ's monetary policy or its credibility. Since fiat money has no obligation of redemption in the first place, the issue of debt repayment never arises regardless of BOJ's appropriate monetary policy and so on. If this is the case, there is no need for BOJ's balance sheet to reconcile BOJ notes in issue, which are recorded in liabilities, with JGBs, stocks, and real estate purchased by BOJ notes, which are recorded in assets.

Then, if the plunge in JGBs, stocks, and real estate is somehow attributable to the failure of BOJ's monetary policy, rather than to an exogenous natural disaster or global financial panic, BOJ will be held accountable and lose the confidence of the public, corporations, and investors. In that case, there will arise the risks that the liabilities including BOJ notes that remain the same would substantially exceed the assets that decline in market value, and the BOJ would become insolvent. Nevertheless, even if the central bank becomes insolvent, it will not go bankrupt immediately because the government will take measures to bail it out, such as injecting capital.

Even if these risks are the result of monetary policy failure and loss of confidence, they are independent of whether BOJ notes are debt instruments or not. Rather, by maintaining this interpretation, the risk of insolvency has increased. What the government is doing to support the private sector in its efforts to fight the new corona infection is to purchase unlimited amounts of government bonds and increase purchases of CP, corporate bonds, etc., and BOJ's notes and deposits in liabilities on the balance sheet are expanding more and more to finance them. Therefore, the recognition that "BOJ notes are debt instruments" is a safety net to curb excessive issuance is also incorrect.

There is no small possibility that BOJ's ultra-easy monetary policy could create significant risks. Rather, what would be more consistent with such a monetary policy would be to recognize "banknotes in issue" as capital and to record them in net assets. The reason why fiat banknotes, which have no obligation to be repaid, have been recorded as liabilities as debt obligations is probably because the practice of the era of convertible banknotes has been dragged on for a long time. If BOJ were to change this practice and declare that it will change the items on its financial statements in the future, the banknotes it issues, which account for nearly 20% of its liabilities, would disappear in an instant, and its net assets would increase accordingly so that even if the value of its assets, including its bonds, is severely damaged, it would not be forced into insolvency.

3.4 Boj Notes Are "Capital Securities" With No Obligation To Repay

Convertible banknotes had been used even after the gold standard was abolished in 1931 and until 1942 when the new BOJ law enabled BOJ to issue unconvertible banknotes. They were issued as negotiable certificates of obligation, circulated among economic agents other than themselves as an asset, "cash", and then redeemed in specie when returned to the central bank (refunds). The properties of modern fiat central banknotes, especially postmodern types after the floating exchange rate system of 1973, are completely different from those. Thus, they are no longer credit money. Of course, they are not material money that retains its own value, either. Then, what exactly is a "debt" that has no obligation to be repaid?

The BOJ was established with a capital of 100 million yen, but it has issued more than 100 trillion yen (1 million times that amount) in banknotes, which continue to circulate as fiat money with no obligation to redeem. To understand this strange reality, we should interpret BOJ notes not as debt instruments but as investment securities, a means of large-scale fund-raising. In other words, modern central banknotes are equity instruments issued by the central bank in the name of "cash" and are interpreted as quasi-securities or utility coupons without voting rights or dividends.

What would change if we understood fiat central banknotes as quasi-securities? First, the meaning of central banknotes as money changes. It becomes possible to explain explicitly that fiat central banknotes are neither material money nor credit money, but a third kind of money, i.e., "ideational money" or "symbolic money". By so recognizing, we can clarify that post-modern money, including not only national currencies but also private currencies such as community currencies and cryptocurrencies, shares unique properties that were not found in earlier material money and credit money. Second, on the balance sheet, capital is distinguished from liabilities and is recorded as net assets on the same credit line. If BOJ were to reinterpret and publicly disclose banknotes in issue as capital, the "banknotes" would disappear from liabilities and be recorded as net assets, eliminating at once the fear of insolvency, even if the value of current assets such as government bonds, real estate, and stocks were to fall sharply in value.

In the case of a central bank, which is almost certain to be bailed out by the government even if it falls into insolvency, it is obvious that the principle of self-responsibility does not apply from the beginning. Rather, it would be better to clearly state in principle that central banks are capitalized by the banknotes they issue because they play a public role in the financial system, and that the risk of failure is therefore much smaller than that of private entities. In the case of central banks, it is much better to solve the problem from the root by changing the accounting rules of monetary and financial systems rather than bailing them out with taxpayer funds. In the case of the central bank, it is much better to solve the problem fundamentally by changing the accounting rules of money and finance than by bailing it out with taxes. At this point, if financial institutions accept JGBs as investment securities, how can the trading of JGBs for "cash" be understood? Each financial institution would be considered to make an investment in kind (not a monetary investment) in securities called JGBs and to receive securities called BOJ notes as an investment. In other words, it is not a sale of a commodity in exchange for money, but an in-kind investment in JGBs in exchange for the delivery of investment securities. In this case, the articles in kind are not goods or services, but securities such as JGBs, corporate bonds, CPs, commercial bills, corporate bonds, ETFs, and REITs, which are mainly exchanged between the BOJ and financial institutions as assets. It is possible at this point in time, when modern financial capitalism has reached the ultimate stage of free investment, to regard central banknotes as investment securities and to place the investment principle at the root of money and finance.

Thus, if the BOJ recorded "banknotes" in issue as capital, rather than liabilities, on its balance sheet and widely discloses such information, the perceptions and behaviors of central and municipal governments, financial institutions, firms, and the public would change significantly.

First, how would the government perceive it? The government's budget deficit has been drastically increasing, and at the end of FY 2019 (end of March 2020), the outstanding balance of government bonds is 997.9 trillion yen, a record high, and the combined long-term debt of the central and local governments is 1,125 yen, or 197% of GDP. The BOJ's JGB holdings at the end of the same period were also 486 trillion yen, with almost half of the JGBs held by the BOJ. If BOJ notes were recorded in net assets as capital, the risk of the BOJ becoming insolvent would be significantly reduced and the BOJ could hold even more JGBs, even in the event of a sharp rise in long-term interest rates and a consequent collapse in the price of JGBs. At present, the central bank's underwriting of new JGBs is prohibited by Article 5 of the Fiscal Law, however, it can be possible if we interpret that the government makes an investment in kind in new JGBs to provide capital to the central bank and received capital equity in the central bank in the name of "central banknotes", instead of receiving "cash" or "legal tender" directly from the BOJ. Then the debt instruments of JGBs would be exchanged into capital securities of the central bank.

Since the central bank ultimately bears such risks, the central government should not be prohibited from providing capital to the central bank. This is rather closer to the situation of integrated government as explained in MMT, but with the different notion of post-modern money regarding cash or legal tender.

Until now, the relationship between the central bank and financial institutions has been a one-way hierarchical relationship, with the central bank assisting and bailing out private financial institutions and supervising and regulating them, as seen in the "bank of banks", "lender of last resort", and the reserve deposit system. However, if BOJ notes were to be clearly stated to be securities in exchange for in-kind investments in BOJ by private financial institutions, which would become capital on the balance sheet, then the opposite effect of financial institutions jointly supporting and assisting the central bank would be clarified and a more two-way and equal relationship between the two would be formed. This would create a more interactive and equal relationship between the two. If the financial institutions are investors in BOJ, there would be risks associated with investing in kind rather than in money. However, even if the value of assets such as government bonds, stocks, and real estate were to suffer significant damage, the risk of BOJ falling into insolvency would be significantly reduced, and the risk of investment for financial institutions would also be reduced. Financial institutions possessed with current accounts at BOJ would not only consider BOJ notes to be securities in exchange for their investment in kind in JGBs and other securities but also recognize that their current accounts represent deposits of investment securities called BOJ notes and that they would receive the same securities when they withdraw their deposits. The current account is a liability for BOJ, but it is investment security of BOJ that must be repaid to the financial institutions. Then, even the unlimited issuance of such securities would not make BOJ unable to repay its debts. Although the author does not agree with this method of money issuance, the present BOJ's unlimited "buying operation" of long-term JGBs to increase the supply of the monetary base, which it has already been doing as QQE, must be more consistent with the above interpretation.

If individuals and companies recognize that cash and deposits are investment securities involving any risks, the conventional monetary consciousness that holding money is safe and that there are no risks in money should change. 6 They would be forced to realize that they are all investors who choose their own portfolios of various assets at their own will and responsibility while being constantly aware of such risks. Then, the nature of free investment capitalism would be further strengthened. 7 However, at the same time, "investment" would become not just quantitative "speculation" aimed at increasing the amount of a single type of national currency. As private currencies other than legal tender become more diversified, investors would select multiple currencies qualitatively that match their values and lifestyles while taking various risks into consideration and would use these currencies to achieve comprehensive quantitative expansion as well as qualitative accomplishments. As private currencies other than legal tender become more diversified, the time should change to include qualitative "projection" in a sense similar to "commitment" with the main purpose of expanding one's possibilities and world as well as aiming for quantitative expansion comprehensively by selecting multiple currencies and using them in a way that matches one's values and style while taking various risks into consideration.

3.5 Fiat Money As Ideational Money Or Symbolic Money

While material money is based on the use value that people find in goods and the utility they derive from their use, credit money is based on the credit-debt relation that arise between two parties. Unlike these, fiat central banknotes strongly rely on the power of ideas and symbols unique to human beings, who have formed and developed society by jointly representing ideas and symbols using and sharing language, numbers and signs. As a third type of money that expresses such characteristics, I will call post-modern money in the age of globalization since the late 1970s "ideational money", "symbolic money" or "token money". It is a money that combines inertial "customs" that persist from the past and movable "expectations" that envision the future, the two main ideas that arise and operate in different time directions, into a monetary value, without depending on materials in the "relations between persons and things" (use and utility relations) or credit in the "relations between persons" (credit-debt relations). Value is generated and maintained in a self-organized manner by the "relations between persons and ideas" in symbols and signs (tokens) alone. It should be noted that "persons" here are not "rational economic agents", but ordinary people who, due to their limited cognitive, computational, and predictive abilities, follow social and cultural rules (rules of thumb, customs, routines), recognize the surrounding context and situation, and make decisions and take actions influenced by emotions as their own inner rules.

As long as all economic agents other than the central bank, i.e., governments, financial institutions, corporations, NPOs, and individuals, keep accepting and using BOJ notes as cash on a daily basis, they will certainly circulate. So how exactly is this possible? The value of BOJ notes appears to be as solid and stable as that of material money such as immortal gold, but it is viable and sustainable only if it is self-supporting as a joint idea of many entities and is accepted as a social institution. 8 Let us now examine the two ideas mentioned above and how they support the value of BOJ notes.

The first idea is the self-realization of past customs and habits. It forms an "inner institution" as a rule shared by many ordinary people. Once this rule of cognition and behavior is accepted, it exerts an inertial force as an "inner institution". It is a shift from "If everyone received it (BOJ note) all the way until yesterday (and could use it without problem), then I can receive it today (and can use it without problem)" to "If someone next receives it today, then I can receive it tomorrow". By repeating this process, we can extend time in a positive direction, from the past to the present, and from the present to the future. As a result, the rule "If you received it all the way until yesterday, you can receive it today" is extended into the future as "if someone next received it all the way until yesterday, I can receive it not only today but also tomorrow". In this way, as a result of the continued self-realization of the acceptability of BOJ notes, this cognitive and behavioral rule generates universal acceptability that it is right to follow. Central banknotes are correctly perceived as stable cash or assets by such ordinary economic agents. This notion of custom, operating from the past to the future on the timeline, plays a major role in the stability and sustainability of central banknotes.

Once social conventions in the "inner institution" are established, they crystallize and exhibit considerable fixity, but they are never unchangeable like physical reflexes. For example, when you travel abroad, the "inner institution" that says: "Until yesterday, cars drove on the left side of the road all the time, so today we must drive cars on the left side of the road" have only to be amended to another cognitive and behavioral rule that includes a conscious perception of the current situation of the country in which you are now located, such as "Until yesterday, cars drove on the left side of the road all the time in Japan, but today I am in the U.S., so we must drive cars on the right side of the road". Even if these conscious cognitive and behavioral rules are maintained temporarily, as they keep staying in the U.S. for a long time, because saving on conscious thoughts begins to work in our mind, the conscious recognition of the current situation will be lost and replaced by another unconscious cognitive and behavioral rule: "Until yesterday, cars drove on the right side of the road all the time, so today we must drive cars on the right side of the road". The older one gets, the harder it becomes to change the inner institution that has cognitively fixed based on past experiences because it gets harder to reconstruct neural networks for setting up cognitive and behavioral rules adapting to a new situation.

In this way, the traffic rule of "driving on the left" or "driving on the right" exists objectively as an "outer institution", but unless drivers can subjectively form an "inner institution" in their mind-or in the program for self-driving cars-that conforms to the outer institution, the traffic rule would not work well. Institutions can exist autonomously, become sustainable, and spread widely if both the "outer institution" and the "inner institution" form a mutually complementary relationship and reinforce its continuing power by repeating this relationship.

The second conception behind BOJ's fiat notes is the self-fulfillment of future expectations. It is mainly an "inner institution" shared by rational speculators, who are different from ordinary economic agents, and is constituted as a cognitive and behavioral rule that says: "If I can expect that someone else will receive BOJ notes tomorrow (and can use them without problems), then I will receive them today". This is a judgment based on an expectation that everyone makes daily, such as "If I can expect today that X will happens tomorrow, I will do Y today", or "If I can expect today that an airplane will fly tomorrow, I will buy a ticket for the airplane today". Nevertheless, it applies especially well when speculators decide their current actions based on their rational expectations of future profits, as in "If I can expect today that the price of a stock will rise tomorrow, then I will buy the stock today".

Once one accepts this cognitive and behavioral rule, it is then possible to say, "If I can expect today that "someone next will receive it tomorrow", then I will receive it today", and further, "If I can expect today that "someone next can expect tomorrow that "someone next will receive it the day after tomorrow"", then I will receive it today", and further, "If I can expect today that "someone next can expect tomorrow that "someone next can expect the day after tomorrow that "someone next will receive it two days after tomorrow""", then I will receive it today", and so on.

The contents of the expectation can be thus nested and rewritten one after another. Since such an expectation about someone in the future can be postponed indefinitely, this cognitive and behavioral rule can be simplified to "If I can expect now that someone will receive it in the infinite future, not the finite future, then I will receive it now". However, since 'rational' expectations about the infinite future are not computable in finite time even with a supercomputer, we must ultimately rely on attitudes that include human emotions, such as optimism with relief or pessimism with anxiety and observations on other agents' such attitudes.

Thus, if 'rational' speculators are optimistic enough to expect that "someone will receive it in the infinite future", they will receive it now. In such a case, the selffulfillment of the expectation positively affects the stable persistence of the central banknote, making it a stable asset, but it has only a small effect compared to the custom we saw earlier. However, if they are pessimistic enough that they cannot expect that "someone will receive it in the infinite future", they will expect that "someone in the finite future will not receive it", and then they will further expect regressively that "someone before someone in the finite future will not receive it" and "someone two before someone in the finite future will not receive it" and so on. Finally, since they can expect that "anybody next will not receive it tomorrow", then they conclude that "we will not receive it today". In that case, the central banknote is considered as an unstable asset. This is a destabilizing factor for central banknotes. Nevertheless, as long as the number of pessimistic speculators who expect in this way is considerably smaller than the number of optimistic speculators, the expectation as a whole is not destabilizing, since the instability factor does not expand enough to overturn the stability factor.

Then, if stabilizing factors of customs from the past and stabilizing or destabilizing factors of expectations on the future act simultaneously, will central banknotes as ideational money be stable enough to be sustainable? This question will come under scrutiny next.

Let x be the number of general public agents who simply follow and imitate social customs, y be the number of speculative agents who believe in their own expectations, of which y 1 be the number of optimistic agents and y 2 be the number of pessimistic agents, and z(= x + y) be the total number of agents as assumed constant . The factor that determines whether a central banknote is stable or unstable is expressed as the ratio of the number of stabilizing agents, that is, the sum of the number of general public agents x and the number of optimistic speculative agentsy 1 , to the number of destabilizing agents, pessimistic speculative agents y 2 . The ratio is written as w = (x + y 1 )∕y 2 = (x + y − y 2 )∕y 2 = (z − y 2 )∕y 2 = (z∕y 2 ) − 1. Let us call this w the "money stability index" of BOJ notes as shown in the upper part (2) of Fig. 5 . We can see from the equation above that w only depends on the number of pessimistic speculators y 2 .

If x is constant, as the number of pessimistic speculative agents y 2 increases from 0 to y, w decreases from ∞ to x∕y. But if x decreases to 0, w decreases to 0 when all agents are pessimistic speculative agents, i.e. z = x + y = y = y 2 . When all agents are general public agents following social customs, namely, z = x and y = y 2 = 0, then w = ∞ where BOJ notes are undoubtedly accepted, and their value stays stable. On the other hand, if all agents are pessimistic speculative agents imitating their own expectations, namely, y 2 = z, then w = 0 where BOJ notes are completely unaccepted, and their value vanishes. w takes a certain value between these two corresponding to y 2 . As long as w is bigger than a certain lower threshold w th for y 2 = y * 2 , i.e., w > w th , y 2 < y * 2 , BOJ notes are accepted by a large number of agents and the value of BOJ notes, expressed as v, remains stable. If w reaches down to the threshold, i.e., w = w th , the phase transition occurs so that v discontinuously and catastrophically plunges as more and more agents cumulatively stop accepting them (Fig. 6) .

In normal conditions, the number of stabilizing agents x who follow conventions is overwhelmingly large, that of speculating agents y is quite small, and therefore that of pessimistic speculating agents y 2 is much smaller than y * 2 . Accordingly, w is large enough to satisfy the condition w > w th so that the value of BOJ note v is stable in most cases.

Next, let us consider how v can be possibly destabilized under the condition that the total number of all agents z is constant. If the general public agents follow current customs and cannot easily convert to speculative agents, x will remain unchanged for the time being, so the number of speculative agents y will also remain constant. Assuming that the total number of agents (government, corporations, NPOs, and individuals) is 150 million, speculative agents are 50 million, of which 20% are pessimistic, the money stability index is w = (150∕10) − 1 = 14 . If the lower threshold is w th = 1 million, then w > w th holds. Even if all speculative agents became pessimistic, w = (150∕50) − 1 = 2 so that w > w th still holds and BOJ notes remain stable. BOJ notes are thus quite robust thanks to the existence of vast general public agents that follow social customs rather than their own expectations, namely, the fact that x is much bigger than y 2 . However, under catastrophic socioeconomic and environmental conditions, even the general economic agents cease to follow the rule of customs and begin to become pessimistic speculative agents. Then, what if all the 150 million agents become speculative, i.e., z = x + y = y ? In this case, if the pessimistic speculator become 40% of that number, that is, y 2 = 60 million, w = 1.5 , at which BOJ notes are still stable. However, if the number of pessimistic speculators increases up to 50%, that is, y 2 = 75 million, then w = w th = 1, then BOJ notes abruptly get into an unstable domain and the value of BOJ notes v sharply falls. Thus, as more speculators shift from optimistic to pessimistic attitude and stop accepting BOJ notes, y 1 decreases and y 2 increases, and w gradually becomes smaller, and at the instant that y 2 finally reach down to 75 million, a stable order of money catastrophically breaks down.

Sooner or later, as the relative frequency of stabilizing agents to destabilizing agents decreases, resulting in w ≤ w th , BOJ notes will suddenly lose its value as purchasing power (Fig. 6, right) . It should be noted here that such purchasing power of money emerged spontaneously in the population dynamics expressed by the movement of the money stability index w , which is the relative ratio of the number of stabilizing agents to the number of destabilizing agents and w has continued to exist in a self-organized manner, not by the coercive force of state law.

Thus, while most of the people are the general public as stabilizing agents as imitating the social conventions and they seem to continue to accept central banknotes according to past customs without worrying about the future, many people must become instantly anxious about the future and turn into pessimistic speculators especially in catastrophic situations such as major natural disasters, wars, economic crises, and the new corona infection at present. But even in less catastrophic cases, small perturbations can be amplified by positive feedback effects in nonlinear chaotic dynamics. If the result is to cause a crisis in the financial markets for stocks, bonds, foreign exchange, or derivatives, the condition w ≤ w th which destabilizes central banknotes, may happen to be satisfied. We cannot overlook the fact that such risks are always present in modern central banknotes.

It is clear that the central banknotes issued monopolistically by modern central banks are not debt instruments that must be repaid as convertible banknotes. Nevertheless, by continuing to list them as liabilities on the balance sheet, they are made to appear as if they were real "certificates of indebtedness", and by providing inappropriate information that might be misleading, the general public as the stabilizing agents, including many businesses, as a result, may be deceived. Rather, it would be more appropriate to recognize the outstanding BOJ notes as equity securities (without dividend or voting rights) similar to those used by private companies to raise capital and to indicate that there is no obligation to redeem them in the event of bankruptcy, not only as a correct description of reality and a prior warning to stabilizing agents but also to record them in net assets on the balance sheet, thereby avoiding insolvency in advance. In other words, a more appropriate policy option substance" and "dematerialization of money media"

In the ongoing digitization of money, if "cash" as fiat central banknotes and "deposits" in private banks are real money, and "value" in electronic money and payment systems are proxy money, then if only one-way charging from cash or deposits to value is possible, a hierarchical relationship in which cash or deposits are overwhelmingly superior to value would be fixed. However, if the "conversion" or "withdrawal" from value to cash or deposits is possible, mutual circulation between the hierarchy like "convertibility" between real money and proxy money may occur, and this derivative hierarchical structure may be broken down, as happened in the conversion from convertible to fiat money. However, the relationship between convertible and fiat money differs in that "cash" and "deposits" are already intangible "value" information, rather than tangible "value" objects such as species (gold/silver coin or bullion) in the case of convertible currency.

The digitalization of money and the shift to cashless transactions, which are currently underway, became possible only on the premise of the dematerialization of money, which was made possible by the emergence and spread of fiat money. This is because the value embodied in fiat money has been completely separated from the physical use value of the specie (gold/silver coin or bullion) used to secure it. By switching from traditional physical value representation media composed of materials such as ink, paper, and printing presses, which are used for printing fiat money, to other physical value representation media composed of hardware such as computers, smart phones, smart cards, as well as software such as operating systems and applications, in addition to infrastructure such as power plants, power lines, optical fibers, radio towers, and artificial satellites, we can replace all the analog information of money with digital information. This has enabled smoother, more efficient, remote, global, and automatic monetary transactions even without human intervention.

The current "dematerialization of money" means the dilution of things as a substance that embody and represent value, rather than things as media that express and transmit value. In other words, the "dematerialization of money" means the "dematerialization of money substance" and not necessarily the "dematerialization of money media". In the ongoing digitalization of money and cashless society, out of the genuine money consisting of "cash" and "deposits", we are trying to reduce the tangible things expressing analog information called "cash" as much as possible by substituting the digital information of "value" of electronic money and digital coins (cashless society) and integrate as much genuine money as possible into intangible figures of digital information called "deposits". In this case, we notice that there are important intangible industrial products such as electricity, electromagnetic waves, light, and sound as well as many tangible industrial products such as electric wires, optical fibers, computers, and smartphones, the latter of which we can only see and touch and that those intangible and tangible industrial products for enabling digital monetary media have rather increased in volumes. In other words, we can see that the "dematerialization of money substance" has currently progressed, but the "dematerialization of money media" has not progressed much (Nishibe 2021) .

In the white paper by Satoshi Nakamoto, Bitcoin was intended to be a "P2P digital cash system" that would use blockchain (Distributed Ledger Technology) to completely digitize "cash" through distributed ledger and distributed issuance (Nakamoto 2008) . Thereafter, the core idea had been forgotten, and Dr. Craig Wright, who is assumed to be one of the core members of the team that stood for Satoshi Nakamoto, has been struggling to reinstate it as Satoshi's original vision and has established the true Bitcoin as Bitcoin SV incorporating Satoshi's Vison (Wright 2019). The original idea of Bitcoin as "P2P digital cash system" is a true representation that Bitcoin is a purely ideational money, neither material money nor credit money, newly emerging in the 21century.

On the other hand, Central Bank Digital Currencies (CBDCs), which would allow the state and central bank to turn cash into digital cash while maintaining the traditional central bank centralized issuance, have been launched in the Bahamas, Cambodia, and Venezuela, and China was the first major country to conduct a social experiment. CBDCs can be either wholesale, which is used only for settlement among financial institutions and businesses without changing the existing coexistence of analog "central banknotes (cash)" and digital "current accounts (deposits)" in the existing central bank currency, or general-purpose, which changes the existing structure of cash and deposits by completely digitizing cash and is used by all agents, including citizens. 10 If we can eliminate analog central banknotes, we will be able to settle funds more efficiently. But even in that case, we must answer to the fundamental question of whether a fiat central banknote as 'cash' is no longer credit money as certificates of obligation and have already become ideational money.

In the past decade, due to the digitization of money, private currencies such as local currencies and cryptocurrencies have coexisted with national legal tenders, and their presence has been rapidly increasing. In addition, a new trend of fusion of local currency's ideas such as the revitalization of the local economy and community, local production for local consumption and cryptocurrency's fintech such as blockchain, QR code payment, smart contract, Defi, NFT, and DAO is spreading, and many examples have emerged in recent years. The distribution sphere is expanding to "communities" that share values and interests, in addition to "regions" as neighborhoods and localities. 11 In June 2019, Facebook, the world's largest social networking provider with 2.4 billion members, announced the creation of a new digital coin, Libra. This news came as a big shock and was talked about everywhere. Libra is usually characterized as a blockchain-based cryptocurrency or stablecoin (a cryptocurrency linked to a legal tender such as the US dollar to give it a stable value) that enables a simple, global payment system and financial infrastructure. However, another view of Libra is that it is a massive glocal (global and local) digital community currency that draws on and empowers the expertise, skills, and potential of its billions of members. Moreover, since the Facebook community is diverse and multi-layered according to value and interest, and its totality is larger than any single country, its sphere of circulation is the largest in the world, and its value is expected to be stable as it is pegged to a basket of national currencies (weighted average value). The original idea is more important, although strong criticism from financial authorities in the U.S. and elsewhere has put a damper on that plan, which has been replaced by the "Diem", a stable coin pegged to the U.S. dollar. It was necessary to reconsider the nature of national currencies, which are now the dominant legal tender in the world in order to properly understand the nature of Libra as private and ideational money in a massive community of interest.

4.1 Diversification And Denationalization Of Money

At the beginning of the twenty-first century, confidence in the key currency, the dollar, was strong, expectations for the expansion of the euro, the unifying currency of Europe, were high, and the day when a single global currency would be realized did not seem far off. However, the subprime crisis of 2008 burst bubbles in the real estate and financial markets, exposing financial instability, and the sovereign debt crisis in Greece in 2009 raised fears of a breakup of the euro, leading to increased corporate bankruptcies and unemployment, widening economic disparities and poverty issues. The realization of the dream of a single global currency was far from certain. Under such circumstances, the cryptocurrency Bitcoin was born in 2008, and altcoins such as Ethereum and Ripple increased dramatically in both quantity and value. In addition, community currencies that spread globally since the last decade of the twentieth century have been revisited. However, the formation and bursting of the cryptocurrency bubble in 2017 also raised fears about the speculation and high volatility of cryptocurrencies, and a number of stablecoins were created that achieve stable value by being linked to legal tender. Cryptocurrencies were then referred to as "crypto-assets" in the legal framework of major developed countries. CityCoins have emerged as tokens on the Ethereum blockchain with the goal to financially support such municipal governments as Miami and New York cities. Thus, since the late 2010s, we have seen the emergence and spread of more diverse private currencies. The age of denationalization of money appears just around the corner.

This can be seen as a realization of the situation described in Hayek's "Denationalization of Money" (Hayek 1976b) , in which multiple heterogeneous currencies compete over quality, and the currency with higher quality is selected. In this situation, it is necessary to activate the principle of "good money drives out bad". The conditions for this are (1) the coexistence of multiple currencies that are different in terms of such quality as a standard of measure, denomination, etc. (like bitcoin against the dollar or yen) and (2) the adoption of a non-fixed rate among the multiple currencies. Although cryptocurrencies are highly speculative due to their price volatility, they satisfy the conditions of (1) and (2). On the other hand, under the different conditions of (1)' the coexistence of multiple currencies with the same standard of measure, denomination, etc. (like the standard currency and proxy currency with "yen" as the same standard of measure and denomination) and (2)' the adoption of a fixed rate (such that the exchange rate of the standard currency to proxy currency is one-to-one), Gresham's law, 12 which states that "bad money drives out good", would be functioning. In the case of free banking, where private banks are free to issue money with the same standard of measure and denomination as the central bank, conditions (1)' and (2)' are satisfied and Gresham's law operates, resulting in free competition in quantity, which leads to qualitative deterioration of money like inflation. In contrast, Hayek believed that "good money" could be created and discovered through competition as long as the monopoly of money issuance by the central bank is abolished and private entities (financial institutions, etc.) are allowed to issue heterogeneous multiple currencies with different denominations, standards of measure, and conditions for issuance, management, and value preservation, so that conditions (1) and (2) are satisfied. Hayek believed that "good money" would be created and discovered through competition. Such competition is "monopolistic competition" over quality through innovation for product differentiation, and Hayek tried to apply it not only to commodities but also to money. Hayek objects to the state's monopoly on the money issue. What he thinks dangerous is "not governments' right to issue the money but the exclusive right to do so and their power to force people to use it and to accept it at a particular price" (Hayek 1976a) . However, there have been many false criticisms based on the misunderstanding that Hayek advocated free banking. It should be understood that Hayek's competition among money is not neoclassical perfect competition as pure price competition but monopolistic competition that is a mixture of price and non-price competition.

From the perspective of evolutionary economics, if we view the monetary system as an "institutional species" with unique "replicators (rules)" just like "biological species" with unique "genes", the coexistence of many monetary species realized through such monopolistic competition can be understood as the evolution of a "monetary institutional ecosystem". 13 This will enable the realization of "good money" with diverse values.

An ecosystem composed of a single species is likely to be unable to survive due to endogenous changes or exogenous shocks. Biodiversity enhances the resilience of ecosystems so that even if a global catastrophe wipes out many species, those species that can flexibly adapt to the harsh environment can survive. Although a single global currency would offer convenience and efficiency, such as the ability to be used for anything, regardless of time or place, it risks being as fragile as the ecosystem of a single species.

Hayek, who experienced hyperinflation in Austria in the 1920s, first mentioned money with a stable value (so-called "neutral money") as "good money". The stability of money is thought to reduce the uncertainty associated with buying and selling, to stimulate real transactions such as consumption and investment, and to expand credit transactions involving money lending and borrowing. From a modern perspective, however, "good money" can have various other characteristics such as resilience, decentralization, diversity, sustainability, trust, fairness, equality, and people's well-being (QOL, Well-being). These are qualities of "good money" that are found spontaneously through monetary choices by users.

Local currencies or community currencies, which have expanded worldwide since the 1980s, have evolved as "integrative communication media" to hybridize the two major human media, money and language, rather than separating them as 13 We have constructed the theoretical model of institutional ecosystems to explain and describe the evolutionary dynamics of currently observed diversified money (Hashimoto and Nishibe 2017). In the model, an institution such as money is a game constrained by given game rules, and a variety of institutions such as diversified money constitute a complex institutional ecosystem subject to a meta-rule composed by players' value consciousness as criteria to evaluate multi-games. Refer to the article if interested in such theoretical aspects of this topic. media in the economic and cultural/social domains (Nishibe 2012) . Its purpose is not only to activate transactions in the local economic sphere, which is declining due to the expansion of globalization, but also to improve the quality of life in local and virtual communities and by promoting mutual aid, reciprocity, and facilitating communication. Community currencies can be understood as a movement to seek new qualities of "good money".

Cryptocurrencies and community currencies as "ideational money" or "symbolic money" are partially independent from the yen, and especially in their initial stage, they cannot depend on "past customs" as the yen does. Until the power of "customs" in the past comes into play, they must form and maintain hopeful and attainable value only with the driving force of "expectations" in the future, such as "sounds fun", "sounds interesting", "sounds profitable", "sounds good", "is exciting because it anticipates the future world," "is ethically excellent", "can realize the value I have been seeking", and so on. It is not always easy. Internet and smartphone technologies and SNS such as Twitter and Facebook have facilitated the formation and growth of various social networks and communities of interest. Therefore, there is a high possibility that more digital currencies circulating in such networks and communities will be created in the future. A typical example is a digital glocal currency such as Facebook's Libra.

If we view money as a service as CaaS (Currency as a Service) rather than a medium of exchange or a store of value as in the past, we can overcome the limitation that conventional money has been a scalar currency, a one-dimensional value measure that expresses a positive/negative relationship in terms of a base number, and we can create a new currency that expresses heterogeneous characteristics in a composite manner. It may evolve into a "vector currency", a multidimensional value measure that expresses heterogeneous characteristics in a composite manner. Scalar currencies have difficulty in expressing diversity because the size of the scalar currency determines the disparity between rich and poor, but vector currencies with different dimensions can express diversity in a more complex and richer way (Nishibe 2019) .

5. The Merits And Demerits Of Mmt

As a result of spread of Bitcoin's core fintech, blockchain or distributed ledger technology (DLT), the theory of the origin of credit money revived recently, and the view that the essence of money is not material money but credit money, and that money is an IOU that circulates based on credit relations, has gradually gained strength.

Randall Wray, a famous post Keynesian and one of the founders of Modern Money Theory (MMT), has developed an endogenous monetary theory based on such credit money (debt money), defined as distinct from liquidity, since the 1990s (Wray 1990 (Wray , 1998 . It combines nominalism, which holds that money is merely a unit of nominal value, and chartalism, which holds that money is created as a means of direct economic activity of the state, such as fiscal spending, with its compulsory right to collect taxes. In Wray's view, modern central banknotes do not represent real value as in the case of material money but are negotiable instruments of indebtedness (IOUs) that represent a unit of account and are issued on the basis of the state's ability to collect taxes. In our view, it is correct that modern central bank notes do not embody real value like material money, but it is incorrect to say that they are negotiable certificates of obligation, or credit money (debt money). Because the central banknote as fiat money is, as we have already seen, neither material money nor credit money, but the postmodern money called ideational or symbolic money without possessing intrinsic use value nor representing human economic relation.

The MMT claims that no matter how much a nation spends beyond its tax revenues and how much it borrows if the central bank can continue to buy government bonds as the government's IOUs by issuing legal tender as the central bank's IOUs, and that the resulting inflation stimulates the economy without leading to uncontrollable hyperinflation and the integrated government will not go into financial default. The argument is based on endogenous money theory, but its conclusion is somewhat similar to that of inflation targeting by QE based on exogenous monetary theory because MMT simply regards money as IOUs.

As of March 31, 2020, 47% of Japan's government bonds are held by the Bank of Japan. This is far from the extreme situation that MMT claims, where the central bank holds all the JGBs, but it has been said that this causes no problem because most of the remaining 53% is held by domestic financial institutions and investors. But foreign investors might sell JGBs as soon as those prices fall and interest rates rise, causing capital flight and possibly a crash in government bonds and currencies. According to MMT, such things often happened in smaller countries around the world, however, in Japan with its sovereignty currency, yen, BOJ and other domestic investors hold JGBs so that there would be no need to worry about this.

MMT develops the endogenous monetary theory that modern money is spontaneously created as certificates of obligation (IOC), deposits of the central bank, based on reflux as tax revenues. If the government increases public works projects due to budget deficits, its financial debt will increase, but the money stock will naturally increase on the balance sheet of the BOJ by holding JGBs necessary to finance it. In this respect, it is a much superior theory compared to the exogenous monetary theory of Friedman and Bernanke, whose theories see money as something to be artificially injected from outside, such as helicopter money, and the inflation targeting theory that relies on it. While more plausible as a modern monetary theory, we believe it is dangerous to apply it directly to reality.

We must take notice that even if MMT regards modern money as credit money (debt money), the original meaning of 'credit/ debt' has been largely changed from the obligation of repay/redemption of specie (gold/gold coin) or cash by money issuers as debtors as in the case of IOUs such as convertible banknotes to the obligation of tax payment by the nations' people and firms as receivers and users of inconvertible banknotes as fiat money. In fact, Wray has become to call it "sovereign currency" based on "monetary sovereignty" of the state 'rather than 'credit money or 'debt money' because he realized that 'credit' or 'debt' is a strange expression for tax payment and emphasize the power of the nation to enforce people to use means of payment to settle debt of tax payment (Wray 2015 ).

But we cannot call the obligation of tax payment 'credit/debt' because the former is completely different from the latter. While 'credit/debt' is normally supposed to occur as a contractual agreement on every term of financial arrangements related to economic transactions between both parties, obligation of tax payment in the modern nation-state arises from the social contract at the initial point in time by establishment of its constitution and from the continued agreement through successive elections between the government and the people on the basic ideas of tax collection necessary for government spending without all more detailed terms. The tax rate changes according to the tax law, and the amount of tax payment is not predetermined before the realization of the income and asset. Then is it true that the nation-state has the compulsory power to enforce people and firms to pay tax? It is doubtful because they can escape from its jurisdiction to foreign domains if they do not satisfy nor agree on the contents of the social and economic policy of the government including tax. At present time, all national currencies are owned by not only domestic people and firms but foreign investors who do not pay tax. Nevertheless, the value of the national currency expressed as its exchange rate with any other foreign currency is basically determined by the difference of interest rate and the capital flow of those foreign investors in the foreign exchange where they are dominant players, not the nation-states. In short, any nation-state cannot determine the value of its own national currency by itself nor give unlimited supply of national currency without its devaluation because it depends on the expectations and behaviors of other nation-states and domestic and foreign investors.

MMT maintains that the sovereign government needs tax not to cover expenditure but to create demand for money, and tax is the mover of money as the business card tax in Warren Mosler's story typically shows. In other words, MMT tries to convince us that all moneys in human history were national currencies, not private currencies. But, as we have seen before, it is not true. There were many examples of non-national money before capitalism. The concept of money proposed by MMT is not only thus unconvincing but also outdated in the following two respects.

First, this argument would have been valid if the national economy had a fixed exchange rate system and foreign trade and investment had not been so large as in the early 1970s, and if the economy had been much closer to a closed economy. In the case, however, under a floating exchange rate system since 1973, and especially under globalization since the 1980s, this is no longer the case. Today, we have a floating exchange rate system and an open economy. The risk of capital flight by foreign and domestic investors who have bought JGBs in the future is considerable. We cannot say it will be safe even if currently domestic financial institutions and institutional investors hold a large share of JGBs. If they expect JGBs to fall, they will reduce their JGB holdings, and if JGB prices really start to fall, they will have no choice but to sell. It would become impossible for BOJ to keep the long-term interest rate low by buying all the JGBs in such situations.

The other issue is related to the expansion of non-national currencies, including cryptocurrencies and community currencies. As seen in the previous section, with the spread of digital technologies such as smartphones and QR codes settlement since the beginning of the twenty-first century, the denationalization of money is already underway. In other words, the state monopoly of money, which is a prerequisite for MMT, is gradually breaking down, and private currencies are spreading. In the future, there is a risk that investors will not only sell their government bonds and flee to other countries' currencies, but also may flow into investment and speculation in bitcoin, altcoins, and tokens. In addition, if ordinary people begin to use cryptocurrencies and community currencies for consumption, investment and even saving, tax revenues from national currencies will likely decrease rather than increase. Even if these events are not large enough at present and the national currency continues to exist as it is, its foundations should be seen as shaky in the future.

The former is somewhat old, but the latter is the latest reality. Since we need to assess the trend of this latest reality in the future, I do not think we should joyfully accept MMT out of hand, even if it is a theoretical argument to keep the consumption tax from being raised.

Let us repeat. First, we believe that MMT underestimates the intensity of global competition by financial speculative entities in a global and open capitalist economy. As we discussed with regard to central banknotes, even domestic financial institutions will not altruistically continue to hold them if government debt crashes. Already, we are beginning to see various signs suggesting that this will be the case. Second, MMT's basic assumption that the central banknote as legal tender under a "one country, one currency" system remain strong forever is fragile although it is seemingly solid, isn't it? In short, the flaw in MMT is that it tends to overestimate the strength of the control on self-generating purchasing power of the central banks or the integrated government because MMT still regards fiat central banknotes as IOUs and ignores the modern trend toward diversification of non-national currencies.

In contrast to MMT, PMMT takes the ongoing dynamics in the evolution and diversity of post-modern moneys and the markets in the twenty-first century as more serious and significant.

6. Conclusion: From Mmt To Pmmt

Here is the summary of PMMT's view on post-modern money that we have seen above. We must release ourselves from the stereotype of a single national currency to seek a new way of adequately understanding the diversity and evolution of postmodern moneys and find a new bottom-up approach for evolutionary theory and policy with a diversity of money, different from conventional top-down approaches found in micro theory without money as well as a macro policy with single money. 14 In evolution of money, "material money" and "credit money" emerged parallel from primitive money, and until pre-capitalism, both moneys were used separately depending on the counterparty (anonymous/nominal) and the scope of transactions (interregional/local) (Fig. 1, 4) .

When the central banking system initiated as Bank of England, which had a monopoly on money issue under the Peel Act of 1844, and the international gold standard called the pound system were established in the United Kingdom, the then capitalist center of the nineteenth century, and spread to other countries, cash currency as legal tender was divided into two types: "material money", which was the specie as gold coins minted by the state, and "credit money", which was convertible central banknotes guaranteed to be redeemable for the specie. Under the dollar gold exchange standard and fixed exchange rate system in the Bretton Woods system after WWII, national currency was divided into two: cash currency, consisting of fiat central banknotes and supplementary coins, and deposit currency, consisting of demand deposits in private banks. In addition, fiat central banknotes as cash currency under the floating exchange rate system has become neither material money nor credit money.

Nevertheless, Modern Monetary Theory (MMT) still understands from the view of its monetary nominalism and chartalism that a central banknote is an analogue of credit money (IOU) as a sovereign currency of the state for enforcing people to pay tax and that even if the government issues vast amounts of government bonds to cover the budget deficit, the monetary base can be unlimitedly increased if the central bank purchases government bonds as assets and increase central banknotes and deposits of the same amount to be recorded as liabilities. Accordingly, MMT further argues that there is no need for considering balanced budgets in expansionary fiscal policy at all, and that an increase in the budget deficit and money stock by the integrated government would successfully bring about higher prices and wages, leading to economic recovery.

However, since 1973, when a floating exchange rate system was introduced, the fiat central banknote is no longer a certificate of obligation (IOU) as a convertible note that guarantees redemption because all national currencies, including the dollar, became fiat currencies after then. In other words, the core of modern money is no longer credit money. It is a new type of money like security or equity, "ideational money" or "symbolic money", that continues to be received and circulated only as two self-fulfilling ideas of customs from the past and expectations in the future. Since ideational money can be visualized as the march of the "naked emperor", 15 whether it is retained as money depends on the present state expressed as the relative frequency of such customs and expectations as self-fulfilling ideas. If the ratio of speculative agents with pessimistic expectations of the stability of the currency value exceeded a certain upper threshold, positive feedback would be triggered and the ratio of speculative agents possessed with pessimistic expectations would cumulatively increase, resulting in a collapse of the stability of the money value expressed in a sharp rise in prices as in hyperinflation and/or a sharp decline in foreign exchange rates as in rapid depreciation of the yen.

We call such a view on money that understands modern legal tender in this way "Post-Modern Money Theory (PMMT)". PMMT criticizes MMT on the ground that it is (1) outdated in that it regards central banknotes as debt money or sovereign money and neglects the emergence of diverse non-national currencies, (2) fallacious in that it equates BOJ notes (ideational money) with JGBs (government debt) although they are heterogeneous and independent, and (3) inappropriate not to consider that there is a certain upper threshold to the increase of government bonds and money stock for covering the budget deficit so as to encourage limitlessly expanding fiscal and monetary policy.

BOJ's balance sheet still shows "banknotes" as liabilities. But this does not provide an adequate statement of its financial condition even if it might be merely a customary rule of the past (Table 1) . But for BOJ, it should be more appropriate to record it not as "liabilities" but as "capital" in the net assets section as investment securities or utility tokens without dividend, interest, or voting rights because it can not only reduce BOJ's risk of insolvency due to the price collapse of JGBs but also make it clear to financial institutions, corporations and individuals that BOJ notes have the same risk as equity or security.

Since the 2010s, especially in the years following the outbreak of the new Coronavirus disaster, the expansion of free trade, free investment, and globalization has come to a halt, and home-first and protectionism have been on the rise. The U.S. under the Trump administration, which advocated "America First", has also taken a major turn toward protectionism. In addition, the number of private currencies, such as cryptocurrencies used globally on the Internet and digital local currencies that can be used for smartphone payments, has increased dramatically (as many as 20,000 altcoin and tokens), and the one-country, one-currency system that is the premise of MMT is collapsing. Significantly, these private currencies also share with legal tender the essence of post-modern money as "ideational currency", and innovation through AI and DX has reached web3, which includes distributed ledger, Defi, DAO, token economy, characterized by autonomy, decentralization, and diversification, and is expected to bring a variety of values such as stability, resilience, sustainability, sharing, "quality of life" improvement in a mutually substitutive and complementary manner.

Declarations

Conflict of interest The author has no conflicts of interest to disclose.

SECTION

For more on local currencies or community currencies, please refer toNishibe (2012Nishibe ( , 2018Nishibe ( , 2019.

For more details on the logic and self-organizing dynamics of the creation of material money, seeChap. 4, Nishibe (2016).

For more on the basic concepts and framework of evolutionary economics, seeAruka (2015),Dopfer, Potts (2008, 2009,Nishibe (2006Nishibe ( , 2012,Nishibe, Yoshida et al (2010).

"Is the Bank of Japan a major shareholder in Japanese corporations?" (in Japanese), https:// www. nikko am. com/ produ cts/ etf/ we-love-etf/ kihon/ kihon 13, Tsuzaka N "Criticism rises as BOJ becomes top shareholder in domestic market" (in Japanese) The Asahi Shinbun, https:// www. asahi. com/ ajw/ artic les/ 14389 584.

"Liquidity preference" introduced byKeynes (1936) was based on the understanding that the reason why the interest on cash currency is zero compared to such financial assets as deposits and bonds, which earn interest, is because the risk of holding money is zero, which would have reflected the normal monetary consciousness of the British, not the German or Austrian such as Hayek who experienced hyperinflation after WWI. 7 This is the author's view that "free investment" rather than "free trade" characterizes post-modern financial capitalism as ultimate goal of long-term tendency of globalization. For more on this, seeNishibe (2020a).

This issue is discussed in more details in Chap. 3,Nishibe (2016).

What exactly is meant here by the situation in which pessimistic speculative agents do not accept BOJ notes? Here, we do not clearly distinguish between BOJ notes as cash and current deposits at BOJ by financial institutions. We treated them altogether to focus on the problem of future expectation of and confidence in the national currency, "yen," although the monetary base that BOJ can operate discretionarily contains many times as much current deposits at BOJ as cash as BOJ notes at its core. This is because we consider that, as already explained in the text, once the new and clearer meaning of BOJ notes is given as the origin, the meaning of current account at BOJ would be derived from it. There are a total of 519 financial institutions with current accounts at BOJ, including 124 banks, 11 trust banks, 50 foreign banks, 248 credit unions, 32 securities firms, and 33 banking associations (https:// www. boj. or. jp/ paym/ torih iki/ ichiran.pdf). These would be the in-kind investors in BOJ in the new interpretation of BOJ notes and proposal of its treatment on the balance sheet of BOJ just mentioned in the text, but they would also be potential candidates to be pessimistic speculative agents. Turning these financial institutions to in-kind investors in BOJ would remove the risk of insolvency from BOJ and prevent them from becoming pessimistic speculators. If these financial institutions try to completely evade from "yen," it is conceivable that they would not be able to conduct domestic financial transactions in the first place. This sounds an extremely unrealistic assumption, but we consider pessimistic speculators about the "yen" are economic agents who, after receiving payment in BOJ notes or deposits, immediately try to convert the "yen" into such other currencies as U.S. dollar, euros and financial assets (stocks, indices, futures) and real estate denominated in such currencies, or even cryptocurrencies such as Bitcoin and altcoins. We cannot expect what happens ex ante, but we would know that ex post.

According to a report (March 2018) by the Bank for International Settlements' Committee on Payments and Market Infrastructures and Markets Committee on Central Bank Digital According to a report on Central Bank Digital Currency (CBDC) (March 2018), CBDC is a new concept that is different from the reserves and settlement balances that commercial banks have with central banks, and there are several design possibilities in terms of access, anonymity, degree of availability and interest. https:// www. bis. org/ cpmi/ publ/ d174. pdf 11 The most famous digital community currencies in Japan are Sarubobo Coin in Hida-Takayama City, Gifu Prefecture, Aqua Coin in Kisarazu City, Chiba Prefecture, Kintetsu Harukas Coin, Yokohama Bay-Stars Coin, and eumo, the sympathetic community currency. The first two are community currencies for neighborhoods, while the others are for communities of interest. However, by being digital currencies, they become community currencies for 'communities of interest' if they include local residents, prospective residents, and foreign tourists. SeeNishibe (2020b, c)

This can be called "Gresham-Copernicus law". For more detail, seeNishibe (2020b)

On plurality and diversity of money, seeGomez (2018), and on the diversity of community currencies, seeNishibe (2018).