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Virtual Money Illusion and the Fundamental Value of Non-Fiat Anonymous Digital Payment Methods Coining a (Bit of) Theory to Describe and Measure the Bitcoin Phenomenon.

Introduction

In economics, the value of an item is defined by its opportunity cost - the next best alternative forgone. To facilitate comparisons of value, it is standard practice to express opportunity cost in currency units or money. For many goods and services, market prices exist and theory suggests that these prices well approximate the value of the marginal unit consumed by individuals. When the items of interest are not widely traded or abstract, then typically some related market price is used as an approximation. For example, the value of a person's time is often approximated using their wage rate.

In the case of money itself, this approach is problematic because it is the unit of account. Nevertheless, there is a well-defined set of forgone functional alternatives to money. In addition to serving as a unit of account, money is also a store of value and a medium for exchange. In the absence of money, one would use alternative resources for these services. Thus far, economists have identified two species of money: commodity and fiat. (1)

Examples of commodity money are gold, silver, gems, sea shells, salt, and cigarettes. Commodity money is distinguished from fiat money because it has an intrinsic value separate from its value as money. Fiat money is created by an act of law by a government that designates a token that has little or no intrinsic value as such. The key feature of fiat money is that it can be used to pay taxes.

Prior to the development of fiat currency, governing authorities (e.g., monarchs) would demand tax payments in commodities. However, with a fiat currency, the government designates all tax obligations in units of the currency and demands that the payments be made in currency. If a taxpayer does not have the financial resources (i.e., money) to pay his tax obligations, the government typically seizes the taxpayer's property and auctions the property to get the money to pay the obligation. The ability of fiat currency to satisfy government payment requests represents an additional source of demand for fiat currency not shared by other forms of money (in particular, Non-Fiat Anonymous Digital Payment Methods (N-FADs)).

The literature on N-FADs, and in particular bitcoin, is beginning to emerge in economics and finance. Both Bohme et al. (2015) and Dwyer (2015) provided good introductions to bit-coin while Cheung et al. (2015), Fry and Cheah (2016), and Corbet et al. (2018) uncovered the existence of price bubbles in the market for bitcoin. In addition to revealing the existence of price bubbles in the market for bitcoin, Cheah and Fry (2015) estimated the fundamental value of bitcoin to be zero. Urquhart (2016) found that the market for bitcoin was not weakly efficient in its infancy but found some evidence of weak efficiency in more recent periods. In a follow-up study, Nadarajah and Chu (2017) provided evidence of a weakly efficient market for bitcoin over the entire time period studied in Urquhart (2016) when the returns were exponentiated by an odd integer. Additionally, Dyhrberg (2016) showed that bitcoin could be used as a hedge against the Financial Times Stock Exchange Index.

Yelowitz and Wilson (2015) initiated an investigation on the potential users of bitcoin, and found evidence that the demand side was comprised of computer programming enthusiasts and those interested in illegal markets. However, the authors used Google Trends data to identify the type of person that was likely purchasing bitcoin. One issue with the method used in Yelowitz and Wilson (2015) is that the more libertarian consumers of bitcoin who are concerned with privacy likely do not use Google as the search engine of choice. Additionally, investors likely receive information on bitcoin through financial publications and websites rather than via internet searches. For these reasons, the lack of significant correlation between investment and libertarian search terms and bitcoin search terms does not necessarily imply that these types of consumers are not demanding bitcoin. Other contributions to the literature provide insights into conditions under which a government may effectively ban N-FAD transactions from competing with fiat currency (Hendrickson and Luther 2017). This paper models how an N-FAD can potentially interfere with monetary policy, supplying an important underlying motive for governments seeking to ban or otherwise restrict N-FAD use as China recently has done (Dawkins 2018).

The paper discusses the different types of demand for N-FADs and how the characteristics of the currency's supply protocols are likely to influence demand. Predictions are derived on how N-FADs will affect monetary policy and vice versa making use of a quantity equation. We are then able to estimate the amount of purchases made using the most widely used N-FAD, bitcoin.

N-FAD Demand

N-FADs are money, but they are neither commodity money nor legal tender (i.e., fiat currency). What are the functional components of N-FADs that have given rise to its demand? Money is defined by three characteristics. Money is: (i) a unit of account, (ii) a store of value, and (iii) a medium of exchange. An asset with these characteristics generates three demand components: transactions demand, precautionary demand, and speculative demand. However, transactions demand makes up the greatest source of demand for most currencies.

Transactions Demand

In the case of N-FADs currently available, the ability of the currency to function as a means of transactions (i.e., medium for exchanging goods and services) has been the traditional barrier to wide-scale adoption. Currently, purchases of general goods and services made using the most widely accepted N-FAD, bitcoin, are expanding. According to Blockchain (2018), the daily number of bitcoin transactions in 2017 ranged between 130,000 and 500,000. Although the amount of these transactions that were purchases of goods and services is unknown, what is known is that the largest retail acceptor of bitcoin, Overstock.com, began selling an average of $15,000 a day worth of goods via bitcoin purchases in 2014 (Money Morning 2014). More recently, the company released its own N-FAD, tZERO (Overstock.com 2018). Additional companies are accepting bitcoin as a method of payment every day such as Microsoft, Dell, Expedia, and Newegg to name a few. However, the majority of transactions are likely not for traditional goods and services. Badev and Chen (2015) presented evidence that the majority of small (less than $100 in value) transactions were attributable to Satoshi Dice, a popular online gambling service.

Bitcoin users encounter a number of difficulties that users of other forms of money do not. For instance, bitcoin is not widely accepted as a form of payment in the day-to-day real economy and it is unlikely that governments will accept bitcoin as a form of payment for government payment requests (e.g., tax obligations) in the near future. There are also significant costs associated with establishing bitcoin accounts and trading that discourage most people from transacting in bitcoin. One must first obtain a virtual wallet to store the bitcoin or purchase online storage at an additional fee. If the currency is stored on a physical drive via a virtual wallet, the entire amount will be permanently lost in the case of a drive failure. This initial technological hurdle requires a significant investment of time to understand bitcoin trading protocols for most users.

There is also a risk-assessment hurdle, which requires a new user to consider the risks of government (public) seizure and theft (private seizure) of bitcoin assets. On July 26th, 2011, the third largest bitcoin exchange (Bitomat) permanently lost all of its customers' bitcoins when its servers were reset (Dotson 2011). When the largest bitcoin exchange, Mt. Gox, was hacked for a second time in 2013, it lost 850,000 of its customer's bitcoin ($460 million). The Department of Homeland Security also seized $5 million from Mt. Gox's U.S. bank account because the company had not registered with the government as a money transmitter, causing individuals with bitcoin stored on Mt. Gox's servers to lose access to their assets (McMillan 2014). Also, as pointed out in Chuen (2015), there is currently no form of insurance comparable to the deposit insurance provided to bank customers.

Lastly, the current tax treatment of bitcoin greatly increases the cost of using N-FAD's for law-abiding citizens. The Internal Revenue Service (IRS) declared bitcoin a "convertible virtual currency" (Internal Revenue Service 2014, p. 1), which implies that it should be treated as property for tax purposes. For example, if an individual purchased a bitcoin for $400 and spent the entire bitcoin after it had appreciated to $500, he would owe taxes on the $100 appreciation. On the other hand, the treatment of N-FADs as property by the IRS may actually be a positive sign for their users as it implies that the U.S. government is unlikely to declare them illegal according to the Stamp Payments Act of 1862. (2)

The technological hurdles and seizure risk uncertainty of N-FADs can be summed up by saying that the general transactions demand for N-FADs is likely to be weak for the time being due to increased set up costs and risk relative to standard fiat currency. Moreover, with a currency such as bitcoin, whose value fluctuates widely, risk assessment for the general populace is very difficult. Unless the uncertainty in bitcoin's ability to serve as a store of value subsides, transactions demand is unlikely to exist at all for the general population.

Figure 1 displays the U.S. dollar/bitcoin exchange rate since 2010 when the price first became positive. In the early years of bitcoin's existence, the market value of a unit of bitcoin (BTC) went from $0 to almost $1,200 only to briefly sink below $200 and then rise back to just under $300. The largest fluctuation to date began in 2017, when the value skyrocketed to over $19,000 in December, only to fall back down to the $14,000 range by the end of the year and then back to the $6,000-7,000 range in 2018. According to Cheung et al. (2015), the early volatility in the price of bitcoin can be largely attributed to many short-lived bubbles in bitcoins valuation and three bubbles lasting 66 days or longer. Using more recent data, Corbet et al. (2018) found evidence that bitcoin was in a bubble from the time it reached a market value of $1,000 in early 2017 until the endpoint of the authors' data, November 9th, 2017.

Many factors have been proposed to explain the volatility of 2017 and 2018. Bitcoin reached an all-time high in March of 2017 as institutional investors became increasingly interested in the asset, only to drop almost 30% when the SEC announced its rejection of a bitcoin exchange-traded fund (Bovaird 2017). It was suggested that the subsequent climb to just under $20,000 was due to the increase in global adoption of NFADs, in particular from China, South Korea, and Japan (Young 2017). The dramatic fall in price in 2018 has multiple potential explanations. Of course without a formal study of the price volatility, one cannot rule out the possibility that much of the decline was simply the bursting of the most recent bubble identified in Corbet et al. (2018). However, the banning of all N-FADs by the governments in China is believed to have caused the price of bitcoin to fall from just over $9,000 to just under $7,000 in the first week of February, 2018. The Chinese issued ban came shortly after similar measures were passed in Vietnam and Indonesia (Jaewon 2017). Lastly, the rise in stolen bitcoin and other N-FADs from exchanges have also likely contributed to the decline in bitcoin's price (Chavez-Dreyfuss 2018).

In addition to consumers and investors, merchants also have an incentive to favor N-FADs over fiat to avoid fees paid to financial institutions. According to the Federal Reserve's 2013 Payments Study, there were 122.8 billion non-cash payments made in 2012, with a total value of $79.0 trillion. Banks, credit card associations (Visa, American Express, etc), and credit card processors charge fees for maintaining the financial infrastructure to process payments on behalf of consumers and merchants. These fees act as an additional tax, driving a wedge between the prices consumers pay and the prices merchants receive.

Merchants providing the option to purchase goods and services with an N-FAD avoid higher transactions fees charged by traditional financial intermediaries. To avoid the risks associated with a highly volatile exchange rate, merchants can utilize services that instantly exchange N-FADs for fiat for a small transaction fee of 1 % or $0.15 for transactions that are $15 or less (Coinbase.com 2015). This fee is considerably less than those paid when transacting with credit cards, which include interchange fees that are typically a few percentage points of the transaction value and other flat fees for use of the credit card's payment system. In addition, Lo and Wang (2014) found preliminary evidence that some online retailers accepting bitcoin may be passing on what they save in avoided fees to consumers, which should serve to increase transactions demand.

Even in the face of technological hurdles, the use of bitcoin has been rising. The phenomenon of increasing bitcoin demand despite its increased risk must be largely due to the other two potential sources of demand: precautionary and speculative demand.

Precautionary Demand

Precautionary demand for money comes from holding an asset in anticipation of some contingency. In the case of N-FADs, this appears to be a central component of their appeal. By definition the transactions carried out using N-FADs are anonymous. (3) Currently, bit-coin allows for anonymity between transacting (i.e., primary) parties and social (i.e., third party) anonymity. The appeal of holding bitcoin in the event that an anonymous primary party transaction becomes necessary depends on the likelihood of such an event arising. For consumers that place a high value on privacy, the desire to carry out financial transactions using N-FADs will always be present.

In the case of the general public, the necessity of transactions requiring primary party anonymity is likely to be small. However, for parties involved in illicit transactions primary party anonymity reduces the risk of sanctions from legal authorities. In determining the strength of precautionary demand for illicit transactions for N-FADs, economic theory suggests that the parties involved in illicit transactions will balance the risk of sanctions involving transactions in other forms of money against the transactions cost, risk of sanctions, and risk of seizure using N-FADs.

The real problem for N-FADs is that unless illicit transactions become sufficiently difficult to detect, and thus too costly to monitor, legal authorities are likely to increase the probability of public seizure such that N-FADs are no longer relatively desirable as a method for conducting illicit transactions. There is some evidence, however, that tracing bitcoin back to an owner is possible, particularly if the owner eventually needs to convert a large amount of bitcoin to a fiat currency (Meiklejohn et al. 2013). Thus, the demand for bitcoin depends on assessing a wide variety of risks that are not well-understood, which leads to speculation. Speculation in this context means assessing risks for which common source of data and techniques have not been established.

Speculative Demand

The speculative demand component of N-FAD demand is due to optimistic assessments of wide-scale adoption in light of the risks previously mentioned, which would lead one to conclude that the value of bitcoin will likely rise in the future. There is also speculation regarding the ability of the bitcoin algorithm to generate a hedge against inflation or a general anticipated decrease in the value of widely accepted fiat currencies (as previously noted, Dyhrberg (2016) showed that bitcoin could be used as a hedge against the FTLSE Index). The inflation risk speculation associated with bitcoin is due to the widely accepted belief that the stock of bitcoins is fixed by the algorithm used to create and track the currency.

Assuming the stock of bitcoins is fixed and that no modifications to the algorithm could be undertaken, there is a critical trade-off that the bitcoin developers likely did not anticipate. (4) Namely, that the inflation-hedging properties of the currency distort a central bank's control over price levels and thus magnify the risks associated with public seizure. This is a main result of the model presented herein. Of course the ability of bitcoin to hedge against inflation may be inconsequential if competing N-FADs dilute bitcoin's value by increasing the supply of N-FADs in use. (5) In what follows, the potential effect an N-FAD may have on monetary policy is modeled abstracting from the competing N-FAD issue. As the inverse relationship between the inflation-hedging property of bitcoin and the probability of public seizure become well-accepted, one would predict that the precautionary motives for holding bitcoin as a medium for illicit transactions will decrease, which will lead to a decrease in the currency's value. The paper formally models the relationship between the supply of an N-FAD and a central bank's ability to control inflation with monetary policy by augmenting the quantity equation.

Model

To better understand the negative relationship between the inflation-hedging properties of bitcoin and the probability of public seizure, consider a robust relationship between inflation, money supply growth, and real economic growth introduced in principles of economics. The model that follows augments the quantity theory of money by adding an additional currency to the equation of exchange. The quantity theory can be described as an accounting identity, or as the reduced form of a behavioral model of the demand for money as in the well-known money-in-the-utility-function (MIU) model (Walsh 2010, p. 229). Independent of the justification, the quantity theory has provided invaluable clarity to theory and monetary policy. The objective in employing the quantity theory here is to add similar clarity to the risks that widespread N-FAD use poses to policy objectives of a monetary authority. A key relationship of quantity theory is

m =[pi] +g (1)

where m is the growth rate of money supply, [pi] is the rate of inflation, and g is the growth rate of the real economy. Central banking monetary authorities have used the relationship of Eq. 1 to manage the growth of the money supply to avoid the negative economic consequences associated with deflation and excessive inflation.

The bitcoin algorithm sets the left-hand side of Eq. 1 to zero (eventually), which implies that the bitcoin policy would generate general deflation. Imagine that all of the technological hurdles with bitcoin are overcome (as optimistic speculators believe) and that the risks of private seizure (i.e., theft) are equal to that of fiat currencies. In other words, imagine that there is no reason to hold fiat currency rather than bitcoins. Then, the desire to avoid inflation would make bitcoin a superior instrument for holding individual wealth.

A Gresham's Law analogy applies to the success, or failure, of N-FADs as a medium of exchange. Gresham's Law, "bad money crowds out the good" (Tobin and Golub 1997, p. 214), suggests that fiat currency, subject to incessant devaluation, would crowd out transactions demand for a bitcoin-type N-FAD, whose scarcity is guaranteed by design. The implication of the fiat-crowding equilibrium implies that bitcoin will only ever be used as a store of wealth and never for transactions. As a counterbalance, bitcoin's volatility and public seizure risks could mean that market participants find fiat currency more desirable, meaning that transactions demand for bitcoin will increase. However, an economy valued in bitcoins or similar N-FADs would be marked by general deflation - a significant threat to economic growth. The incentive of governments to prevent such an outcome would greatly increase the probability of public seizure or a ban on bitcoin transactions as happened recently in China (Dawkins 2018). There are additional reasons to believe that the potential of bitcoin to undermine the ability of governments to control the price level would increase the likelihood of public seizure, but the scenario described points to an equilibrium outcome that bitcoin's algorithm embeds in the currency by design. Not all N-FADs would generate the same level of seizure risk. The current analysis applies to situations where the balance of the considerations mentioned allows significant transaction volumes in both the N-FAD and fiat currency.

Imagine an economy with only two payment methods: fiat currency (f) and an N-FAD (n). Equation 1 is derived from the oft-mentioned equation of exchange, which relates the velocity of money (V) to the price level (P) and real output (Q): (6)

MV = PQ. (2)

Equation 2 can be modified to allow for the presence of an N-FAD by noting that some portion of real output ([Q.sub.n]) will be exchanged using the N-FAD:

[M.sub.f][V.sub.f] = [P.sub.f][Q.sub.f]. (3)

This is the key observation. [Q.sub.f] is no longer total output, Q. Rather, [Q.sub.f] is only that fraction of real purchases that occur in the fiat currency.

Q = [Q.sub.f] + [Q.sub.n] (4)

Solving Eq. 4 for [Q.sub.f], substituting the result into Eq. 3 and taking the total derivative yields:

[DELTA][M.sub.f][V.sub.f] + [M.sub.f][DELTA][V.sub.f] = [DELTA][P.sub.f]Q- [DELTA][P.sub.f][Q.sub.n] + [P.sub.f][DELTA]Q - [P.sub.f][DELTA][Q.sub.n]. (5)

Dividing Eqs. 5 by 3 reveals the relationship between the related rates of change as in Eq. 1.

[mathematical expression not reproducible] (6)

Equation 6 shows the relationship between the growth rate of the fiat money supply, [m.sub.f], the velocity of transactions, [v.sub.f], the fiat currency inflation rate, [[pi].sub.f], and the growth of fiat transactions, which depend on real growth, [DELTA]Q, and the growth in N-FAD transactions, [DELTA][Q.sub.n].

The paucity of assumptions leading to the relationship exposed in Eq. 6 makes the result general. With a minor restriction, the main point of the analysis can be laid bare. If, as usual, [V.sub.f] is assumed to be constant, then [DELTA] [Q.sub.n] represents a leakage of transactions. Transaction leakage caused by the N-FAD implies additional complexity for the monetary authority due to the disruption of the relationship between real growth, [mathematical expression not reproducible] and fiat inflation. The analysis suggests that widespread use of a bitcoin-type N-FAD for transactions is limited by the interests of the monetary authority.

Purchasing Power Parity

In the remainder of this analysis, the additional assumption is made of purchasing power parity between the N-FAD and fiat currency. In the case of a bitcoin-type N-FAD, the assumption is supported by stylized facts concerning the purchase of goods with bitcoin. Typically, businesses accepting payment in bitcoin convert the dollar price of goods to bit-coin using real-time exchange rate data to determine the price in bitcoin. Nevertheless, the results exposed hold more generally.

[M.sub.f] [V.sub.f] + [[euro].sub.f] [M.sub.n] [V.sub.n] = [P.sub.f] [Q.sub.f] + [e.sub.f] [P.sub.n] [Q.sub.n] (7)

where [epsilon] f is the exchange rate of fiat per unit N-FAD.

Assuming that there is purchasing power parity between the two currencies and that the stock of real output is divided between the two payment methods provides the additional restriction, [P.sub.f] = [[epsilon].sub.f] [P.sub.n]. Thus, Eq. 7 can be written as

[M.sub.f] [V.sub.f] + [.sub.f] [M.sub.n] [V.sub.n] =[P.sub.f]([Q.sub.f]+ [Q.sub.n]) (8)

Taking the total differential of Eq. 8 and assuming that the velocity of monies do not change yields:

[mathematical expression not reproducible] (9)

Dividing both sides by Mf and making use of purchasing power parity and Eqs. 3 and 4, a new equation can be derived describing money supply growth in the presence of a second currency:

[mathematical expression not reproducible] (10)

where [mathematical expression not reproducible], for [mathematical expression not reproducible], and [mathematical expression not reproducible]. With the assumption of purchasing power parity, Eq. 10 implies that in the presence of an N-FAD, the monetary authority needs to additionally monitor the growth of the economic activity carried out with the N-FAD, the change in the exchange rate, and the change in the N-FAD money supply. (7) Furthermore, these new variables affecting monetary policy are all weighted according to the proportion of goods and services purchased with the N-FAD. Note that if no purchases are made with the N-FAD, [Q.sub.n] = 0, Eq. 10 reduces to Eq. 1. The main point of these exercises was to show that N-FADs have the potential to undermine the ability of central bank monetary authorities to carry out their principle objective of price stabilization.

Measuring Purchases Made with N-FADs

Regardless of the rules under which the N-FAD changes in supply, the monetary authority overseeing the fiat currency will have to adjust their policies according to the amount of purchases made with the N-FAD. Estimating such a measure is a difficult task since the purpose of many N-FADs in use is to mask what is being purchased along with the parties involved. Although every transaction of bitcoin from one virtual wallet to another is recorded in a public record, the purpose of the transaction (sale of a good, illicit money laundering, etc) is not. However, with the additional assumption that the velocity of money for N-FADs is equal to that for fiat, an estimate of how much goods and services were purchased with N-FADs can be calculated using this simple model.

Assuming purchasing power parity holds and that the velocity of money is the same across currencies, the quantity of goods and services purchased with N-FADs can be written as

[mathematical expression not reproducible]

where [epsilon]n = 1/[[epsilon].sub.f] is the exchange rate of N-FAD for fiat. Equation 11 can be calculated using publicly available data. Although many N-FADs have surfaced since 2008, bitcoin continues to claim the largest market share. We choose to analyze a time period where bitcoin was practically the only N-FAD for transactions to simplify data collection. In the sample time period, bitcoin's market capitalization reached $3.5 million while the distant second ranked currency, Ripple, had only $0.4 million in market capitalization and all other N-FADs had a market capitalization under $70,000. (8) As such, the calculation of [Q.sub.n] was approximated by using data solely on bitcoin. Proceeding in this manner, [M.sub.n] and [[euro].sub.n] are easily obtained from Bitcoincharts (2018), for Vf the measure of velocity of M2 money provided by the Federal Reserve was used, (9) and Pf was measured by the CPI.

Quarterly estimates are displayed of bitcoin purchases of goods and services converted to millions of U.S. 2014 dollars as well as actual transactions (transfers of bitcoin from one wallet to another) and transactions net of trades for fiat for comparison in Fig. 2. The transactions data come from Blockchain (2018), which takes the data directly from bitcoin's public ledger. The net transactions are calculated by adding up all recorded transactions of bitcoin for currency on all the exchange markets listed on Bitcoincharts (2018) and subtracting them from the total amount of transactions. (10) In this way, a large portion of transactions is removed that can be confirmed were not for goods and services but for other (sometimes fiat, sometimes N-FAD) currency.

Although what was purchased with each transaction is not observed and therefore cannot directly comment on how well the model predicts purchases made with bitcoin, the series do line up remarkably well. The remaining net transactions not accounted for by estimated purchases of goods and services would include payments of debt, trades for fiat not occurring on the exchanges, and of course transactions between wallets owned by the same individual or entity meant to obfuscate the movement of funds. (11) Furthermore, not all purchases carried out with bitcoin occur in the U.S. Since the net transaction volume in Fig. 2 measures all transactions regardless of geography, the graph is an upper bound of potential purchases of goods and services using bitcoin in the U.S. That being said, Dwyer (2015) provided evidence that the purchases of bitcoin were tied to the typical trading times of assets in the U.S. during much of the time period studied here. Lastly, as mentioned previously, bitcoin is not the only N-FAD in use. However, in the sample time period, their acceptance by merchants and market capitalization is negligible compared to bitcoin. Therefore the difference between net transactions of all N-FADs (not just bitcoin) and the predicted purchases of goods and services using bitcoin is likely a little more than what is observed in Fig. 2 but would be greater if one used recent data. With these caveats in mind, the calculations suggest that quarterly purchases of goods and services via N-FADs ranged from approximately $42 million to $13 billion between 2011 and 2015.

N-FAD and Monetary Policy

The model can also calculate how much the presence of the N-FAD distorts the monetary authority's ability to target inflation. With the presence of the N-FAD, inflation will no longer increase one-for-one with an increase in the money supply, but rather it will increase proportionately with money supply according to the fraction of goods and services purchased with the fiat currency. Solving Eq. 10 for [[pi].sub.f] and taking the partial derivative with respect to the fiat money supply, we have

[mathematical expression not reproducible] (12)

The more the economy switches from using fiat to the N-FAD, holding Q constant, the less control the monetary authority will have over inflation in fiat prices. As of today, the presence of N-FADs is likely not yet interfering with monetary policy but, theoretically, it has the potential to do so.

Lastly, consider inflation tax avoidance as motivation for using N-FADs. By symmetry of our model, it follows that

[mathematical expression not reproducible] (13)

so that the introduction of the N-FAD will not completely protect users from the inflation tax imposed by a central bank as is ideal for many N-FAD creators and users. It will, however, dampen the effect in proportion to the economic activity carried out via the N-FAD.

Discussion

The introduction of N-FADs into financial markets has created new ways of transferring wealth without the use of a centralized monetary authority. In addition, users of N-FADs enjoy a degree of anonymity not available when conducting financial transactions using fiat currencies. We derive relationships illustrating that the presence of an N-FAD makes a price stabilizing policy more difficult to implement for monetary authorities. This characteristic of N-FADs will magnify as transactions in the currencies increase.

Part of the motivation behind the creation of bitcoin was to avoid monetary authorities' ability to deflate the value of currency held by increasing the money supply. What we show with our simple model is that the wide-scale adoption of an N-FAD would help consumers partially avoid the inflation tax, but it would also dampen the monetary authority's ability to control inflation of prices denominated in fiat. However, it must be noted that in reality the number of N-FADs available are increasing rapidly. As other N-FADs beyond bitcoin become readily accepted by merchants, the supply of all N-FADs in use increases, deflating their values. As of the writing of this paper, bitcoin's share of market capitalization has shrunk to a little under 50% according to CoinMarketCap (2018). So although the value of bitcoin is somewhat protected from inflation, it is not protected from the adoption of competing currencies.

Given that the demand for N-FADs is currently derived from a relatively small number of individuals, the likelihood of public seizure or interference prior to widespread transacting is likely. With the recent IRS notification that N-FAD transactions are taxable, those using N-FADs for illicit transactions can add tax evasion to their list of legal offenses. When those using bitcoin realize that the precautionary motive (i.e., the need for avoiding sanctions associated with illicit transactions) is no longer valid because of the high probability of public seizure and increasing punishments, they may abandon the currency and the value of bitcoin would dramatically decrease if these users are the majority.

However, there are parities outside of consumers who have much to gain from the presence of N-FADs. Merchants may have an even stronger demand for N-FADs than consumers. With $79 trillion dollars transacted in 2012 via non-cash payments, even a small reduction in fees paid by merchants for switching to N-FADs could reap trillions of dollars of savings. Since merchants collectively have much to gain from avoiding credit card fees, one might expect a movement by merchants to protect the legality of N-FADs.

While the regulation and adoption of N-FADs continues to increase, according to our estimates the current amount of goods and services purchased with the main N-FAD, bit-coin, is extremely small relative to total GDP of the U.S. economy. In the first few years of existence, the upper bound on quarterly purchase of goods and services in the U.S. economy with bitcoin is estimated to range from only $42 million to $13 billion. Thus, it is unlikely that N-FADs will soon interfere with monetary policy although they do posses the ability to do so given wide-scale adoption.

Our paper provides a foundation for additional research into important questions of theory, measurement, and policy. Using tools to study questions of monetary policy conceived to deal with one currency, we have successfully re-purposed these tools to expose a more complex problem of understanding the relationship between N-FAD supply, fiat money supply, and general inflation. Yet, the tools themselves, given the competing currencies problem and available data, generate partial answers too weak to provide rules-of-thumb for monetary authorities similar to the well-settled principles that have been disturbed. Theoretically, our extension demonstrates the need for better tools for modeling the interaction between "near-monies" and fiat money supply. We anticipate future contributions that examine competing currency questions and accommodate the analysis of monetary policy rules to provide better policy guidance. Additionally, the policy significance of this analysis is an empirical question. Future work providing analyses of the ever expanding set of digital payment methods will provide sharper estimates of the size of the N-FAD transactions issue. Lastly, there is the question of effective monetary policy itself in the age of ever expanding N-FAD use. What policy tools are needed in the central banker's tool box to manage inflationary pressures? Do policymakers merely try to ban the use of N-FAD's in an attempt to return to the status quo? Is there an enlightened way to manage N-FAD use? For example, might there be a demand by central bankers in the future that N-FAD algorithms include a set of monetary policy rules that support the decisions of central banks by linking N-FAD supply to a target interest rate? These questions are left for future research.

Acknowledgements Funding for this research was provided by the CSU Chancellors office through California State Polytechnic University. We would like to thank Gabriele Camera, Edmond Wu, and an anonymous reviewer for useful comments that improved this paper.

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[??] Craig Kerr

cakerr@cpp.edu

Greg W. Hunter

gwhunter@cpp.edu

Greg W. Hunter (1*) Craig Kerr (1) [iD]

(1) Economics Department, California State Polytechnic University, Pomona, CA 91768, USA

(1)Selgin (2015) categorized monies according to not only their intrinsic value, but also according to their scarcity being absolute or contingent on a decision maker, thus deriving four species of money. What the author denoted "synthetic commodity" money is what this paper refers to as non-fiat anonymous digital payment methods.

(2) According to the Stamp Payments Act of 1862, "Whoever makes, issues, circulates, or pays out any note, check, memorandum, token, or other obligation for a less sum than $ 1, intended to circulate as money or to be received or used in lieu of lawful money of the United States, shall be fined under this title or imprisoned not more than six months, or both". (Stamp Payments Act of 1862, 18 U.S.C. [section]336, 2012, p. 98)

(3)All transactions of bitcoin between virtual wallets are recorded in a public ledger. Therefore, the transactions are anonymous so long as users keep their wallet ID private. Since the fixed cost of creating a new wallet is essentially zero, many users who value the anonymity create a new wallet for every transaction.

(4) Hypothetically, if a single entity were to control over half of the bitcoin network's computing power, it could change the supply of bitcoin. However, the simulations run in Nakamoto (2008) showed the hypothetical situation to be a practical impossibility.

(5)We thank an anonymous reviewer for pointing this out.

(6)Taking the total differential of both sides of the equation of exchange yields: [DELTA]MV + M [DELTA] V = [DELTA]PQ + P[DELTA]Q. Assuming velocity is a unitary constant and dividing by M = PQ gives Eq. 1.

(7)Of course nothing up to this point in the model has distinguished the N-FAD from the fiat currency. We have simply assumed two currencies in a single economy.

(8)As of the writing of this paper, bitcoin's market capitalization exploded to $110 billion while Ripple's increased to $17 billion and a new currency, Ethereum has overtaken Ripple's place behind bitcoin with a market capitalization of $20 billion.

(9) Although the model assumes velocity is constant, the M2 measure of velocity did not change greatly over the time period and replacing it with the average value in the time frame does not alter the predictions substantially.

(l0) The trade data on Bitcoincharts (2018) is self-reported by the exchanges and so is not guaranteed to contain all currency trades. In particular, it will not include currency trades that occurred between private parties not using exchanges.

(11) Badev and Chen (2015) may provide a better measure of bitcoin used to purchase goods and services as the authors measured how active wallets are a function of the period of time between transactions. One could potentially calculate a direct estimate of the number of times a bitcoin changes wallets for the purpose of a purchase verses the purpose of masking transactions. This would involve assumptions on what type of behavior is likely masking activity.

https://doi.org/10.1007/sl 1294-019-09737-4
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Author:Hunter, Greg W.; Kerr, Craig
Publication:International Advances in Economic Research
Date:May 1, 2019
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