William J. Luther
Date of original submission: 6 February 2014
Date of acceptance: 18 June 2014
We maintain that the crypto-currency bitcoin is a practical application of what is termed “memory” in the monetary economics literature. After reviewing the theoretical literature on money and memory, we offer a brief overview of the bitcoin protocol and argue that, like memory, bitcoin functions as a public record-keeping device. Finally, we provide evidence that—in line with the standard theoretical account of memory—bitcoin use has soared as the expected cost of storing traditional monies increased.
bitcoin; crypto-currency; currency competition; medium of exchange; memory; monetary standard; money; payment system
In four frequently cited articles, Kocherlakota and Wallace (1998) and Kocherlakota (1998a; 1998b; 2002b) consider the similarities and substitutability of money and memory. The authors conclude that, in many cases, money and memory are analytically equivalent. Their results are typically offered as a justification for the widespread acceptance of intrinsically useless monies: if humans lack a perfect record-keeping device (i.e., memory), using money might be socially beneficial. However, one might just as well conclude that technological developments in record keeping or increasing costs associated with money might reduce the beneficial scope of those monies commonly employed in the past.
A new and relatively successful crypto-currency called bitcoin is an example of such a technology. In what follows, we review the theoretical literature on money and memory, provide a brief overview of the bitcoin protocol, and argue that bitcoin might serve as a practical application of the theory. Specifically, we explain that bitcoin functions as a public record-keeping device. As such, it serves as an alternative to historically accepted monies while enabling transactions in much the same way. Consistent with the standard theoretical account of memory, we provide evidence that bitcoin use has soared as the expected cost of storing traditional monies increased.
Money and Memory
The principle finding of the money and memory literature is that both devices are capable of facilitating exchange. Using OLG, turnpike, and random matching models, Kocherlakota (1998a) considers whether money is inessential when agents have access to memory. He defines money as hand-to-hand currency buyers and sellers can use to transact. Memory, on the other hand, is a publicly observable (and instantaneously updated) record of past transactions that buyers and sellers can consult prior to transacting. Kocherlakota confirms that the set of incentive-feasible allocations with money is contained in the set of those with memory. Indeed, if money is divisible, Kocherlakota (2002b) shows it effectively functions by providing an observable record of past transactions—that is, agents can tell whether a potential trader is running a current deficit or surplus with society by looking at the money balances that trader is carrying. Hence, money is memory.
Kocherlakota and Wallace (1998) extend the earlier model by allowing for imperfect memory and non-zero cost money. Imperfect memory is modeled as a record-keeping device that is not updated instantaneously. As a result, agents must take into account the probability that the public record accurately reflects the status of their trading partner. The authors also recognize individuals might incur costs storing or verifying the legitimacy of a hand-to-hand currency. In this modified environment, Kocherlakota and Wallace demonstrate the existence of equilibria where both money and memory are used. Moreover, they show that, when the probability of observing an up-to-date record is sufficiently high, agents will choose not to employ costly money.
The money and memory literature is often cited to explain why money circulates. If money is a primitive form of memory, record-keeping must be sufficiently imperfect to warrant the use of media of exchange (Shi 2006, p. 662). The prevalence of hand-to-hand currencies throughout the world would seem to imply that human subjects lack a perfect record-keeping device. At the same time, however, we observe areas of life where human subjects rely exclusively on record-keeping devices (e.g., banking and payment systems based on credit). As Kahn and Roberds (2009, p. 19) note, “Informational limitations are not set in stone. At a cost, they can be and are overcome. […] If the beneﬁt is high enough the institutions for gathering or recording the information develop.” Hence, one cannot rule out the use of record-keeping devices entirely; and, following Kocherlakota and Wallace (1998), it is useful to consider how the tradeoffs between money and memory might change over time and place.
Bitcoin as a Medium of Exchange
Bitcoin is an open source, peer-to-peer crypto-currency developed by Nakamoto (2008) and launched in 2009. The system relies on public-private key technology and the decentralized clearing of payments to enable quasi-anonymous transactions. To understand how the bitcoin protocol functions, consider a typical payment. Both parties in a transaction have a public and a private key. The payer uses its private key to verify that it is the rightful owner of a balance of bitcoin. The payer identifies the payee by the latter’s public key. Submitting this information via the bitcoin software effectively amounts to requesting that all other peers on the network acknowledge the transaction is valid. Once the transaction is authenticated (discussed below), all other peers are notified that the payee now holds the balance transferred from the payer. To spend these coins, the new owner repeats the process—becoming the payer to a payee identified only by its public key.
The bitcoin system allows transactions to be authenticated without need for a central clearing authority. Transactions are grouped together for processing. Authenticating the block of transactions requires the solution to a complicated cryptography problem. Peers on the network effectively guess until a solution is found. The first peer to complete this “proof-of-work” shares the solution with all of the others by adding the bundle of transactions to the blockchain—a public record of all past transactions. Since all peers can observe the record, ownership is easy to substantiate and an agent cannot spend the same balance more than once.
Completing the “proof-of-work” requires costly computing power. Members of the network are willing to incur this cost to solve the problem (and authenticate the transactions of others) because the system rewards the successful number cruncher with ownership of newly created bitcoin. This decentralized clearing process is often referred to as mining—a reference to commodity monies of the past. An algorithm, which runs every 2,016 blocks, regulates the rate of block creation (and, hence, the rate of new money creation) by altering the digit length of a string of zeros in the proof-of-work. Under the current protocol, a new block is created every ten minutes.
Bitcoin has several clear strengths. As mentioned above, bitcoin allows quasi-anonymous transactions. A user’s key does not contain any personally traceable information in and of itself. If a user takes precautions to never associate their personal identity with their public key, the bitcoin system provides anonymity through obscurity. We say that transactions are “quasi-anonymous” since bitcoins can be transferred without either party revealing their real-world identity in transactions that are neither face-to-face nor require the physical delivery of goods or services. However, users purchasing bitcoin on an exchange must link some piece of self-identifying information such as a credit card or bank account number; cash purchases of bitcoin require physical delivery of the hand-to-hand money; and, in order to take possession of a good or service purchased with bitcoin, one may need to reveal identifying information such as a shipping address or point of pickup.
Another strength of bitcoin is the predictability of its production. Since there is no central authority, and the speed of hashing is regulated, bitcoin is not subject to monetary supply shocks. Indeed, as Selgin (2013) explains, it performs better in this respect than commodity monies: “whereas the discovery of a more efficient way to mine a precious metal results in an increase in the overall rate of metal output, […] with Bitcoin such innovations alter output shares only, and not total coin output, which is exogenously determined.” As such, the supply of bitcoin grows at a steady, predictable pace.
Although the system offers several advantages over traditional fiat currencies, bitcoin is not without weaknesses. Perhaps most notably, it was not designed to accommodate shocks to money demand. Since the supply of bitcoin follows a predetermined trajectory, changes in demand cause its purchasing power to fluctuate. In March 2013, the dollar/bitcoin exchange rate crashed when an update to the system was not simultaneously adopted by all users on the network. On the other hand, those acquiring bitcoin on speculation that they will be able to sell it at a higher price in the future and/or positive developments in the broader bitcoin network (e.g., ATMs, third-party payment processors, etc.) have tended to push its purchasing power up. The price has risen from roughly $13 on January 1, 2013 to a high of $1132 on November 28, 2013.. And, perhaps because speculators became less confident in the future of bitcoin, its price fell. At the end of May 2014, bitcoin was trading at $631. The existence of demand shocks like these makes the purchasing power of bitcoin relatively unstable.
Bitcoin might also suffer from relatively high transaction costs. Recall that, at present, a block of transactions is processed roughly every ten minutes. Such a long processing time might hinder some spot market transactions. Moreover, the problem is exacerbated if multiple bundles are vying to be added to the blockchain simultaneously since, once one block is verified, all others must restart the cryptography problem. Some transactors try to overcome this problem by including a small bounty of bitcoin for the first peer to successfully hash the block containing their transaction. Although these bounties are relatively small and uncommon at present, many believe they will increase in size and frequency as the number of bitcoins created through mining declines. Hence, in the future, the transaction costs of using bitcoin could be substantial.
Bitcoin also suffers from a network effects problem. Few retailers accept bitcoin as a form of payment due to the small user base; and many consumers will not consider using bitcoin until a significant number of retailers accept bitcoin payments. Simply put: network effects favor the status quo. This makes it difficult for bitcoin to get off the ground. As Luther (2013b) shows, bitcoin may fail to gain widespread acceptance even if it were superior to existing monies—that is, even if everyone prefers a situation in which everyone uses bitcoin (and no one prefers one where anyone uses anything else). Although it is difficult to isolate and gauge the magnitude of the network effects problem, there is reason to believe it is non-trivial.
Despite the network effects problem, bitcoin has managed to gain some acceptance. The market for bitcoin is continually evolving and, today, users have an increasing number of ways to acquire and spend bitcoin. Mining, as mentioned above, is one way to obtain bitcoin. Many of the early holders of bitcoin obtained their balances exclusively through mining. However, advances in computer technology have made it nearly impossible for the average user to obtain bitcoin by mining. Completing proof-of-work is so computationally intensive at present that only users with a network of custom-built computers can obtain bitcoin at a point where the market value of the bitcoin mined exceeds the costs of mining. Today, it is far more common for users to acquire bitcoin via an online exchange. Exchanges like BitStamp and OKCoin convert bitcoin to/from many currencies, including USD, EUR, JPY, CAD, GBP, CHF, RUB, AUD, SEK, DKK, HKD, PLN, CNY, SGD, THB, NZD, and NOK. In December 2012, Bitcoin-Central became the first exchange officially licensed (by France) as a payment services provider.
Ongoing efforts aim at making it easier to acquire and use bitcoin. BitcoinATM, Lamassu Bitcoin Ventures, and Robocoin have all developed automatic teller machines where users can exchange cash for bitcoins. Lamassu and Robocoin are in the process of launching their hardware. Lamassu boasts that its machines accept notes from over 200 countries. BitcoinATM, in contrast, is trying to market its software to existing ATMs. Others, including Bitinstant, are preparing to launch debit cards that can be connected to one’s Bitcoin account. Casascius has even developed physical bitcoin, which are linked to digital bitcoin. These metal coins, which are presumably intended to circulate as a hand-to-hand currency, contain a private key needed to access its electronic counterpart. By making bitcoin easier to acquire and spend, these developers hope to tip the balance in favor of the crypto-currency.
An increasing number of Internet middlemen have also made it easier to transact with bitcoin. PizzaForCoins, for example, allows users to place an online pizza delivery order at existing pizza chains using bitcoin as payment. Since the existing pizza chains do not accept bitcoin, PizzaForCoins accepts the crypto-currency on their behalf. It then pays the pizza chain in its preferred currency. Another company, Bitpay, provides similar services for over 4,000 businesses, including Black Lotus and WordPress. These services take on the exchange rate risk and allow retailers to accept bitcoin without having to manage multiple accounts.
Because of the privacy it provides, bitcoin has become especially popular in black market transactions. The Silk Road, a popular online marketplace for drugs and other illicit goods had roughly $22 million in annual sales in 2011. Additionally, many online gambling sites, such as Satoshi dice, use bitcoin as the currency of choice. Bitcoin’s quasi-anonymous nature makes the platform ideal for tax evasion, money laundering, and other currency transfer scenarios where the parties wish to remain anonymous.
Perhaps as a result of the currency’s unique features, the bitcoin network has expanded markedly. Ron and Shamir (2012) estimate there were as many as 2.46 million unique bitcoin users trading in the system in 2012. The market capitalization at that time was just over $100 million. Demand has since increased significantly. In May 2014, the market capitalization exceeded $6,200 million. The extent to which bitcoin will gain widespread acceptance in the future is, of course, unknown; but it is already being employed as a medium of exchange in some markets.
Bitcoin as an Application of Memory
The bitcoin system serves as a functioning application of memory. Peers on the bitcoin network store a complete copy of all past transactions, similar to the public ledger Kocherlakota (1998a) terms memory. Moreover, the bitcoin protocol effectively checks new transactions against this ledger prior to authorization. Unlike the theoretical construct, where past transactions are attributed to a particular agent, the bitcoin system records transactions by account. Given that an agent might possess several accounts and cryptography is used to obscure one’s identity, it is difficult to get a full picture of the past transactions of a particular agent. In other words, the unit of analysis in the bitcoin system differs from that of the theoretical construct. Nonetheless, it is reasonable to describe the bitcoin system as memory.
As in Kocherlakota and Wallace (1998), there is some probability that, at a particular moment, the public ledger will be compete and up-to-date. The bitcoin protocol works to keep that probability high. Since proof-of-work is difficult to repeat, distorting the public record is costly. A malicious user intent on double spending bitcoin would need computational power sufficient to redo all the proof-of-work between the two transactions. The user would then need to hash a new fraudulent block before any other user hashes a legitimate block. While technically possible, such a feat would be very costly to pull off. Adding to this possibility the time it takes to process a transaction and the potential for updating errors discussed above, it seems reasonable to conclude that there is a non-zero (but perhaps small) probability of accessing an incomplete record of transactions.
Having contended that bitcoin resembles an imperfect form of memory, we next consider whether recent experience with bitcoin is consistent with the theoretical literature on memory. In particular, we consider the following three implications:
- Both money and memory might facilitate exchange.
- If memory is imperfect and money is costly to store and/or verify, equilibria exist where both money and memory are employed.
- As the expected cost of storing and/or verifying money increases, memory is more likely to be used.
We discuss each in turn.
It is rather straightforward to show that the bitcoin experience is consistent with the first two implications of the theory. As described above, bitcoin is used to facilitate exchange in a variety of contexts. Cyber security, web domains, and leisure activities—just to name a few items—can be (and have been) acquired with bitcoin. In these contexts, bitcoin works in much the same way as traditional monies. At the same time, it is certainly not the case that bitcoin has replaced traditional monies entirely. Rather, bitcoin is often one of many payment options. In other words, since bitcoin is an imperfect form of memory and traditional monies are costly to store and/or verify, both are employed to facilitate exchange.
Recent experience in Europe provides some evidence that, as the expected cost of storing and/or verifying traditional monies increases, bitcoin is more likely to be used. On March 16, 2013, the European Commission, European Central Bank, and International Monetary Fund offered Cyprus a €10 billion bailout package on condition that Cyprus would issue a one-time levy on all domestic bank accounts. Deposits up to €100,000 would be subject to a 6.7% levy; deposit balances in excess of this threshold would be subject to a 9.9% levy. Although the Cypriot parliament rejected the deal three days later, and the final agreement reached on March 25 required no such levies, the damage had already been done. The terms of the initial offer suggested that, in the event of a severe banking crisis in the eurozone, insured depositors might suffer losses—a state of affairs most had previously thought to be off the table. The result was a shock to expectations: deposit holders across Europe believed their deposits were somewhat less secure. As such, the expected cost of storing traditional monies had increased.
Less than two days after the announcement, Kuittinen (2013) noticed a surge in downloads of bitcoin-related applications to iPhones in Spain. In just one day, he noted, the ranking for “Bitcoin Gold shot up in the Spanish iPhone Finance category from 498 to 72, and another app called Bitcoin Ticker zoomed from 526 to 52.” Both apps monitor exchange rates between bitcoin and other currencies on Mt. Gox. According to Kuittinen, it was no mere coincidence that bitcoin-related apps became more popular while “Spaniards brooded over the Cyprus crisis.” As we demonstrate below, the increase in enthusiasm for bitcoin apps was not limited to the Spanish market.
Table 1. BitCoin Gold download rankings, by country, iPhone finance category, March 9-22, 2013
In table 1, we present iPhone finance category download rankings collected by AppAnnie, an app store analytics company, for the BitCoin Gold app from March 9 to 22, 2013. We include data for Cyprus, Portugal, Ireland, Italy, Greece, and Spain—all believed to have troubled banking systems at the time—as well as France and Germany, which were widely seen as safe. Two non-eurozone countries—the United Kingdom (UK) and United States (US)—are also included for comparison. We calculate average rankings for the seven-day periods before and after the bailout announcement for all ten countries. Then, we subtract the average ranking for the March 16-22 period from the average ranking for the March 9-15 ranking to gauge the seven-day average rank increases for each country.
Figure 1. BitCoin Gold download rankings by country, before and after bailout announcement, March 9-22, 2013
The AppAnnie download ranking data is consistent with the view that, in response to the shock to expectations, bitcoin use increased. In particular, we find that iPhone users in countries suspected of having troubled banking systems were more likely to download BitCoin Gold relative to other apps in the seven-day period immediately following the bailout announcement than in the prior seven-day period. We also find that the increase in download rankings over these periods were typically larger in countries suspected of having troubled banking systems than those occurring in non-troubled eurozone and non-euro countries. Cyprus (+589), Italy (+240), Spain (+236), Ireland (+213), and Portugal (+66) experienced the biggest average increases in Bitcoin Gold download rankings. German (+35) and French (+8) rankings increased only slightly. The US (+48) experienced a small increase on average in its rankings. The average ranking fell in the UK (-26). On average, rankings increased by 224.90 in the six countries suspected of having troubled banking systems over the period, as compared with increases of 21.43 in the non-troubled eurozone countries and 10.50 in the non-eurozone countries. BitCoin Gold download rankings before and after the initial bailout announcement are depicted for each country in figure 1.
The available exchange rate data is also consistent with the view that demand for bitcoin increased significantly following the initial bailout announcement. From January 1 to March 15, 2013, the dollar price of bitcoin increased at an average annualized rate of 630.50 percent. From March 16 to April 8, 2013, the dollar price of bitcoin increased at an astounding rate of 2,195.76 percent. Its price has since fallen back down a bit. Even still, from March 16 to June 5, 2013, the dollar price of bitcoin increased at an average annualized rate of 996.62 percent—much higher than that observed before the initial bailout announcement. The daily bitcoin closing price on the Mt. Gox exchange, in US dollars, from January 1 to June 5, 2013 is presented in figure 2.
Figure 2. Daily bitcoin closing price, Mt. Gox (USD), January 1 – June 5, 2013
Finally, that the US government has devoted considerable attention to bitcoin in recent months serves as supporting evidence that its use is on the rise. On March 18, 2013, the Financial Crimes Enforcement Network (FinCEN), a bureau of the Treasury tasked with enforcing the Bank Secrecy Act, issued guidance on regulations pertaining to those administering, exchanging, or using virtual currencies. “A user of virtual currency is not [a money services business (MSB)] under FinCEN’s regulations and therefore is not subject to MSB registration, reporting, and recordkeeping regulations,” FinCEN (2013) affirmed. “However, an administrator or exchanger is an MSB under FinCEN’s regulations, specifically, a money transmitter, unless a limitation to or exemption from the definition applies to the person.” In other words, bitcoin exchanges like Mt. Gox were required to register and comply with FinCEN’s regulations.
Mt. Gox did not register as a money services business with FinCEN. On May 14, 2013, the Department of Homeland Security and U.S. District Court for the District of Maryland served Dwolla, a mobile payment service used to transfer funds to/from Mt. Gox, with a seizure warrant for funds associated with Mt. Gox’s Dwolla account. Complying with the court order, Dwolla immediately ceased processing payments to/from the account and transferred Mt. Gox’s balance to the government. According to the affidavit submitted in support of the seizure warrant, the accounts were seized because Mt. Gox was not registered as an MSB with FinCEN.
Bitcoin resembles an imperfect form of memory. It functions by providing transactors with a public record of past transactions. Moreover, recent experience with bitcoin is consistent with the theoretical literature on memory. Bitcoin facilitates exchange alongside traditional monies; and, as the expected cost of storing money increased in the eurozone, some transactors seem to have turned to bitcoin. This claim has been supported by the greater download rankings of bitcoin-related apps in the affected countries, an increase in the growth trajectory of the dollar-bitcoin exchange rate, and increased attention from US regulators following the shock. As such, we conclude that bitcoin is memory.
Previous studies have tended to treat memory as a theoretically useful concept necessary to justify the use of traditional monies. In contrast, we show that theories of memory have practical applications. Specifically, we explain that the crypto-currency bitcoin is an example of such a technology. The bitcoin protocol functions by providing a public record of past transactions. As such, it is capable of facilitating exchange in much the same way as traditional hand-to-hand currencies. Moreover, since bitcoin is an imperfect form of memory and traditional monies are costly to store and/or verify, it is possible for the two types of exchange medias to coexist.
Perhaps most importantly, we have provided evidence that—in line with the standard theoretical account of memory—bitcoin use soared as the expected cost of storing and/or verifying traditional monies increased. Following the initial announcement of the Cyprus bailout—and the realization that insured deposit accounts in the Eurozone were not as secure as previously thought—there was a surge in downloads for popular bitcoin apps and a significant increase in the growth trajectory of the dollar price of bitcoin. US government oversight of bitcoin also seems to have intensified over this period.
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* The authors wish to thank the Institute for Human Studies at George Mason University for generously supporting this research.
 See also: Araujo and Camargo (2008, 2010).
 See, for example, Kocherlakota (2002a).
 Indeed, the former is the motivation offered by Kocherlakota and Wallace (1998, p. 272), who note that “Technological developments, especially during the past two or three decades, have greatly enhanced our ability to keep up-to-date records.”
 Corbae et al. (2002) consider money and memory in an endogenous, or directed, matching model.
 The block-chain currently includes all past transactions, but the software retains the ability to shorten the chain if necessary (Nakamoto 2008). The record of all current bitcoin owner’s public keys, however, will never be dropped from the chain (Babaioff et al. 2012).
 Adding a zero exponentially increases the difficulty of finding a solution (Nakamoto 2008).
 Grinberg (2012) offers an alternative view, describing bitcoin’s five-member development team as a “de facto central bank.” See also: Selgin (2013).
 Luther and Young (2014) consider the significance and magnitude of various demand shocks to the value of bitcoin.
 The March 12, 2013 software update was particularly problematic in that, during the mix up, some funds were double spent. An initial response saw bitcoin’s value fall by 22 percent in an hour. It rebounded promptly.
 On December 3, 2013, it would hit $1132 again.
 Luther and White (2014) consider whether bitcoin’s unstable purchasing power precludes it from becoming a major currency.
 Nair and Cachanosky (2014) discuss entrepreneurial efforts to break the network effect.
 Of course, it also gives bitcoin a first-mover advantage over alternative cryptocurrencies. If some cryptocurrency is to succeed, bitcoin would seem to be the most likely in that it has the largest network. On the likelihood that bitcoin will succeed, see Luther and Gochenour (2014).
 The difficulty stems from the usual entanglement of network effects and legal restrictions (Luther 2013a). However, Luther and White (2011) present a case where agents continue using a relatively poor money in the absence of legal restrictions, suggesting that the network effects problem is significant.
 The average user, operating on a much smaller scale than specialized miners, will be able to earn similar expected returns (though, at a much higher variance) as mining hardware becomes commoditized. Profit-sharing arrangements could be employed to lower the effective variance.
 A majority of the bitcoin exchanges work on a bid-ask model.
 As an anonymous referee points out, Bitcoin-Central accomplished this by partnering with an existing provider already in possession of the appropriate license; the partner deals with the regulatory and banking aspects of operations.
 The private key is protected by a tamper-evident hologram to prevent one from spending the digital coin before passing off the physical coin.
 The Silk Road operates on TOR. TOR is an online virtual private network (VPN) service that relays messages through its encrypted network to better protect users’ identity and location data.
 The fraudulent block serves to verify the second transaction as legitimate, even though the malicious user had already spent the balance in an earlier transaction. If another user hashes a legitimate block before the malicious user can redo the proof-of-work and pass the fraudulent block, the malicious user will have to start over in order to include the new legitimate block in the proof-of-work. The more legitimate blocks hashed between the two transactions, the more difficult altering the block chain to double spend the balance becomes.
 Indeed, the malicious user would almost certainly earn a higher rate of return employing this computational power as an honest user.
 As an anonymous referee points out, evidence supporting these three implications does not constitute proof that bitcoin is memory since such evidence would also be consistent with alternative hypotheses. To be clear: we do not interpret any evidence that follows as proof of the hypothesis that bitcoin is memory. Rather, we have argued that the characteristics of bitcoin warrant its classification as an imperfect form of memory and, in what follows, merely consider whether the experience of bitcoin is consistent with the implications from the theoretical literature on memory.
 Bitcoin Ticker also monitors BtcE, Bitstamp, Btc24, Bitcurex, VirtEx, and BTC China exchanges.
 Note that an increased ranking implies that the rank number is lower (i.e., a rank of 1 is greater than a rank of 100).
 The seizure warrant did not name Mt. Gox, but rather Mutum Sigillum LLC, a Deleware-based Mt. Gox subsidiary. The connection to Mt. Gox was referenced explicitly in the affidavit submitted by Homeland Security Investigations Special Agent Michael McFarland in support of the seizure warrant.