6. Can We Stabilize the Price of a Cryptocurrency? Understanding the Design of Bitcoin and Its Potential to Compete with Central Bank Money

Bitcoin (Nakamoto, 2008) is an electronic cash system designed to work without central management. Despite recent enthusiasm, Bitcoin (BTC) and other so-called cryptocurrencies are not ideal as means for payment, because of instability of their market prices against major currencies. This chapter explores the problem of such instability from the viewpoint of economics and proposes a new monetary policy for stabilizing the values of these cryptocurrencies. First, we begin by describing the institutional details of Bitcoin.

Circulation of Bitcoin¹ as a digital asset is guaranteed by an authentication process between traders. This process consists both of an asymmetric key cryptosystem and by competition between coin-releasing “miners” who validate transactions to prevent double spends by traders. It is important to recognize that it is operationally feasible for traders to authorize transactions by means of a digital signature, based on an asymmetric key cryptosystem. It is by far more difficult to validate transactions of Bitcoin, or other digital assets, whilst preventing double spending of assets. For paper money and checks, anti-counterfeit technology, such as holograms and signatures, prevents forgery. But the state of digital assets never deteriorates and it is not a simple task to identify a genuine transaction from a forged one.

Many electronic securities and electronic money systems employ either a centralized (a node with hub function) trading system or an IC card system with a secret key that prevents such doubled spending. The former system requires a centralized administration with a reasonable governance structure. The latter system requires an IC card operation. These systems may transfer incidents of regulation and other institutional risks to the owners of digital assets.

In Bitcoin the validation of transactions (preventing double spending) is made possible by sharing the virtual registry book that contains all information on transactions and ownership of Bitcoin. The virtual registry book is always open to every participant, so any double spend is easily identified. Bitcoin gives the impression that it is a set of independent gold-like coinage assets with its co-option of “mining” and “coin” phrases. But Bitcoin more closely resembles a real estate register or record in which the new owner of each lot of real estate is recorded whenever a new transaction takes place. This virtual real estate register record contains 21 million lots (i.e., 21 million BTCs) before sub-dividing.² To issue Bitcoin is to attach an ID number to each BTC lot, and a settlement of BTC is to replace the ID number by a new number.³

As of October 2018, a total of 17.31 million BTCs had been issued in the market with ID numbers (about 82% of 21 million BTCs). As of 2018, roughly every ten minutes on average, 12.5 BTCs were being issued with new IDs. This procedure of new issue is implemented as a reward for the first person/group to validate transactions without double spends that have been collected in a block. This is a competition of validation via computation, with the aim of solving a specific mathematical problem.⁴ This computation is described as mining, and those who conduct mining are miners. The speed of new issue of Bitcoin on the register record is set to be halved every four years. At the beginning of the Bitcoin system in January 2009, the reward was 50 BTCs per ten minutes; it was halved to 25 BTCs per ten minutes on November 28, 2012. It remained the same reward per ten minutes until it was halved to 12.5 BTCs per ten minutes on July 9, 2016,⁵ and this halving process will continue until 2140, when the new issue of BTC will be terminated. Total circulation of BTC will be fixed at a little less than 21 million BTCs.

There are differences between a real estate registry system and the Bitcoin system. In Japan, for instance, the real estate register record is kept exclusively by the Legal Affairs Bureau and the public is only allowed to read the record. In contrast, the virtual registry book that contains all information on Bitcoin transactions and ownership is maintained individually among participants. This decentralized nature of virtual registry bookkeeping activity may create some inconsistencies among participants. In the Bitcoin protocol, when an identical Bitcoin segment is used twice for different payments—leading to a Bitcoin segment having two branches (double spends)—the majority decision rule is used to determine which payment is genuine. To be more precise, the Bitcoin protocol authenticates a genuine Bitcoin registry book in which a chain of blocks or blockchain, after branching, extends the longest.⁶ The advantage of majority decision rule is to solve a deadlock situation in which two parties disagree with each other. However, as Eyal and Sirer (2013) argue, the majority decision is not enough to protect against collective selfish mining that commands more than one-third of the whole resources,⁷ given the delayed finality confirmation structure we describe in the next section.

The bookkeeping method of ownership transaction is not restricted to a type of real estate registry system in which the ownership of each segment is recorded. Deposit account data in a banking system keep transaction and balance records for individuals; in Bitcoin phrasing, this is equivalent to the number of segments the deposit account holder has previously used and can currently use. The advantage of this method is that it allows the management of the large number of segments with a relatively small number of accounts.⁸ The reason the Bitcoin protocol employs the real estate-like registry system, rather than the bank deposit-like account system, is probably because Nakamoto and his collaborators think that it is suitable for decentralized processing.

The Bitcoin protocol uses a hash value⁹ of a beneficiary’s public key as its ID number. A hash value is a sort of digest of original data, which is obtained after a designated calculation process by some specific algorithm (we will come back to this later). By using a hash value as an ID number, together with a public key itself, the Bitcoin protocol is able to maintain anonymity with as well as trustworthiness of trade.

The essence of the Bitcoin protocol is its structure that guarantees the uniqueness of the segment information “registry book”. This confirmation process broadly corresponds to one provided by the centralized payment system in the case of traditional banking. The Bitcoin protocol validates all transactions by means of open competition among profit-seeking miners as described above. This whole process is referred to as confirmation in the Bitcoin protocol.

The winner of the open competition provides the hash value as a stamp on the registry book, marking a validation of the trades in the specific block. At the same time, this winner receives newly created Bitcoin, and is recorded as the owner of such in the registry book. This process is called mining. In this chapter we distinguish the confirmation process in which all mining activities are involved from the validation process in which the winner of competition provides the hash value as a stamp on the registry book.

Miners play an important role in the validation of Bitcoin transactions which guarantees the uniqueness of the registry book. We call them miners because they are not a trusted third party that is assigned to prevent double spend events, but are voluntary participants seeking a reward from the open competition of validation. Only the winner receives Bitcoins in reward; all other miners receive nothing and must pay their mining costs. This is perhaps a cruel system from the viewpoint of miners.

This competition of validation is open every ten minutes on average. Trades collected by a miner before such ten-minute intervals form a block. After the validation, a new block is added to the existing blocks—a process called extending a blockchain. Newly created Bitcoins received as a reward for validation can be used for payment after a reasonably long blockchain is extended (i.e., long enough to prevent disputes over double spends).¹⁰ The Bitcoin protocol employs a delayed finality confirmation structure in which Bitcoins cannot be used immediately after a transaction from the other party, even after validation of a transaction is made. This structure is quite different from the centralized payment system employed by the banking sector.

The Bitcoin protocol sets a variable difficulty of computation factor, to be solved by the miners in approximately ten minutes. When the miners’ computation speed becomes faster (i.e., less than ten minutes on average), a parameter that determines a difficulty of computation is reset to make the block interval approximately ten minutes.¹¹

This delayed finality confirmation structure is regarded as a weakness of the Bitcoin system from alternative cryptocurrency creators’ points of view. However, there certainly exists a trade-off between approaching real-time finality and increasing risk in alterations of validated transactions.

Let us clarify the validation process in the Bitcoin protocol. This is a block extension process after confirming all past transactions:

In the Bitcoin protocol, h₀ and q are exogenously given (these figures depend on the past history of trades), and miners have to search r to satisfy the condition h₁≦t (target). This exercise is called the proof of work. The concept of proof of work comes from Dwork and Naor (1992) and Back (2002). They provide a computational technique for combatting junk mail and controlling access to a shared resource. Their main contribution is requiring a user to compute a moderately hard, but not intractable, function in order to gain access to the resource, thus preventing frivolous use. In the Bitcoin system, this concept is used to give confirmation of the transactions via the mining competition. In exchange the winner of the competition receives a reward. This incentive mechanism is the most innovative part of the Bitcoin system, and it works well.

Let us clarify the meaning of the problem the Bitcoin protocol imposes on the miners. The problem is “to search x to satisfy the condition h₁ ≦t (target in 256 bits) where the hash value h₁ is generated from (h₀, q, x). Put solution x as r.” If we do not impose any restriction on r (that is, t = 2²⁵⁶ − 1), any number would satisfy the problem. If we set t to be small, a probability of finding r in the hash function would drop sharply.¹² If the difficulty (as measured by parameter n) of this problem goes beyond a certain point, any standard personal computer cannot find a solution within a certain period of time (ten minutes in this case).

This implementation differs from the original design by Nakamoto (2008). The original design states that “to search a hash value h₁obtained form (h₀, q, x) whose first n bit is zero. Put solution x as r.” In this design, a difficulty parameter n for the proof of work can be adjusted but allows only for a discrete change. The current design is superior and encompasses the original design.¹³

However, the original design by Nakamoto is intuitive. Note, in this chapter, we use t and n interchangeably since t = 2²⁵⁶⁻ⁿ− 1. Then,

By adjusting the difficulty parameter n, together with exogenous technological change and miner entry and exit, the speed of a block formation can be controlled. Parameters t or n enable the speed of block formation to stay more or less constant at ten minutes on average.

As is clear from the above discussion, a choice of parameter t or n in the proof of work depends on computational power, technological change, and the numbers of miners.¹⁴ The impact of technological change is intuitive: if the computational power doubles, the difficulty of the problem must double: n must shift to n + 1. The impact of the number of miners is basically similar, but more important in practice as it is more likely the number of miners will double than would computational power.

Let us further elaborate upon the issues related to the proof of work. The essence of this issue is that we assume a miner’s probability of finding a solution to some arbitrarily large number of calculations is independent even if there are reasonable numbers of miners. Let us assume the rare event of a miner’s finding some r that satisfies the required conditions within a ten-minute interval is set to probability λ (provided all miners have the same computational power), and M miners participate in the mining competition, the probability of no miner finding r within an interval is given as (1 − λ)^M, the probability of a miner’s finding r within an interval is 1 − (1 − λ)^M. We also assume that a probability of such a rare independent event follows the Poisson distribution. Then an average waiting timeθfor such a rare event is an inverse of the probability of the event, thus \(\frac{1}{\uptheta }\) is defined as 1−(1 − λ)^M. Approximating \(\frac{1}{\uptheta }\) by the first-order Taylor expansion at λ = 0 leads to \(\frac{1}{\uptheta }\approx M\uplambda \), or

Miners try to find some number less than or equal to \({2}^{256-n}\) among \({2}^{256}\) possibilities. Consequently, the winning probabilityλis proportional to \(\frac{{2}^{256-n}}{{2}^{256}}\) at the coefficient of computational power \(K\).

Substituting Eq. (6.2) into Eq. (6.1), we obtain

The average time of a block validation (the average waiting time for the miner to find r) is determined as follows:

These observations hint at the nature of proof of work as the core concept of the Bitcoin system. As shown above, difficulty parameter n has nothing to do with the quality of validation of a block. That is why n can be raised and reduced flexibly without affecting a validation process. That is, the proof of work is not an issue in maintaining the quality of Bitcoin, but is the cost to maintain a steady speed of new issues of Bitcoin (at the moment, it is 12.5 BTCs per approximately ten minutes). In order to evaluate the nature of proof of work, this role must be examined. If the role is properly carried out, it would be considered reasonable. Otherwise it would not be the proof of work, but it would be the proof of waste, because it would be a mechanism to provide rewards for the mining competition with excessively large computational cost.

It is essential for the Bitcoin system to provide an incentive for those who contribute to the maintenance of the system. In case of standard electronic money, an issuer of electronic money receives participation fees directly from the retail shops; they are paid not by the electronic money they issue, but by central bank notes. Central banks themselves pay maintenance costs and receive service rewards in the money they issue.

In the case of Bitcoin, the miner who contributes to the maintenance of the system receives Bitcoins as their reward, so it resembles the central bank system. A difference between the Bitcoin system and the central bank system lies in the fact that the former gives a reward to a miner who happens to win the mining competition while the latter receives a reward constantly. If there is a single miner in the Bitcoin system, r can be any arbitrary 256 bit value (n can be zero). In such a case, the competition mechanism that guarantees a validity of proof of work does not work and we require some alternative. If an alternative works, it could be sufficient to prevent double spends. This situation can be described as the mint model of cryptocurrency.

The mint model differs from the Bitcoin model in the sense that the former model uses a finality confirmation structure with legal enforcement, while the latter model uses a finality confirmation structure via mining competition. Note again that the winner of the competition is the only competitor to be rewarded with Bitcoin. The probability of winning a reward must be based on the proportional computational power of an individual miner to the total computational power of all mining participants: all miners may expect to receive rewards proportional to their computational power after a reasonable number of mining competitions.¹⁵

Then we must ask ourselves, can the proof of work contribute to the stability of Bitcoin value? Nakamoto (2008) states that “once a predetermined number of coins have entered circulation, the incentive can transition entirely to transaction fees and be completely inflation-free”(p. 4).

The answer is no. As Fig. 6.2 amply illustrates, the values of Bitcoin as measured in U.S. dollars fluctuate wildly compared with those of other foreign currencies. The reason for this high volatility is apparent. Demand for Bitcoin, regardless of the motivation for holding (i.e., payment or speculation), increases as its price decreases and vice versa. As Fig. 6.3 shows, the demand curve of Bitcoin, therefore, would be downward sloping¹⁶ while supply the curve of Bitcoin at any point of time would be vertical. All demand shocks (such as E^* or E^**) must be absorbed in price adjustments (such as P^* or P^**).

A line graph with increasing and decreasing curves represent the average of U S D market prices across major bitcoin exchanges. The peak is over 19000 U S D in December 2017.

A decreasing line graph between value versus quantity of supply and demand of bitcoin. At any point in time, the curve would be vertical while supply.

We note Bitcoin pricing differs from the pricing mechanism under the gold standard in two aspects. First, the supply of gold as natural resource must be adjusted to the marginal cost (i.e., the miner would set its production so as to make the market value of gold equal to the marginal cost of gold mining). Secondly, gold can be used for industrial and jewelry purposes as well as for money. If the price of gold coins goes up, the gold used for industrial and jewelry would be converted to gold coins and vice versa.

Gold coins should consequently be expected to manifest an upward sloping supply curve. In this case, as shown in Fig. 6.4, demand shocks can be absorbed in both prices and quantities. Compared with that of Bitcoin, the price of gold coins would be consequently less volatile due to this supply elasticity.¹⁷ The price volatility of Bitcoin may reflect a rather naïve understanding by the designers of the Bitcoin system that the monetary value of Bitcoin would be stabilized with a fixed money supply rule.

A decreasing curved line demand curve and an upward sloping supply curve between value and quantity of gold coins.

Let us consider the miner’s behavior from a broad cost/benefit analytic perspective. Miners voluntarily participate in the mining competition and invest in their computational power, and would exit if mining costs exceed its benefits. In principle, this situation of entry and exit is common to all industries. The only difference from standard industries is that supply of Bitcoin is independent from miners’ entry and exit.

To elaborate upon this point, we divide the miners’ computational power into M units. M varies according to miners’ entry and exit. But the reward for the winner of mining competition is fixed as about Z per hour (at the moment, 12.5 BTC per ten minutes, Z would be about 75) regardless of entry and exit of miners.¹⁸ Assuming that the Bitcoin protocol sets n properly, Z would be fixed for a length of an hour. This fact is reflected in the vertical supply curve of Fig. 6.3.

As we make two assumptions, (1) the winning probability is proportional to the computational power, and (2) the power is evenly distributed among M miners, the expected reward/benefit per unit per hour is Z/M. If the market value of Bitcoin is given as P, the market value of expected reward is PZ/M. We argue that this equals the marginal cost of mining (mc) at equilibrium.

If the mining cost is lower than PZ/M, then the miners obtain net benefit/return, and vice versa. Let us reflect on these aspects in the past one year or so.

From the above observations, it is clear that the Bitcoin system intrinsically manifests dual instability. The first instability stems from an inflexible supply curve of Bitcoin, which amplifies Bitcoin price volatility; the miners’ revenue/reward fully absorbs any price changes. There is no price stabilization mechanism. The second instability comes from risks to the sustainability of mining. During a Bitcoin price boom, miners engage in mining activity which guarantees the supply of Bitcoin. But during a Bitcoin price depression, no smooth way to induce exits from mining exists.²⁴ The current situation of the Bitcoin system can be interpreted as a freezing equilibrium with dual instability. See Fig. 6.5 as share of mining pool as of October 7, 2018.

A pie chart represents the share of mining pool, where B T C dot com has the highest at 16.6 %, bit coin Russia and C K Pool have the lowest at 0.2 %.

Cryptocurrencies like Bitcoin do not depend on a central bank. With some amendments to its design, we can use this cryptocurrency (we call this currency, an extension to Bitcoin, Improved Bitcoin, or IBC) to implement some equivalent policy effects as a central bank conducting monetary policy. It is indeed monetary policy without the central bank. To do so, we need to conquer the dual instability issues discussed in Sect. 6.4.

Why did Bitcoin not exist until recently? Decentralized money provision, and similar economic systems with peer-to-peer (P2P) technology, were proposed well before Bitcoin, but these trials failed to grow like Bitcoin. Perhaps early challengers may have taken the nature of money and autonomy of economic activity too seriously.

The major drivers behind Bitcoin’s success are (1) a naïve understanding of currency, (2) the employment of an easy-to-understand asymmetric key cryptosystem for validation of transactions and a virtual register system, and (3) the creation of a participatory system with a P2P network maintained by the elliptic curve digital signature algorithm and a hash function. This framework has attracted many programmers and collaborators to improve user software and that, in turn, attract many users of Bitcoin.

In addition, the originator of Bitcoin–Satoshi Nakamoto—and his collaborators demonstrated they can create a currency without a central bank via proof of work, and that there exists a demand for such a currency.

A unexpected feature of Bitcoin is that, contrary to the original belief of Satoshi Nakamoto et al. that they can create currency without inflation by means of controlling and preannouncing a total supply of Bitcoin, the market value/price of Bitcoin fluctuates up (deflation or the value of Bitcoin goes up) and down (inflation or the value of Bitcoin goes down). We hope that Nakamoto’s important contributions can nullify their misunderstandings. We are grateful to him for the imperfect Bitcoin innovation. There remains much room for improvement and for discussion of our future monetary system.