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Bitcoin and its mining on the equilibrium path


Bitcoin as a major cryptocurrency has come up as a shooting star of the 2017 and 2018 headlines. After exploding its price twenty times just in the twelve months of 2017, the tone has changed dramatically in 2018 after major price corrections and increasing concerns about its mining power consumption and overall sustainability. The dynamics and interaction between Bitcoin price and its mining costs have become of major interest. Here we show that these two quantities are tightly interconnected and they tend to a common long-term equilibrium. Mining costs adjust to the cryptocurrency price with the adjustment time of several months up to a year. Current developments suggest that we have arrived at a new era of Bitcoin mining where marginal (electricity) costs and mining efficiency play the prime role. Presented results open new avenues towards interpreting past and predicting future developments of the Bitcoin mining framework and their main possible directions are outlined and discussed here as well.

1. Introduction

Bitcoin (Nakamoto, 2008) emerged in the aftermath of the global financial crisis in 2008 as a decentralized alternative to standard (fiat) currency systems, which are under scrutiny of central banks. The decentralization stems from the blockchain technology as a public ledger where all verified transactions are being recorded. The verification itself is not conducted by any central authority but by a large network of nodes that undertake and solve complex mathematical problems (hashes). This cryptographical element has given the name to the whole family of cryptocurrencies. As a reward for the verification, a pre-specified number of bitcoins is emitted forming an algorithmically given monetary supply (or growth). In parallel to fiat money being historically backed up by gold, which needs to be physically mined, the process of Bitcoin creation is also referred to as mining as work of the network is needed to verify the transactions and be rewarded as a miner. As all the transactions are being recorded, the system boasts transparency, even though the actual addresses of sending and receiving parties are represented by alphanumerical chains that cannot be directly linked to a specific geographic location or a person. In addition, creating a new address (wallet) is trivial and free so that hypothetically, a new one can be created for every single transaction.

Such anonymity had formed the topics of the early Bitcoin (and cryptocurrency in general) studies that dealt primarily with safety and legal issues (Barber et al., 2012Reid and Harrigan, 2013Velde, 2013). And even though the legality of its early adoption and utility can be and has been questioned repeatedly (Jacobs, 2011Barratt, 2012), it started to be traded first over the counter and then at specialized Bitcoin exchanges. As the economic saying goes, when supply meets demand on a market, there is a price and an asset. Combining the decentralization, anonymity, little or no regulation, and thus also extreme risk, the Bitcoin price dynamics has never been close to stable. Research on drivers of the price fluctuations logically followed (Ciaian et al., 2016Garcia et al., 2014Kondor et al., 2014Kristoufek, 2013Kristoufek, 2015) and showed that even though Bitcoin price is strongly driven by speculations, there are fundamental components in the price formation process. These results have been further validated by newer studies (Bouri et al., 2017Baur and Hong, 2018Phillips and Gorse, 2018Mai et al., 2018Ciaian and Rajcaniova, 2018).

And even though public awareness of and interest in Bitcoin and crypto-world in general have been tightly connected to its bubble and bust cyclical dynamics, the year of 2017 and mainly its second half experienced a literal crypto-craze, when not only Bitcoin increased its price twenty-fold in a year but also other cryptocurrencies (altcoins) and tokens (derived from smart contract wielding cryptocurrencies such as majorly Ethereum) went through massive gains (Ethereum price grew more than 100 times, Ripple almost 400 times, and Litecoin almost 70 times to name a few). Late 2017 saw an influx of speculative capital and the FOMO (“fear of missing out”) effect was tangible across groups of eventual investors that perhaps had never heard about cryptocurrencies just few months back.

This was the most evident manifestation of the herding behavior but in the background, also the mining community was expanding. Gamers might never forget Winter Holidays of 2017 when the graphical cards were either out of stock completely or available with large markups due to Bitcoin and Ethereum miners expanding their mining rigs or just getting into the mining business as miners’ daily revenues shot up from around $2 M at the beginning of 2017 to the high of $53 M in December 2017. As a result, the competition in the crypto-mining industry became fiercer, more computational power was needed to be rewarded the same amount of bitcoins as before, and the overall power demand of the mining network was increasing rapidly. The increase had been so immense that the power consumption of the cryptocurrency mining network and general understanding of its dynamics has come into the spotlight not only in the public and the crypto-community but also for the researchers. Technical aspects and tendency towards oligopoly in the mining systems are covered by Arnosti and Weinberg (2018) who show, using a simple model, that asymmetric costs and economies of scale lead to concentration of the mining power (that we in fact observe in the real market). Ma et al. (2018) go further, identifying the mining protocol as an extension of standard research and development racing models, and suggest market regulation is needed for community benefiting from the blockchain operations. Moving from the research in the field of industrial organization and market structure, the comparison of Bitcoin and traditional assets that are being mined is presented by Krause and Tolaymat, 2018Cocco et al., 2019Krause and Tolaymat (2018) indicate that crypto-mining consumes more energy than mining of copper, gold, platinum and rare earth oxides to produce an equivalent market dollar value. However, Cocco et al. (2019) emphasize that crypto-assets have a much smaller social and economic impact than traditional financial systems (covering gold as the traditional mined asset) and they allow facing modern environmental challenges better than gold. This leads us to the topic of environmental impacts of Bitcoin (and cryptocurrency in general) mining. Thum (2018) boldly states that Bitcoin mining is a waste of resources. In a more detailed treatment, Mora et al. (2018) suggest that Bitcoin mining could contribute to global warming and by itself increase temperatures by two degrees centigrade within less than three decades. And Li et al. (2019) provide an experimental study on nine cryptocurrencies and their mining impacts. With a special focus on Monero, they summarize that the discussion of energy consumption and sustainable development should be studied in more detail.

Following the presented discussion, we focus on the relationship that is basal and essential for the whole mining discussion and its possible further extensions into environmental issues and sustainability. Most of the studies listed above state that the energy consumption of Bitcoin mining is large. However, the discussion of drivers and dynamics of this consumption is mostly missing. Even though Mora et al. (2018) go into detail and predict energy consumption several decades into future, their model is mostly built on assuming that the hashpower (and thus energy consumption) will follow the explosive dynamics of late 2017 and beginning of 2018. The coming months of 2018 and year 2019 have shown that the exponential dynamics is not sustainable and the market has cooled down, even though the new levels stabilized much higher than before the rally. Our study builds on ideas and results of our previous research showing that the Bitcoin system behaves closely to the standard market where the market forces are at work (Kristoufek, 2015Kristoufek, 2019). These results go against the popular belief that the crypto-markets are irrational and chaotic. In the same vein, we are interested in an equilibrium relationship between Bitcoin price and its mining costs. We are also interested in examining the directionality of this behavior both in the short-term and in the long-term to see whether the mining costs are driven (in addition to the technical factors such as electricity price, mining efficiency, and mining network power consumption) by Bitcoin price forming a hysteresis-like dynamics when a (possibly bubble/speculation induced) price increases are being caught up by increasing mining costs which then form a new support level for potential future price increases and/or whether the increasing mining costs are driving price up as well which would suggest a long-term explosive dynamics of the price. To answer and examine these questions, we utilize the standardly used combination of cointegration and (vector) error-correction models (Engle and Granger, 1987Phillips, 1991Hendry and Juselius, 2001Juselius, 2006), specifically the maximum likelihood estimation that has been shown superior to other alternatives (Gonzalo, 1994). Power of such models has been repeatedly shown in various fields of economics and finance, specifically their ability to identify long-run equilibrium dynamics between series as well as further description of their short-term interactions (Corbae and Ouliaris, 1988Yu and Jin, 1992Chaudhuri and Daniel, 1998Mark and Sul, 2003Ziao et al., 2008Bernstein and Medlener, 2015Aye et al., 2016).

In the following section, details on the dataset construction are given as it forms an essential part of the whole problem solution. The next section describes the methodological framework, specifically the cointegration and vector error-correction model, and the model selection procedure. The Results section is split into three parts. First, the estimated mining costs and profitability are presented. Second, the equilibrium relationship between mining costs and Bitcoin price is established. And third, interactions within the error-correction model are discussed together with the short-term and long-term causality. We conclude with a general discussion of the Bitcoin mining market and its possible future developments.

2. Data sources and dataset construction

There are two variables of interest relationship of which is being quantified in this study – Bitcoin price and costs of mining/creating a single bitcoin. The former one is rather simple to obtain as there are various Bitcoin (and cryptocurrency in general) exchanges that provide needed data to analyze. As the price might differ (but not considerably) across exchanges, we utilize the Bitcoin Price Index, which is based on an average price across the most liquid exchanges. The details and downloadable series can be found on https://www.coindesk.com/price. As for the latter, the situation is a bit more complicated. The necessary steps are described in the following sections1.

2.1. Marginal/operational costs specification

Bitcoins are mined as a reward for transactions verification to miners who contribute their computational power to the network. The awarded bitcoins are distributed among the miners practically proportionally2 with respect to the computation power they have delivered to the system. The production cost of a single bitcoin can be thus quantified as costs towards its mining. There are two major costs – purchasing costs of a miner and electricity costs spent on the mining itself. From the standard economics perspective, the former can be seen as a fixed cost and the latter can be seen as a marginal cost. The troubling part of the miners purchasing costs is data availability. Even though prices can be found for the specific miners (e.g. https://shop.bitmain.com), there are at least three issues. First, the presented prices are not final as they do not include tariffs, taxes and similar additional costs. Second, the presented prices do not include the costs of power cords, SD cards, and other necessary hardware costs. And third, the prices change in time. The prices of the same miner at the top of the late 2017 bull run were as high as ten times the prices now and it is not possible to keep track of these changes, more so connected with the previous two points. Rumor has it (crypto-community speculates) that producers of the miners set the prices so that the initial costs are amortized in 10 months3. As we do not want to include such speculations into our analysis, as it would be an important parameter in calculating the costs and it could influence the outcomes strongly, we take a standard economics/finance approach and consider only marginal/operational costs into the price formation dynamics. The purchasing costs are then assumed to be a fixed percentage markup to the marginal costs included in the intercept of the final log-log cointegration model.

2.2. Network power consumption

The operational mining costs are not directly available. However, they can be inferred from available data and knowledge of the mining procedures. Mining rewards are given for verification of each block of transactions and the number of bitcoins rewarded is known. The current reward is 12.5 BTC and it halves every 210000 blocks. Block time is approximately 10 minutes. This makes a halving period of around 4 years. Power consumption of the network is represented as a number of hashes per second, i.e. the hashrate of the network. Each mining hardware, apart from its own hashrate (power), has a given power consumption, which put together form a miner efficiency measured in joules per hash. Combining these, we are able to get the amount of joules (kilowatt-hours) spent on creation of a single bitcoin. Putting this together with the price of a kilowatt hour, we arrive at the final operational mining costs. Out of these, all variables are available for the Bitcoin network on https://blockchain.info but two – electricity price and miners’ efficiency.

2.3. Electricity price

We take an average electricity price over countries that are considered to be the main players in the mining industry and they have available and variable electricity prices4 – Canada, Estonia, Georgia, Sweden, and the USA. Electricity price series are available at respective agencies and providers – Independent Electricity System Operator (IESO, http://www.ieso.ca) for Canada, Nordpool (https://www.nordpoolgroup.com) for Estonia and Sweden, Electricity Market Operator (ESCO, https://www.nordpoolgroup.com) for Georgia, and U.S. Energy Information Administration (EIA, https://www.eia.gov) for the USA. The necessary exchange rates have been obtained from the National Bank of Georgia (https://www.nbg.gov.ge) and the Federal Reserve Bank of St. Louis (https://www.stlouisfed.org). These prices are available with monthly frequency which sets the frequency for the overall analysis. Other variables that are available on daily basis are then taken as monthly averages.

2.4. Mining efficiency

Information about efficiency of specific chips and miners, especially their introduction date and actual use, is not easily available as some mining chips are being kept secret (at least for a period of time) before being made available for public and bulk purchases. However, power consumption with respect to performed hashes is a crucial piece of the puzzle in calculating the marginal mining costs of cryptocurrencies. We use the data available at https://en.bitcoin.it/wiki/List_of_Bitcoin_mining_ASICs. These have been also checked with respect to the available information at the respective manufacturers. Mining chips for the analyzed period are listed in Tab. 1. The mining efficiency evolution is then illustrated in Fig. 1 where, in addition to the specific miners’ efficiency, we also add information about the best possible miner at the time as well as an informative hyperbolic fit to the efficiency development. The best available mining chip for a given month is then used in the marginal mining costs calculation.

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source ScienceDirect

About Jude Savage

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