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ORIGINAL RESEARCH
published: 30 April 2020
doi: 10.3389/frai.2020.00021
Frontiers in Artificial Intelligence | www.frontiersin.org 1April 2020 | Volume 3 | Article 21
Edited by:
Alessandra Tanda,
University of Pavia, Italy
Reviewed by:
Jürgen Hakala,
Leonteq Securities AG, Switzerland
Marika Vezzoli,
University of Brescia, Italy
*Correspondence:
Cinzia Baldan
cinzia.baldan@unipd.it
Specialty section:
This article was submitted to
Artificial Intelligence in Finance,
a section of the journal
Frontiers in Artificial Intelligence
Received: 19 November 2019
Accepted: 20 March 2020
Published: 30 April 2020
Citation:
Baldan C and Zen F (2020) The
Bitcoin as a Virtual Commodity:
Empirical Evidence and Implications.
Front. Artif. Intell. 3:21.
doi: 10.3389/frai.2020.00021
The Bitcoin as a Virtual Commodity:
Empirical Evidence and Implications
Cinzia Baldan*and Francesco Zen
Department of Economics and Management, University of Padova, Padua, Italy
The present work investigates the impact on financial intermediation of distributed ledger
technology (DLT), which is usually associated with the blockchain technology and is at
the base of the cryptocurrencies’ development. “Bitcoin” is the expression of its main
application since it was the first new currency that gained popularity some years after
its release date and it is still the major cryptocurrency in the market. For this reason, the
present analysis is focused on studying its price determination, which seems to be still
almost unpredictable. We carry out an empirical analysis based on a cost of production
model, trying to detect whether the Bitcoin price could be justified by and connected to
the profits and costs associated with the mining effort. We construct a sample model,
composed of the hardware devices employed in the mining process. After collecting
the technical information required and computing a cost and a profit function for each
period, an implied price for the Bitcoin value is derived. The interconnection between
this price and the historical one is analyzed, adopting a Vector Autoregression (VAR)
model. Our main results put on evidence that there aren’t ultimate drivers for Bitcoin
price; probably many factors should be expressed and studied at the same time, taking
into account their variability and different relevance over time. It seems that the historical
price fluctuated around the model (or implied) price until 2017, when the Bitcoin price
significantly increased. During the last months of 2018, the prices seem to converge
again, following a common path. In detail, we focus on the time window in which Bitcoin
experienced its higher price volatility; the results suggest that it is disconnected from the
one predicted by the model. These findings may depend on the particular features of the
new cryptocurrencies, which have not been completely understood yet. In our opinion,
there is not enough knowledge on cryptocurrencies to assert that Bitcoin price is (or
is not) based on the profit and cost derived by the mining process, but these intrinsic
characteristics must be considered, including other possible Bitcoin price drivers.
Keywords: Bitcoin, FinTech, Vector Autoregression model, distributed ledger technology, cryptocurrencies price
determination
JEL Codes: G12, C52, D40
INTRODUCTION
A strict definition of FinTech seems to be missing since it embraces different companies and
technologies, but a wider one could assert that FinTech includes those companies that are
developing new business models, applications, products, or process based on digital technologies
applied in finance.
Baldan and Zen Bitcoin as a Virtual Commodity
Financial Stability Board (FSB) (2017) defines FinTech as
“technology-enabled innovation in financial services that could
result in new business models, applications, processes, or
products with an associated material effect on the provision of
financial services.”
OECD (2018) analyzes instead various definitions from
different sources, concluding that none of them is complete
since “FinTech involves not only the application of new digital
technologies to financial services but also the development of
business models and products which rely on these technologies
and more generally on digital platform and processes.”
The services offered by these companies are indeed various:
some are providing financial intermediation services (FinTech
companies), while others offer ancillary services relating to
the financial intermediation activity (TechFin companies).
Technology is, for FinTech firms, an instrument, a productive
factor, an input, while for TechFin firms, it is the final
product, the output. The latter are already familiar with different
technologies and innovation; hence, they could easily diversify
their production by adding some digital and financial services
to the products they already offer. They enjoy a situation of
privileged competition because they are already known in the
market due to their previous non-financial services and thus
could take advantage of their customers’ information to enlarge
their supply of financial services. TechFin firms are the main
competitors for FinTech companies (Schena et al., 2018). Indeed
FinTech, or financial technology, is changing the way in which
financial operations are carried out by introducing new ways to
save, borrow, and invest, without dealing with traditional banks.
FinTech platforms, firms, and startups rose after the global
financial crisis in 2008 as a consequence of the loss of trust in
the traditional financial sector. In addition, digital natives (or
millennials, born between 1980 and 2000) seemed interested
in this new approach proposed by FinTech entrepreneurs.
Millennials were old enough to be potential customers, who feel
much more related to these new, fresh mobile services offered
through mobile platforms and apps, rather than bankers. The
strength of these new technologies lies in their transparent and
easy-to-use interfaces that was seen as an answer to the trust crisis
toward banks (Chishti and Barberis, 2016).
After the first Bitcoin (Nakamoto, 2008) has been sent in
January 2009, hundreds of new cryptocurrencies started being
traded in the market, whose common element is to rely on a
public ledger (or blockchain technology; Hileman and Rauchs,
2017). In fact, in addition to Bitcoin, other cryptocurrencies
gained popularity, such as: Ethereum (ETH), Dash, Monero
(XMR), Ripple (XRP), and Litecoin (LTC). Ethereum (ETH) was
officially launched in 2015 and is a decentralized computing
platform characterized by its own programming language. Dash
was introduced in 2014 but its market value was rising in 2016.
The peculiarity of this digital coin is that, in contrast with
other cryptocurrencies, block rewards are equally shared among
community participants and a revenue percentage (equal to
10%) is stored in the “treasury” to fund further improvements,
marketing, and network operations. Monero (XMR), launched
in 2014, is a system that guarantees anonymous digital cash by
hiding the features of the transacted coins. Its market value raised
in 2016. Ripple (XRP) has the unique feature to be based on a
“global consensus ledger” rather than on blockchain technology.
Its protocol is adopted by large institutions like banks and money
service businesses. Litecoin (LTC) appeared for the first time in
2011 and is characterized by a large supply of 84 million LTC.
Its functioning is based on that of Bitcoin, but some parameters
were altered (the mining algorithm is based on Scrypt rather than
Bitcoin’s SHA-265).
Despite the creation of these new cryptocurrencies, Bitcoin
remains the main coin in terms of turnover. The main advantage
of this new digital currency seems to be the low cost of transaction
(even if this is actually a myth, since BTC transactions topped
out at 50 USD per transaction in 2017–2018, while private banks
charge less these days) and, contrary on what many people think,
anonymity was not one of its main features when this network
was designed. An individual could attempt to make his identity
less obvious but the evidences available by now do not support
the claim that it could be hidden easily; it may be probably
impossible. To this purpose, fiat physical currencies remain the
best option.
Hayes (2015, 2017, 2019) analyzes the Bitcoin price formation.
In particular, he assumes the cryptocurrency as a virtual
commodity, starting from the different ways by which an
individual could obtain it. A person could buy Bitcoins
directly in an online marketplace by giving in exchange fiat
currencies or other types of cryptocurrencies. Alternatively,
he can accept them as payment and finally an individual
can decide to “mine” Bitcoins, which consists in producing
new units, by using computer hardware designed for this
purpose. This latter case involves an electrical consumption
and a rational agent would not be involved in the mining
process if the marginal costs of this operation exceed its
marginal profits. The relation between these values determines
price based on the cost of production that is the theoretical
value underlying the market price, around which it is
supposed to gravitate. Abbatemarco et al. (2018) resume Hayes’
studies introducing further elements missed in the previous
formulation. The final result confirms Hayes’ findings: the
marginal cost model provides a good proxy for Bitcoin market
price, but the development of a speculative bubble is not
ruled out.
We study the evolution of Bitcoin price by considering a
cost of production model introduced by Hayes (2015, 2017,
2019). Adding to his analysis some adjustment proposed by
Abbatemarco et al. (2018), we recover a series for the hypothetical
underlying price; then, we study the relationship between this
price and the historical one using a Vector Autoregression
(VAR) model.
The remainder of the paper proceeds as follows: in
section Literature Review, we expose a literature overview,
presenting those papers that investigate other drivers for Bitcoin
price formation, developing alternative approaches. In section
Materials and Methods, we exploit the research question,
describing the methodology behind the implemented cost of
production model, the sources accessed to collect data, the
hardware sample composition, and the formula derivations. In
section Main Outcomes, we analyze and comment on the main
findings of the analysis; section Conclusions concludes the work
with our comments on main findings and their implications.
Frontiers in Artificial Intelligence | www.frontiersin.org 2April 2020 | Volume 3 | Article 21
Baldan and Zen Bitcoin as a Virtual Commodity
LITERATURE REVIEW
Researchers detect a number of economic determinants for
Bitcoin price; it seems that given the new and particular
features of this cryptocurrency, price drivers will change over
time. For this reason, several authors analyze various potential
factors, which encompass technical aspects (such as the hashrate
and output volume), user-based growth, Internet components
(as Google Trends, Wikipedia queries, and Tweets), market
supply and demand, financial indexes (like S&P500, Dow Jones,
FTSE100, Nikkei225), gold and oil prices, monetary velocity, and
exchange rate of Bitcoin expressed in US dollar, euro, and yen.
Among others, Kristoufek (2015) focuses on different sources
of price movements by examining their interconnection during
time. He considers different categories: economic drivers, as
potential fundamental influences, followed by transaction and
technical drivers, as influences on the interest in the Bitcoin.
The results show how Bitcoin’s fundamental factors, such as
usage, money supply and price level, drive its price over the
long term. With regard to the technical drivers, a rising price
encourages individuals to become miners but this effect eclipses
over time, since always more specialized mining hardware have
increased the difficulty. Evidences show that price is even driven
by investors’ interest. According to previous studies (Kristoufek,
2013; Garcia et al., 2014), the relationship appears as most
evident in the long run, but during episodes of explosive
prices, this interest drives prices further up, while during rapid
declines, it pushes them further down. He then concludes that
Bitcoin is a unique asset with properties of both a speculative-
financial asset, and a standard one and because of his dynamic
nature and volatility, it is obvious to expect that its price
drivers will change over time. The interest element seems to
be particularly relevant when analyzing the behavior of Bitcoin
price, leading many researchers to study its interconnection with
Internet components, such as Google Trends, Wikipedia queries,
and Tweets.
Even Matta et al. (2015) investigate whether information
searches and social media activities could predict Bitcoin price
comparing its historical price to Google Trends data and volume
of tweets. They used a dataset based only on 60 days, but, in
addition to the other papers regarding this topic, they implement
an automated sentiment analysis technique that allows one to
automatically identify users’ opinions, evaluations, sentiments,
and attitudes on a particular topic. They use a tool called
“SentiStrength,” which is based on a dictionary only made by
sentiment words, where each of them is linked to a weight
representing a sentiment strength. Its aim is to evaluate the
strength of sentiments in short messages that are analyzed
separately, and the result is summed up in a single value: a
positive, negative, or neutral sentiment. The study reveals a
significant relationship between Bitcoin price and volumes of
both tweets and Google queries.
Garcia et al. (2014) study the evolution of Bitcoin price based
on the interplay between different elements: historical price,
volume of word-of-mouth communication in on-line social
media (information sharing, measured by tweets, and posts on
Facebook), volume of information search (Google searches and
Wikipedia queries), and user base growth. The results identify an
interdependence between Bitcoin price and two signals that could
form potential price bubbles: the first concerns the word-of-
mouth effect, while the other is based on the number of adopters.
The first feedback loop is a reinforcement cycle: Bitcoin interest
increases, leading to a higher search volume and social media
activity. This new popularity encourages users to purchase the
cryptocurrency driving the price further up. Again, this effect
would raise the search volume. The second loop is the user
adoption cycle: after acquiring information, new users join the
network, growing the user base. Demand rises but since supply
cannot adjust immediately but changes linearly with time, Bitcoin
price would increase.
Ciaian et al. (2016) adopt a different approach to identify
the factors behind the Bitcoin price formation by studying both
the digital and traditional ones. The authors point out the
relevance of analyzing these factors simultaneously; otherwise,
the econometric outputs could be biased. To do so, they specify
three categories of determinants: market forces of supply and
demand; attractiveness indicators (views on Wikipedia and
number of new members and posts on a dedicated blog), and
global macro-financial development. The results show that the
relevant impact on price is driven by the first category and it tends
to increase over time. About the second category, they assert that
the short-run changes on price following the first period after
Bitcoin introduction are imputable to investors’ interest, which
is measured by online information search. Its impact eases off
during time, having no impact in the long run and may be due
to an increased trust among users who become more willing to
adopt the digital currency. On the other hand, the results suggest
that investor speculations can also affect Bitcoin price, leading to
a higher volatility that may cause price bubbles. To conclude, the
study does not detect any correspondences between Bitcoin price
and macroeconomics and financial factors.
Kjærland et al. (2018) try to identify the factors that have an
impact on Bitcoin price formation. They argue that the hashrate,
CBOE volatility index (VIX), oil, gold, and Bitcoin transaction
volume do not affect Bitcoin price. The study shows that price
depends on the returns on the S&P500, past price performance,
optimism, and Google searches.
Bouoiyour and Selmi (2015) examine the links between
Bitcoin price and its potential drivers by considering investors’
attractiveness (measured by Google search queries); exchange–
trade ratio; monetary velocity; estimated output volume;
hashrate; gold price; and Shanghai market index. The latter
value is due to the fact that the Shanghai market is seen as the
biggest player in Bitcoin economy, which could also drive its
volatility. The evaluation period is the one from 5th December
2010 to 14th July 2014 and it is investigated through the adoption
of an ARDL Bounds Testing method and a VEC Grander
causality test. The results highlight the speculative nature of
this cryptocurrency stating that there are poor chances that it
becomes internationally recognized.
Giudici and Abu-Hashish (2019) propose a model to explain
the dynamics of bitcoin prices, based on a correlation network
VAR process that models the interconnections between different
crypto and classic asset price. In particular, they try to assess
Frontiers in Artificial Intelligence | www.frontiersin.org 3April 2020 | Volume 3 | Article 21
Baldan and Zen Bitcoin as a Virtual Commodity
whether bitcoin prices in different exchange markets are
correlated with each other, thus exhibiting “endogenous” price
variations. They select eight exchange markets, representative
of different geographic locations, which represent about 60% of
the total daily volume trades. For each exchange market, they
collect daily data for the time period May 18th, 2016 to April
30th, 2018. The authors also try to understand whether bitcoin
price variations can also be explained by exogenous classical
market prices. Hence, they use daily data (market closing price)
on some of the most important asset prices: gold, oil, and SP500,
as well as on the exchange rates USD/Yuan and USD/Eur. Their
main empirical findings show that bitcoin prices from different
exchanges are highly interrelated, as in an efficiently integrated
market, with prices from larger and/or more connected trading
exchanges driving the others. The results also seem to confirm
that bitcoin prices are typically unrelated with classical market
prices, thus bringing further support to the “diversification
benefit” property of crypto assets.
Katsiampa (2017) uses an Autoregressive model for the
conditional mean and a first-order GARCH-type model for
the conditional variance in order to analyze the Bitcoin price
volatility. The study collects daily closing prices for the Bitcoin
Coindesk Index from 18th July 2010 to 1st October 2016 (2,267
observations); the returns are then calculated by taking the
natural logarithm of the ratio of two consecutive prices. The
main findings put on evidence that the optimal model in terms
of goodness of fit to the data is the AR-CGARCH, a result
that suggests the importance of having both a short-run and a
long-run component of conditional variance.
Chevallier et al. (2019) investigate the Bitcoin price
fluctuations by combining Markov-switching models with
Lévy jump-diffusion to match the empirical characteristics of
financial and commodity markets. In detail, they try to capture
the different sub-periods of crises over the business cycle, which
are captured by jumps, whereas the trend is simply modeled
under a Gaussian process. They introduce a Markov chain with
the existence of a Lévy jump in order to disentangle potentially
normal economic regimes (e.g., with a Gaussian distribution) vs.
agitated economic regimes (e.g., crises periods with stochastic
jumps). By combining these two features, they offer a model
that captures the various crashes and rallies over the business
cycle, which are captured by jumps, whereas the trend is simply
modeled under a Gaussian framework. The regime-switching
Lévy model allows identifying the presence of discontinuities for
each market regime, and this feature constitutes the objective of
the proposed model.
MATERIALS AND METHODS
We study the evolution of Bitcoin price by considering a cost
of production model introduced by Hayes (2015, 2017). Adding
to his analysis some adjustment proposed by Abbatemarco et al.
(2018), we recover a series for the hypothetical underlying
price, and we study the relationship between this price and
the historical one using a VAR model. In detail, Hayes back-
tests the pricing model against the historical market price to
consolidate the validity of his theory. The findings show how
Bitcoin price is significantly described by the cryptocurrency’s
marginal cost of production and suggest that it does not depend
on other exogenous factors. The conclusion is that during periods
in which price bubbles happen, there will be a convergence
between the market price and the model price to shrink the
discrepancy. Abbatemarco et al. (2018) resume Hayes’ studies
introducing further elements missed in the previous formulation.
The final result confirms Hayes’ findings: the marginal cost
model provides a good proxy for Bitcoin market price, but the
development of a speculative bubble is not ruled out. Since
these studies were published before Bitcoin price raise reached
its peak on 19th December 2017 (the value was $19,270), the
aim of our work is to extend the analysis considering a larger
time frame and verify if, even in this case, the results are
unchanged. In particular, we consider the period from 9th April
2014 to 31st December 2018. We start with some unit root
tests to verify if the series are stationary in level or need to
be integrated and then we identify the proper number of lags
to be included in the model. We then check for the presence
of a cointegrating relationship to verify whether we should
adopt a Vector Error Correction Model (VECM) or a VAR
model; the results suggest that a VAR model is the best suited
for our data1. We thus collect the final results of the analysis
and we improve them by correcting the heteroscedasticity in
the regressions.
The marginal cost function, which estimates the electrical
costs of the devices used in the mining process, is presented as
Equation (1):
COST $
day
=Hhash
s
∗Eff J
hash
∗CE $
kWh
∗24 h
day (1)
Where:
Hhash/sis the hashrate (measured by hash/second);
EFFJ/hash is the energy efficiency of the devices involved in the
process and it is measured by Joule/hash;
CE$/kWh is the electricity cost expressed in US dollar
per kilowatt/hour;
24 is the number of hours in a day;
A marginal profit function, which estimates the reward of the
mining activity, is instead depicted as Equation (2):
PROFIT BTC
day
=BRBTC ∗"3, 600 s
h∗24 h
day
BTs #(2)
Where:
1According to Abbatemarco et al. (2018), the nature of the variables considered
suggests that they probably are mutually interdependent. Lütkepohl and Krätzig
(2004) state that the analysis of interdependencies between time series is subject
to the endogenous problem; part of the literature proposes to specify a Vector
Auto Regressive model (VAR) that analyzes the causality between the two
series estimated by the model. Engle and Granger (1987), instead, demonstrated
that the estimate of such a model in the presence of non-stationary variables
(i.e., with mean and variance non-constant over time) can lead to erroneous
model specification and hence to unconditional regressions (spurious regressions).
Scholars’ intuition suggests that the price trend of a cryptocurrency and that of its
estimated equilibrium prices are non-stationary time series, as there is a constant
increase in their values over time.
Frontiers in Artificial Intelligence | www.frontiersin.org 4April 2020 | Volume 3 | Article 21
Baldan and Zen Bitcoin as a Virtual Commodity
BRBTC is the block reward that refers to new Bitcoins
distributed to miners who successfully solved a block (hence it
is measured by BTC) and it is given by a geometric progression
(Equation 3):
BRBTC =BR1∗1
2
n−1
(3)
nincreases by 1 every 210,000 blocks. At the beginning, it was
BR1=50, but during the course of time, it halved twice: on 29th
November 2012 and on 10th July 2016.
3,600 is the number of seconds in an hour;
24 is again the number of hours in a day;
BTsis the block time, which is expressed as the seconds needed
to generate a block (around 600 s =10 min), and it is computed
as Equation (4):
BTs=D∗232
H(4)
Where H=hashrate and D=difficulty. The latter variable
specifies how hard it is to generate a new block in terms of
computational power given a specific hashrate. This is the value
that changes frequently to ensure a BTsclose to 10 min2.
In addition to the variables already considered, we introduce
some adjustments proposed by Abbatemarco et al. (2018), who
thought there were two elements missing in Hayes’ formulations.
They add, on the cost side, the one required to maintain and
update miners’ hardware (MAN, expressed in US dollar), and
on the profit side, the fees (FEES) received by miners who place
transactions in a block3.
Maintenance costs are computed as a ratio between the
weighted devices’ price and their weighted lifespan (5), while fees,
expressed in BTC, are measured as a ratio between the daily total
transaction fees and the number of daily transactions4(6).
MAN$=Weighted Devices Price$
Weighted Lifespan (5)
FEESBTC =Total Transaction Fees (BTC)
Daily Transaction Fees (6)
The new equations become:
COST $
day
=Hhash
s
∗Eff J
hash
∗CE $
kWh
∗24 h
day
+MAN$(7)
PROFIT BTC
day
=BRBTC ∗"3, 600 s
h∗24 h
day
BTs #+FEESBTC (8)
Moreover, due to the equality 1 joule =1 watt∗second, Equation
(7) could be expressed as follows:
COST$/day =Hhash/s∗EffW∗s
hash ∗CE $
kWh
∗24h/day +MAN$(9)
2Results are shown in Table A.1 (Supplementary Material). In order to simplify
the presentation, we display only the values for the last day of each month.
3Bitcoin could be obtained through both the mining process and the registration
of transactions but, since Bitcoin supply is limited to 21 million, once it is reached,
fees become the only remuneration source in the future.
4Fees computation results are displayed in Table A.1 (Supplementary Material).
TABLE 1 | Sources.
Variables Sources
Phist$Historical price in US
dollar
https://Bitcoinvisuals.com
Hhash/sHashrate
BRBTC Block reward
DDifficulty
BTsBlock time Computed using Dand Hhash/s
FEESBTC Transaction fees https://charts.Bitcoin.com/bch/
CE$/kWh Cost of energy Computed using data from:
en.Bitcoin.it/wiki/Mining_
hardware_comparison
https://archive.org/web/
MAN$Hardware maintaining
cost
EFFJ/hash Hardware energy
efficiency
Source: Authors’ elaboration.
By converting watt in kilowatt/hour, it can be written as:
COST$/day =Hhash/s∗
Eff W∗s
hash
1000 ∗CE $
kWh
∗24h/day +MAN$
(10)
COST$/day =Hhash/s∗EffkWh ∗s
hash
∗CE $
kWh
∗24h/day +MAN$
(11)
According to the competitive market economic theories, the ratio
between the cost and profit functions must lead to the price under
equilibrium condition (Equation 12):
P$/BTC =
COST $
day
PROFIT BTC
day
(12)
A historical price below the one predicted by the model would
force a miner out of the market, since he is operating in loss, but
at the same time, the removal of its devices from the network
increases others’ marginal profits (competition decreases), and
at the end, the system would return to equilibrium. On the
other hand, a historical price higher than what predicted by
the model attracts more miners, thus increasing the number of
devices operating in the network and decreasing others’ marginal
profits (competition increases). Again, the system would return
in balance (Hayes, 2015).
We must remark that the assumption of an energy price per
hemisphere is not very realistic. In fact, for large consumers,
energy price is contractually set differently for peak times and
less busy times. There is a lot of variation in the energy price of
mines in different countries and circumstances (see, for example,
Iceland with its geothermal cheap energy as a cheap energy
example; Soltani et al., 2019). Taking more variation around
energy prices into account would probably add a wider range of
BTC prices (de Vries, 2016); due to the difficulties on collecting
comparable data, we adopted a simplified proxy of the cost
of energy.
Frontiers in Artificial Intelligence | www.frontiersin.org 5April 2020 | Volume 3 | Article 21
Baldan and Zen Bitcoin as a Virtual Commodity
Table 1 presents the sources used to collect and compute the
required information.
We start the analysis by constructing a hardware sample that
evolves during a chosen time window (2010–2018), which is
divided in semesters associated with the introduction of a specific
device (Table 2).
Since the first Bitcoin was traded, there has been an
evolution of the devices used by miners. The first ones
adopted were GPU (Graphical Processing Unit) and later
FPGA (Field-Programmable Gate Array), but these days, only
ASIC (Application-Specific Integrated Circuit) is suitable for
mining purposes.
For each device model, we collect the efficiency, expressed in
Mhash/J, and the dollar price at the release day.
Technical data were collected from the Wikipedia pages
https://en.Bitcoin.it/wiki/Mining__hardware__comparison
and https://en.Bitcoin.it/wiki/Non-specialized__hardware__
comparison by using in addition the online archive https://
archive.org/web/, which allows the recovery of different
webpages at the date in which they were modified, enabling the
comparison before and after reviews5.
Since only ASIC devices were created with specifications
to mining purpose, there is homogeneity among FPGA and
especially among GPU hardware. Due to this fact and considering
the difficulty to recover the release prices, we make some
simplified assumptions about them based on the information
available online. This means that given the same computational
power, we assume price homogeneity among devices when they
were not available for specific models6.
Given the hardware sample, we construct a weights
distribution matrix (Table A.3 in Supplementary Material)
that represents the evolution of the devices used during each
semester of the time window selected, which are replaced
following a substitution rate that increases over time. In fact,
until 2012, before FPGA took roots, it is equal to 0.05; until 2016,
we set it equal to 0.1, and in the last 2 years of the analysis, it is
equal to 0.157.
All computations are based on this matrix; indeed,
we multiplied it by a specific column of the hardware
sample table to obtain the biannual Efficiency (Table A.4 in
Supplementary Material) (J/Hash), Weighted Devices’ Prices
($) (Table A.5 in Supplementary Material), and Weighted
Lifespans (Table A.6 in Supplementary Material). Regarding
this latter matrix, we made further assumptions on the
device lifespans by implementing Abbatemarco et al. (2018)
assumptions. Hence, we set a lifespan equal to 2,880 days for
5When possible, we double check Wikipedia prices with those on the websites of
the companies producing mining hardware, and if they are not identical, we choose
the latter.
6In detail, we approximate the prices of ATI FirePro M5800, Sapphire Radeon
5750 Vapor-X, GTX460, FireProV5800, Avnet Spartan-6 LX150T, and AMD
Radeon 7900.
7Despite that ASIC devices have been released for the first time in 2013, they
became the main devices used in the mining process only in 2015–2016. In the
last 2 years of the analysis, we increase the substitution rate up to 0.15 because the
competition among miners has been driven up as more sophisticated hardware was
developed with a larger frequency.
FIGURE 1 | Historical market price vs. implied model price (July
2010–December 2018). Source: Authors’ elaboration.
GPU, 1,010 days for FPGA, and 540 days for ASIC, but after
2017, due to a supposed market growth phase, we halved these
numbers (Table 2).
To evaluate the cost of energy, we follow the assumptions
suggested by the cited researchers and we divide the world into
two parts relative to Europe: East and West, each one with a fix
electricity price equal to 0.04 and 0.175 $/kWh, respectively. The
weights’ evolution of the mining pool is set up in 2010 equal to
0.7 for the West part and 0.3 for the East part and it changes
progressively until reaching in 2018 a 0.2 for the West and 0.8
for the East. We obtained a biannual cost of energy evolution
measured by $/kWh by multiplying the biannual weights to the
electricity costs and summing up the value for the West and
the East (Table A.7 in Supplementary Material).
At this point, to smooth the values across the
time window, we take the differences between
biannualMAN$,biannualEFFJ/Hash, and biannualCE$/kWh at
time tand t– 1 and we divide these values by the number of days
in each semester, obtaining DeltaMAN,DeltaEFF, and DeltaCE
(Table A.8 in Supplementary Material). Starting the first day
of the analysis with the first value of the biannual matrixes, we
compute the final variables as follows:
MAN$(t)=MAN$(t−1)+DeltaMAN (13)
EFF J
hash
(t)=EFFJ/hash (t−1)+DeltaEFF (14)
CE $
kWh
(t)=CE $
kWh
(t−1)+DeltaCE (15)
MAIN OUTCOMES
By applying Equations (8), (11), and (12), we obtain the model
price8and compare its evolution to the historical one (Figure 1).
The evolution of the model (or implied) price shows a spike
during the second semester of 2016, probably because on 10th
July 2016, the Block Reward halved from 25 to 12.5, leading to a
reduction on the profit side and a consequent price increase.
Despite this episode, the historical price seems to fluctuate
around the implied one until the beginning of 2017, the period
8Table A.2 (Supplementary Material) displays all the variables required to
compute the model price and compares it with the historical price. Since our time
window involves 3,107 observation days, for the sake of simplicity, we present only
the results for the last day of each month.
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Baldan and Zen Bitcoin as a Virtual Commodity
TABLE 2 | Hardware sample.
TYPE MODEL TIME EFF. (Mhash/J) PRICE (USD) LIFESPAN
Before ′17 After ′17
GPU ATI FirePro M5800 2 s. 2010 1.45 175 2,880 1,440
GPU Sapphire Radeon 5750 Vapor-X 2 s. 2010 1.35 160 2,880 1,440
GPU GTX460 2 s. 2010 1.73 200 2,880 1,440
GPU FirePro V5800 1 s. 2011 2.08 469 2880 1,440
FPGA Avnet Spartan-6 LX150T 2 s. 2011 6.25 995 1,010 505
FPGA AMD Radeon 7900 1 s. 2012 10.40 680 1,010 505
FPGA Bitcoin Dominator X5000 2 s. 2012 14.70 750 1,010 505
FPGA X6500 1 s. 2013 23.25 989 1,010 505
ASIC Avalon 1 2s. 2013 107.00 1,299 540 270
ASIC Bitmain AntMiner S1 1 s. 2014 500.00 1,685 540 270
ASIC Bitmain AntMiner S2 2 s. 2014 900.00 2,259 540 270
ASIC Bitmain AntMiner S3 1 s. 2015 1,300.00 1,350 540 270
ASIC Bitmain AntMiner S4 2 s. 2015 1,429.00 1,400 540 270
ASIC Bitmain AntMiner S5 1 s. 2016 1,957.00 1,350 540 270
ASIC Bitmain AntMiner S5+2 s. 2016 2,257.00 2,307 540 270
ASIC Bitmain AntMiner S7 1 s. 2017 4,000.00 1,832 540 270
ASIC Bitmain AntMiner S9 2 s. 2017 10,182.00 2,400 540 270
ASIC Ebit E9++ 1 s. 2018 10,500.00 3,880 540 270
ASIC Ebit E10 2 s. 2018 11,100.00 5,230 540 270
Source: Authors’ elaboration.
in which Bitcoin price started raising exponentially, reaching its
peak with a value equal to $19,270 on 19th December 2017. It
declined during 2018, converging again to the model price.
Another divergence was detected at the end of 2013, but it was
of a lower amount and resolved quickly.
Given the historical and implied price series, we make a
further step than what Hayes (2019) and Abbatemarco et al.
(2018) did, by including in the analysis a time frame even in the
divergence phase. Therefore, we consider the period from 9th
April 2014 to 31st December 2018. We select this time window
also to base the analysis on solid data. Because of the difficulty to
obtain reliable information on the hardware used in the mining
process, we make some simplified assumptions on their features.
By choosing this time window, we include the hardware sample
whose data are more precise.
Unit Root Tests
We first try to determine with different unit root tests whether
the time series is stationary or not. The presence of a unit
root indicates that a process is characterized by time-dependent
variance and violates the weak stationarity condition9. We test
the presence of a unit root with three procedures: the augmented
Dickey–Fuller test (Dickey and Fuller, 1979), the Phillips–Perron
test (Phillips and Perron, 1988), and the Zivot–Andrews test
(Zivot and Andrews, 1992).
Given a time series {yt}, both the augmented Dickey–Fuller
test (Dickey and Fuller, 1979) and the Phillips–Perron test are
9The condition of weak stationarity asserts that Var(rt)=γo, which means that
the variance of the process is time invariant and equal to a finite constant.
based on the general regression (Equation 16):
1yt=α+βt+θyt−1+δ11yt−1+...+δp−11yt−p+1+εt
(16)
Where 1ytindicates changes in time series, αis the constant, tis
the time trend, pis the order of the autoregressive process, and ε
is the error term (Boffelli and Urga, 2016).
For both tests, the null hypothesis is that the time series
contains a unit root; thus, it is not stationary (H0:θ=0), while
the alternative hypothesis asserts stationarity (H0:θ < 0).
Considering only the augmented Dickey–Fuller test, its basic
idea is that if a series {yt} is stationary, then {1yt} can be
explained only by the information included in its lagged values
(1yt−1. . . 1yt−p+1) and not from those in yt−1.
For each variable, we conduct this test firstly with a constant
term and later by including also a trend10.
Table 3 presents the main findings of the test.
The Phillips–Perron test points out that the process generating
ytmight have a higher order of autocorrelation than the one
admitted in the test equation. This test corrects the issue, and it is
10In order to select the proper number of lags to include in this test, we used, only
for this part of the analysis, the open-source software Gretl. Its advantage is to
apply clearly the Schwert criterion for the maximum lag (pmax) estimation, which
is given by: pmax =integer part of 12 ∗T
100 1/4, where Tis the number of
observations. The test is conducted firstly with the suggested value of pmax , but if
the absolute value of the tstatistic for testing the significance of the last lagged value
is below the threshold 1.6, pmax is reduced by 1 and the analysis is recomputed. The
process stops at the first maximum lag that returns a value >1.6. When this value
is found, the augmented Dickey–Fuller test is estimated.
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Baldan and Zen Bitcoin as a Virtual Commodity
robust in case of unspecified autocorrelation or heteroscedasticity
in the disturbance term of the equation. Table 4 displays the
test results.
The main difference between these tests is that the
latter applies Newey–West standard errors to consider serial
correlation, while the augmented Dickey–Fuller test introduces
additional lags of the first difference.
Since the previous tests do not allow for the possibility of a
structural break in the series, Zivot and Andrews (1992) propose
to examine the presence of a unit root including the chance of
an unknown date of a break-point in the series. They elaborate
three models to test for the presence of a unit root considering a
one-time structural break:
a) permits a one-time change in the intercept of the series:
1yt=α+βt+θyt−1+γDUt+δ11yt−1+...
+δp−1yt−p+1+εt(17)
b) permits a one-time change in the slope of the trend function:
1yt=α+βt+θyt−1+ϑDTt+δ11yt−1+...
+δp−11yt−p+1+εt(18)
c) combines the previous models:
1yt=α+βt+θyt−1+γDUt+ϑDTt+δ11yt−1+...
+δp−11yt−p+1+εt(19)
Where DUtis a dummy variable that relates to a mean shift at a
given break-date, while DTtis a trend shift variable.
The null hypothesis, which is the same for all three models,
states that the series contains a unit root (H0:θ=0), while the
alternative hypothesis asserts that the series is a stationary process
with a one-time break occurring at an unknown point in time
(H0:θ < 0) (Waheed et al., 2006).
The results in Table 5 confirm what the other tests predict:
both series are integrated of order 1. Since this last test identifies
for 1lnPrice the presence of a structural break on 18th December
2017 and after this date the Bitcoin price reaches its higher value
to start declining later, we add to the analysis a dummy variable
related to this observation, in order to take into account a broken
linear trend in a series.
Identifying the Number of Lags
The preferred lag length is the one that generates the lowest value
of the information statistic considered. We follow Lütkepohl’s
intuition that “the SBIC and HQIC provide consistent estimates
of the true lag order, while the FPE and AIC overestimate the lag
order with positive probability” (Becketti, 2013). Therefore, for
our analysis, we select 1 lag (Table 6)11.
11To identify the proper lag length to be included in the VAR model, we use the
“varsoc” command in Stata that displays a table of test statistics, which reports
for each lag length, the log of the likelihood functions (LL), a likelihood-ratio
test statistic with the related degrees of freedom and pvalue (LR, df, and p),
and also four information criteria: Akaike’s final prediction error (FPE); Akaike’s
information criterion (AIC), Hannan and Quinn’s information criterion (HQIC),
Identifying the Number of Cointegrating
Relationships
A cointegrating relationship is a relationship that describes the
long-term link among the levels of a number of the non-
stationary variables. Given Knon-stationary variables, they can
have at most K– 1 cointegrating relationships. Since we have
only two non-stationary variables (lnPrice and lnModelPrice), we
could obtain, at most, only one cointegrating relationship.
If series show cointegration, a VAR model is no more the best
suited one for the analysis, but it is better to implement a Vector
Error-Correction Model (VECM), which can be written as (20):
1yt=µ+δt+αβ′ut−1+
p−1
X
i=1
Ŵi1yt−i+εt(20)
Where the deterministic components µ+δtare, respectively, the
linear and the quadratic trend in ytthat can be separated into the
proper trends in ytand those of the cointegrating relationship.
This depends on the fact that in a first-difference equation: a
constant term is a linear trend in the level of the variables (yt=
κ+λt→1yt=λ), while a linear trend derives from the
quadratic one in the regression in levels (yt=κ+λt+ωt2→
1yt=λ+2ωt−ω). Therefore, µ≡αν +γ, and δt=αρt+τt.
By substituting in the previous expression, the VECM can be
expressed as Equation (21):
1yt=αβ′yt−1+ν+ρt+
p−1
X
i=1
Ŵi1yt−i+γ+τt+εt(21)
Where the first part αβ′ut−1+ν+ρtrepresents
the cointegrating equations, while the second
Pp−1
i=1Ŵi1yt−i+γ+τt+εtrefers to the variables in levels.
This representation allows specifying five cases that Stata tests:
1) Unrestricted trend: allows for quadratic trend in the level
of yt(τtappears in the equation) and states that the
cointegrating equations are trend stationary, which means
they are stationary around time trends.
2) Restricted trend (τ=0): excludes quadratic trends but
includes linear trends (ρt). As in the previous case, it allows
the cointegrating equations to be trend stationary.
3) Unrestricted constant (τ=0, ρ=0): lets linear trends in
ytto present a linear trend (γ) but the cointegrating equations
are stationary around a constant means (ν).
4) Restricted constant (τ=0, ρ=0, γ=0): rules out
any trends in the levels of the data but the cointegrating
relationships are stationary around a constant mean (ν).
and Schwarz’s Bayesian information criterion (SBIC). Every information criteria
provide a trade-off between the complexity (e.g., the number of parameters) and
the goodness of fit (based on the likelihood function) of a model. Since the output
is sensitive to the maximum lag considered, we try different options by changing
the one included in the command computation. We tried with 4, 8, 12, 16, 20, and
24 lags. After selecting a maximum lag length equal to 16, the optimal number of
lags suggested changes: while the previous results agree recommending 1 lag with
each information criteria, now the FPE and AIC diverge and propose 13 lags.
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Baldan and Zen Bitcoin as a Virtual Commodity
TABLE 3 | Augmented Dickey–Fuller test.
Augmented Dickey–Fuller test
Constant Constant +trend Result
tstat p-value t-stat p-value
lnPrice −0.606 0.8696 −1.839 0.6856 NO stationary
lnModelPrice −0.467 0.8982 −1.669 0.7644 NO stationary
1lnPrice −7.694 0.0000 −7.697 0.0000 Stationary
1lnModelPrice −8.041 0.0000 −8.038 0.0000 Stationary
Critical values
Constant Constant +trend
1% 5% 10% 1% 5% 10%
−3.430 −2.860 −2.570 −3.960 −3.410 −3.120
Source: Authors’ elaboration.
TABLE 4 | Phillips–Perron test.
Phillips–Perron test
Constant Constant +trend Result
tstat p-value tstat p-value
lnPrice −0.437 0.9037 −1.546 0.8130 NO stationary
lnModelPrice −0.637 0.8624 −1.805 0.7021 NO stationary
1lnPrice −34.394 0.0000 −34.385 0.0000 Stationary
1lnModelPrice −42.972 0.0000 −42.959 0.0000 Stationary
Critical values
Constant Constant +trend
1% 5% 10% 1% 5% 10%
−3.430 −2.860 −2.570 −3.960 −3.410 −3.120
Source: Authors’ elaboration.
5) No trend (τ=0, ρ=0, γ=0, ν=0): considers no
non-zero means or trends.
Starting from these different specifications, the Johansen test can
detect the presence of a cointegrating relationship in the analysis.
The null hypothesis states, again, that there are no cointegrating
relationships against the alternative that the null is not true. H0is
rejected if the trace statistic is higher than the 5% critical value.
We run the test with each case specification and the results
agree to detect zero cointegrating equations (a maximum rank
of zero). Only the unrestricted trend does not display any
conclusion from the test but, since the other results matched, we
consider rank =0 the right solution. This implies that the two
time series could be fitted into a VAR model.
VAR Model
The VAR model allows investigating the interaction of several
endogenous time series that mutually influence each other. We
do not only want to detect if Bitcoin price could be determined
by the one suggested by the cost of production model; we also
want to check if the price has an influence on the model price.
This latter relation can occur if, for example, a price increase
leads to a higher cost for the mining hardware. In fact, a raise
in the price represents also a higher reward if the mining process
is successfully conducted, with the risk to push hardware price
atop, which in turn could boost the model price up.
To explain how a VAR model is constructed, we present
a simple univariate AR(p) model, disregarding any possible
exogenous variables, which can be written as (22):
yt=µ+φ1yt−1+...+φpyt−p+εt(22)
Or, in a concise form (23):
φ(L)yt=µ+εt(23)
where ytdepends on its pprior values, a constant (µ) and a
random disturbance (εt).
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Baldan and Zen Bitcoin as a Virtual Commodity
TABLE 5 | Zivot–Andrews test.
Zivot–Andrews test
Intercept Trend Intercept +trend Result
tstat Break Date tstat Break Date tstat Break Date
lnPrice −2.964 1,083 26/03/2017 −2.049 261 25/12/2014 −2.562 1,196 17/07/2017 NON-stationary
lnModelPrice −3.221 281 14/01/2015 −3.357 408 21/05/2015 −3.914 620 19/12/2015 NON-stationary
1lnPrice −34.905 1,350 18/12/2017 −34.626 1,285 14/10/2017 −34.895 1,350 18/12/2017 Stationary
1lnModelPrice −42.848 582 11/11/2015 −42.781 1,469 16/04/2018 −42.858 582 11/11/2015 Stationary
Critical values
Intercept Trend Intercept +trend
1% 5% 10% 1% 5% 10% 1% 5% 10%
−5.34 −4.8 −4.58 −4.93 −4.42 −4.11 −5.57 −5.08 −4.82
Source: Authors’ elaboration.
TABLE 6 | Proper number of lags.
Lag LL LR df P FPE AIC HQIC SBIC
0 7160.95 8.0e−07 −8.36581 −8.3611 −8.35308
1 7190.57 59.237 4 0.000 7.7e−07 −8.39575 −8.38633* −8.37029*
2 7192.42 3.7134 4 0.446 7.8e−07 −8.39325 −8.37911 −8.35506
3 7194.48 4.1059 4 0.392 7.8e−07 −8.39097 −8.37231 −8.34005
4 7195.74 2.5346 4 0.638 7.8e−07 −8.38778 −8.36422 −8.32413
5 7197.81 4.1319 4 0.388 7.8e−07 −8.38552 −8.35725 −8.30914
6 7199.73 3.8486 4 0.427 7.8e−07 −8.38309 −8.35011 −8.29399
7 7201.63 3.8014 4 0.434 7.9e−07 −8.38064 −8.34295 −8.2788
8 7204.56 5.8468 4 0.211 7.9e−07 −8.37938 −8.33698 −8.26482
9 7208.36 7.6003 4 0.107 7.9e−07 −8.37914 −8.33204 −8.25185
10 7212.23 7.7429 4 0.101 7.9e−07 −8.37899 −8.32717 −8.23897
11 7213.48 2.5086 4 0.643 7.9e−07 −8.37578 −8.31925 −8.22304
12 7225.63 24.303 4 0.000 7.8e−07 −8.38531 −8.32407 −8.21983
13 7243.57 35.872* 4 0.000 7.7e−07* −8.4016* −8.33565 −8.2234
14 7244.29 1.4495 4 0.836 7.7e−07 −8.39777 −8.32711 −8.20684
15 7246.50 4.4025 4 0.354 7.7e−07 −8.39567 −8.3203 −8.19201
16 7248.86 4.7357 4 0.316 7.8e−07 −8.39376 −8.31368 −8.17737
Source: Authors’ elaboration.
A vector of njointly endogenous variables is express as (24):
yt=
y1,t
y2,t
.
.
.
yn,t
(24)
This n-element vector can be rearranged as a function (Equation
25) of nconstants, pprior values of Yt, and a vector of nrandom
disturbances, ǫt:
yt=µ+φ1yt−1+...+φpyt−p+ǫt(25)
Where µis a vector (Equation 26) of the n-constants:
µ=
µ1
µ2
.
.
.
µp
(26)
the matrix of coefficients 8iis Equation (27):
81=
φi,11 φi,12 ··· φi,1n
φi,21 φi,22 ··· φi,2n
.
.
..
.
.....
.
.
φi,n1φi,n2. . . φi,nn
(27)
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Baldan and Zen Bitcoin as a Virtual Commodity
TABLE 7 | Regressions of the Vector Autoregression model.
Variables (1) (2)
dlnPrice dlnModelPrice
L.dlnPrice 0.18330223*** 0.00799770
(0.02359822) (0.02055802)
L.dlnModelPrice −0.00655017 −0.02899205
(0.02762476) (0.02406582)
Dummy −0.00588960*** 0.00027999
(0.00185465) (0.00161571)
Constant 0.00236755*** 0.00149779**
(0.00086910) (0.00075713)
Observations 1,726 1,726
R20.04178812 0.00092579
Standard errors in parentheses.
***p<0.01, **p<0.05, and *p<0.1.
Source: Authors’ elaboration.
and ǫtconsists in Equation (28):
ǫt=
ε1
ε2
.
.
.
εp
(28)
With Eǫt=0 and Eǫtǫ′s=6,t=s
0, t6= s
the elements of ǫtcan be contemporaneously correlated.
Given these specifications, a pth-order VAR can be presented
as Equation (29):
8(L)ut=µ+ǫt(29)
To clarify this expression, the ith endogenous time series can be
extracted from these basic VAR and be represented as (30):
yi,t=µi+φ1,i1y1,t−1+...+φ1,in yn,t−1
+φ2,i1y1,t−2+...+φ2,in yn,t−2+...
+φp,i1y1,t−p+...+ +φp,in yn,t−p+εi,t(30)
The result of the VAR model considering the dummy variable is
presented in Table 7:
As expected, the dummy is significant in the dlnPrice function
but not in dlnModelPrice.
Looking at the significance of the parameters, we can see how
dlnPrice depends on its lagged value, on the dummy and on the
constant term, but it seems not to be linked with the lagged value
of dlnModelPrice. The regression of dlnModelPrice appears not
to be explained by any variable considered in the model. We then
check the stationarity of the model. The results confirm that the
model is stable and there is no residual autocorrelation (Table A.9
in Supplementary Material).
Heteroscedasticity Correction
Given the series’ path and the daily frequency of the data, the
variables included in the model are probably heteroskedastic.
TABLE 8 | Regressions with robust standard errors.
Variables (1) (2)
dlnPrice dlnModelPrice
L.dlnPrice 0.18330223*** 0.00799770
(0.04306718) (0.01592745)
L.dlnModelPrice −0.00655017 −0.02899205***
(0.02681078) (0.00979148)
Dummy −0.00588960*** 0.00027999
(0.00225058) (0.00142356)
Constant 0.00236755*** 0.00149779*
(0.00078480) (0.00078942)
Observations 1,726 1,726
R20.04178812 0.00092579
Robust standard errors in parentheses.
***p<0.01, **p<0.05, and *p<0.1.
Source: Authors’ elaboration.
This feature does not compromise the unbiasedness or the
consistency of the OLS coefficients but invalidates the usual
standard errors. In time series analysis, heteroscedasticity is
usually neglected, as the autocorrelation of the error terms is seen
as the main problem due to its ability to invalidate the analysis.
Since it is not possible to check and correct heteroscedasticity
while performing the VAR model, we run each VAR regression
separately and check the presence of heteroscedasticity by
running the Breusch-Pagan test, whose null hypothesis states
that the error variance are all equal (homoscedasticity) against
the alternative hypothesis that the error variances change over
time (heteroscedasticity).
H0:σ2
1=σ2
2=... =σ2(31)
The null hypothesis is rejected if the probability value of the chi-
square statistic (Prob <chi2) is <0.05. The results of the test for
both regressions show that the null hypothesis is always rejected,
implying the presence of heteroscedasticity in the residuals (Table
A.10 in Supplementary Material).
We try to correct the issue using heteroscedasticity-robust
standard errors. The results are displayed in Table 8.
These new robust standard errors are different from the
standard errors estimated with the VAR model, while the
coefficients are unchanged. The first difference of lnPrice depends
even in this case on its lag, but, contrary from the VAR, now
the first difference of lnModelPrice is not independent from its
previous values. This new specification confirms the previous
finding that each variable does not depend on the lagged value
of the other one. Therefore, it seems that during the time window
considered, the Bitcoin historical price is not connected with the
price derived by Hayes’ formulation, and vice versa.
Recalling Figure 1, it seems that the historical price fluctuated
around the model (or implied) price until 2017, the year in
which Bitcoin price significantly increased. During the last
months of 2018, the prices seem to converge again, following a
common path. In our analysis, we focus on the time window
in which Bitcoin experienced its higher price volatility (Figure
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Baldan and Zen Bitcoin as a Virtual Commodity
A.1 in Supplementary Material) and the results suggest that it
is disconnected from the one predicted by the model. These
findings may depend on the features of the new cryptocurrencies,
which have not been completely understood yet.
The previous analyses, conducted on different time periods,
by Hayes (2019) and Abbatemarco et al. (2018) assert that
Bitcoin price could be justified by the costs and revenues of its
blockchain network, leading to an opposite result from ours. We
suggest that the difference could be based on the time window
analyzed since we make a further step evaluating also the months
in which Bitcoin price was pushed atop and did not follow a
stable path. We think that there is not enough knowledge on
cryptocurrencies to assert that Bitcoin price is (or is not) based
on the profit and cost derived by the mining process, but these
intrinsic characteristics must be considered and checked also in
further analysis that include other possible Bitcoin price drivers
suggested by the literature.
CONCLUSIONS
The main findings of the analysis presented show how, in the
considered time frame, the Bitcoin historical prices are not
connected with the price derived from the model, and vice versa.
This result is different from the one obtained by Hayes
(2019) and Abbatemarco et al. (2018), who conclude
that the Bitcoin price could be explained by the cost of
production model.
The reason behind these opposite outcomes could be the
considered time window. In fact, our analysis includes also
those months where Bitcoin price surges up, reaching a peak of
$19,270 on 19th December 2017, without following a seasonal
path (Figure A.1 in Supplementary Material). This has a relevant
impact on the results even if the historical price started declining
in 2018, converging again to the model one. Looking at the overall
time frame, it seems that the increasing value of the historical
price from the beginning of 2017 to the end of 2018 is a unique
episode that required some months to get back to more standard
behavior (Caporale et al., 2019).
It seems now possible to assert that Bitcoin could not be
seen as a virtual commodity, or better not only. According to
Abbatemarco et al. (2018), the implemented approach does not
rule out the possibility of a bubble development and, given the
actual time frame, this is the reason why it would be more
precise to explain Bitcoin price not only with the one implied
by the model, but also with other explanatory variables that
the literature seems to identify as meaningful. Therefore, to
avoid misleading results, Bitcoin intrinsic characteristics must be
considered and checked by adding to the profit and cost functions
also these suggested parameters that range from technical aspects
and Internet components to financial indexes, commodity prices,
and exchange rate. This could open new horizons for research,
which, despite the traditional drivers, should consider also new
factors such as Google Trends, Wikipedia queries, and Tweets.
These elements are related to the Internet component and
appear to be particularly relevant given the social and digital
Bitcoin’s nature.
Kristoufek’s (2013) intuition, which considers Bitcoin as a
unique asset that presents properties of both a speculative
financial asset and a standard one, whose price drivers will change
over time considering its dynamic nature and volatility, seems to
be confirmed.
The explanatory power of the VAR specification we
implemented to inspect fundamental vs. market price dynamics
could be quite low, which is to ascribe to missing factors and
volatility. Further researches could include more tests on the
VAR specification also including other controls/factors to
check whether, for example, the VIX is another and important
explanatory factor. More involved analyses should also explore
for latent factors and/or time-varying relationships with
stochastic and jump components.
Although there are highlighted elements of uncertainty,
Bitcoin has undoubtedly introduced to the market a new
way to think about money transfers and exchanges. The
distributed ledger technology could be a disruptive innovation
for the financial sector, since it can ease communication
without the need of a central authority. Moreover, the
spread of private cryptocurrencies, which enter into
competition with the public forms of money, could affect
the monetary policy and the financial stability pursued by
official institutions. For these reasons, central banks all
over the world are seeking to understand if it is possible
to adopt this technology in their daily operations, with the
aim of including it in the financial system and controlling
its implementations, enhancing its benefits, and reducing its
risks (Gouveia et al., 2017; Bank for International Settlements,
2018).
DATA AVAILABILITY STATEMENT
All datasets generated for this study are included in the
article/Supplementary Material.
AUTHOR CONTRIBUTIONS
FZ: Introduction, Literature Review, and Conclusions.
CB: Materials and Methods, Main Outcomes,
and Conclusions.
ACKNOWLEDGMENTS
We acknowledge useful comments and suggestions
from two anonym ous referees that have helped to
substantially improve the paper. We are also grateful
to Alessia Rossi, who has helped us in collecting and
processing data.
SUPPLEMENTARY MATERIAL
The Supplementary Material for this article can be found
online at: https://www.frontiersin.org/articles/10.3389/frai.2020.
00021/full#supplementary-material
Frontiers in Artificial Intelligence | www.frontiersin.org 12 April 2020 | Volume 3 | Article 21
Baldan and Zen Bitcoin as a Virtual Commodity
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Conflict of Interest: The authors declare that the research was conducted in the
absence of any commercial or financial relationships that could be construed as a
potential conflict of interest.
Copyright © 2020 Baldan and Zen. This is an open-access article distributed
under the terms of the Creative Commons Attribution License (CC BY). The use,
distribution or reproduction in other forums is permitted, provided the original
author(s) and the copyright owner(s) are credited and that the original publication
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Frontiers in Artificial Intelligence | www.frontiersin.org 13 April 2020 | Volume 3 | Article 21
