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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.

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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

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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.

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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.

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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

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