Does the Hashrate Affect the Bitcoin Price?

Abstract

This paper investigates the relationship between the bitcoin price and the hashrate by disentangling the effects of the energy efficiency of the bitcoin mining equipment, bitcoin halving, and of structural breaks on the price dynamics. For this purpose, we propose a methodology based on exponential smoothing to model the dynamics of the Bitcoin network energy efficiency. We consider either directly the hashrate or the bitcoin cost-of-production model (CPM) as a proxy for the hashrate, to take any nonlinearity into account. In the first examined subsample (01/08/2016–04/12/2017), the hashrate and the CPMs were never significant, while a significant cointegration relationship was found in the second subsample (11/12/2017–24/02/2020). The empirical evidence shows that it is better to consider the hashrate directly rather than its proxy represented by the CPM when modeling its relationship with the bitcoin price. Moreover, the causality is always unidirectional going from the bitcoin price to the hashrate (or its proxies), with lags ranging from one week up to six weeks later. These findings are consistent with a large literature in energy economics, which showed that oil and gas returns affect the purchase of the drilling rigs with a delay of up to three months, whereas the impact of changes in the rig count on oil and gas returns is limited or not significant.

Full text

Journal of
Risk and Financial
Management
Article
Does the Hashrate Affect the Bitcoin Price?
Dean Fantazzini 1,* and Nikita Kolodin 2
1Moscow School of Economics, Moscow State University, Leninskie Gory, 1, Building 61,
Moscow 119992, Russia
2Higher School of Economics, Moscow 109028, Russia; nakolodin@edu.hse.ru
*Correspondence: fantazzini@mse-msu.ru; Tel.: +7-4955105267; Fax: +7-4955105256
Received: 30 September 2020; Accepted: 27 October 2020; Published: 30 October 2020


Abstract:
This paper investigates the relationship between the bitcoin price and the hashrate by
disentangling the effects of the energy efficiency of the bitcoin mining equipment, bitcoin halving,
and of structural breaks on the price dynamics. For this purpose, we propose a methodology based on
exponential smoothing to model the dynamics of the Bitcoin network energy efficiency. We consider
either directly the hashrate or the bitcoin cost-of-production model (CPM) as a proxy for the hashrate,
to take any nonlinearity into account. In the first examined subsample (01/08/2016–04/12/2017),
the hashrate and the CPMs were never significant, while a significant cointegration relationship was
found in the second subsample (11/12/2017–24/02/2020). The empirical evidence shows that it is
better to consider the hashrate directly rather than its proxy represented by the CPM when modeling
its relationship with the bitcoin price. Moreover, the causality is always unidirectional going from the
bitcoin price to the hashrate (or its proxies), with lags ranging from one week up to six weeks later.
These findings are consistent with a large literature in energy economics, which showed that oil and
gas returns affect the purchase of the drilling rigs with a delay of up to three months, whereas the
impact of changes in the rig count on oil and gas returns is limited or not significant.
Keywords: bitcoin; energy efficiency; mining; hashrate; bitcoin price
JEL Classification: C22; C32; C51; C53; E41; E42; E47; E51; G17
1. Introduction
There is a growing interest in bitcoin price dynamics both among the general public and in academia,
see Burniske and Tatar (2018); Brummer (2019); Fantazzini (2019); Schar and Berentsen (2020). The price
is not only important for purely speculative reasons but also for its role in the energy consumption
of the Bitcoin network, and in affecting the future behavior of miners—agents who power the Bitcoin
infrastructure by issuing new blocks containing the latest transactions.
There is a long-lived perception that the bitcoin price and the hashrate (i.e., the number
of computations done by bitcoin miners) are connected, see for example Cointelegraph (2020).
Some works in the financial literature went further and theorized that the movements of the hashrate
are useful in predicting the bitcoin price (Hayes 2017;Hayes 2019;Aoyagi and Hattori 2019). At first
glance, such a notion might seem wrong because producers are price-takers in competitive markets,
and the amount of effort they put into the production of a good or service have no impact over the
market price. However, this might not be the case for the bitcoin market. First, there are only a few
mining pool operators, so that they can coordinate their actions in an attempt to control the market
price. Second, the fact that bitcoin supply is inelastic and the mining business is very competitive
might force miners to operate differently: they might be willing to cap their income by hedging their
losses with the bitcoin futures introduced by the Chicago Mercantile Exchange and the CBOE in
December 2017 (Chicago Mercantile Exchange 2017) as discussed in the cryptocurrency professional
J. Risk Financial Manag. 2020,13, 263; doi:10.3390/jrfm13110263 www.mdpi.com/journal/jrfm

J. Risk Financial Manag. 2020,13, 263 2 of 29
literature (see, for example, the several articles published on
coindesk.com
and
cointelegraph.com
)
1
.
The exact economical behavior of miners is unknown and its modeling is beyond the scope of this
paper. However, if we focus only on the influence of the hashrate on the bitcoin price dynamics,
we can resort either to econometric models or to a general equilibrium model that omits the inner
workings of miners’ decision-making but directly models the relationship between the hashrate and
the price. Such an approach was first proposed by Hayes (2017), who put forward a methodology
able to predict the bitcoin price using the total hashrate and the miners’ energy efficiency as inputs.
Hayes (2019) showed that this model provided a surprisingly good fit and its equilibrium price was
able to Granger-cause the bitcoin price. On the other hand, several works explained the dynamics of
the bitcoin price using econometric models and various sets of explanatory variables, and they mostly
found that the hashrate is not statistically significant and it does not help in predicting the bitcoin
price, see Kjærland et al. (2018) and references therein.
These conflicting results drew our attention and became the main motivation for this work:
we initially thought that this contradictory evidence could have been due to different sample periods
(hence different price drivers at different times), but this is not the case: they largely intersect. A possible
explanation could be that the hashrate is not useful in predicting the bitcoin price on its own, but it has
a more complex relationship with it, as discussed by Hayes (2017).
In this paper, we examine the relationship between the hashrate (or the bitcoin cost-of-production
price) and the market price, and we try to reconcile the previous contradictory findings by disentangling
the effects of the energy efficiency of the bitcoin mining equipment, bitcoin halving, and of structural
breaks on the price dynamics.
The first contribution of the paper is a methodology based on exponential smoothing to model
the dynamics of the Bitcoin network energy efficiency as a whole. This type of smoothing naturally
trails the data and it does not use future values: the data related to future mining equipment cannot
be used to infer today’s performance to avoid any form of look-ahead bias. Moreover, this approach
easily models the gradual replacement of old equipment with the new units.
The second contribution of the paper is a set of multivariate models to investigate the nature of
the relationship between the bitcoin market price and the hashrate, both directly or through the proxy
of production costs.
The third contribution of the paper is a robustness check to verify how our results change when
computing the bitcoin cost-of-production using an electricity price no more fixed to a constant but equal
to the daily data of the Nord pool system price, which is the unconstrained market-clearing reference
price for the European Nordic region.
The paper is organized as follows: Section 2briefly reviews the literature devoted to bitcoin and
the cost-of-production model, while the methods proposed to investigate the relationship between the
bitcoin market price and the hashrate are discussed in Section 3. The empirical results are reported
in Section 4, while a robustness check is discussed in Section 5. Section 6briefly concludes. A brief
overview of Bitcoin’s operation is reported in the Appendix A.
2. Literature Review
One of the main approaches to model the bitcoin price behavior was introduced by Hayes (2017),
and it is usually known as the “cost-of-production model” (CPM). The core of this approach is the
attempt to derive the bitcoin cost of production for a given miner from the current state of the network,
the energy prices, and the energy efficiency of the miner’s equipment. The CPM thus gives the
1
However, we want to remark that in the period examined in this paper, the daily transaction volume was approximately
1–2 million BTCs, while the daily trading volume on the exchanges was up to 5–7 million BTCs. Instead, the total daily
supply of new bitcoins was equal to 1800 BTCs, which indicates that the miners’ influence on the bitcoin price may be
actually very small. The authors want to thank the anonymous CIO of one of the world’s leading full-service blockchain
technology companies for highlighting this issue.

J. Risk Financial Manag. 2020,13, 263 3 of 29
break-even cost of mining, which any individual miner would use when trying to define whether he
should be involved in mining bitcoin. Hayes (2017) generalized this approach for the whole network.
Hayes (2017) makes a few assumptions to estimate the main drivers of the bitcoin price. The first
one is that the more computational power is employed by the Bitcoin network, the higher its value
is. The second assumption simply states that all miners are rational, meaning that they are only
willing to mine for bitcoin if they are looking to extract profit. This also implicitly means that any
other cryptocurrency with no demand for it would have zero value and zero mining effort employed,
and a rational miner would redirect its resources elsewhere. The third and final assumption is that the
network difficulty can be used as a proxy of the aggregate mining power. Within the Bitcoin network,
this assumption is directly supported by the algorithm governing it: difficulty always readjusts to
ease off the effect of increased mining power or, in the opposite case, to make up for its decrease.
Hayes (2017) builds a framework aimed at showing the connection between the computational power
employed by a miner and its expected profit given the current network conditions. When a single
miner estimates its baseline profitability, it first calculates the expected number of bitcoins produced
per day:
BTC
day =βρ ·sechr
δ·232 hrday
where
β
is block reward (bitcoin per block),
δ
is the difficulty (expressed in units of Giga-Hash/block),
ρ
is the hashing power employed by a miner expressed in Giga-Hash/second,
sechr
is the number
of seconds in an hour,
hrday
is a number of hours in a day and 1
/
2
32
is a normalized probability of a
single hash “solving” a block and is an attribute of the mining algorithm. These three constants can be
fit into a single parameter θ, so the formula takes the following view:
BTC
day =βρ
δθ,θ=hrday ·sechr/232 (1)
The daily cost of mining can be expressed as follows,
Eday =ρ
1000 GH/s $
kWh
·EEF ·hrday(2)
where
Eday
is the cost per day for a producer,
$/kW h
is the price of a kilowatt-hour, and
EEF
is the
energy consumption efficiency of the miner’s hardware. Given the assumption of perfect competition
so that the marginal cost of production and the marginal profit are equal, the equilibrium price takes
the following form:
P=Eday
BTC/day =
$
kWh
·EEF ·hrday ·δ
β·1000 GH/s·θ(3)
where we set
ρ=
1000 GH/s as in Hayes (2017). The CPM offers a simple but effective framework
for estimating the cost of production price. However, it simplifies the mining expenses by dismissing
several other important factors, such as the capital and the operational expenses of the running mining
operation. Another important drawback of this model emerges around the times of the bitcoin halving
events, when the reward in bitcoins for finding new blocks is cut in half: unlike real-world miners,
this model does not anticipate this change and therefore it produces unreliable results (this issue will
be discussed later in this paper). Interestingly, Hayes (2019) found that the CPM Granger-causes the
market price but not the other way around.
It is important to remark that the CPM proposed by Hayes (2017,2019) requires a few inputs
which cannot be directly observed or reliably approximated: one such input is the electricity cost, which
is assumed by Hayes to be a constant equal to USD 0.135 per kWh—an average rate for electricity
worldwide at the time of publishing those two papers. Of course, this is not always the case for miners:
there are multiple reports of some miners having free energy (either as a form of subsidy or just by
using it covertly), which are cited and discussed in Stoll et al. (2019). Another input is the parameter for

J. Risk Financial Manag. 2020,13, 263 4 of 29
the equipment’s energy efficiency: while it is possible to determine the best mining equipment available at
a certain point in time, it is impossible to know the distribution of this equipment among miners and
thus the average energy efficiency of the network. Moreover, there are ASIC models whose presence
on the market is very limited, but the impact may be high, like—for example—the GMO miners
(gmominer.z.com/en). Therefore, this situation makes it very difficult to assess the real picture of the
total energy efficiency. The CPM relies heavily on the above-mentioned data (particularly the energy
efficiency), so one has to be very careful when fixing these two parameters.
Kristoufek (2015) was among the first to highlight that the drivers behind the bitcoin price tend to
vary over time due to the “dynamic nature of bitcoin and its rapid price fluctuations”. This idea was later
developed and expanded by Kjærland et al. (2018), who used several major commodities and indices,
different metrics from the Bitcoin network, and the Google Trends data as explanatory variables to find
which factors affect the bitcoin price dynamics. Kjærland et al. (2018) transformed the original daily
data into weekly averages to avoid potential issues related to autocorrelation. Moreover, they also deal
with outliers in the data and structural breaks. The data sample was then divided into three smaller
periods, and Autoregressive Distributed Lag (ARDL) and Generalized Autoregressive Conditional
Heteroscedasticity (GARCH) were estimated. Contrary to the findings reported by Hayes (2017,2019),
Kjærland et al. (2018) found that the hashrate of the bitcoin network does not impact the bitcoin market
price, and the only period when it seemed to do so was during the bitcoin exponential growth in 2017.
They concluded that, if anything, it is more likely that the bitcoin price impacts the hashrate than
vice-versa. Interestingly, they also found that the efficient market hypothesis appears not to hold, as the
current bitcoin price can be explained by its own lags: they assume that investors are probably affected
by the momentum effect of rising prices and vice versa where, as the price rapidly rises, “investors
see get-rich-quick potential by buying now and selling to a greater fool next week”, see
Santoni (1987)
for a
review of the “Greater Fool theory” and Jegadeesh and Titman (1993,2001) for a detailed discussion
of the “Momentum theory”. Furthermore, they also showed that Google Trends data has a positive
and significant impact on bitcoin price (similar to previous studies), and the S&P500 has a positive
impact on bitcoin price as well, interpreting this index as an indicator of investors’ overall optimism
and willingness to invest in any assets. Gold and oil are found to be insignificant, as well as the VIX
index2(except for one period).
3. Materials and Methods
The main goal of this paper is to investigate the nature of the relationship between the bitcoin
market price and the hashrate, either directly or through the proxy of production costs. Since we do
not know the true nature of this relationship, we try to model it with a large set of econometric models.
First, we look for any direct relationship between the market price and the hashrate, or between
the market price and the cost of production price. This process follows these steps:
1. We test each variable for unit roots allowing for a structural break.
2.
If the null of a unit root is rejected and a significant break is found, the sample is divided into two
subperiods, and we test for cointegration between the market price and the cost-of-production
price, or between the market price and the hashrate, in all sub-samples. Depending on the test
result, either a bivariate cointegrated model or a bivariate vector-autoregression (VAR) model
with variables in the first differences is estimated.
3.
We test for Granger causality using the approach by Toda and Yamamoto (1995), which is
consistent even if the processes may be integrated or cointegrated of arbitrary order.
More specifically, this approach requires the determination of the optimal VAR lag length
k
for the variables in levels using information criteria, and then to estimate a (
k+dmax
)th-order
2
The VIX Index is an estimate of the 30-day expected volatility of the U.S. stock market, based on real-time, mid-quote prices
of SP500 Index call and put option, see http://www.cboe.com/vix for more details.

J. Risk Financial Manag. 2020,13, 263 5 of 29
VAR where
dmax
is the maximum order of integration for our group of time-series. Toda and
Yamamoto (1995) show that we can test linear or nonlinear restrictions on the first
k
coefficient
matrices using standard asymptotic theory, while the coefficient matrices of the last
k+dmax
lagged vectors must be ignored. This Granger-causality test is performed in all subsamples.
Even though this bivariate analysis can be a useful starting point, a full multivariate analysis
is needed to analyze the bitcoin price dynamics and to avoid any potential omitted-variable bias.
We considered the set of variables used by Kjærland et al. (2018) because these explanatory variables
represent a good summary of what the literature has found so far in terms of factors affecting the
bitcoin price. This set was augmented with the cost-of-production price, which served as an alternative
to the hashrate.
To select the best multivariate model, we followed the structural relationship identification
methodology discussed by Sa-ngasoongsong et al. (2012) and Fantazzini and Toktamysova (2015). In a
nutshell, the first step is to identify the order of integration using unit root tests and, if all variables
are stationary, VAR or VARX (Vector Autoregressive with exogenous variables) models are used.
The second step determines the exogeneity of each variable using the sequential reduction method
for weak exogeneity by Greenslade et al. (2002), who consider weakly exogenous each variable for
which the test is not rejected and re-test the remaining variables until all weakly exogenous variables
are identified. For non-stationary variables, cointegration rank tests are employed to determine the
presence of a long-run relationship among the endogenous variables: if this is the case, VECM or
VECMX (Vector Error Correction model with exogenous variables) models are used, otherwise,
VAR or VARX models with variables in differences are applied, see Sa-ngasoongsong et al. (2012)
and
Fantazzini and Toktamysova (2015)
for more details. However, our approach differs from the
latter in that we employ unit root tests allowing for a structural break: if a significant break is found,
the sample is divided into two subsamples and the next steps are computed with these samples
separately, similarly to the analysis performed by Kjærland et al. (2018) with bitcoin prices.
We remark that the cost-of-production price is strongly affected by three parameters: the energy
efficiency of the Bitcoin network, the electricity price, and the bitcoin reward when a new block is
created. Setting the first two parameters is not straightforward and several variants can be used,
while the third parameter can cause undesired effects at the time of the bitcoin halving events when
the bitcoin reward is cut in half. We discuss these issues in the next sections, while a summary of our
modeling strategy is presented in Figure 1.
Figure 1.
Modeling strategy to investigate the nature of the relationship between the bitcoin market
price and the hashrate (either directly or through the proxy of production costs).

J. Risk Financial Manag. 2020,13, 263 6 of 29
3.1. An Exponential Smoothing Approach to Model the Dynamics of the Bitcoin Network Energy Efficiency
One of the most important parameters of the CPM described by Equations (1)–(3) is the energy
efficiency of the mining equipment for the whole Bitcoin network. Finding a reliable estimate for
this parameter is a very challenging task due to the scarcity of data for most mining pools, if not the
complete lack of data. Hayes (2019) computed this parameter by extracting energy efficiency data from
Bitcoin mining hardware manufacturer websites and by checking them against a dedicated wiki page
that catalogs the efficiency of the mining hardware (https://en.bitcoin.it/wiki/Mining_hardware_
comparison). He then . . . “collected these data for each date of difficulty change in the Bitcoin network,
scraped from the web using the internet archive’s wayback machine”. The network energy efficiency was
finally computed using a power log-function applied to these data
3
. We tried to replicate and extend
the Hayes’ estimated energy efficiency by web scraping data from the previous “Mining hardware
comparison” webpage. However, when we overlaid the energy efficiency estimated by Hayes (2019)
with the scraped ASIC data, we found some anomalies, see Figure 2: at the end of 2015 and until the
beginning of 2016, the estimated energy efficiency suddenly changes but the ASIC release data do not.
Moreover, during the first months of 2018, several new releases were introduced but the estimated
energy efficiency always stays above these releases. Furthermore, there is a line of violet dots constant
at 1 Joule/GH which corresponds to USB miners, which are no longer competitive products but they
still seem to be included in the computation of the energy efficiency even in 2017–2018.
Figure 2.
Energy efficiency of ASIC data scraped from the “Mining hardware comparison” webpage,
and the network energy efficiency reported by Hayes (2019). Logarithmic scale.
Given these issues, we decided to follow a different approach. First, we examined a
couple of websites that catalog the bitcoin mining equipment (see ASIC Miner Value 2020 and
Crypto Mining Tools 2020
), and we scraped their data and cross-checked it with vendor websites
and online marketplaces to find any possible discrepancies. Then, following the idea proposed by
Stoll et al. (2019)
to compute lower and upper bands for the energy efficiency, we decided to use two
alternative Holt-Winters double exponential smoothing with the scraped data to model the dynamics
of the energy efficiency for the whole Bitcoin network. We chose this kind of methodology for the
following reasons:
3The authors want to thank Adam Hayes for providing this information through private communications.

J. Risk Financial Manag. 2020,13, 263 7 of 29
1.
This type of smoothing naturally trails the data and it can model the gradual replacement of old
equipment with the new one. Changing the coefficients of the smoothing function impacts the
length of such lag.
2. It accounts for a trend that is present in the data.
3.
The energy efficiency of future ASICs cannot be used to infer today’s performance, so any
smoothing function referring to future values cannot be used.
The Holt-Winters double exponential smoothing function and its parameters for two alternative
models are reported below:
St=αyt+ (1−α)(St−1+bt−1)
bt=β(St−St−1) + (1−β)bt−1
S1=y1;b1=y2−y1
Model 1 : α=0.02, β=0.06
Model 2 : α=0.1, β=0.2
(4)
where
yt
is the raw data sequence of ASICs energy efficiencies (measured in Joule/Giga-Hash),
St
is the smoothed value at time
t
and it represents an estimate of the energy efficiency for the whole
Bitcoin network, while
bt
is the estimate of the trend at time
t
. The parameters for the two alternative
smoothing models were chosen to give the equipment a reasonable replacement rate of 2–3 months
4
,
and to get two smoothed curves: one with slow and smooth energy efficiency development over
time and the other with more abrupt changes around the release dates of new hardware. Using this
approach, we computed the change of the network energy efficiency over time that is reported in
Figure 3.
Figure 3.
Energy efficiency curves estimated with models 1 and 2 in (4) for the whole Bitcoin network,
and the respective ASIC releases. The reported data are measured in Joule/Giga-Hash.
3.2. The Cost-of-Production Model and Electricity Prices
The electricity price was fixed to a constant (0.13 dollars per kWh), similarly to Hayes (2017,2019).
Even though the actual electricity price might be lower for miners—after all, they are active seekers of
4
When buying new ASICs in the market, it usually takes 6-8 months from the release date to the widespread implementation.
Instead, if the company employs its miners, then the implementation time is down to 1 month from the release. The authors
want to thank again the anonymous CIO of one of the world’s leading full-service blockchain technology companies for
providing this information.

J. Risk Financial Manag. 2020,13, 263 8 of 29
cheap electricity—we chose this level for two reasons: (1) there is no better-educated guess; (2) if we
assume electricity prices which are potentially higher than the real ones, we can capture the effect of
some other mining operational expenses, as discussed by Stoll et al. (2019). This assumption will be
relaxed in Section 5, where we will discuss a robustness check involving electricity prices changing
every day.
3.3. The Cost-of-Production Model and the Bitcoin Reward Halving
The bitcoin halving happens once approximately every four years and cuts the block reward
(and thus the future cash flows of miners) in half. The cost-of-production model does not account
for this effect, but miners are aware of it and anticipate it. This is why the market price does not
change significantly near the times of halving, whereas the cost-of-production model shows a sudden
break in its equilibrium price. This effect is shown in Figure 4where a cost-of-production model is
considered with two different inputs for the network energy efficiency: one as originally published by
Hayes (2019) and another estimated using the first smoothing model in Equation (4).
Figure 4.
A sudden jump can be seen just before August 2016, highlighting the drawback of cost of
production model. Logarithmic scale.
Even though the two models differ due to the different methodologies used for computing the
network energy efficiency, they both show the same jump in prices at the time of the halving event in
July 2016. It is for this reason that our empirical analysis considered only bitcoin market prices between
August 2016 and February 2020 to exclude the two halving events which took place in July 2016 and
May 2020, respectively. Accounting for these breaks and the change in miners’ behavior would have
required additional assumptions and model complexities that would have probably weakened the
overall analysis. This is why we leave it as an avenue for further research, and we refer the interested
reader to Pagnotta and Buraschi (2018) and Pagnotta (2020) for two recent theoretical models dealing
with this issue5 6.
5
Pagnotta and Buraschi (2018) and Pagnotta (2020) developed two theoretical models to address the determination of bitcoin
prices, which involve the bitcoin hashrate, the reward halving, and several other variables. They showed that the effect
of the reward halving on the bitcoin price is rather complex, and may be positive or negative, depending on the other
market factors.
6
All the cryptocurrencies professionals that we contacted for this research work informed us that the effect of the reward
halving on the bitcoin price may take up to 9–12 months, from the official moment when the bitcoin reward is halved, up to
the moment it is reflected in the market prices.

J. Risk Financial Manag. 2020,13, 263 9 of 29
4. Results
4.1. Data
The dataset examined in this paper consists of weekly data ranging from 1 August 2016 till
29 February 2020: similarly to Kjærland et al. (2018), we transformed the original daily data into
weekly averages to avoid potential issues related to autocorrelation. The motivation for such a time
sample was to get the most recent data but, at the same time, to avoid any bitcoin halving events: as
we discussed in Section 3.3, the nature of these events is unique and should be studied separately.
The variables used in this paper and the reasons for using them largely follow
Kjærland et al. (2018)
. However, there are also three important differences. First, we did not
consider oil prices and VIX in our analysis: they were shown to be not statistically significant in
Kjærland et al. (2018)
and they kept being not significant in our study, so we preferred to have a
smaller set of variables to increase the efficiency of our final estimates. Second, we added a variable
measuring the transaction fees: this variable does not just show the public interest in bitcoin but rather
reveals the real “invested” interest: that is, the actual amount of money that the users are willing
to give up in commissions to move their bitcoins. Third, we consider the CPM estimated using the
inputs discussed in Section 3as an alternative to the hashrate. A description of the variables used
in the empirical analysis is reported in Table 1, while their plots are reported in Figure 5. Instead,
the cost-of-production model prices computed using the two smoothed energy efficiency curves
discussed in Section 3.1 are shown in Figure 6, together with the bitcoin market price.
Table 1. Description of the explanatory variables used in the analysis.
Variable Description Source
Bitcoin price
(USD)
Coinmarketcap computes an average price weighted by the trade
volume of the exchanges that offer bitcoin trading pairs. Coinmarketcap.com
Hashrate It is measured in tera-hashes per second (one hash is equal to a
double SHA-256 computation) Coinmetrics.io
Transaction
fees (USD)
This is the total amount of money paid by the users for the
service of moving their funds. It is computed as the weekly
average of the total daily transaction fees in bitcoin multiplied
with the weekly average of the bitcoin price.
Coinmetrics.io
Transaction
volume (USD)
This is the total value transacted on the Bitcoin network
multiplied with the weekly average of the bitcoin price. Coinmetrics.io
Google Trends
Weekly search data for the word “bitcoin” worldwide trends.google.com
Gold Price
($/Ounce)
Price in USD per troy ounce as reported by the London Bullion
Market Association. Gold is often compared with bitcoin, and the
reported similarities include: limited supply, low correlation with
stock markets, and its main use as store of value rather than unit
of account.
Quandl.com
SP500
This index is taken as an indicator of the general public
perception of the global markets. We assume public optimism
towards investment to play a certain role in the demand
for bitcoin.
Yahoo Finance

J. Risk Financial Manag. 2020,13, 263 10 of 29
0
5,000
10,000
15,000
20,000
III IV I II III IV I II III IV I II III IV I
2016 2017 2018 2019 2020
BITCOIN PRICE (BTC/USD)
2,000
2,400
2,800
3,200
3,600
III IV I II III IV I II III IV I II III IV I
2016 2017 2018 2019 2020
SP500 INDEX
0
20,000,000
40,000,000
60,000,000
80,000,000
100,000,000
120,000,000
140,000,000
III IV I II III IV I II III IV I II III IV I
2016 2017 2018 2019 2020
HASHRATE (Ter a-Hashes per se cond)
0
4,000,000
8,000,000
12,000,000
16,000,000
III IV I II III IV I II III IV I II III IV I
2016 2017 2018 2019 2020
TRANSACTION FEE S (USD)
0
2,000,000,000
4,000,000,000
6,000,000,000
8,000,000,000
10,000,000,000
III IV I II III IV I II III IV I II III IV I
2016 2017 2018 2019 2020
TRANSACTION VOLUME (USD)
0
20
40
60
80
100
120
III IV I II III IV I II III IV I II III IV I
2016 2017 2018 2019 2020
GOOGLE TRENDS
1,100
1,200
1,300
1,400
1,500
1,600
1,700
III IV I II III IV I II III IV I II III IV I
2016 2017 2018 2019 2020
GOLD PRICE ($/OUNCE)
Figure 5. Variables used in the analysis.
0
4,000
8,000
12,000
16,000
20,000
III IV I II III IV I II III IV I II III IV I
2016 2017 2018 2019 2020
BITCOIN MARKET PRICE
COST-OF-PRODUCTION MODEL 1
COST-OF-PRODUCTION MODEL 2
Figure 6. Cost-of-production model prices: Model 1 and Model 2 from Equation (4).
We analyzed the stationarity of our variables using a set of unit root tests allowing for a potential
endogenous structural break, both under the null of a unit root and under the alternative. We justify this
choice considering that there is literature showing that there was a financial bubble in the bitcoin prices

J. Risk Financial Manag. 2020,13, 263 11 of 29
in 2016–2017 that burst at the beginning of 2018, see Corbet et al. (2018);
Fry (2018)
;
Gerlach et al. (2019)
;
and Xiong et al. (2020). Moreover, there is also a debate on whether the introduction of bitcoin
futures in December 2017 crashed the market prices: in this regard, the evidence is more mixed with
Hattori and Ishida (2020)
concluding that bitcoin futures did not lead to the crash of the bitcoin market,
whereas Liu et al. (2019) and Jalan et al. (2019) affirm that they were to an extent responsible for the
crash of bitcoin prices in 2018. However, Baig et al. (2020) and Köchling et al. (2019) showed that
the introduction of bitcoin futures indeed improved the efficiency of the bitcoin markets. Given this
evidence, we employed two types of unit root tests: the Vogelsang and Perron (1998) test and the
Lee and Strazicich (2003)
test, both of them allowing for one endogenous break. The results of these
tests for the log-transformed variables and their log-returns are reported in Table 2.
Table 2. Unit root tests. Null hypothesis: the time series has a unit root. * Significant at the 5% level.
Vogelsang and Perron (1998) Lee and Strazicich (2003)
Variable t-Statistic Break Date t-Statistic Break Date
Log(Bitcoin price) −3.43 20/03/2017 −1.72 10/07/2017
Log(Hashrate) −3.46 06/11/2017 −2.05 06/11/2017
Log(Transaction_fees) −2.69 04/12/2017 −2.56 18/06/2018
Log(Transaction_volume) −3.55 17/04/2017 −2.07 24/07/2017
Log(Google) −3.01 24/04/2017 −2.11 15/05/2017
Log(Gold) −3.14 03/06/2019 −2.59 05/08/2019
Log(SP500) −2.84 17/12/2018 −3.36 15/10/2018
DLog(Bitcoin price) −13.45 * 04/12/2017 −7.89 * 27/11/2017
DLog(Hashrate) −25.75 * 30/07/2018 −4.32 * 19/11/2018
DLog(Transaction_fees) −11.68 * 01/04/2019 −5.73 * 27/11/2017
DLog(Transaction_volume) −15.66 * 04/12/2017 −7.71 * 15/01/2018
DLog(Google) −15.18 * 27/11/2017 −8.45 * 06/11/2017
DLog(Gold) −12.61 * 19/12/2016 −5.22 * 16/04/2018
DLog(SP500) −15.20 * 17/02/2020 −8.54 * 03/12/2018
The results in Table 2show that all time series are not stationary, with structural breaks mainly
located at the end of 2017 (particularly for bitcoin-related variables), which is consistent with the
past financial literature dealing with bitcoin prices. Given this evidence, we fixed a break date on
10 December 2017, which is the day when the first bitcoin futures were introduced on the CBOE,
and we divided our dataset into two samples: 01/08/2016–04/12/2017 and 11/12/2017–24/02/2020.
The next steps of our empirical analysis were then performed with these samples separately.
4.2. Bivariate Analysis
The next step of our investigation was to test for cointegration (in all subsamples) between
the market price and the cost-of-production price or between the market price and the hashrate.
We also tested for Granger causality using the approach by Toda and Yamamoto (1995), which is
consistent even if the processes may be integrated or cointegrated of arbitrary order. Note that the
Granger representation theorem by Engle and Granger (1987) assures us that if two or more time-series
are cointegrated, then there must be Granger causality between them because the error correction
term enters at least one of the equations of the error correction model. However, the presence of
Granger causality (either one-way or in both directions) does not necessarily imply that the series are
cointegrated, see Lütkepohl (2005)-chapters 6–7 and references therein for more details. The results
of the Granger causality tests using the Toda and Yamamoto (1995) approach and of the bivariate
Johansen cointegration tests are reported in Tables 3and 4, respectively.

J. Risk Financial Manag. 2020,13, 263 12 of 29
Table 3.
p-values for the Granger causality tests using the Toda and Yamamoto (1995) approach.
The tests for the CPM(model 1)-CPM(model 2), CPM(model 1)-Hashrate, and CPM(model 2)-Hashrate
pairs were not computed for obvious reasons, given how the CPMs are constructed. p-values smaller
than 0.05 are in bold font.
First Sample: 01/08/2016–04/12/2017
Dependent variable (Y)
Log(Bitcoin Price) Log(CPM_model_1) Log(CPM_model_2) Log(Hashrate)
Log(Bitcoin price) / 0.92 0.66 0.82
Regressor Log(CPM_model_1) 0.92 / / /
(X) Log(CPM_model_2) 0.95 / / /
Log(Hashrate) 0.52 / / /
Second sample: 11/12/2017–24/02/2020
Dependent variable (Y)
Log(Bitcoin Price) Log(CPM_model_1) Log(CPM_model_2) Log(Hashrate)
Log(Bitcoin price) / 0.06 0.01 0.00
Regressor Log(CPM_model_1) 0.90 / / /
(X) Log(CPM_model_2) 0.33 / / /
Log(Hashrate) 0.10 / / /
Table 4.
Bivariate Johansen cointegration tests. The null hypothesis is the absence of cointegration.
All the tests considered the case of an intercept in the cointegration equation (CE) only.
Bivariate Variable Pair 01/08/2016–04/12/2017 11/12/2017–24/02/2020
N. of CEs at 5% Level N. of CEs at 5% Level
Log(Bitcoin price), Log(CPM_model_1) 0 1
Log(Bitcoin price), Log(CPM_model_2) 0 1
Log(Bitcoin price), Log(Hashrate) 0 1
Tables 3and 4show that there is neither evidence of Granger-causality nor cointegration in the
first sample (01/08/2016–04/12/2017), whereas there is evidence of unidirectional Granger-causality
and cointegration in the second sample (11/12/2017–24/02/2020), going from the bitcoin price to the
hashrate (or to the CPM) but not vice versa. The final estimated bivariate models for both subsamples
are reported in Tables A1–A6 in Appendix B, while the misspecification tests for these models are
reported in Table 5
7
. In this regard, we computed the following battery of misspecification tests with
the models’ residuals: the multivariate Lagrange Multiplier (LM) test for residual serial correlation
up to a specified order, the multivariate Jarque-Bera normality test, and the multivariate White
heteroskedasticity test, see Johansen (1995) and Lütkepohl (2005) for more details. We also calculated
the BDS test by Broock et al. (1996) to test whether the residuals are independent and identically
distributed (iid) and which is robust against a variety of possible deviations from independence,
including linear dependence, nonlinear dependence, or chaos. Finally, we computed block exogeneity
Wald tests to check whether the bitcoin price can be treated as exogenous, by testing for the joint
significance of each of the other lagged endogenous variables in the bitcoin equation (provided that
lagged variables are present). If VECMs were used, we also tested that the factor loading associated
with the error correction term in the bitcoin equation was not statistically different from zero. For ease
of reference, we referred to the block exogeneity Wald test in Table 5as short-run, while to the test on
the factor loading as long-run.
7
The numbers of lags in the final VAR/VEC models were selected using the Akaike information criteria and to make the
residuals no more auto-correlated.

J. Risk Financial Manag. 2020,13, 263 13 of 29
Table 5.
Misspecification tests on the residuals from the bivariate models. p-values smaller than 5% are
reported in bold font.
First Sample: 01/08/2016–04/12/2017
Bivariate variable pair: Bivariate variable pair: Bivariate variable pair:
Log(Bitcoin price), Log(Bitcoin price), Log(Bitcoin price),
Log(CPM_model_1) Log(CPM_model_2) Log(Hashrate)
Model selected VAR(0) for Log-returns VAR(0) for Log-returns VAR(1) for Log-returns
Multivariate LM test (lag 4) 0.33 0.59 0.45
Multivariate LM test (lag 8) 0.87 0.85 0.26
Multivariate LM test (lag 12) 0.45 0.64 0.60
Multivariate White test 0.00 0.08 0.00
Multivariate Normality test 0.00 0.00 0.58
BDS (dim = 6) residuals 1st eq. 0.16 0.16 0.47
BDS (dim = 6) residuals 2nd eq. 0.48 0.31 0.50
Is bitcoin price weakly exogenous? Yes Yes Yes (short-run: pvalue = 0.29)
Second sample: 11/12/2017–24/02/2020
Bivariate variable pair: Bivariate variable pair: Bivariate variable pair:
Log(Bitcoin price), Log(Bitcoin price), Log(Bitcoin price),
Log(CPM_model_1) Log(CPM_model_2) Log(Hashrate)
Model selected VECM(0) VECM(2) VECM(6)
Multivariate LM test (lag 4) 0.08 0.15 0.20
Multivariate LM test (lag 8) 0.44 0.21 0.36
Multivariate LM test (lag 12) 0.64 0.54 0.91
Multivariate White test 0.00 0.00 0.07
Multivariate Normality test 0.00 0.00 0.58
BDS (dim = 6) residuals 1st eq. 0.00 0.00 0.02
BDS (dim = 6) residuals 2nd eq. 0.02 0.85 0.88
Is bitcoin price weakly exogenous? Yes (long-run: pvalue = 0.08) Yes (long-run: pvalue = 0.37) Yes (long-run: pvalue = 0.06)
(short-run: pvalue = 0.97) (short-run: pvalue = 0.07)
Tables A1–A6 and Table 5show that simple bivariate random walk models and a VAR(1) for
log-returns were sufficient to model the weak dynamics of the bitcoin prices and the hashrate/CPMs
in the first sample, while vector error correction models (VECMs) were used in the second sample.
It is possible to note that the hashrate and the CPMs did not have any effect on the bitcoin price
in any period and model, whereas the bitcoin price affected the hashrate/CPMs with lags ranging
from one week up to six weeks later, depending on the model specification. Interestingly, the models
using the hashrate showed always better misspecification tests than those using the CPMs. Moreover,
the lagged effects of bitcoin prices on the hashrate were generally longer than the same effects on the
CPMs, and these longer lags are more realistic given that it takes time to update the mining equipment.
Therefore, this initial bivariate evidence seems to highlight that it is better to consider the hashrate
directly rather than its proxy represented by the bitcoin cost-of-production model when modeling its
relationship with the bitcoin price.
4.3. Multivariate Analysis
The next step in our analysis was to select the best multivariate model using the
structural relationship identification methodology suggested by Sa-ngasoongsong et al. (2012) and
Fantazzini and Toktamysova (2015)
and the variables described in Section 4.1. The results of the
sequential reduction method for weak exogeneity using the Wald test by Toda and Yamamoto (1995)
are reported in Table 6: only Google search data and transaction fees were found to be endogenous
during the first subsample (01/08/2016–04/12/2017), while the transaction volume, the hashrate, and
the CPMs 1 and 2 were endogenous variables in the second subsample (11/12/2017–24/02/2020).
We then proceeded to test for cointegration using the variables which were deemed endogenous
according to the previous sequential test procedure, and the results of the Johansen cointegration tests
are reported in Table 7. The final estimated multivariate models for both subsamples are reported in
Tables A7–A10 in Appendix B, while the misspecification tests for these models are reported in Table 8.

J. Risk Financial Manag. 2020,13, 263 14 of 29
Table 6.
Weak exogeneity tests: variables for which the null hypothesis of weak exogeneity can be
rejected after re-testing at the 5% probability level.
First Sample: 01/08/2016–04/12/2017
Log(Transaction Fees) Log(Transaction Volume) Log(Hashrate) Log(SP500) Log(GOLD) Log(Google)
V
Log(Transaction Fees) Log(Transaction Volume) Log(CPM_model_1) Log(SP500) Log(GOLD) Log(Google)
V
Log(Transaction Fees) Log(Transaction Volume) Log(CPM_model_2) Log(SP500) Log(GOLD) Log(Google)
V
Second Sample: 11/12/2017–24/02/2020
Log(Transaction Fees) Log(Transaction Volume) Log(Hashrate) Log(SP500) Log(GOLD) Log(Google)
V
Log(Transaction Fees) Log(Transaction Volume) Log(CPM_model_1) Log(SP500) Log(GOLD) Log(Google)
V V
Log(Transaction Fees) Log(Transaction Volume) Log(CPM_model_2) Log(SP500) Log(GOLD) Log(Google)
V
Table 7.
Multivariate Johansen cointegration tests. The null hypothesis is the absence of cointegration.
The tests considered either the case of an intercept in the cointegration equation (CE) and a trend in the
variables (first sample) or the case of an intercept in the CE only (second sample). (*) The final model
turned out to be the same, independently of whether we used the hashrate, or the CPM1, or the CPM2.
First Sample: 01/08/2016-04/12/2017
Variables N. of CEs at 5% level
Log(Bitcoin_price), Log(Google) (*) 1
Log(Bitcoin_price), Log(Google) (*) 1
Log(Bitcoin_price), Log(Google) (*) 1
Second sample: 11/12/2017-24/02/2020
Variables N. of CEs at 5% level
Log(Bitcoin_price), Log(Hashrate) 1
Log(Bitcoin_price), Log(CPM_model_1), Log(Transaction volume) 1
Log(Bitcoin_price), Log(CPM_model_2) 1
In the first subsample, the hashrate and the CPM1/CPM2 were never significant, neither as
endogenous nor as exogenous variables, and the final model was a bivariate VECM(1) for the Bitcoin
price and Google search data, with transaction volume and transaction fees as exogenous variables.
The bitcoin price was found again to be weakly exogenous, and the direction of causality was from the
bitcoin price to the Google search data. Similarly to the bivariate analysis, a significant cointegration
relationship was found in the second subsample between the bitcoin price and the hashrate or its
proxies, while Google data, transaction volume, and transaction fees were found mostly to be significant
exogenous variables. Again, the model using the hashrate showed better misspecification tests than
those using the CPMs, and the lagged effects of bitcoin prices on the hashrate were generally longer
than the same effects on the CPMs. No particular difference was found when using the CPM1 or
the CPM2. Therefore, this multivariate evidence confirms the previous bivariate analysis, showing
that it is better to consider directly the hashrate rather than its proxy represented by the bitcoin
cost-of-production model when modeling its relationship with the bitcoin price. Moreover, the causality
is always unidirectional going from the bitcoin price to the hashrate/CPM1/CPM2, with lags ranging
from one week up to six weeks later. Furthermore, this evidence confirmed that there was a sharp
change in market behavior from the first period to the second one, thus corroborating the past financial
literature. The burst of the bubble at the end of 2017 and the simultaneous introduction of bitcoin
futures represented a major change in the market dynamics, by filtering the group of bitcoin traders
(only those better informed and financially robust survived the market crash) and by improving the
market efficiency, respectively.

J. Risk Financial Manag. 2020,13, 263 15 of 29
Table 8.
Misspecification tests on the residuals from the multivariate models. p-values smaller than 5%
are reported in bold font. (*) The final model turned out to be the same, independently of whether we
used the hashrate, or the CPM1, or the CPM2.
First Sample: 01/08/2016–04/12/2017
Variables: Variables: Variables:
Log(Bitcoin_price), Log(Bitcoin_price), Log(Bitcoin_price),
Log(Google) Log(Google) Log(Google)
(*) (*) (*)
Model selected VECMX(1) VECMX(1) VECMX(1)
Multivariate LM test (lag 4) 0.99 0.99 0.99
Multivariate LM test (lag 8) 0.88 0.88 0.88
Multivariate LM test (lag 12) 0.45 0.45 0.45
Multivariate White test 0.10 0.10 0.10
Multivariate Normality test 0.00 0.00 0.00
BDS (dim = 6) residuals 1st eq. 0.73 0.73 0.73
BDS (dim = 6) residuals 2nd eq. 0.28 0.28 0.28
Is bitcoin price weakly exogenous? Yes (long-run: pvalue = 0.72) Yes (long-run: pvalue = 0.72) Yes (long-run: pvalue = 0.72)
(short-run: pvalue = 0.83) (short-run: pvalue = 0.83) (short-run: pvalue = 0.83)
Second sample: 11/12/2017–24/02/2020
Variables: Variables: Variables:
Log(Bitcoin_price), Log(Bitcoin_price), Log(Bitcoin_price),
Log(Hashrate) Log(CPM_model_1) Log(CPM_model_2)
Log(Transaction volume)
Model selected VECMX(6) VECMX(2) VECMX(2)
Multivariate LM test (lag 4) 0.58 0.34 0.68
Multivariate LM test (lag 8) 0.21 0.59 0.18
Multivariate LM test (lag 12) 0.99 0.73 0.28
Multivariate White test 0.40 0.00 0.04
Multivariate Normality test 0.93 0.03 0.00
BDS (dim = 6) residuals 1st eq. 0.01 0.05 0.03
BDS (dim = 6) residuals 2nd eq. 0.70 0.01 0.66
BDS (dim = 6) residuals 3rd eq. /0.01 /
Is bitcoin price weakly exogenous? Yes (long-run: pvalue = 0.60) Yes (long-run: pvalue = 0.86) Yes (long-run: pvalue = 0.88)
(short-run: pvalue = 0.09) (short-run: pvalue = 0.81) (short-run: pvalue = 0.07)
These findings are consistent with a large literature in energy economics, which showed that
oil and gas returns affect the purchase of the drilling rigs with a delay of up to three months,
whereas the impact of changes in the rig count on oil and gas returns is limited or not significant,
see
Khalifa et al. (2017)
for a large discussion and a detailed review of this literature. Differently from
Khalifa et al. (2017) who found a nonlinear relationship, with oil returns affecting changes in rig
counts much stronger when the oil returns take on very negative values, the BDS tests on our models’
residuals did not highlight any strong missing nonlinearity. We also tested our data for nonlinear
Granger causality using the test implemented in the NlinTS R package by Hmamouche (2020) that is
based on Schreiber (2000) and Kraskov et al. (2004), as well as for threshold nonlinear cointegration
using the Seo (2006) test, but we did not find any significant evidence of nonlinearity
8
. This difference
can probably be explained by the relatively small dimension of our dataset (2016–2020) compared
to the one used by Khalifa et al. (2017) (1990–2015). Moreover, Khalifa et al. (2017) showed that the
evidence of nonlinearity has softened in the most recent years, and similar evidence was also reported
by Ansari and Kaufmann (2019) who used a linear cointegrated model.
5. Robustness Checks
We wanted to check how our previous results changed when computing the bitcoin
cost-of-production using an electricity price no more fixed to a constant but able to reflect the changing
dynamics of daily electricity markets. To achieve this goal, we employed the daily data of the Nord
8These results are not reported for the sake of space and interest and are available from the authors upon request.

J. Risk Financial Manag. 2020,13, 263 16 of 29
pool
9
system price, which is the unconstrained market clearing reference price for the European Nordic
region, computed without any congestion restrictions by setting capacities to infinity
10
. These daily
prices (originally in Euro/MWh) were transformed into $/kWh using the daily fixing of the EURUSD
pair, and they are shown in Figure 7.
.00
.02
.04
.06
.08
.10
.12
.14
III IV I II III IV I II III IV I II III IV I
2016 2017 2018 2019 2020
Figure 7. Nord Pool system price and the fixed electricity price of 0.13 $/kWh.
The Nord Pool is particularly interesting in our case because it reflects the increasing importance
of renewable energy in the European energy mix (see Jones 2017-chapter 5 for a discussion at the
textbook level), and the “majority of Bitcoin mining is mainly powered by what would otherwise be a wasted
surplus of renewable energy” (de Vries 2019), particularly hydro-power, see Bendiksen et al. (2018) for the
full details.
The CPMs computed using the Nord Pool electricity prices and the two energy efficiency curves
presented in Section 3.1 as well as the CPMs computed with constant electricity prices are reported in
Figure 8, together with the bitcoin market prices.
The CPMs computed using Nord Pool electricity prices are much lower than the CPMs computed
with a fixed electricity price of 0.13 $/kWh, because Nord Pool prices are significantly lower than this
constant price level. As we discussed in Section 3.2, an higher electricity price can capture the effect
of some other mining operational expenses, so the CPMs computed using Nord Pool prices can be
considered as proxies for the marginal cost of production, see Fantazzini (2019)-chapter 4 for a broad
discussion of this issue.
The results of the sequential reduction method for weak exogeneity using the Wald test
by
Toda and Yamamoto (1995)
and the CPMs using Nord Pool prices are reported in Table A11
(Appendix B), while the results of the Johansen cointegration tests are reported in Table A12
(Appendix B). The misspecification tests for the final selected models are reported in Table A13
(Appendix B)11.
The results using the CPMs with the Nord pool prices are not very dissimilar from the baseline
case: in the first subsample, the CPM1/CPM2 were never significant, and the final model was again
a bivariate VECM(1) for the Bitcoin price and Google search data, with transaction volume and
9
The Nord Pool is a European power exchange owned by Euronext and the continental Nordic and Baltic countries’
Transmission system operators (TSOs). At the time writing this paper, the Nord Pool operates power trading markets in
Norway, Denmark, Sweden, Finland, Estonia, Latvia, Lithuania, Germany, the Netherlands, Belgium, Austria, Luxembourg,
France, and the United Kingdom. See www.nordpoolgroup.com and references therein for more details.
10 See www.nordpoolgroup.com/trading/Day-ahead-trading/Price-calculation for more details about its calculation.
11
The estimated parameters of the final models for both subsamples are not reported here for the sake of interest and space
and are available from the authors upon request.

J. Risk Financial Manag. 2020,13, 263 17 of 29
transaction fees as exogenous variables. In the second subsample, there were no endogenous variables
according to the sequential reduction method for weak exogeneity, and the Johansen tests similarly
found no evidence of cointegration between the bitcoin market price and the CPMs. The final models
turned out to be a simple bivariate random walk (VAR(0)) and a VAR(4) model for the log-returns of
the bitcoin price and the CPM1/CPM2, respectively, with misspecification tests slightly worse than the
baseline case.
In general, the use of the Nord Pool prices to compute the CPMs tend to soften their relationship
with the bitcoin market price: this fact is already evident when looking at the correlation matrices of
the log-returns for the bitcoin price, the baseline CPMs, and the CPMs computed with the Nord pool
prices, which are reported in Table A14 in Appendix B.
0
4,000
8,000
12,000
16,000
20,000
III IV I II III IV I II III IV I II III IV I
2016 2017 2018 2019 2020
MARKET PRICE CPM1 (CONSTANT ELECTRICITY PRICE)
CPM1 (NORD POOL) CPM2 (CONSTANT ELECTRICITY PRICE)
CPM2 (NORD POOL)
Figure 8.
Bitcoin cost-of-production prices computed using both constant electricity prices and Nord
Pool prices, together with the bitcoin market price.
6. Conclusions
This paper investigated the relationship between the bitcoin price and the hashrate by
disentangling the effects of the energy efficiency of the bitcoin mining equipment, bitcoin halving,
and of structural breaks on the price dynamics. To reach this aim, we proposed a new
methodology based on exponential smoothing to model the dynamics of the Bitcoin network energy
efficiency. We considered either directly the hashrate or the bitcoin cost-of-production model by
Hayes (2017,2019)
as a proxy for the hashrate, to take any nonlinearity into account. We found
that there was neither evidence of Granger-causality nor cointegration in the first examined sample
(01/08/2016–04/12/2017), whereas there was evidence of unidirectional Granger-causality and
cointegration in the second sample (11/12/2017–24/02/2020), going from the bitcoin price to the
hashrate (or to the CPMs) but not vice versa. This evidence is thus consistent with a large literature in
energy economics, which showed that oil and gas returns affect the purchase of the drilling rigs with a
delay of up to three months, whereas the impact of changes in the rig count on oil and gas returns
is limited or not significant. Moreover, our analysis showed that it is better to consider directly the
hashrate rather than its proxy represented by the bitcoin cost-of-production model when modeling
its relationship with the bitcoin price. These results also held after we performed a robustness check
to verify how our previous results changed when computing the bitcoin cost-of-production using an
electricity price no more fixed to a constant but equal to the daily data of the Nord pool system price.
The evidence reported in this work shows that the bitcoin market has become a more mature
and efficient market after the introduction of regulated futures markets in December 2017. The usual
technical drivers (bitcoin supply and demand), attractiveness indicators, and macroeconomic variables

J. Risk Financial Manag. 2020,13, 263 18 of 29
appear to have become either lagging indicators or no more significant in explaining the dynamics
of the bitcoin price, thus confirming similar results reported by Kapar and Olmo (2020). In this
regard, we want to remark that Shanaev et al. (2019) recently showed that some of the previously
reported positive relationships between crypto-coins prices and their hashrate, or between crypto-coins
prices and their transaction counts, were either spurious due to serial correlation or inconsistent
due to endogeneity. Therefore, the development of “second-generation valuation metrics” for
cryptocurrencies (Lehner et al. 2019;Shanaev et al. 2019) able to accommodate both modern empirical
finance asset-pricing models and theory-driven valuation models is definitively a compelling avenue
for further research.
Author Contributions:
Conceptualization, N.K.; Methodology, N.K. and D.F.; software, N.K. and D.F.; validation,
N.K. and D.F.; formal analysis, N.K. and D.F. investigation, N.K. and D.F.; resources, N.K. and D.F.; data curation,
N.K. and D.F.; writing–original draft preparation, N.K. and D.F.; writing–review and editing, D.F.; visualization,
N.K. and D.F.; supervision, D.F.; project administration, D.F.; funding acquisition, D.F. All authors have read and
agreed to the published version of the manuscript.
Funding: This research was funded by Dean Fantazzini grant number 20-68-47030.
Acknowledgments:
We would like to thank all the participants of the VII International Conference in Modern
Econometric Tools and Applications (META2020), which was held in September 2020 and was organized by
the Higher School of Economics in Nizhny Novgorod (Russia). We also want to thank Sergei Tikhomirov,
an anonymous founder of a crypto-exchange, and the anonymous chief information officer (CIO) of one of the
world’s leading full-service blockchain technology companies, who provided important feedback. The first-named
author gratefully acknowledges financial support from the grant of the Russian Science Foundation n. 20-68-47030.
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A. A Brief Overview of Bitcoin’s Operation
The complete description of how the Bitcoin network works can be found in the original
whitepaper published by Nakamoto (2008) and it is beyond the scope of this paper. However, certain
aspects of its operation are briefly reviewed here to better understand the research discussed in this
paper. The bitcoin supply is completely inelastic, and it is determined by a fixed emission schedule: for
the first four years, 50 bitcoins are created on average every 10 min. After the first four years, the rate of
emission halves, and only 25 bitcoins appear within the network every 10 min. The creation of bitcoin
is again halved every four years, and this pattern is repeated until the smallest possible unit is created
12
. and, after this event, the emissions stop completely. The total amount of bitcoin to be created will
be equal to 21 million bitcoin. Due to the nature of the bitcoin protocol, the rate of emission cannot be
manipulated or altered in any way, so that we already know that emission of bitcoin will cease in the
year 2140.
Newly created bitcoins come with what is called a block: a chunk of transactions “packaged” in a
special way. The size of each block is limited, so there is a competition among those using the Bitcoin
network to have their transactions inserted into the earliest block, which gives rise to a fee market.
There is also a competition to confirm the latest transactions and produce a new block: this process
is incentivized by the (1) reward offered by the Bitcoin network (for being the first to confirm a new
block) and by the (2) fees collected from all transactions included in the block. To control the rate
of the block issuance, the bitcoin protocol has certain rules in place. Each newly created block has
to provide a so called proof of work to be considered valid. The proof of work is a hard, unforgeable
digital evidence of the “work” performed to confirm a block of transactions. In other words, to create
a valid block, one has to expend a certain amount of computational resources and then presents the
evidence of that expenditure within the block. Given that the combined computational power of all
those interested in creating a block may increase or decrease, the Bitcoin network has a concept of
difficulty: it tells how much computations on average a miner has to do before he gets a valid proof of
12 A one hundred millionth of a bitcoin is the smallest unit of the bitcoin currency and it is called a Satoshi.

J. Risk Financial Manag. 2020,13, 263 19 of 29
work. If the total computational power in the network suddenly surges, blocks start to come out at a
higher rate: the network notices that and readjusts the difficulty target to slow the rate back down.
Thus, the average time between the blocks is always kept at 10 min, independently from the changes
in the total computational power. The process of providing the proof of work for a block is called
mining and its participants are called miners. The equipment used by miners is usually called “miners”
as well. Today such equipment is dominated by application-specific integrated circuit (ASIC) chips.
The computations that miners do involve a double SHA-256 hash function, so the computational
power is often called hashrate and is measured in hashes per second. The miners are always in an arms
race for higher energy efficiency (EEF) of their ASICs and for a higher number of hashes per second
(usually measured in Ghash/sec). The current state of the network is such that even a large miner can
only hope to find a block once every year or so. Because of that, miners pool their efforts together to
increase their combined hashrate and hope to find blocks at a much faster and steadier rate. The pool
operators coordinate the miners and take a small management fee for that. In this way, an individual
miner gives up some of his expected profit in exchange for steady and predictable payouts. Each miner
incurs certain costs when mining for a block: these costs are both fixed (real estate, equipment, set-up
costs) and variable (energy, labor, cooling, etc.). By far, energy costs are the highest cost: they may be
so big that other costs might be safely neglected, see Stoll et al. (2019) for more details.
Due to the nature of the Bitcoin network, some of its parameters can be directly observed and
their past values are forever kept in its public blockchain: see, for example, the block reward, the total
transaction fees Blockchain.com (2020c), the hashrate Blockchain.com (2020b), and the difficulty
Blockchain.com (2020a). They are widely used in bitcoin-related research.
Appendix B. Model Estimates
Each equation is reported by column, while each cell reports the parameter estimate, its standard
error, and t-statistic.
Appendix B.1. Bivariate Analysis
Table A1.
VAR(0) for the Log-returns of the pair: Log(Bitcoin price), Log(CPM model 1). First sample:
01/08/2016–04/12/2017.
Variables DLog(Bitcoin Price) DLog(CPM_model_1)
Constant 0.046586 0.019783
−0.01353 −0.0046
[3.44263] [4.30423]
Table A2.
VAR(0) for the Log-returns of the pair: Log(Bitcoin price), Log(CPM model 2). First sample:
01/08/2016–04/12/2017.
Variables DLog(Bitcoin Price) DLog(CPM_model_2)
Constant 0.046586 0.021165
−0.01353 −0.00536
[3.44263] [3.94997]

J. Risk Financial Manag. 2020,13, 263 20 of 29
Table A3.
VAR(1) for the Log-returns of the pair: Log(Bitcoin price), Log(Hashrate). First sample:
01/08/2016–04/12/2017.
Variables DLog(Bitcoin Price) DLog(Hashrate)
DLog(Bitcoin price(−1)) 0.011607 −0.02143
−0.13052 −0.16834
[0.08893] [−0.12730]
DLog(Hashrate(−1)) −0.08538 −0.596435
−0.07991 -0.10306
[−1.06849] [−5.78708]
Constant 0.049622 0.047781
−0.01481 −0.0191
[3.35113] [2.50179]
Table A4.
VECM(0) for the variables Log(Bitcoin price) and Log(CPM model 1). Second sample:
11/12/2017–24/02/2020.
Error Correction (EC) Term
Log(Bitcoin price(−1)) 1
Log(CPM_model_1(−1)) −0.663981
−0.21282
[−3.11985]
Constant −2.97009
−1.81363
[−1.63765]
Variables DLog(Bitcoin price) DLog(CPM_model_1)
EC −0.03118 0.044423
−0.01726 −0.00559
[−1.80600] [7.95227]
Table A5.
VECM(2) for the variables Log(Bitcoin price) and Log(CPM model 2). Second sample:
11/12/2017–24/02/2020.
Error Correction (EC) Term
Log(Bitcoin price(−1)) 1
Log(CPM_model_2(−1)) −0.692219
−0.21357
[−3.24116]
Constant −2.806945
−1.84646
[−1.52017]
Variables D(Log(Bitcoin price)) D(Log(CPM_model_2))
EC −0.029855 0.042844
−0.03116 −0.01095
[−0.95809] [3.91310]
0.098178 0.02819
D(Log(Bitcoin price(−1))) −0.09641 −0.03388
[1.01832] [0.83217]
−0.039484 0.045213
D(Log(Bitcoin price(−2))) −0.09497 −0.03337
[−0.41575] [1.35492]
−0.004661 0.171544
D(Log(CPM_model_2(−1))) −0.24632 −0.08655
[−0.01892] [1.98206]
−0.05507 0.274415
D(Log(CPM_model_2(−2))) −0.23794 −0.0836
[−0.23145] [3.28235]

J. Risk Financial Manag. 2020,13, 263 21 of 29
Table A6.
VECM(6) for Log(Bitcoin price) and Log(Hashrate). Second sample: 11/12/2017–24/02/2020.
Error Correction (EC) Term
Log(Bitcoin price(−1)) 1
Log(Hashrate(−1)) −0.409183
−0.1125
[−3.63727]
Constant −1.256762
−2.00595
[−0.62652]
Variables D(Log(Bitcoin price)) D(Log(Hashrate))
EC −0.049126 0.147903
−0.02597 −0.02708
[−1.89180] [ 5.46226]
D(Log(Bitcoin price(−1))) 0.183584 −0.050318
−0.09211 −0.09605
[1.99306] [−0.52390]
D(Log(Bitcoin price(−2))) −0.032037 0.157578
−0.08781 −0.09156
[−0.36485] [1.72106]
D(Log(Bitcoin price(−3))) 0.108266 0.04156
−0.08754 −0.09127
[1.23682] [0.45532]
D(Log(Bitcoin price(−4))) −0.14961 −0.149548
−0.08646 −0.09016
[−1.73033] [−1.65877]
D(Log(Bitcoin price(−5))) −0.034145 0.077298
−0.08735 −0.09108
[−0.39092] [0.84871]
D(Log(Bitcoin price(−6))) 0.170596 0.072128
−0.08667 −0.09038
[1.96824] [0.79808]
D(Log(Hashrate(−1))) −0.076181 −0.736701
−0.08894 −0.09273
[−0.85659] [−7.94419]
D(Log(Hashrate(−2))) 0.009311 −0.438379
−0.10961 −0.11429
[0.08495] [−3.83559]
D(Log(Hashrate(−3))) 0.099676 −0.273345
−0.11133 −0.11608
[0.89533] [−2.35471]
D(Log(Hashrate(−4))) 0.105471 −0.275003
−0.11083 −0.11556
[0.95169] [−2.37976]
D(Log(Hashrate(−5))) −0.005624 −0.29404
−0.1056 −0.11011
[−0.05326] [−2.67035]
D(Log(Hashrate(−6))) 0.171554 −0.154059
−0.08442 −0.08803
[2.03213] [−1.75014]

J. Risk Financial Manag. 2020,13, 263 22 of 29
Appendix B.2. Multivariate Analysis
Table A7.
VECMX(1) for Log(Bitcoin price) and Log(Google), with Log(transaction volume) and
Log(Transaction fees) as exogenous variables. First sample: 01/08/2016–04/12/2017. This model
turned out to be the same, independently of whether we used the hashrate, or the CPM1, or the CPM2.
Error Correction (EC) Term
Log(Bitcoin price(−1)) 1
Log(Google(−1)) −1.000538
−0.04603
[−21.7368]
Constant −5.4321
Variables D(Log(Bitcoin price)) D(Log(Google))
EC −0.020082 0.604649
−0.05422 −0.12658
[−0.37039] [4.77691]
D(Log(Bitcoin price(−1))) −0.071363 0.143743
−0.09649 −0.22527
[−0.73957] [0.63810]
D(Log(Google(−1))) −0.012273 0.134782
−0.04903 −0.11446
[−0.25031] [1.17753]
Constant 0.02109 0.010608
−0.01033 −0.02413
[2.04073] [0.43967]
D(Log(Transaction fees)) 0.172323 0.040111
−0.04195 −0.09793
[4.10790] [0.40958]
D(Log(Transaction Volume)) 0.335968 0.443305
−0.06704 −0.15652
[5.01110] [2.83227]
Table A8.
VECMX(6) for Log(Bitcoin price), Log(Hashrate) and Log(Transaction fees),
with Log(transaction volume), Log(Google), and Log(Transaction fees) as exogenous variables. Second
sample: 11/12/2017-24/02/2020.
Error Correction (EC) Term
Log(Bitcoin price(−1)) 1
Log(Hashrate(−1)) −0.442911
−0.12766
[−3.46936]
Constant −0.620773
−2.27623
[−0.27272]
Variables D(Log(Bitcoin price)) D(Log(Hashrate))
EC −0.009204 0.143938
−0.01909 −0.02662
[−0.48217] [ 5.40721]
D(Log(Bitcoin price(−1))) 0.105778 −0.053536
−0.07226 −0.10077
[1.46388] [−0.53126]

J. Risk Financial Manag. 2020,13, 263 23 of 29
Table A8. Cont.
Error Correction (EC) Term
Variables D(Log(Bitcoin price)) D(Log(Hashrate))
D(Log(Bitcoin price(−2))) 0.032122 0.159914
−0.06866 −0.09575
[0.46786] [ 1.67010]
D(Log(Bitcoin price(−3))) −0.026725 0.040566
−0.06826 −0.0952
[−0.39151] [ 0.42612]
D(Log(Bitcoin price(−4))) −0.04931 −0.138195
−0.06636 −0.09255
[−0.74303] [−1.49317]
D(Log(Bitcoin price(−5))) −0.064049 0.073961
−0.06817 −0.09507
[−0.93961] [0.77800]
D(Log(Bitcoin price(−6))) 0.132207 0.070274
−0.06677 −0.09312
[ 1.97995] [0.75465]
D(Log(Hashrate(−1))) −0.119478 −0.741459
−0.06751 −0.09415
[−1.76969] [−7.87490]
D(Log(Hashrate(−2))) −0.016763 −0.442022
−0.08292 −0.11564
[−0.20217] [−3.82241]
D(Log(Hashrate(−3))) 0.077149 −0.277793
−0.08467 −0.11808
[0.91118] [−2.35258]
D(Log(Hashrate(−4))) −0.033626 −0.285352
−0.08528 −0.11893
[−0.39432] [−2.39936]
D(Log(Hashrate(−5))) −0.035212 −0.297643
−0.08005 −0.11164
[−0.43989] [−2.66622]
D(Log(Hashrate(−6))) 0.075737 −0.157866
−0.06518 −0.09091
[1.16190] [−1.73659]
DLog(Google) −0.164882 0.015363
−0.04637 −0.06467
[−3.55586] [0.23757]
DLog(Transaction fees) 0.074418 0.004869
−0.02798 −0.03902
[2.65972] [0.12477]
DLog(Transaction Volume) 0.326196 0.020172
−0.04868 −0.06789
[6.70053] [0.29711]

J. Risk Financial Manag. 2020,13, 263 24 of 29
Table A9.
VECMX(2) for Log(Bitcoin price), Log(CPM model 1), and Log(Transaction volume),
with Log(transaction fees), Log(Google), and Log(SP500) as exogenous variables. Second sample:
11/12/2017–24/02/2020.
Error Correction (EC) Term
Log(Bitcoin price(−1)) 1
Log(CPM_model_1(−1)) −0.631559
−0.07653
[−8.25280]
Log(Transaction Volume(−1)) −0.767616
−0.06355
[−12.0782]
Constant 12.95172
−1.78079
[7.27301]
Variables D(Log(Bitcoin price)) D(Log(CPM_model_1)) D(Log(Transaction Volume))
EC 0.012154 0.144569 0.024845
−0.07358 −0.02403 −0.11201
[0.16519] [6.01564] [0.22181]
D(Log(Bitcoin price(−1))) −0.033971 −0.051945 0.214159
−0.13416 −0.04382 −0.20424
[−0.25321] [−1.18544] [1.04859]
D(Log(Bitcoin price(−2))) −0.080567 0.02964 −0.16257
−0.11971 −0.0391 −0.18223
[−0.67304] [0.75810] [−0.89212]
D(Log(CPM_model_1(−1))) −0.222182 −0.052122 0.520264
−0.25878 −0.08452 −0.39394
[−0.85858] [−0.61668] [1.32066]
D(Log(CPM_model_1(−2))) −0.175314 0.122105 −0.855809
−0.25048 −0.08181 −0.38131
[−0.69991] [1.49252] [−2.24437]
D(Log(Transaction Volume(−1))) −0.000195 0.05502 −0.342822
−0.08185 −0.02673 −0.1246
[−0.00238] [2.05804] [−2.75130]
D(Log(Transaction Volume(−2))) −0.011235 0.028662 −0.220672
−0.07227 −0.0236 −0.11002
[−0.15546] [1.21424] [−2.00577]
DLog(Transaction fees) 0.170783 −0.007478 0.27153
−0.03007 −0.00982 −0.04578
[5.67931] [−0.76138] [5.93147]
DLog(Google) −0.139925 0.013245 0.106468
−0.05695 −0.0186 −0.0867
[−2.45686] [0.71203] [1.22800]
DLog(SP500) 0.323125 0.287191 0.429537
−0.38611 −0.12611 −0.58779
[0.83686] [2.27729] [0.73077]

J. Risk Financial Manag. 2020,13, 263 25 of 29
Table A10.
VECMX(2) for Log(Bitcoin price) and Log(CPM model 2), with Log(transaction
fees), Log(Google), and Log(Transaction volume) as exogenous variables. Second sample:
11/12/2017–24/02/2020.
Error Correction (EC) Term
Log(Bitcoin price(−1)) 1
Log(CPM_model_2(−1)) −0.788774
−0.22735
[−3.46937]
Constant −1.965044
−1.96566
[−0.99969]
Variables D(Log(Bitcoin price)) D(Log(CPM model 2))
EC −0.003327 0.04146
−0.02119 −0.01049
[−0.15697] [3.95174]
D(Log(Bitcoin price(−1))) 0.054894 0.029597
−0.07037 −0.03484
[0.78005] [0.84959]
D(Log(Bitcoin price(−2))) 0.054567 0.041797
−0.0712 −0.03525
[0.76640] [1.18588]
D(Log(CPM model 2(−1))) −0.367229 0.173548
−0.17893 −0.08858
[−2.05231] [1.95926]
D(Log(CPM model 2(−2))) 0.2832 0.287279
−0.17388 −0.08608
[1.62872] [3.33752]
D(Log(Google)) −0.181629 0.030859
−0.04477 −0.02216
[−4.05680] [1.39236]
DLog(Transaction fees) 0.072612 −0.00575
−0.02712 −0.01342
[2.67784] [−0.42836]
DLog(Transaction Volume) 0.372787 0.000915
−0.04758 −0.02355
[7.83514] [0.03883]
Appendix B.3. Robustness Checks
Table A11.
Weak exogeneity tests: variables for which the null hypothesis of weak exogeneity can be
rejected after re-testing at the 5% probability level.
First sample: 01/08/2016–04/12/2017
Log(Transaction Fees) Log(Transaction Volume) Log(CPM_model_1) Log(SP500) Log(GOLD) Log(Google)
V
Log(Transaction Fees) Log(Transaction Volume) Log(CPM_model_2) Log(SP500) Log(GOLD) Log(Google)
V
Second sample: 11/12/2017–24/02/2020
Log(Transaction Fees) Log(Transaction Volume) Log(CPM_model_1) Log(SP500) Log(GOLD) Log(Google)
Log(Transaction Fees) Log(Transaction Volume) Log(CPM_model_2) Log(SP500) Log(GOLD) Log(Google)

J. Risk Financial Manag. 2020,13, 263 26 of 29
Table A12.
Multivariate Johansen cointegration tests. The null hypothesis is the absence of
cointegration. The tests considered either the case of an intercept in the cointegration equa- tion
(CE) and a trend in the variables (first sample) or the case of an intercept in the CE only (second sample).
(*) The final model turned out to be the same, independently of whether we used the CPM1 or the
CPM2.
First Sample: 01/08/2016–04/12/2017
Variables N. of CEs at 5% level
Log(Bitcoin_price), Log(Google) (*) 1
Second sample: 11/12/2017–24/02/2020
Variables N. of CEs at 5% level
Log(Bitcoin_price), Log(CPM_model_1) 0
Log(Bitcoin_price), Log(CPM_model_2) 0
Table A13.
Misspecification tests on the residuals from the multivariate models. p-values smaller than
5% are reported in bold font. (*) The final model turned out to be the same, independently of whether
we used the CPM1 or the CPM2.
First Sample: 01/08/2016–04/12/2017
Variables: Variables:
Log(Bitcoin_price), Log(Bitcoin_price),
Log(Google) (*) Log(Google) (*)
Model selected VECMX(1) VECMX(1)
Multivariate LM test (lag 4) 0.99 0.99
Multivariate LM test (lag 8) 0.88 0.88
Multivariate LM test (lag 12) 0.45 0.45
Multivariate White test 0.10 0.10
Multivariate Normality test 0.00 0.00
BDS (dim = 6) residuals 1st eq. 0.53 0.53
BDS (dim = 6) residuals 2nd eq. 0.37 0.37
Is bitcoin price weakly exogenous? Yes (long-run: pvalue = 0.72) Yes (long-run: pvalue = 0.72)
(short-run: pvalue = 0.83) (short-run: pvalue = 0.83)
Second sample: 11/12/2017–24/02/2020
Variables: Variables:
Log(Bitcoin_price), Log(Bitcoin_price),
Log(CPM_model_1) Log(CPM_model_2)
Model selected VAR(0) for log-returns VAR(4) for log-returns
Multivariate LM test (lag 4) 0.05 0.18
Multivariate LM test (lag 8) 0.29 0.17
Multivariate LM test (lag 12) 0.95 0.87
Multivariate White test 0.00 0.02
Multivariate Normality test 0.01 0.09
BDS (dim = 6) residuals 1st eq. 0.00 0.00
BDS (dim = 6) residuals 2nd eq. 0.00 0.00
Is bitcoin price weakly exogenous? Yes Yes (short-run: pvalue = 0.16)

J. Risk Financial Manag. 2020,13, 263 27 of 29
Table A14.
Correlation matrices of the log-returns for the bitcoin price, the baseline CPMs with constant
electricity, and the CPMs computed with the Nord pool prices.
First Sample: 01/08/2016–04/12/2017
Bitcoin Market CPM1 (constant CPM2 (constant CPM1 (Nord CPM1 (Nord
price electricity price) electricity price) Pool price) Pool price)
Bitcoin Market p. 1
CPM1 (constant e. p.) 0.09 1
CPM2 (constant e.p.) 0.16 0.89 1
CPM1 (Nord P. p.) −0.08 0.12 0.12 1
CPM2 (Nord P. p.) −0.04 0.13 0.22 0.98 1
Second sample: 11/12/2017–24/02/2020
Bitcoin Market CPM1 (constant CPM2 (constant CPM1 (Nord CPM2 (Nord
price electricity price) electricity price) Pool price) Pool price)
Bitcoin Market p. 1
CPM1 (constant e. p.) −0.13 1
CPM2 (constant e.p.) −0.12 0.89 1
CPM1 (Nord P. p.) −0.07 0.40 0.42 1
CPM2 (Nord P. p.) −0.07 0.42 0.51 0.98 1
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