Fan azzini, Dean; Kolodin, Niki a
A icle
Does he hash a e a ec he bi coin p ice?
Jou nal o Risk and Financial Managemen
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MDPI – Mul idisciplina y Digi al Publishing Ins i u e, Basel
Sugges ed Ci a ion: Fan azzini, Dean; Kolodin, Niki a (2020) : Does he hash a e a ec he bi coin
p ice?, Jou nal o Risk and Financial Managemen , ISSN 1911-8074, MDPI, Basel, Vol. 13, Iss. 11, pp.
1-29,
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Jou nal o
Risk and Financial
Managemen
A icle
Does he Hash a e A ec he Bi coin P ice?
Dean Fan azzini 1,* and Niki a Kolodin 2
1Moscow School o Economics, Moscow S a e Uni e si y, Leninskie Go y, 1, Building 61,
Moscow 119992, Russia
2Highe School o Economics, Moscow 109028, Russia; [email p o ec ed]
*Co espondence: [email p o ec ed]u; Tel.: +7-4955105267; Fax: +7-4955105256
Recei ed: 30 Sep embe 2020; Accep ed: 27 Oc obe 2020; Published: 30 Oc obe 2020


Abs ac :
This pape in es iga es he ela ionship be ween he bi coin p ice and he hash a e by
disen angling he e ec s o he ene gy e iciency o he bi coin mining equipmen , bi coin hal ing,
and o s uc u al b eaks on he p ice dynamics. Fo his pu pose, we p opose a me hodology based on
exponen ial smoo hing o model he dynamics o he Bi coin ne wo k ene gy e iciency. We conside
ei he di ec ly he hash a e o he bi coin cos -o -p oduc ion model (CPM) as a p oxy o he hash a e,
o ake any nonlinea i y in o accoun . In he i s examined subsample (01/08/2016–04/12/2017),
he hash a e and he CPMs we e ne e signi ican , while a signi ican coin eg a ion ela ionship was
ound in he second subsample (11/12/2017–24/02/2020). The empi ical e idence shows ha i is
be e o conside he hash a e di ec ly a he han i s p oxy ep esen ed by he CPM when modeling
i s ela ionship wi h he bi coin p ice. Mo eo e , he causali y is always unidi ec ional going om he
bi coin p ice o he hash a e (o i s p oxies), wi h lags anging om one week up o six weeks la e .
These indings a e consis en wi h a la ge li e a u e in ene gy economics, which showed ha oil and
gas e u ns a ec he pu chase o he d illing igs wi h a delay o up o h ee mon hs, whe eas he
impac o changes in he ig coun on oil and gas e u ns is limi ed o no signi ican .
Keywo ds: bi coin; ene gy e iciency; mining; hash a e; bi coin p ice
JEL Classi ica ion: C22; C32; C51; C53; E41; E42; E47; E51; G17
1. In oduc ion
The e is a g owing in e es in bi coin p ice dynamics bo h among he gene al public and in academia,
see Bu niske and Ta a (2018); B umme (2019); Fan azzini (2019); Scha and Be en sen (2020). The p ice
is no only impo an o pu ely specula i e easons bu also o i s ole in he ene gy consump ion
o he Bi coin ne wo k, and in a ec ing he u u e beha io o mine s—agen s who powe he Bi coin
in as uc u e by issuing new blocks con aining he la es ansac ions.
The e is a long-li ed pe cep ion ha he bi coin p ice and he hash a e (i.e., he numbe
o compu a ions done by bi coin mine s) a e connec ed, see o example Coin eleg aph (2020).
Some wo ks in he inancial li e a u e wen u he and heo ized ha he mo emen s o he hash a e
a e use ul in p edic ing he bi coin p ice (Hayes 2017;Hayes 2019;Aoyagi and Ha o i 2019). A i s
glance, such a no ion migh seem w ong because p oduce s a e p ice- ake s in compe i i e ma ke s,
and he amoun o e o hey pu in o he p oduc ion o a good o se ice ha e no impac o e he
ma ke p ice. Howe e , his migh no be he case o he bi coin ma ke . Fi s , he e a e only a ew
mining pool ope a o s, so ha hey can coo dina e hei ac ions in an a emp o con ol he ma ke
p ice. Second, he ac ha bi coin supply is inelas ic and he mining business is e y compe i i e
migh o ce mine s o ope a e di e en ly: hey migh be willing o cap hei income by hedging hei
losses wi h he bi coin u u es in oduced by he Chicago Me can ile Exchange and he CBOE in
Decembe 2017 (Chicago Me can ile Exchange 2017) as discussed in he c yp ocu ency p o essional
J. Risk Financial Manag. 2020,13, 263; doi:10.3390/j m13110263 www.mdpi.com/jou nal/j m
J. Risk Financial Manag. 2020,13, 263 2 o 29
li e a u e (see, o example, he se e al a icles published on
coindesk.com
and
coin eleg aph.com
)
1
.
The exac economical beha io o mine s is unknown and i s modeling is beyond he scope o his
pape . Howe e , i we ocus only on he in luence o he hash a e on he bi coin p ice dynamics,
we can eso ei he o econome ic models o o a gene al equilib ium model ha omi s he inne
wo kings o mine s’ decision-making bu di ec ly models he ela ionship be ween he hash a e and
he p ice. Such an app oach was i s p oposed by Hayes (2017), who pu o wa d a me hodology
able o p edic he bi coin p ice using he o al hash a e and he mine s’ ene gy e iciency as inpu s.
Hayes (2019) showed ha his model p o ided a su p isingly good i and i s equilib ium p ice was
able o G ange -cause he bi coin p ice. On he o he hand, se e al wo ks explained he dynamics o
he bi coin p ice using econome ic models and a ious se s o explana o y a iables, and hey mos ly
ound ha he hash a e is no s a is ically signi ican and i does no help in p edic ing he bi coin
p ice, see Kjæ land e al. (2018) and e e ences he ein.
These con lic ing esul s d ew ou a en ion and became he main mo i a ion o his wo k:
we ini ially hough ha his con adic o y e idence could ha e been due o di e en sample pe iods
(hence di e en p ice d i e s a di e en imes), bu his is no he case: hey la gely in e sec . A possible
explana ion could be ha he hash a e is no use ul in p edic ing he bi coin p ice on i s own, bu i has
a mo e complex ela ionship wi h i , as discussed by Hayes (2017).
In his pape , we examine he ela ionship be ween he hash a e (o he bi coin cos -o -p oduc ion
p ice) and he ma ke p ice, and we y o econcile he p e ious con adic o y indings by disen angling
he e ec s o he ene gy e iciency o he bi coin mining equipmen , bi coin hal ing, and o s uc u al
b eaks on he p ice dynamics.
The i s con ibu ion o he pape is a me hodology based on exponen ial smoo hing o model
he dynamics o he Bi coin ne wo k ene gy e iciency as a whole. This ype o smoo hing na u ally
ails he da a and i does no use u u e alues: he da a ela ed o u u e mining equipmen canno
be used o in e oday’s pe o mance o a oid any o m o look-ahead bias. Mo eo e , his app oach
easily models he g adual eplacemen o old equipmen wi h he new uni s.
The second con ibu ion o he pape is a se o mul i a ia e models o in es iga e he na u e o
he ela ionship be ween he bi coin ma ke p ice and he hash a e, bo h di ec ly o h ough he p oxy
o p oduc ion cos s.
The hi d con ibu ion o he pape is a obus ness check o e i y how ou esul s change when
compu ing he bi coin cos -o -p oduc ion using an elec ici y p ice no mo e ixed o a cons an bu equal
o he daily da a o he No d pool sys em p ice, which is he uncons ained ma ke -clea ing e e ence
p ice o he Eu opean No dic egion.
The pape is o ganized as ollows: Sec ion 2b ie ly e iews he li e a u e de o ed o bi coin and
he cos -o -p oduc ion model, while he me hods p oposed o in es iga e he ela ionship be ween he
bi coin ma ke p ice and he hash a e a e discussed in Sec ion 3. The empi ical esul s a e epo ed
in Sec ion 4, while a obus ness check is discussed in Sec ion 5. Sec ion 6b ie ly concludes. A b ie
o e iew o Bi coin’s ope a ion is epo ed in he Appendix A.
2. Li e a u e Re iew
One o he main app oaches o model he bi coin p ice beha io was in oduced by Hayes (2017),
and i is usually known as he “cos -o -p oduc ion model” (CPM). The co e o his app oach is he
a emp o de i e he bi coin cos o p oduc ion o a gi en mine om he cu en s a e o he ne wo k,
he ene gy p ices, and he ene gy e iciency o he mine ’s equipmen . The CPM hus gi es he
1
Howe e , we wan o ema k ha in he pe iod examined in his pape , he daily ansac ion olume was app oxima ely
1–2 million BTCs, while he daily ading olume on he exchanges was up o 5–7 million BTCs. Ins ead, he o al daily
supply o new bi coins was equal o 1800 BTCs, which indica es ha he mine s’ in luence on he bi coin p ice may be
ac ually e y small. The au ho s wan o hank he anonymous CIO o one o he wo ld’s leading ull-se ice blockchain
echnology companies o highligh ing his issue.
J. Risk Financial Manag. 2020,13, 263 3 o 29
b eak-e en cos o mining, which any indi idual mine would use when ying o de ine whe he he
should be in ol ed in mining bi coin. Hayes (2017) gene alized his app oach o he whole ne wo k.
Hayes (2017) makes a ew assump ions o es ima e he main d i e s o he bi coin p ice. The i s
one is ha he mo e compu a ional powe is employed by he Bi coin ne wo k, he highe i s alue
is. The second assump ion simply s a es ha all mine s a e a ional, meaning ha hey a e only
willing o mine o bi coin i hey a e looking o ex ac p o i . This also implici ly means ha any
o he c yp ocu ency wi h no demand o i would ha e ze o alue and ze o mining e o employed,
and a a ional mine would edi ec i s esou ces elsewhe e. The hi d and inal assump ion is ha he
ne wo k di icul y can be used as a p oxy o he agg ega e mining powe . Wi hin he Bi coin ne wo k,
his assump ion is di ec ly suppo ed by he algo i hm go e ning i : di icul y always eadjus s o
ease o he e ec o inc eased mining powe o , in he opposi e case, o make up o i s dec ease.
Hayes (2017) builds a amewo k aimed a showing he connec ion be ween he compu a ional powe
employed by a mine and i s expec ed p o i gi en he cu en ne wo k condi ions. When a single
mine es ima es i s baseline p o i abili y, i i s calcula es he expec ed numbe o bi coins p oduced
pe day:
BTC
day =βρ ·sech
δ·232 h day
whe e
β
is block ewa d (bi coin pe block),
δ
is he di icul y (exp essed in uni s o Giga-Hash/block),
ρ
is he hashing powe employed by a mine exp essed in Giga-Hash/second,
sech
is he numbe
o seconds in an hou ,
h day
is a numbe o hou s in a day and 1
/
2
32
is a no malized p obabili y o a
single hash “sol ing” a block and is an a ibu e o he mining algo i hm. These h ee cons an s can be
i in o a single pa ame e θ, so he o mula akes he ollowing iew:
BTC
day =βρ
δθ,θ=h day ·sech /232 (1)
The daily cos o mining can be exp essed as ollows,
Eday =ρ
1000 GH/s $
kWh
·EEF ·h day(2)
whe e
Eday
is he cos pe day o a p oduce ,
$/kWh
is he p ice o a kilowa -hou , and
EEF
is he
ene gy consump ion e iciency o he mine ’s ha dwa e. Gi en he assump ion o pe ec compe i ion
so ha he ma ginal cos o p oduc ion and he ma ginal p o i a e equal, he equilib ium p ice akes
he ollowing o m:
P=Eday
BTC/day =
$
kWh
·EEF ·h day ·δ
β·1000 GH/s·θ(3)
whe e we se
ρ=
1000 GH/s as in Hayes (2017). The CPM o e s a simple bu e ec i e amewo k
o es ima ing he cos o p oduc ion p ice. Howe e , i simpli ies he mining expenses by dismissing
se e al o he impo an ac o s, such as he capi al and he ope a ional expenses o he unning mining
ope a ion. Ano he impo an d awback o his model eme ges a ound he imes o he bi coin hal ing
e en s, when he ewa d in bi coins o inding new blocks is cu in hal : unlike eal-wo ld mine s,
his model does no an icipa e his change and he e o e i p oduces un eliable esul s ( his issue will
be discussed la e in his pape ). In e es ingly, Hayes (2019) ound ha he CPM G ange -causes he
ma ke p ice bu no he o he way a ound.
I is impo an o ema k ha he CPM p oposed by Hayes (2017,2019) equi es a ew inpu s
which canno be di ec ly obse ed o eliably app oxima ed: one such inpu is he elec ici y cos , which
is assumed by Hayes o be a cons an equal o USD 0.135 pe kWh—an a e age a e o elec ici y
wo ldwide a he ime o publishing hose wo pape s. O cou se, his is no always he case o mine s:
he e a e mul iple epo s o some mine s ha ing ee ene gy (ei he as a o m o subsidy o jus by
using i co e ly), which a e ci ed and discussed in S oll e al. (2019). Ano he inpu is he pa ame e o
J. Risk Financial Manag. 2020,13, 263 4 o 29
he equipmen ’s ene gy e iciency: while i is possible o de e mine he bes mining equipmen a ailable a
a ce ain poin in ime, i is impossible o know he dis ibu ion o his equipmen among mine s and
hus he a e age ene gy e iciency o he ne wo k. Mo eo e , he e a e ASIC models whose p esence
on he ma ke is e y limi ed, bu he impac may be high, like— o example— he GMO mine s
(gmomine .z.com/en). The e o e, his si ua ion makes i e y di icul o assess he eal pic u e o he
o al ene gy e iciency. The CPM elies hea ily on he abo e-men ioned da a (pa icula ly he ene gy
e iciency), so one has o be e y ca e ul when ixing hese wo pa ame e s.
K is ou ek (2015) was among he i s o highligh ha he d i e s behind he bi coin p ice end o
a y o e ime due o he “dynamic na u e o bi coin and i s apid p ice luc ua ions”. This idea was la e
de eloped and expanded by Kjæ land e al. (2018), who used se e al majo commodi ies and indices,
di e en me ics om he Bi coin ne wo k, and he Google T ends da a as explana o y a iables o ind
which ac o s a ec he bi coin p ice dynamics. Kjæ land e al. (2018) ans o med he o iginal daily
da a in o weekly a e ages o a oid po en ial issues ela ed o au oco ela ion. Mo eo e , hey also deal
wi h ou lie s in he da a and s uc u al b eaks. The da a sample was hen di ided in o h ee smalle
pe iods, and Au o eg essi e Dis ibu ed Lag (ARDL) and Gene alized Au o eg essi e Condi ional
He e oscedas ici y (GARCH) we e es ima ed. Con a y o he indings epo ed by Hayes (2017,2019),
Kjæ land e al. (2018) ound ha he hash a e o he bi coin ne wo k does no impac he bi coin ma ke
p ice, and he only pe iod when i seemed o do so was du ing he bi coin exponen ial g ow h in 2017.
They concluded ha , i any hing, i is mo e likely ha he bi coin p ice impac s he hash a e han
ice- e sa. In e es ingly, hey also ound ha he e icien ma ke hypo hesis appea s no o hold, as he
cu en bi coin p ice can be explained by i s own lags: hey assume ha in es o s a e p obably a ec ed
by he momen um e ec o ising p ices and ice e sa whe e, as he p ice apidly ises, “in es o s
see ge - ich-quick po en ial by buying now and selling o a g ea e ool nex week”, see
San oni (1987)
o a
e iew o he “G ea e Fool heo y” and Jegadeesh and Ti man (1993,2001) o a de ailed discussion
o he “Momen um heo y”. Fu he mo e, hey also showed ha Google T ends da a has a posi i e
and signi ican impac on bi coin p ice (simila o p e ious s udies), and he S&P500 has a posi i e
impac on bi coin p ice as well, in e p e ing his index as an indica o o in es o s’ o e all op imism
and willingness o in es in any asse s. Gold and oil a e ound o be insigni ican , as well as he VIX
index2(excep o one pe iod).
3. Ma e ials and Me hods
The main goal o his pape is o in es iga e he na u e o he ela ionship be ween he bi coin
ma ke p ice and he hash a e, ei he di ec ly o h ough he p oxy o p oduc ion cos s. Since we do
no know he ue na u e o his ela ionship, we y o model i wi h a la ge se o econome ic models.
Fi s , we look o any di ec ela ionship be ween he ma ke p ice and he hash a e, o be ween
he ma ke p ice and he cos o p oduc ion p ice. This p ocess ollows hese s eps:
1. We es each a iable o uni oo s allowing o a s uc u al b eak.
2.
I he null o a uni oo is ejec ed and a signi ican b eak is ound, he sample is di ided in o wo
subpe iods, and we es o coin eg a ion be ween he ma ke p ice and he cos -o -p oduc ion
p ice, o be ween he ma ke p ice and he hash a e, in all sub-samples. Depending on he es
esul , ei he a bi a ia e coin eg a ed model o a bi a ia e ec o -au o eg ession (VAR) model
wi h a iables in he i s di e ences is es ima ed.
3.
We es o G ange causali y using he app oach by Toda and Yamamo o (1995), which is
consis en e en i he p ocesses may be in eg a ed o coin eg a ed o a bi a y o de .
Mo e speci ically, his app oach equi es he de e mina ion o he op imal VAR lag leng h
k
o he a iables in le els using in o ma ion c i e ia, and hen o es ima e a (
k+dmax
) h-o de
2
The VIX Index is an es ima e o he 30-day expec ed ola ili y o he U.S. s ock ma ke , based on eal- ime, mid-quo e p ices
o SP500 Index call and pu op ion, see h p://www.cboe.com/ ix o mo e de ails.

J. Risk Financial Manag. 2020,13, 263 5 o 29
VAR whe e
dmax
is he maximum o de o in eg a ion o ou g oup o ime-se ies. Toda and
Yamamo o (1995) show ha we can es linea o nonlinea es ic ions on he i s
k
coe icien
ma ices using s anda d asymp o ic heo y, while he coe icien ma ices o he las
k+dmax
lagged ec o s mus be igno ed. This G ange -causali y es is pe o med in all subsamples.
E en hough his bi a ia e analysis can be a use ul s a ing poin , a ull mul i a ia e analysis
is needed o analyze he bi coin p ice dynamics and o a oid any po en ial omi ed- a iable bias.
We conside ed he se o a iables used by Kjæ land e al. (2018) because hese explana o y a iables
ep esen a good summa y o wha he li e a u e has ound so a in e ms o ac o s a ec ing he
bi coin p ice. This se was augmen ed wi h he cos -o -p oduc ion p ice, which se ed as an al e na i e
o he hash a e.
To selec he bes mul i a ia e model, we ollowed he s uc u al ela ionship iden i ica ion
me hodology discussed by Sa-ngasoongsong e al. (2012) and Fan azzini and Tok amyso a (2015). In a
nu shell, he i s s ep is o iden i y he o de o in eg a ion using uni oo es s and, i all a iables
a e s a iona y, VAR o VARX (Vec o Au o eg essi e wi h exogenous a iables) models a e used.
The second s ep de e mines he exogenei y o each a iable using he sequen ial educ ion me hod
o weak exogenei y by G eenslade e al. (2002), who conside weakly exogenous each a iable o
which he es is no ejec ed and e- es he emaining a iables un il all weakly exogenous a iables
a e iden i ied. Fo non-s a iona y a iables, coin eg a ion ank es s a e employed o de e mine he
p esence o a long- un ela ionship among he endogenous a iables: i his is he case, VECM o
VECMX (Vec o E o Co ec ion model wi h exogenous a iables) models a e used, o he wise,
VAR o VARX models wi h a iables in di e ences a e applied, see Sa-ngasoongsong e al. (2012)
and
Fan azzini and Tok amyso a (2015)
o mo e de ails. Howe e , ou app oach di e s om he
la e in ha we employ uni oo es s allowing o a s uc u al b eak: i a signi ican b eak is ound,
he sample is di ided in o wo subsamples and he nex s eps a e compu ed wi h hese samples
sepa a ely, simila ly o he analysis pe o med by Kjæ land e al. (2018) wi h bi coin p ices.
We ema k ha he cos -o -p oduc ion p ice is s ongly a ec ed by h ee pa ame e s: he ene gy
e iciency o he Bi coin ne wo k, he elec ici y p ice, and he bi coin ewa d when a new block is
c ea ed. Se ing he i s wo pa ame e s is no s aigh o wa d and se e al a ian s can be used,
while he hi d pa ame e can cause undesi ed e ec s a he ime o he bi coin hal ing e en s when
he bi coin ewa d is cu in hal . We discuss hese issues in he nex sec ions, while a summa y o ou
modeling s a egy is p esen ed in Figu e 1.
Figu e 1.
Modeling s a egy o in es iga e he na u e o he ela ionship be ween he bi coin ma ke
p ice and he hash a e (ei he di ec ly o h ough he p oxy o p oduc ion cos s).
J. Risk Financial Manag. 2020,13, 263 6 o 29
3.1. An Exponen ial Smoo hing App oach o Model he Dynamics o he Bi coin Ne wo k Ene gy E iciency
One o he mos impo an pa ame e s o he CPM desc ibed by Equa ions (1)–(3) is he ene gy
e iciency o he mining equipmen o he whole Bi coin ne wo k. Finding a eliable es ima e o
his pa ame e is a e y challenging ask due o he sca ci y o da a o mos mining pools, i no he
comple e lack o da a. Hayes (2019) compu ed his pa ame e by ex ac ing ene gy e iciency da a om
Bi coin mining ha dwa e manu ac u e websi es and by checking hem agains a dedica ed wiki page
ha ca alogs he e iciency o he mining ha dwa e (h ps://en.bi coin.i /wiki/Mining_ha dwa e_
compa ison). He hen ...“collec ed hese da a o each da e o di icul y change in he Bi coin ne wo k,
sc aped om he web using he in e ne a chi e’s wayback machine”. The ne wo k ene gy e iciency was
inally compu ed using a powe log- unc ion applied o hese da a
3
. We ied o eplica e and ex end
he Hayes’ es ima ed ene gy e iciency by web sc aping da a om he p e ious “Mining ha dwa e
compa ison” webpage. Howe e , when we o e laid he ene gy e iciency es ima ed by Hayes (2019)
wi h he sc aped ASIC da a, we ound some anomalies, see Figu e 2: a he end o 2015 and un il he
beginning o 2016, he es ima ed ene gy e iciency suddenly changes bu he ASIC elease da a do no .
Mo eo e , du ing he i s mon hs o 2018, se e al new eleases we e in oduced bu he es ima ed
ene gy e iciency always s ays abo e hese eleases. Fu he mo e, he e is a line o iole do s cons an
a 1 Joule/GH which co esponds o USB mine s, which a e no longe compe i i e p oduc s bu hey
s ill seem o be included in he compu a ion o he ene gy e iciency e en in 2017–2018.
Figu e 2.
Ene gy e iciency o ASIC da a sc aped om he “Mining ha dwa e compa ison” webpage,
and he ne wo k ene gy e iciency epo ed by Hayes (2019). Loga i hmic scale.
Gi en hese issues, we decided o ollow a di e en app oach. Fi s , we examined a
couple o websi es ha ca alog he bi coin mining equipmen (see ASIC Mine Value 2020 and
C yp o Mining Tools 2020
), and we sc aped hei da a and c oss-checked i wi h endo websi es
and online ma ke places o ind any possible disc epancies. Then, ollowing he idea p oposed by
S oll e al. (2019)
o compu e lowe and uppe bands o he ene gy e iciency, we decided o use wo
al e na i e Hol -Win e s double exponen ial smoo hing wi h he sc aped da a o model he dynamics
o he ene gy e iciency o he whole Bi coin ne wo k. We chose his kind o me hodology o he
ollowing easons:
3The au ho s wan o hank Adam Hayes o p o iding his in o ma ion h ough p i a e communica ions.
J. Risk Financial Manag. 2020,13, 263 7 o 29
1.
This ype o smoo hing na u ally ails he da a and i can model he g adual eplacemen o old
equipmen wi h he new one. Changing he coe icien s o he smoo hing unc ion impac s he
leng h o such lag.
2. I accoun s o a end ha is p esen in he da a.
3.
The ene gy e iciency o u u e ASICs canno be used o in e oday’s pe o mance, so any
smoo hing unc ion e e ing o u u e alues canno be used.
The Hol -Win e s double exponen ial smoo hing unc ion and i s pa ame e s o wo al e na i e
models a e epo ed below:
S =αy + (1−α)(S −1+b −1)
b =β(S −S −1) + (1−β)b −1
S1=y1;b1=y2−y1
Model 1 : α=0.02, β=0.06
Model 2 : α=0.1, β=0.2
(4)
whe e
y
is he aw da a sequence o ASICs ene gy e iciencies (measu ed in Joule/Giga-Hash),
S
is he smoo hed alue a ime
and i ep esen s an es ima e o he ene gy e iciency o he whole
Bi coin ne wo k, while
b
is he es ima e o he end a ime
. The pa ame e s o he wo al e na i e
smoo hing models we e chosen o gi e he equipmen a easonable eplacemen a e o 2–3 mon hs
4
,
and o ge wo smoo hed cu es: one wi h slow and smoo h ene gy e iciency de elopmen o e
ime and he o he wi h mo e ab up changes a ound he elease da es o new ha dwa e. Using his
app oach, we compu ed he change o he ne wo k ene gy e iciency o e ime ha is epo ed in
Figu e 3.
Figu e 3.
Ene gy e iciency cu es es ima ed wi h models 1 and 2 in (4) o he whole Bi coin ne wo k,
and he espec i e ASIC eleases. The epo ed da a a e measu ed in Joule/Giga-Hash.
3.2. The Cos -o -P oduc ion Model and Elec ici y P ices
The elec ici y p ice was ixed o a cons an (0.13 dolla s pe kWh), simila ly o Hayes (2017,2019).
E en hough he ac ual elec ici y p ice migh be lowe o mine s—a e all, hey a e ac i e seeke s o
4
When buying new ASICs in he ma ke , i usually akes 6-8 mon hs om he elease da e o he widesp ead implemen a ion.
Ins ead, i he company employs i s mine s, hen he implemen a ion ime is down o 1 mon h om he elease. The au ho s
wan o hank again he anonymous CIO o one o he wo ld’s leading ull-se ice blockchain echnology companies o
p o iding his in o ma ion.
J. Risk Financial Manag. 2020,13, 263 8 o 29
cheap elec ici y—we chose his le el o wo easons: (1) he e is no be e -educa ed guess; (2) i we
assume elec ici y p ices which a e po en ially highe han he eal ones, we can cap u e he e ec o
some o he mining ope a ional expenses, as discussed by S oll e al. (2019). This assump ion will be
elaxed in Sec ion 5, whe e we will discuss a obus ness check in ol ing elec ici y p ices changing
e e y day.
3.3. The Cos -o -P oduc ion Model and he Bi coin Rewa d Hal ing
The bi coin hal ing happens once app oxima ely e e y ou yea s and cu s he block ewa d
(and hus he u u e cash lows o mine s) in hal . The cos -o -p oduc ion model does no accoun
o his e ec , bu mine s a e awa e o i and an icipa e i . This is why he ma ke p ice does no
change signi ican ly nea he imes o hal ing, whe eas he cos -o -p oduc ion model shows a sudden
b eak in i s equilib ium p ice. This e ec is shown in Figu e 4whe e a cos -o -p oduc ion model is
conside ed wi h wo di e en inpu s o he ne wo k ene gy e iciency: one as o iginally published by
Hayes (2019) and ano he es ima ed using he i s smoo hing model in Equa ion (4).
Figu e 4.
A sudden jump can be seen jus be o e Augus 2016, highligh ing he d awback o cos o
p oduc ion model. Loga i hmic scale.
E en hough he wo models di e due o he di e en me hodologies used o compu ing he
ne wo k ene gy e iciency, hey bo h show he same jump in p ices a he ime o he hal ing e en in
July 2016. I is o his eason ha ou empi ical analysis conside ed only bi coin ma ke p ices be ween
Augus 2016 and Feb ua y 2020 o exclude he wo hal ing e en s which ook place in July 2016 and
May 2020, espec i ely. Accoun ing o hese b eaks and he change in mine s’ beha io would ha e
equi ed addi ional assump ions and model complexi ies ha would ha e p obably weakened he
o e all analysis. This is why we lea e i as an a enue o u he esea ch, and we e e he in e es ed
eade o Pagno a and Bu aschi (2018) and Pagno a (2020) o wo ecen heo e ical models dealing
wi h his issue5 6.
5
Pagno a and Bu aschi (2018) and Pagno a (2020) de eloped wo heo e ical models o add ess he de e mina ion o bi coin
p ices, which in ol e he bi coin hash a e, he ewa d hal ing, and se e al o he a iables. They showed ha he e ec
o he ewa d hal ing on he bi coin p ice is a he complex, and may be posi i e o nega i e, depending on he o he
ma ke ac o s.
6
All he c yp ocu encies p o essionals ha we con ac ed o his esea ch wo k in o med us ha he e ec o he ewa d
hal ing on he bi coin p ice may ake up o 9–12 mon hs, om he o icial momen when he bi coin ewa d is hal ed, up o
he momen i is e lec ed in he ma ke p ices.
J. Risk Financial Manag. 2020,13, 263 15 o 29
Table 8.
Misspeci ica ion es s on he esiduals om he mul i a ia e models. p- alues smalle han 5%
a e epo ed in bold on . (*) The inal model u ned ou o be he same, independen ly o whe he we
used he hash a e, o he CPM1, o he CPM2.
Fi s Sample: 01/08/2016–04/12/2017
Va iables: Va iables: Va iables:
Log(Bi coin_p ice), Log(Bi coin_p ice), Log(Bi coin_p ice),
Log(Google) Log(Google) Log(Google)
(*) (*) (*)
Model selec ed VECMX(1) VECMX(1) VECMX(1)
Mul i a ia e LM es (lag 4) 0.99 0.99 0.99
Mul i a ia e LM es (lag 8) 0.88 0.88 0.88
Mul i a ia e LM es (lag 12) 0.45 0.45 0.45
Mul i a ia e Whi e es 0.10 0.10 0.10
Mul i a ia e No mali y es 0.00 0.00 0.00
BDS (dim = 6) esiduals 1s eq. 0.73 0.73 0.73
BDS (dim = 6) esiduals 2nd eq. 0.28 0.28 0.28
Is bi coin p ice weakly exogenous? Yes (long- un: p alue = 0.72) Yes (long- un: p alue = 0.72) Yes (long- un: p alue = 0.72)
(sho - un: p alue = 0.83) (sho - un: p alue = 0.83) (sho - un: p alue = 0.83)
Second sample: 11/12/2017–24/02/2020
Va iables: Va iables: Va iables:
Log(Bi coin_p ice), Log(Bi coin_p ice), Log(Bi coin_p ice),
Log(Hash a e) Log(CPM_model_1) Log(CPM_model_2)
Log(T ansac ion olume)
Model selec ed VECMX(6) VECMX(2) VECMX(2)
Mul i a ia e LM es (lag 4) 0.58 0.34 0.68
Mul i a ia e LM es (lag 8) 0.21 0.59 0.18
Mul i a ia e LM es (lag 12) 0.99 0.73 0.28
Mul i a ia e Whi e es 0.40 0.00 0.04
Mul i a ia e No mali y es 0.93 0.03 0.00
BDS (dim = 6) esiduals 1s eq. 0.01 0.05 0.03
BDS (dim = 6) esiduals 2nd eq. 0.70 0.01 0.66
BDS (dim = 6) esiduals 3 d eq. /0.01 /
Is bi coin p ice weakly exogenous? Yes (long- un: p alue = 0.60) Yes (long- un: p alue = 0.86) Yes (long- un: p alue = 0.88)
(sho - un: p alue = 0.09) (sho - un: p alue = 0.81) (sho - un: p alue = 0.07)
These indings a e consis en wi h a la ge li e a u e in ene gy economics, which showed ha
oil and gas e u ns a ec he pu chase o he d illing igs wi h a delay o up o h ee mon hs,
whe eas he impac o changes in he ig coun on oil and gas e u ns is limi ed o no signi ican ,
see
Khali a e al. (2017)
o a la ge discussion and a de ailed e iew o his li e a u e. Di e en ly om
Khali a e al. (2017) who ound a nonlinea ela ionship, wi h oil e u ns a ec ing changes in ig
coun s much s onge when he oil e u ns ake on e y nega i e alues, he BDS es s on ou models’
esiduals did no highligh any s ong missing nonlinea i y. We also es ed ou da a o nonlinea
G ange causali y using he es implemen ed in he NlinTS R package by Hmamouche (2020) ha is
based on Sch eibe (2000) and K asko e al. (2004), as well as o h eshold nonlinea coin eg a ion
using he Seo (2006) es , bu we did no ind any signi ican e idence o nonlinea i y
8
. This di e ence
can p obably be explained by he ela i ely small dimension o ou da ase (2016–2020) compa ed
o he one used by Khali a e al. (2017) (1990–2015). Mo eo e , Khali a e al. (2017) showed ha he
e idence o nonlinea i y has so ened in he mos ecen yea s, and simila e idence was also epo ed
by Ansa i and Kau mann (2019) who used a linea coin eg a ed model.
5. Robus ness Checks
We wan ed o check how ou p e ious esul s changed when compu ing he bi coin
cos -o -p oduc ion using an elec ici y p ice no mo e ixed o a cons an bu able o e lec he changing
dynamics o daily elec ici y ma ke s. To achie e his goal, we employed he daily da a o he No d
8These esul s a e no epo ed o he sake o space and in e es and a e a ailable om he au ho s upon eques .

J. Risk Financial Manag. 2020,13, 263 16 o 29
pool
9
sys em p ice, which is he uncons ained ma ke clea ing e e ence p ice o he Eu opean No dic
egion, compu ed wi hou any conges ion es ic ions by se ing capaci ies o in ini y
10
. These daily
p ices (o iginally in Eu o/MWh) we e ans o med in o $/kWh using he daily ixing o he EURUSD
pai , and hey a e shown in Figu e 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
Figu e 7. No d Pool sys em p ice and he ixed elec ici y p ice o 0.13 $/kWh.
The No d Pool is pa icula ly in e es ing in ou case because i e lec s he inc easing impo ance
o enewable ene gy in he Eu opean ene gy mix (see Jones 2017-chap e 5 o a discussion a he
ex book le el), and he “majo i y o Bi coin mining is mainly powe ed by wha would o he wise be a was ed
su plus o enewable ene gy” (de V ies 2019), pa icula ly hyd o-powe , see Bendiksen e al. (2018) o he
ull de ails.
The CPMs compu ed using he No d Pool elec ici y p ices and he wo ene gy e iciency cu es
p esen ed in Sec ion 3.1 as well as he CPMs compu ed wi h cons an elec ici y p ices a e epo ed in
Figu e 8, oge he wi h he bi coin ma ke p ices.
The CPMs compu ed using No d Pool elec ici y p ices a e much lowe han he CPMs compu ed
wi h a ixed elec ici y p ice o 0.13 $/kWh, because No d Pool p ices a e signi ican ly lowe han his
cons an p ice le el. As we discussed in Sec ion 3.2, an highe elec ici y p ice can cap u e he e ec
o some o he mining ope a ional expenses, so he CPMs compu ed using No d Pool p ices can be
conside ed as p oxies o he ma ginal cos o p oduc ion, see Fan azzini (2019)-chap e 4 o a b oad
discussion o his issue.
The esul s o he sequen ial educ ion me hod o weak exogenei y using he Wald es
by
Toda and Yamamo o (1995)
and he CPMs using No d Pool p ices a e epo ed in Table A11
(Appendix B), while he esul s o he Johansen coin eg a ion es s a e epo ed in Table A12
(Appendix B). The misspeci ica ion es s o he inal selec ed models a e epo ed in Table A13
(Appendix B)11.
The esul s using he CPMs wi h he No d pool p ices a e no e y dissimila om he baseline
case: in he i s subsample, he CPM1/CPM2 we e ne e signi ican , and he inal model was again
a bi a ia e VECM(1) o he Bi coin p ice and Google sea ch da a, wi h ansac ion olume and
9
The No d Pool is a Eu opean powe exchange owned by Eu onex and he con inen al No dic and Bal ic coun ies’
T ansmission sys em ope a o s (TSOs). A he ime w i ing his pape , he No d Pool ope a es powe ading ma ke s in
No way, Denma k, Sweden, Finland, Es onia, La ia, Li huania, Ge many, he Ne he lands, Belgium, Aus ia, Luxembou g,
F ance, and he Uni ed Kingdom. See www.no dpoolg oup.com and e e ences he ein o mo e de ails.
10 See www.no dpoolg oup.com/ ading/Day-ahead- ading/P ice-calcula ion o mo e de ails abou i s calcula ion.
11
The es ima ed pa ame e s o he inal models o bo h subsamples a e no epo ed he e o he sake o in e es and space
and a e a ailable om he au ho s upon eques .
J. Risk Financial Manag. 2020,13, 263 17 o 29
ansac ion ees as exogenous a iables. In he second subsample, he e we e no endogenous a iables
acco ding o he sequen ial educ ion me hod o weak exogenei y, and he Johansen es s simila ly
ound no e idence o coin eg a ion be ween he bi coin ma ke p ice and he CPMs. The inal models
u ned ou o be a simple bi a ia e andom walk (VAR(0)) and a VAR(4) model o he log- e u ns o
he bi coin p ice and he CPM1/CPM2, espec i ely, wi h misspeci ica ion es s sligh ly wo se han he
baseline case.
In gene al, he use o he No d Pool p ices o compu e he CPMs end o so en hei ela ionship
wi h he bi coin ma ke p ice: his ac is al eady e iden when looking a he co ela ion ma ices o
he log- e u ns o he bi coin p ice, he baseline CPMs, and he CPMs compu ed wi h he No d pool
p ices, which a e epo ed 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)
Figu e 8.
Bi coin cos -o -p oduc ion p ices compu ed using bo h cons an elec ici y p ices and No d
Pool p ices, oge he wi h he bi coin ma ke p ice.
6. Conclusions
This pape in es iga ed he ela ionship be ween he bi coin p ice and he hash a e by
disen angling he e ec s o he ene gy e iciency o he bi coin mining equipmen , bi coin hal ing,
and o s uc u al b eaks on he p ice dynamics. To each his aim, we p oposed a new
me hodology based on exponen ial smoo hing o model he dynamics o he Bi coin ne wo k ene gy
e iciency. We conside ed ei he di ec ly he hash a e o he bi coin cos -o -p oduc ion model by
Hayes (2017,2019)
as a p oxy o he hash a e, o ake any nonlinea i y in o accoun . We ound
ha he e was nei he e idence o G ange -causali y no coin eg a ion in he i s examined sample
(01/08/2016–04/12/2017), whe eas he e was e idence o unidi ec ional G ange -causali y and
coin eg a ion in he second sample (11/12/2017–24/02/2020), going om he bi coin p ice o he
hash a e (o o he CPMs) bu no ice e sa. This e idence is hus consis en wi h a la ge li e a u e in
ene gy economics, which showed ha oil and gas e u ns a ec he pu chase o he d illing igs wi h a
delay o up o h ee mon hs, whe eas he impac o changes in he ig coun on oil and gas e u ns
is limi ed o no signi ican . Mo eo e , ou analysis showed ha i is be e o conside di ec ly he
hash a e a he han i s p oxy ep esen ed by he bi coin cos -o -p oduc ion model when modeling
i s ela ionship wi h he bi coin p ice. These esul s also held a e we pe o med a obus ness check
o e i y how ou p e ious esul s changed when compu ing he bi coin cos -o -p oduc ion using an
elec ici y p ice no mo e ixed o a cons an bu equal o he daily da a o he No d pool sys em p ice.
The e idence epo ed in his wo k shows ha he bi coin ma ke has become a mo e ma u e
and e icien ma ke a e he in oduc ion o egula ed u u es ma ke s in Decembe 2017. The usual
echnical d i e s (bi coin supply and demand), a ac i eness indica o s, and mac oeconomic a iables
J. Risk Financial Manag. 2020,13, 263 18 o 29
appea o ha e become ei he lagging indica o s o no mo e signi ican in explaining he dynamics
o he bi coin p ice, hus con i ming simila esul s epo ed by Kapa and Olmo (2020). In his
ega d, we wan o ema k ha Shanae e al. (2019) ecen ly showed ha some o he p e iously
epo ed posi i e ela ionships be ween c yp o-coins p ices and hei hash a e, o be ween c yp o-coins
p ices and hei ansac ion coun s, we e ei he spu ious due o se ial co ela ion o inconsis en
due o endogenei y. The e o e, he de elopmen o “second-gene a ion alua ion me ics” o
c yp ocu encies (Lehne e al. 2019;Shanae e al. 2019) able o accommoda e bo h mode n empi ical
inance asse -p icing models and heo y-d i en alua ion models is de ini i ely a compelling a enue
o u he esea ch.
Au ho Con ibu ions:
Concep ualiza ion, N.K.; Me hodology, N.K. and D.F.; so wa e, N.K. and D.F.; alida ion,
N.K. and D.F.; o mal analysis, N.K. and D.F. in es iga ion, N.K. and D.F.; esou ces, N.K. and D.F.; da a cu a ion,
N.K. and D.F.; w i ing–o iginal d a p epa a ion, N.K. and D.F.; w i ing– e iew and edi ing, D.F.; isualiza ion,
N.K. and D.F.; supe ision, D.F.; p ojec adminis a ion, D.F.; unding acquisi ion, D.F. All au ho s ha e ead and
ag eed o he published e sion o he manusc ip .
Funding: This esea ch was unded by Dean Fan azzini g an numbe 20-68-47030.
Acknowledgmen s:
We would like o hank all he pa icipan s o he VII In e na ional Con e ence in Mode n
Econome ic Tools and Applica ions (META2020), which was held in Sep embe 2020 and was o ganized by
he Highe School o Economics in Nizhny No go od (Russia). We also wan o hank Se gei Tikhomi o ,
an anonymous ounde o a c yp o-exchange, and he anonymous chie in o ma ion o ice (CIO) o one o he
wo ld’s leading ull-se ice blockchain echnology companies, who p o ided impo an eedback. The i s -named
au ho g a e ully acknowledges inancial suppo om he g an o he Russian Science Founda ion n. 20-68-47030.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Appendix A. A B ie O e iew o Bi coin’s Ope a ion
The comple e desc ip ion o how he Bi coin ne wo k wo ks can be ound in he o iginal
whi epape published by Nakamo o (2008) and i is beyond he scope o his pape . Howe e , ce ain
aspec s o i s ope a ion a e b ie ly e iewed he e o be e unde s and he esea ch discussed in his
pape . The bi coin supply is comple ely inelas ic, and i is de e mined by a ixed emission schedule: o
he i s ou yea s, 50 bi coins a e c ea ed on a e age e e y 10 min. A e he i s ou yea s, he a e o
emission hal es, and only 25 bi coins appea wi hin he ne wo k e e y 10 min. The c ea ion o bi coin
is again hal ed e e y ou yea s, and his pa e n is epea ed un il he smalles possible uni is c ea ed
12
. and, a e his e en , he emissions s op comple ely. The o al amoun o bi coin o be c ea ed will
be equal o 21 million bi coin. Due o he na u e o he bi coin p o ocol, he a e o emission canno be
manipula ed o al e ed in any way, so ha we al eady know ha emission o bi coin will cease in he
yea 2140.
Newly c ea ed bi coins come wi h wha is called a block: a chunk o ansac ions “packaged” in a
special way. The size o each block is limi ed, so he e is a compe i ion among hose using he Bi coin
ne wo k o ha e hei ansac ions inse ed in o he ea lies block, which gi es ise o a ee ma ke .
The e is also a compe i ion o con i m he la es ansac ions and p oduce a new block: his p ocess
is incen i ized by he (1) ewa d o e ed by he Bi coin ne wo k ( o being he i s o con i m a new
block) and by he (2) ees collec ed om all ansac ions included in he block. To con ol he a e
o he block issuance, he bi coin p o ocol has ce ain ules in place. Each newly c ea ed block has
o p o ide a so called p oo o wo k o be conside ed alid. The p oo o wo k is a ha d, un o geable
digi al e idence o he “wo k” pe o med o con i m a block o ansac ions. In o he wo ds, o c ea e
a alid block, one has o expend a ce ain amoun o compu a ional esou ces and hen p esen s he
e idence o ha expendi u e wi hin he block. Gi en ha he combined compu a ional powe o all
hose in e es ed in c ea ing a block may inc ease o dec ease, he Bi coin ne wo k has a concep o
di icul y: i ells how much compu a ions on a e age a mine has o do be o e he ge s a alid p oo o
12 A one hund ed million h o a bi coin is he smalles uni o he bi coin cu ency and i is called a Sa oshi.
J. Risk Financial Manag. 2020,13, 263 19 o 29
wo k. I he o al compu a ional powe in he ne wo k suddenly su ges, blocks s a o come ou a a
highe a e: he ne wo k no ices ha and eadjus s he di icul y a ge o slow he a e back down.
Thus, he a e age ime be ween he blocks is always kep a 10 min, independen ly om he changes
in he o al compu a ional powe . The p ocess o p o iding he p oo o wo k o a block is called
mining and i s pa icipan s a e called mine s. The equipmen used by mine s is usually called “mine s”
as well. Today such equipmen is domina ed by applica ion-speci ic in eg a ed ci cui (ASIC) chips.
The compu a ions ha mine s do in ol e a double SHA-256 hash unc ion, so he compu a ional
powe is o en called hash a e and is measu ed in hashes pe second. The mine s a e always in an a ms
ace o highe ene gy e iciency (EEF) o hei ASICs and o a highe numbe o hashes pe second
(usually measu ed in Ghash/sec). The cu en s a e o he ne wo k is such ha e en a la ge mine can
only hope o ind a block once e e y yea o so. Because o ha , mine s pool hei e o s oge he o
inc ease hei combined hash a e and hope o ind blocks a a much as e and s eadie a e. The pool
ope a o s coo dina e he mine s and ake a small managemen ee o ha . In his way, an indi idual
mine gi es up some o his expec ed p o i in exchange o s eady and p edic able payou s. Each mine
incu s ce ain cos s when mining o a block: hese cos s a e bo h ixed ( eal es a e, equipmen , se -up
cos s) and a iable (ene gy, labo , cooling, e c.). By a , ene gy cos s a e he highes cos : hey may be
so big ha o he cos s migh be sa ely neglec ed, see S oll e al. (2019) o mo e de ails.
Due o he na u e o he Bi coin ne wo k, some o i s pa ame e s can be di ec ly obse ed and
hei pas alues a e o e e kep in i s public blockchain: see, o example, he block ewa d, he o al
ansac ion ees Blockchain.com (2020c), he hash a e Blockchain.com (2020b), and he di icul y
Blockchain.com (2020a). They a e widely used in bi coin- ela ed esea ch.
Appendix B. Model Es ima es
Each equa ion is epo ed by column, while each cell epo s he pa ame e es ima e, i s s anda d
e o , and -s a is ic.
Appendix B.1. Bi a ia e Analysis
Table A1.
VAR(0) o he Log- e u ns o he pai : Log(Bi coin p ice), Log(CPM model 1). Fi s sample:
01/08/2016–04/12/2017.
Va iables DLog(Bi coin P ice) DLog(CPM_model_1)
Cons an 0.046586 0.019783
−0.01353 −0.0046
[3.44263] [4.30423]
Table A2.
VAR(0) o he Log- e u ns o he pai : Log(Bi coin p ice), Log(CPM model 2). Fi s sample:
01/08/2016–04/12/2017.
Va iables DLog(Bi coin P ice) DLog(CPM_model_2)
Cons an 0.046586 0.021165
−0.01353 −0.00536
[3.44263] [3.94997]
J. Risk Financial Manag. 2020,13, 263 20 o 29
Table A3.
VAR(1) o he Log- e u ns o he pai : Log(Bi coin p ice), Log(Hash a e). Fi s sample:
01/08/2016–04/12/2017.
Va iables DLog(Bi coin P ice) DLog(Hash a e)
DLog(Bi coin p ice(−1)) 0.011607 −0.02143
−0.13052 −0.16834
[0.08893] [−0.12730]
DLog(Hash a e(−1)) −0.08538 −0.596435
−0.07991 -0.10306
[−1.06849] [−5.78708]
Cons an 0.049622 0.047781
−0.01481 −0.0191
[3.35113] [2.50179]
Table A4.
VECM(0) o he a iables Log(Bi coin p ice) and Log(CPM model 1). Second sample:
11/12/2017–24/02/2020.
E o Co ec ion (EC) Te m
Log(Bi coin p ice(−1)) 1
Log(CPM_model_1(−1)) −0.663981
−0.21282
[−3.11985]
Cons an −2.97009
−1.81363
[−1.63765]
Va iables DLog(Bi coin p ice) DLog(CPM_model_1)
EC −0.03118 0.044423
−0.01726 −0.00559
[−1.80600] [7.95227]
Table A5.
VECM(2) o he a iables Log(Bi coin p ice) and Log(CPM model 2). Second sample:
11/12/2017–24/02/2020.
E o Co ec ion (EC) Te m
Log(Bi coin p ice(−1)) 1
Log(CPM_model_2(−1)) −0.692219
−0.21357
[−3.24116]
Cons an −2.806945
−1.84646
[−1.52017]
Va iables D(Log(Bi coin p ice)) D(Log(CPM_model_2))
EC −0.029855 0.042844
−0.03116 −0.01095
[−0.95809] [3.91310]
0.098178 0.02819
D(Log(Bi coin p ice(−1))) −0.09641 −0.03388
[1.01832] [0.83217]
−0.039484 0.045213
D(Log(Bi coin p ice(−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 o 29
Table A6.
VECM(6) o Log(Bi coin p ice) and Log(Hash a e). Second sample: 11/12/2017–24/02/2020.
E o Co ec ion (EC) Te m
Log(Bi coin p ice(−1)) 1
Log(Hash a e(−1)) −0.409183
−0.1125
[−3.63727]
Cons an −1.256762
−2.00595
[−0.62652]
Va iables D(Log(Bi coin p ice)) D(Log(Hash a e))
EC −0.049126 0.147903
−0.02597 −0.02708
[−1.89180] [ 5.46226]
D(Log(Bi coin p ice(−1))) 0.183584 −0.050318
−0.09211 −0.09605
[1.99306] [−0.52390]
D(Log(Bi coin p ice(−2))) −0.032037 0.157578
−0.08781 −0.09156
[−0.36485] [1.72106]
D(Log(Bi coin p ice(−3))) 0.108266 0.04156
−0.08754 −0.09127
[1.23682] [0.45532]
D(Log(Bi coin p ice(−4))) −0.14961 −0.149548
−0.08646 −0.09016
[−1.73033] [−1.65877]
D(Log(Bi coin p ice(−5))) −0.034145 0.077298
−0.08735 −0.09108
[−0.39092] [0.84871]
D(Log(Bi coin p ice(−6))) 0.170596 0.072128
−0.08667 −0.09038
[1.96824] [0.79808]
D(Log(Hash a e(−1))) −0.076181 −0.736701
−0.08894 −0.09273
[−0.85659] [−7.94419]
D(Log(Hash a e(−2))) 0.009311 −0.438379
−0.10961 −0.11429
[0.08495] [−3.83559]
D(Log(Hash a e(−3))) 0.099676 −0.273345
−0.11133 −0.11608
[0.89533] [−2.35471]
D(Log(Hash a e(−4))) 0.105471 −0.275003
−0.11083 −0.11556
[0.95169] [−2.37976]
D(Log(Hash a e(−5))) −0.005624 −0.29404
−0.1056 −0.11011
[−0.05326] [−2.67035]
D(Log(Hash a e(−6))) 0.171554 −0.154059
−0.08442 −0.08803
[2.03213] [−1.75014]
J. Risk Financial Manag. 2020,13, 263 22 o 29
Appendix B.2. Mul i a ia e Analysis
Table A7.
VECMX(1) o Log(Bi coin p ice) and Log(Google), wi h Log( ansac ion olume) and
Log(T ansac ion ees) as exogenous a iables. Fi s sample: 01/08/2016–04/12/2017. This model
u ned ou o be he same, independen ly o whe he we used he hash a e, o he CPM1, o he CPM2.
E o Co ec ion (EC) Te m
Log(Bi coin p ice(−1)) 1
Log(Google(−1)) −1.000538
−0.04603
[−21.7368]
Cons an −5.4321
Va iables D(Log(Bi coin p ice)) D(Log(Google))
EC −0.020082 0.604649
−0.05422 −0.12658
[−0.37039] [4.77691]
D(Log(Bi coin p ice(−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]
Cons an 0.02109 0.010608
−0.01033 −0.02413
[2.04073] [0.43967]
D(Log(T ansac ion ees)) 0.172323 0.040111
−0.04195 −0.09793
[4.10790] [0.40958]
D(Log(T ansac ion Volume)) 0.335968 0.443305
−0.06704 −0.15652
[5.01110] [2.83227]
Table A8.
VECMX(6) o Log(Bi coin p ice), Log(Hash a e) and Log(T ansac ion ees),
wi h Log( ansac ion olume), Log(Google), and Log(T ansac ion ees) as exogenous a iables. Second
sample: 11/12/2017-24/02/2020.
E o Co ec ion (EC) Te m
Log(Bi coin p ice(−1)) 1
Log(Hash a e(−1)) −0.442911
−0.12766
[−3.46936]
Cons an −0.620773
−2.27623
[−0.27272]
Va iables D(Log(Bi coin p ice)) D(Log(Hash a e))
EC −0.009204 0.143938
−0.01909 −0.02662
[−0.48217] [ 5.40721]
D(Log(Bi coin p ice(−1))) 0.105778 −0.053536
−0.07226 −0.10077
[1.46388] [−0.53126]
J. Risk Financial Manag. 2020,13, 263 23 o 29
Table A8. Con .
E o Co ec ion (EC) Te m
Va iables D(Log(Bi coin p ice)) D(Log(Hash a e))
D(Log(Bi coin p ice(−2))) 0.032122 0.159914
−0.06866 −0.09575
[0.46786] [ 1.67010]
D(Log(Bi coin p ice(−3))) −0.026725 0.040566
−0.06826 −0.0952
[−0.39151] [ 0.42612]
D(Log(Bi coin p ice(−4))) −0.04931 −0.138195
−0.06636 −0.09255
[−0.74303] [−1.49317]
D(Log(Bi coin p ice(−5))) −0.064049 0.073961
−0.06817 −0.09507
[−0.93961] [0.77800]
D(Log(Bi coin p ice(−6))) 0.132207 0.070274
−0.06677 −0.09312
[ 1.97995] [0.75465]
D(Log(Hash a e(−1))) −0.119478 −0.741459
−0.06751 −0.09415
[−1.76969] [−7.87490]
D(Log(Hash a e(−2))) −0.016763 −0.442022
−0.08292 −0.11564
[−0.20217] [−3.82241]
D(Log(Hash a e(−3))) 0.077149 −0.277793
−0.08467 −0.11808
[0.91118] [−2.35258]
D(Log(Hash a e(−4))) −0.033626 −0.285352
−0.08528 −0.11893
[−0.39432] [−2.39936]
D(Log(Hash a e(−5))) −0.035212 −0.297643
−0.08005 −0.11164
[−0.43989] [−2.66622]
D(Log(Hash a e(−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(T ansac ion ees) 0.074418 0.004869
−0.02798 −0.03902
[2.65972] [0.12477]
DLog(T ansac ion Volume) 0.326196 0.020172
−0.04868 −0.06789
[6.70053] [0.29711]
J. Risk Financial Manag. 2020,13, 263 24 o 29
Table A9.
VECMX(2) o Log(Bi coin p ice), Log(CPM model 1), and Log(T ansac ion olume),
wi h Log( ansac ion ees), Log(Google), and Log(SP500) as exogenous a iables. Second sample:
11/12/2017–24/02/2020.
E o Co ec ion (EC) Te m
Log(Bi coin p ice(−1)) 1
Log(CPM_model_1(−1)) −0.631559
−0.07653
[−8.25280]
Log(T ansac ion Volume(−1)) −0.767616
−0.06355
[−12.0782]
Cons an 12.95172
−1.78079
[7.27301]
Va iables D(Log(Bi coin p ice)) D(Log(CPM_model_1)) D(Log(T ansac ion Volume))
EC 0.012154 0.144569 0.024845
−0.07358 −0.02403 −0.11201
[0.16519] [6.01564] [0.22181]
D(Log(Bi coin p ice(−1))) −0.033971 −0.051945 0.214159
−0.13416 −0.04382 −0.20424
[−0.25321] [−1.18544] [1.04859]
D(Log(Bi coin p ice(−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(T ansac ion Volume(−1))) −0.000195 0.05502 −0.342822
−0.08185 −0.02673 −0.1246
[−0.00238] [2.05804] [−2.75130]
D(Log(T ansac ion Volume(−2))) −0.011235 0.028662 −0.220672
−0.07227 −0.0236 −0.11002
[−0.15546] [1.21424] [−2.00577]
DLog(T ansac ion ees) 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]