Does the hashrate affect the bitcoin price?

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 P o ided in Coope a ion wi h: 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, h ps://doi.o g/10.3390/j m13110263 This Ve sion is a ailable a : h ps://hdl.handle.ne /10419/239364 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. 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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]