Understanding risk of bubbles in cryptocurrencies

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ContentslistsavailableatScienceDirect

Journal of Economic Behavior and Organization

journalhomepage:www.elsevier.com/locate/jebo

Understanding risk of bubbles in cryptocurrencies

F.A. Enoksen

^a

, Ch.J. Landsnes

^a

, K. Lu ˇcivjanská

^b^,¹

, P. Molnár

^a^,^c^,²^,^∗

aUniversity of Stavanger, Stavanger, Norway

bŠafárik University in Košice, Slovakia and University of Economics, Prague, Czechia

cNicolaus Copernicus University in Torun, Torun, Poland and University of Economics, Prague, Czechia

a r t i c l e i n f o

Article history:

Received 15 September 2019 Revised 5 May 2020 Accepted 9 May 2020 Available online 5 June 2020 Keywords:

Cryptocurrencies Bubbles PSY test Uncertainty

a b s t r a c t

Ascryptocurrenciesemergedonlyrecently,theyaresubjecttoonlyverylimitedﬁnancial regulations.Inthispaperwestudywhichvariablescan predictbubblesinthepricesof eightmajorcryptocurrencies,focusingonuncertainty measuresaspredictors.We detect multiplebubbleperiodsforalleightcryptocurrencies,particularlyin2017andearly2018.

Weﬁndthat highervolatility, tradingvolumeand transactionsarepositivelyassociated withthepresenceofbubblesacrosscryptocurrencies.Regardingtheuncertaintyvariables, the VIX-index consistentlydemonstrates negativerelationships with bubble occurrence, whiletheEPU-indexmostlyexhibitspositiveassociationswithbubbles.Theseresultsmay assistauthoritiesindesigningappropriateregulations.

ThisisanopenaccessarticleundertheCCBYlicense.

(http://creativecommons.org/licenses/by/4.0/)

1. Introduction

Emergenceofcryptocurrencieswasoneofthemostremarkableﬁnancialinnovationsofthelast decade.Theirfuturistic propertiesandextremepricebehaviorhaveattractedexcessivemediacoverage,aswellasregulators’andresearchers’atten- tion.Mostcryptocurrenciesareknowntohavevolatilepricesandhaveexperienceddramaticpriceincreasesandcollapses intherecentyears.Thishastriggereddiscussionsastowhethercryptocurrencies experiencebubblesandhowcryptocur- renciesshouldberegulated.

Bitcoin,thefirstcryptocurrency,hasexperiencedseverepricefluctuations;itspricereachedapeakinlate2017.Bitcoin wasoriginally intendedto functionasdigitalmoney:itwasdesignedtobea reliableandtrustworthytransactionsystem withlowcosts (Grinberg,2012). Bitcoinandother cryptocurrencies havethepotential toreplacethe intermediaterole of financial third parties. Thoughit was intended to be utilized as money, its decentralized and unregulated market have attractedcriticism(Grinberg,2012)andexpertshavediscussedwhetheritshouldbeclassifiedaseitheraspeculativeasset orasameansofexchange.Yermack(2015) andGlaseretal.(2014) concludedintheir researchthat itwasprimarily held asaspeculativeasset.Givenitsapparentriskynatureandextremepricebehavior,thepresenceofbubblesinthiscurrency isnaturallyaninterestingtopicforresearch.

∗ Corresponding author.

E-mail address: [email protected] (P. Molnár).

1Lu ˇcivjanská was supported by the Czech Science Foundation under grant no. 20-16786S and by the Slovak Research and Development Agency under grant no. APVV-17-0568.

2Molnár was supported by the Czech Science Foundation under grant no. 20-16786S and by the National Science Centre, Poland under grant no.

2017/26/E/HS4/00858.

https://doi.org/10.1016/j.jebo.2020.05.005

( http://creativecommons.org/licenses/by/4.0/ )

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Table 1

Time Period Employed for Each Cryptocurrency Price dataset start and end dates for each of the eight cryptocurrencies.

Cryptocurrency From To # of days

Bitcoin (BTC) 27.12.2013 15.02.2019 1876

Ethereum (ETH) 27.07.2016 15.02.2019 933

Ripple (XRP) 31.12.2013 15.02.2019 1872

Litecoin (LTC) 27.12.2013 15.02.2019 1876

Monero (XMR) 16.04.2015 15.02.2019 1401

Dash coin (DASH) 20.01.2015 15.02.2019 1487

Nem coin (XEM) 29.03.2016 15.02.2019 1053

Dogecoin (DOGE) 16.12.2014 15.02.2019 1522

In thispaperwe detect bubbles in all themajor cryptocurrencies and studywhichfactors can predict thesebubbles.

Suchinformationcanbeusefulforbothinvestorsandregulators.Weconsiderfactorsspecifictoparticularcryptocurrencies, such astradingvolume,aswell asglobaluncertaintymeasures suchaseconomicpolicy uncertainty(EPU).ThedailyEPU measurereflectsuncertaintyaboutlegislationandregulation.Sincefinancialregulationofcryptocurrenciesisonlyemerging now, uncertaintyinthisareacould havea majorimpacton cryptocurrencies.Severalpapershaveanalyzed theimpactof suchuncertainty(measuredbyEPUortheVIXindex)onBitcoin(Bourietal.,2017;Aalborgetal.,2018;Demiretal.,2018;

Wangetal.,2019;Wuetal.,2019).However,thesepapershaveonlystudiedonecryptocurrency(Bitcoin)andnoneofthem havelookedatthepresenceofbubbles.

Fromaneconomicperspective,abubbleisadeviationfromthefundamentalvalue.However,wherecryptocurrenciesare concerneditishardtopinpointwhatthefundamentalvalueis.Wethereforedeﬁneabubbleasexplosivepricebehaviour, asproposed by Phillipset al.(2015a,b).There have beennumerousattempts to develop statisticalprocedures toidentify bubbles.DibaandGrossman(1988)appliedaunit roottestto detectexplosivebehaviorinassetprices.Extensions ofthis methodbased on variousforms ofthe augmentedDickey-Fuller test weresuggested by Phillipsetal.(2011)andPhillips etal.(2015a,b)toidentifybubbles,andthesemethodsbecomeknownasacronymsoftherespectiveauthors’names,PWY andPSY.Phillipsetal.(2015a,b)showthatthePSYmethodoutperformsthePWYmethodindetectingmultiplebubbles.We thereforeusethePSYmethod.

ThePSYframeworkwasinitiallydevelopedtoidentifypricebubbles.SubsequentresearchbyPhillips(2017)hasshown that the PSYprocedure canalso be usedasa warningdevice forcrisis, asthe methodcan be extendedto covermarket collapsedynamics.PhillipsandShi(2018)incorporatedthiscrisisdetectionaspectintothePSYmethodpresentedinPhillips etal.(2015a,b)andimprovedthePSYprocedurebyoptimizingtherecursiveevolvingtestalgorithm.

Severalpapers haveusedthe PSYframework to detectbubbles incryptocurrencies. Cheungetal.(2015) andSu etal.

(2018) date-stampbubblesinBitcoinpriceandﬁndthat thebubble periodscoincide withmajor eventsthat affectedthe Bitcoinmarket.Corbetetal.(2018)andBourietal.(2018)usethePSYframeworktoidentifybubblesinmultiplecryptocur- rencies. Corbetetal.(2018) look atBitcoinandEthereum anddetect bubblebehavior inboth, particularlyat theend of their sampleperiod(mid2017). Bourietal.(2018) identifybubblesinBitcoin, Ripple,Ethereum,Litecoin,NEM,Dash and Stellarandﬁndthat thelikelihoodofbubbleperiodsinonecryptocurrencyisrelatedto theexistenceofbubblesinother cryptocurrencies. Various methods havealso beenused to studythe presenceof speculativebubbles, see Cheah andFry (2015)andFryandCheah(2016).However,noneofthesepapershaveattemptedtopredictcryptocurrencybubbles.

Wesetouttostudywhichfactorscanpredictbubblesforalargersetofcryptocurrencies.Theabilitytopredictbubblesis valuablenotonlyforunderstandingthecryptocurrencies’pricedynamics,butalsoformarketmonitoring.First,weusethe PSYframeworktolocatebubblesforthecryptocurrenciesBitcoin,Ethereum,Ripple,Litecoin,Monero,Dashcoin,Nemcoin andDogecoin.Next,westudywhetheranyoffourvariablesrelatedtotheparticularcryptocurrency(Googlesearchqueries forthecryptocurrency’sname,itspricevolatility,numberoftransactions,tradingvolume)orthreevariablescapturingun- certaintyingeneralﬁnancialmarkets(theeconomicpolicyuncertainty(EPU)index,theVIX-indexandtheTED-spread)can predict thosebubbles. We ﬁndthat volatilityandtrading volumeconsistently exhibit a positive relationshipwithbubble behavior. High EPU levels imply a greater likelihood ofbubbles, while highVIX-index levels implya lower likelihoodof bubbles.

Theremainderofthepaperisstructured asfollows:Section2describesthedataonthecryptocurrenciesandthevari- ablesthatmaypredictbubbles.InSection3wepresentouranalysisofthedetectedbubblesandtheirpotentialpredictors.

Weofferconclusionsinsection4. 2. Data

The dataused inthe analysiscover thetime period December27, 2013to February15, 2019. Thestarting datesvary dependingon the availabilityof datafor theindividual cryptocurrencies studied, seeTable 1.The cryptocurrencies to be consideredwerechosenbasedonthelengthoftheirdatasets,theirpopularityandtheirtotalmarketvalue.TheVIX-index, whichwe useinouranalysis,isnot reportedonweekendsoroncertain holidays.Thesedaysarethereforeomittedfrom ouranalysis.

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Dailypriceandtrading volumedata forthecryptocurrencies were collectedfromCoinMarketCapthroughan API inR Studio.TransactionvolumewascollectedfromCoinmetrics.Thoughitispossibletoobtainearlierdatafromother sources, wechosetousethesedatasetsduetotheir apparentreliabilitycomparedtootheravailablesources.Theeconomicpolicy uncertaintyindex(EPU)datawascollectedfromtheEconomicPolicyUncertaintyweb page.Data ontheTED-spreadand VIX-indexwerecollectedfromtheFREDdatabase,theFederalReserveBankofSt.Louis.Fortheremainderofthepaper,we frequentlyusetickersymbolswhenwerefertoeachcryptocurrency.ThetickersaredisplayedinparenthesesinTable1.

Tomeasure thevolatility of thecryptocurrencies we use the estimatorbased ontrading pricerange duringa day,as proposed byGarman andKlass (1980). Themethod,which offers an improvementinaccuracycompared to thecommon method ofmeasuring volatility by standard deviation of returns (Molnár, 2012), has recently gained popularity(Molnár, 2016;BaštaandMolnár,2018;Fiszeder,2018;FiszederandFałdzi´nski,2019;Fiszederetal., 2019).Daily volatilityiscalcu- latedasfollows:

Volatility_t=

1

2

(

^ht−lt

)

²−

(

²^log²−1

)

^c²t, (1)

wherect=log(^close^t)−log(ôpent),lt=log(^low^t)−log(ôpent)ând^h^t=log(^hight)−log(ôpent)^.Înôrder^to^deal^with^pos- sibleweekly seasonality,weconverttheprecedingdailyvaluesintoa7-dayarithmeticaveragebythefollowingequation:

Volatility_t=1 7

t τ=t−6

Volatility_τ. (2)

Cryptocurrencytransfers can be classiﬁedinto transfers betweena useranda cryptocurrencyexchange, andtransfers between two users. In general, transfers between users are assumed to represent purchases of goods or services using cryptocurrency,whereastransfers withexchangesrepresentbuyingorsellingcryptocurrency(inexchangeforconventional currency).It isthereforeusefultodifferentiatebetweentheseformsoftransfers.Inourpaper,transactionvolume (TV)is classiﬁedasthevolumeoftransfersofacryptocurrencybetweenusers.Transactionvolumeisstandardizedinthesameway asinAalborgetal.(2018),asadeviationfromtheaveragevolumeoverthelastyeardividedbythestandarddeviationover thesameperiod:

Transactionst=TVt−TV

σ (

^TV

)

^. ⁽³⁾

Tradingvolume, on the other hand,is classified as transfers over an exchange, and doesnot includedirect transfers betweenusers. The time seriesfor Bitcoin’s tradingvolume hashistorically exhibited both linear and exponential trend components(Balcilaretal., 2017).Byfollowing theprocedureofGebka andWohar(2013) we canremovethesefromthe series,which is necessary to make thevariable stationary. The trend elementscan be estimated by converting the data tologarithmic formandregressinga constant, (t/T) and (t/T)² on volume,where T istotal observations. Followingthese estimations,each observationiscorrectedbysubtractingthetrendcomponents.Trendsexistforallcryptocurrencies,asall theestimatedcoefficientsarestatisticallysignificant.

Weemploysearch volumefromGoogletrendsinouranalysisbecauseitmeasurespublicinterestineachspeciﬁccryp- tocurrency.Thisvariableisconstructedastherelativelevelofwebsearches providedbyGoogle, andhaspreviously been demonstrated to havepredictive potential, asChoi and Varian (2009),Choi and Varian (2012), Bijl etal. (2016), Molnár andBašta(2017)havereported.Thisdatacan becollectedforvarioustime scalesandismeasuredasanindexofrelative searchvolume(SVI)between0and100.Thedailydatacanonlybecollectedinsampleswithamaximumtimespanof10 months.Inordertomake observationsbetweendatasetsintoone completeset,we applythemethodology describedby BleherandDimpﬂ (2018).Thesearchresultsarenotcasesensitiveandthekeywordsusedare:”Bitcoin”,“Litecoin”,“Ripple”,

“Ethereum”,“Monero”,“Dashcoin”,“Nemcoin” and“Dogecoin”.

WestandardizethedatafollowingtheprocedureusedinDaetal.(2011)andKimetal.(2019).Eachdailyobservation ismeasuredasadeviationfromthemedian.Themeasureiscalculatedasthedifference fromthemedianoftheprevious 8correspondingweekdays.Forexample,iftheobservationisonaMondayitiscomparedagainstthe8previousMondays.

Moreprecisely,itisgivenbythefollowingequation:

Google_t=log[SVIt]−log[Median

(

^SVIt−7,SVI_t−14,...,SVI_t−56

)

^]^. ⁽⁴⁾

TheEPU-indexcanbeconsideredaproxyforeconomicpolicyuncertaintyintheUSeconomy,asperceivedbythepublic.

It isconstructed by measuring and standardizing thevolume of newsarticles that contain a combination ofcertain key words,suchas”economy+regulation+uncertainty”,fromover1000USnewsoutlets(EconomicPolicyUncertainty,2019).In anattempttoreducenoiseinthedataseriesanddealwithpossibleweeklyseasonality,weusethemovingaverageofthe mostrecent7daysinouranalysis:

EPUt=log

1 7

t τ=t−6

EPU_τ

. (5)

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Table 2

Descriptive statistics for currency-speciﬁc variables.

BTC ETH XRP LTC

Mean St. Dev. Mean St. Dev. Mean St. Dev. Mean St. Dev.

Volatility 0.027 0.018 0.043 0.025 0.037 0.034 0.037 0.026

Transactions 1.078 1.133 1.289 1.572 0.644 1.380 0.276 1.435

Volume 16.639 0.804 14.799 0.835 11.932 1.345 15.446 1.214

Google 0.026 0.309 0.045 0.481 0.017 0.317 0.018 0.331

XMR DASH XEM DOGE

Mean St. Dev. Mean St. Dev. Mean St. Dev. Mean St. Dev.

Volatility 0.055 0.026 0.049 0.027 0.062 0.034 0.048 0.031

Transactions 0.450 1.385 0.539 1.494 0.944 1.470 0.222 1.281

Volume 8.213 1.072 9.891 1.055 9.479 1.334 11.263 1.255

Google 0.007 0.303 -0.688 0.805 -0.129 1.038 0.018 0.308

Table 3

Descriptivestatistics for macroeconomic variables.

Variables N Mean St. Dev. Min Max Skew Kurtosis

EPU 1259 4.370 0.323 3.526 5.649 0.386 3.407

VIX 1259 2.669 0.254 2.213 3.707 0.751 3.374

TED 1259 −1.199 0.336 −1.897 −0.386 0.282 2.059

Table 4

Correlation Matrix. The average correlations between the independent variables used in the analysis are reported in the table. We apply the same methodology as Da et al. (2011) . First, we estimate each correlation individually for the speciﬁc cryptocurrencies. Then, we average the results across all cryptocurrencies.

Google Volatility Transactions Volume EPU-index VIX-index TED-spread

Google 1.00

Volatility 0.22 1.00

Transactions 0.36 0.40 1.00

Volume 0.25 0.47 0.41 1.00

EPU-index 0.04 0.14 0.13 0.07 1.00

VIX-index 0.27 0.14 0.31 0.19 0.06 1.00

TED-spread 0.09 0.16 0.16 0.25 0.20 0.12 1.00

The VIX-index isa measure of perceived short termprice uncertaintyin the stockmarket andis commonly calleda fearindex.ItisconstructedfromoptionpricesbasedontheS&P500,withanexpirationdateofapproximatelyonemonth (CBOE,2019).Forthepurposesofouranalysis,thisvariablehasundergonelogarithmictransformation.

The levelof creditrisk inthe economyis proxiedby the TED-spread,whichis constructedasthe difference between theUS interbankrateandtherisk-freeUS Treasuryrate.The intuitionbehindthismetricisthat thespreadbetweenthe interbankinterestrateandTreasuryrateincreaseswhenthepossibilityofcounterpartydefaultincreases.Historically,when the ﬁnancialsector hasexperienced periods ofuncertaintyandhigherdefaultrisk, theTED-spread hasbeenhigh(Boudt etal.,2017).Forthepurposesofouranalysis,thisvariablehasundergonelogarithmictransformation.

Table2providesthedescriptivestatisticsofthecurrency-speciﬁcvariablesincludedintheanalysisandTable3reports thedescriptivestatisticsofthemacroeconomicvariables.Fortheremainderofthispaper,inregressiontablesandequations, EPU,VIXandTEDareusedasabbreviationsfortheEPU-index,VIX-indexandTED-spread,respectively.

ThecorrelationsbetweenthevariablesarepresentedinTable4.Itisnotablethatthecorrelationsbetweenvolumeand volatilityandbetweenvolumeandtransactionsare relativelyhigh,withcoeﬃcientsof0.47and0.41,respectively.Further- more,weseethatthecorrelationbetweentheuncertaintyvariables (EPU-index,VIX-indexandTED-spread)arequitelow.

Thisindicatesthatcollinearityisnotaproblemandthatthevariablescapturedifferentaspectsorformsofuncertainty.

3. Results

Webeginby discussingtheresultsfromthePSYalgorithmandprovidingan overviewofthe bubbleperiods.Wethen studywhichvariablescanpredictcryptocurrencybubbles.DetailsofthePSYmethodologycanbefoundinAppendixB. 3.1. BubbleDetection-PSYTest

Fig. 1illustrates the PSYtest, when applied tothe logarithm ofBitcoinprice(black line). The red linerepresentsthe 95%-levelcriticalvalueofthebootstrappedDickey-Fullerteststatisticsgeneratedbythisframework.Theexplosiveperiods

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Fig. 1. PSY Test of Bitcoin Bubbles.

Table 5

Statistics of Bubble Periods. Panel A reports the number of bubble days (days when the cryptocurrency was experiencing a bubble) for the individual cryptocurrencies. Panel B reports the same data but this time expressed as percentage of the total number of days in each given year and over the whole sample period.

BTC ETH XRP LTC XMR DASH XEM DOGE Sum

Panel A: Number of bubble days

2013 0 – 0 0 – – – – 0

2014 1 – 25 4 – – – 0 30

2015 3 – 0 11 0 0 – 0 14

2016 12 1 0 1 24 0 11 2 51

2017 129 79 57 91 44 174 66 54 694

2018 48 11 18 11 24 14 2 8 136

2019 0 0 0 0 0 0 0 0 0

Sum bubble days 193 91 100 118 92 188 79 64 925

Panel B: % of days with explosiveness Average

2013 0.0 % – 0.0% 0.0% – – – – 0.0%

2014 0.3% – 6.8% 1.1% – – – 0.0% 2.1%

2015 0.8% – 0.0% 3.0% 0.0% 0.0% – 0.0% 0.6%

2016 3.3% 0.3% 0.0% 0.3% 6.6% 0.0% 3.0% 0.5% 1.7 %

2017 35.3% 21.6% 15.6% 24.9% 12.1% 47.7% 18.1% 14.8% 23.8%

2018 13.2% 3.0% 4.9% 3.0% 6.6% 3.8% 0.5% 2.2% 4.7%

2019 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

Total% 7.6% 6.2% 3.9% 4.6% 5.0% 10.3% 5.4% 2.9% 5.7%

occurwhenthePSYtestvalues,illustratedbytheblueline,exceedthecriticalvalue.Evidently,therewerenumerousbubble periodsinBitcoinduringtheobservedsampleperiod.

Fig.2plotsthetime-stampedbubbleperiodsfromthePSYtest againstdevelopmentoftheuncertaintyvariables(VIX- index,EPU-indexandTED-spread)employed intheregressionmodels.Mostoftheexplosive periodslastedonlyforafew days,althoughafewweremuchlonger-lived.Theshort-livedbubblesoccurredatdifferenttimesfordifferentcryptocurren- cies.Thelonger-livedbubblescoincidedtoagreaterextentacrossthecryptocurrenciesthantheshort-livedbubbles.

The prices of all the cryptocurrencies studied in this paper increaseddramatically during 2017. As Fig. 2 shows, the PSYalgorithmrevealsthattherewere bubblesinmostofthecryptocurrencies forlargepartsof2017.Bitcoininparticular exhibitslong-livedbubbleperiodsinboth2017and2018.Thedate-stampedbubbleperiodsforeachcryptocurrencyended sometimeafterthepricecollapseinJanuary2018.Notably,thatpricecollapseseemstohavecoincidedwithasubstantial increaseintheVIX-index.ByFebruary15,2019,theanalyzedcryptocurrencieshaddeclinedonaverage90%fromtheirpeak inDecember2017/January2018.

Anoverviewof thebubble periods weidentiﬁed is provided inTable 5.Panel Apresentsthe numberof bubbledays (days whenthe cryptocurrencywaswasin a bubblestate).The cryptocurrencies BTC andDASH experienced thehighest

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Fig. 2. Bubble Periods in Cryptocurrencies and Uncertainty Variables. The colored areas in this ﬁgure mark the explosive periods in the individual cryp- tocurrencies detected by the PSY framework. The black lines for the cryptocurrencies represent the price in $. The lines start when the dataset of prices begins for each individual cryptocurrency and end on February 15, 2019. The black lines for the uncertainty variables VIX-index, EPU-index and TED-spread display their historical development.

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Table 6

Summary ofregression models.

Sample Dependent Variable Estimator

All Bubble dummy Panel probit with random effects & cluster robust standard errors All PSY statistics Panel Prais-Winsten with panel corrected standard errors, in Appendix Individual Bubble dummy Probit with optimal cluster robust standard errors

Individual PSY statistics OLS with optimal lag Newey-West standard errors, in Appendix

total number ofbubble days: 193 and 188 days,respectively. Mostbubble days occured in 2017.DASH hadthe highest frequencyofbubbledaysin2017(174days).PanelBindicatesthatthepercentageofdayswithexplosivenesswashigherin 2017thaninother years.DASHfeatured explosivenessmostfrequently(on10.3% ofdaysoverthetimeperiod2015–2019) andDOGEleastfrequently(on2.9%ofdaysoverthetimeperiod2014–2019).

3.2.Bubblepredictors

Havingapplied thePSYframework,wegeneratedthePSY statisticsforeach ofthecryptocurrencies.Wethen analyzed the results by performing various regressions in order to evaluate which variables can predict cryptocurrency bubbles.

Weestimatedboth probitmodelsandregular linearregressionmodels (the resultsofthelinear modelsare presentedin AppendixA).First,wepresentestimatesofpanelmodelswithallcryptocurrenciesinthesamesample.Second,wepresent estimatesofmodelsforeachcryptocurrencyseparately.

Thetwo dependent variables (the bubbledates dummyandthe PSYtest statistic) applied inthe regressions measure thesamepropertytosomeextent,astheyarebothderivedfromthePSYstatistics.AswedescribedinSection2,previous studies haveshownthat there are correlationsbetweencryptocurrency pricesand variablessuch asGoogle Trends,EPU, volatilityandtradingvolumeetc.Thisresearchprovidesastartingpointforthepredictorselectioninouranalysis.

Thedependentbinaryvariableoftheprobitmodels,denotedBUB_i,tforpanelprobitregressionsandBUBtfortimeseries regressions,takesvaluesofoneandzero.BUB_i,tandBUB_tissetto1whenthePSYstatisticfortherespectiveobservationis abovethegeneratedcriticalvalue fortheconsideredcryptocurrency(i.e.thereisa bubble),andzerowhenthisstatisticis belowthecriticalvalue(i.e.thereisnobubble):

BUBi,t=

₁_, _if_P_SY

i,t

(

^r0

)

>c

v

i,t

( β

^T

)

0, ifPSY_i,t

(

^r0

)

<c

v

_i,t

( β

^T

)

Thepanelprobitmodelandtimeseriesprobitmodelcan,respectively,beexpressedas:

P

(

^BUBi,t=1

)

=

( β

^xⁱ,t−1+

ν

ⁱ

)

, (6)

P

(

^BUBt=1

)

=

( β

^xt−1

)

, (7)

where⁽·) isthe normalcumulative distributionfunction. Inthe panel probitmodels, x_i,t−1 is thevector oflagged pre- dictorsincryptocurrencyi=BTC,ETH,...,DOGE attime t−1 and

ν

i

iid∼N

0,

σ

_ν²

corresponds torandom effects.x_t₋₁ is a vectorof laggedpredictors inthemodels forindividual cryptocurrencies.The linearregression modelsusethe generated PSYstatistic asadependent variable.The PSY statisticis thesupremum oftheestimated ADFstatisticforthe respective observation,generatedby thealgorithm,asdeﬁnedinAppendixBin Eq.(15).The estimatedprobitmodels consideronly whetherthePSYteststatisticisbeloworabovethegeneratedcriticalvalue;theydonotusetheactualvalueofPSYstatistic.

WethereforealsoconsideranalternativelinearmodelwhichemploysthePSYstatisticdirectly.Thelinearpanelregression modelisspeciﬁedasfollows:

PSY_i,t

(

^r0

)

=

β

⁰⁺

β

¹^Googlei,t−1+

β

²^Volatilityi,t−1+

β

³Transactions_i,t−1+

β

⁴^Volumei,t−1

+

β

⁵^EPU^t−1+

β

⁶^VIX^t−1+

β

⁷^TED^t−1+

i,t, (8) whilethelineartimeseriesregressionmodeltakestheform:

PSYt

(

^r0

)

=

β

⁰⁺

β

¹^Googlet−1+

β

²^Volatilityt−1+

β

³Transactionst−1+

β

⁴^Volume^t−1

+

β

⁵^EPU^t−1+

β

⁶^VIX^t−1+

β

⁷^TED^t−1+

^t^. ⁽⁹⁾

Anoverviewofthemodels usedispresented inTable6.Toimprovethispaper’sreadability, we reportthe resultsofthe linearmodelsonlyinAppendixA.Thedatasampleisalwayseitheranindividualcryptocurrencyorallthecryptocurrencies together.Duetopotentialautocorrelationandheteroscedasticity,we applymodelssuitablefordealingwiththisissue.The panelprobitmodelsareestimatedwithrandomeffectsandrobuststandarderrors,clusteredbycryptocurrency.Thelinear panel models use a Prais–Winstenestimator with standard errors corrected for AR(1) autocorrelation, heteroscedasticity andcross-sectional correlation. Both thesemethods are suggestedby Hoechle (2007).The lineartime seriesmodels are

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Table 7

Probit Regression Results - Panel Regression. The table reports average marginal effects for standardized explanatory variables. The dependent binary variable BUB i,tonly takes the values 1 (explosive dates) and 0 (non-explosive dates). The independent variables are described in Section 2 and are standardized by substracting the sample mean and dividing by the sample standard deviation. The sample includes all cryptocurrencies (see Table 1 for the individual time spans). ^∗, ^∗∗and ^∗∗∗ represents signiﬁcance at the 10%, 5% and 1% level, respectively. The panel model is estimated with random effects. All the reported estimates are coeﬃcients with corresponding cluster-robust standard errors, by cryptocurrency.

Dependent variable: BUB i,t

(1) (2) (3) (4) (5) (6) (7) (8)

Google _i,t−1 0.153 ^∗∗∗ 0.0198

(0.0350) (0.0294)

Volatility _i,t−1 2.968 ^∗∗∗ 0.794 ^∗∗∗

(0.537) (0.239)

Transactions _i,t−1 0.0590 ^∗∗∗ 0.0141

(0.0125) (0.0109)

Volume i,t−1 0.0796 ^∗∗∗ 0.0713 ^∗∗∗

(0.00619) (0.00796)

EPU i,t−1 0.115 ^∗∗∗ 0.0474 ^∗

(0.0247) (0.0285)

VIX _i,t−1 −0.449 ^∗∗∗ -0.158 ^∗∗∗

(0.0713) (0.0448)

TED _i,t−1 −0.107 ^∗∗∗ 0.0166

(0.0337) (0.0228)

Observations 8060 8060 8060 8060 8060 8060 8060 8060

McFadden R-squared 0.1083 0.1510 0.1507 0.0515 0.0198 0.152 0.0123 0.3613

estimatedwithNewey-Weststandarderrors(NeweyandWest,1987),treatingthegapsasequallyspaced,assuggestedby DattaandDu(2012).Optimallagsare5forallmodels,followingthelagselectionprocedurepresentedinGreene(2007).³

Forthemeasureofﬁtmetrics,regularR-squaredistheshareofvarianceinthedependentvariablethatcanbeexplained by theestimatedmodel.InterpretationofthetheMcFaddenR-squaredisnotasstraightforward,butstill applicablewhen comparing the ﬁtness of different models. It is constructed by utilizingthe log-likelihood ratio of the models with and withoutexplanatoryvariables(McFadden,1973).

3.2.1. Panelregressions:Allcryptocurrenciestogether

The regression results from the probit panel regressions are provided in Table 7 (the PSY statistic panel regressions in Table A.3). We use panel regressions to analyze the variables’ predictive effects across cryptocurrencies. We estimate univariatemodelsinvestigatingoneexplanatoryvariableatatimeandamultivariatemodelwithallvariables.

Foraproperevaluationof(notonlystatisticalsignificance,butalso)economicsignificance,westandardizetheexplana- toryvariables by subtracting thesamplemean anddividingit by thesamplestandard deviation. Furthermore,we report average marginaleffects. Forthe probitregression,theseare the mostinformativeand similaralternative to simplebeta coefficientsinaclassicallinearregression.

Positivecoefficientsindicatea higherpredictedprobability.Anincreaseinthevariableisthusassociatedwithahigher likelihood ofbubbles. Anegativecoefficient wouldindicate a lower likelihoodofbubbles. Ahigher absolutevalue ofthe coefficientindicatesstrongereconomicsignificance.

Itisimportanttoemphasizethatweutilizetwotypesofexplanatoryvariables:variablesrelatedtoparticularcryptocur- rencies(volatility,transactions,volume,Googlesearches),andvariablescapturingvariousaspectsofuncertaintyingeneral ﬁnancialmarkets(theEPUindex,theVIXindexandtheTEDspread).

Letusfirstdiscussthecryptocurrency-specificvariables.Inbothunivariateandmultivariatepanelmodels,highervolatil- ityraisesthelikelihoodofbubblestates.Theresearch byBekirosetal.(2017)statesthatherdingbehaviorisusuallymore prevalent inperiods ofexcessivevolatility, which mightmake volatilitya naturalproperty ofbubbles.Volume exhibitsa positive relationship withbubbleoccurrenceinall models. Higher tradingvolume isalso associatedwitha higherlikeli- hoodofbubbles.Thiscanpossiblybeexplainedbytheoriessuchasrationalbubbles⁴orherdingbehavior.Tradingvolume is naturallyrelatedto the pricedynamics ofcryptocurrencies, andis thus assumedto be closely connectedwithbubble behavior.ThisdiffersfromtheresearchbyBlau(2017),whichdoesnotfindanyconnectionbetweenspeculativetradingand extrememarketbehavior. Googlesearchesandtransactionshavepositiveeffectsonbubblebehaviorinallunivariate panel models,although theseeffectsare notsignificant whenother variables arecontrolled forinthemultivariate probitpanel model.Wesuspectthatboththesevariablesarecloselyconnectedtothetradingvolume,whichmayexplainwhytheeffects are notsignificant inthemultivariate probitpanel model,whentradingvolume isincluded.Tosome extent,thevolume,

3Optimal lag size is calculated by the smallest integer of T ¹⁴, where T is total sample size. This procedure is presented on page 463 in Greene (2007) .

4The concept of rational bubbles was established by Blanchard and Watson (1982) , who indicates that temporary price levels above the intrinsic value can be consistent with rationality, if the expected future price is higher than the current price.

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Table 8

Probit Regression Results - Time Series. The table reports average marginal effects for standardized explanatory variables. The dependent binary variable BUB t only takes the values 1 (explosive dates) and 0 (non-explosive dates). Independent variables are described in Section 2 and are standardized by subtracting the sample mean and dividing by the sample standard deviation. The sample includes all dates for the respective cryptocurrency (see Table 1 for individual time spans). ^∗, ^∗∗and ^∗∗∗ represents signiﬁcance at the 10%, 5% and 1% level, respectively. All the reported estimates are coeﬃcients with corresponding robust standard errors.

Dependent variable: BUB t

BTC ETH XRP LTC XMR DASH XEM DOGE

Google _t−1 0.172 ^∗∗∗ 0.154 ^∗∗∗ 0.00520 0.0340 ^∗∗ 0.0765 ^∗∗∗ −0.0621 ^∗∗∗ −0.000346 0.00999 (0.0279) (0.0237) (0.0109) (0.0152) (0.0250) (0.0147) (0.00645) (0.0115) Volatility _t−1 2.609 ^∗∗∗ 0.897 ^∗∗ 0.298 ^∗∗∗ 0.452 ^∗∗ 1.240 ^∗∗∗ 1.245 ^∗∗∗ 0.703 ^∗∗∗ −0.0817

(0.488) (0.368) (0.112) (0.187) (0.246) (0.398) (0.272) (0.145)

Transactions _t−1 −0.0332 ^∗∗∗ 0.0470 ^∗∗∗ 0.000528 0.0215 ^∗∗∗ 0.0148 ^∗∗ 0.0217 ^∗∗ 0.0356 ^∗∗∗ −0.00563 (0.00807) (0.00977) (0.00441) (0.00539) (0.00669) (0.00919) (0.00757) (0.00444) Volume t−1 0.111 ^∗∗∗ 0.0154 0.0606 ^∗∗∗ 0.0412 ^∗∗∗ 0.0520 ^∗∗∗ 0.105 ^∗∗∗ 0.0319 ^∗∗∗ 0.0582 ^∗∗∗

(0.0130) (0.00978) (0.00609) (0.00781) (0.00843) (0.0162) (0.00877) (0.00545) EPU t−1 −0.0693 ^∗∗ 0.0467 0.0223 −0.00279 0.0234 (0.0162) 0.0685 ^∗∗ 0.0518 ^∗∗∗

(0.0304) (0.0330) (0.0217) (0.0228) (0.0261) (0.0162) (0.0284) (0.0143) VIX _t−1 −0.192 ^∗∗∗ 0.111 ^∗∗∗ −0.0675 ^∗∗∗ −0.0418 −0.0413 (0.0162) −0.0936 ^∗∗ −0.117 ^∗∗∗

(0.0363) (0.0372) (0.0226) (0.0279) (0.0430) (0.0162) (0.0426) (0.0337)

TED t−1 0.108 ^∗∗∗ −0.0343 −0.0557 ^∗∗ 0.0237 0.0569 ^∗ (0.0162) −0.0536 ^∗ 0.0330 ^∗∗

(0.0239) (0.0313) (0.0237) (0.0172) (0.0294) (0.0162) (0.0304) (0.0156)

Observations 1258 625 1256 1258 939 998 707 1019

McFadden R-squared 0.4854 0.5383 0.5781 0.5531 0.4651 0.5674 0.3959 0.6876

Googlesearches andtransactionsvariables aresimilar, asthey areall relatedtothe marketdemand forcryptocurrencies.

Thefactthattheydemonstratethesamedirectionofeffectssupportsthisintuition.

When it comes to uncertainty variables, the TED-spread is significant and negatively associated withbubbles in the univariateprobitmodel,buttheeffectisnotsignificantwhenothervariablesareincludedinthemultivariateregression.Of thethreevariablescapturinguncertaintyinfinancialmarkets,TEDspreadmatterstheleastforcryptocurrencybubbles.

TheEPU-indexis positiveandsigniﬁcant forboththe univariate andmultivariateprobitmodels. Thisimpliesthat the probabilityofcryptocurrencybubblesishigherwheneconomicpolicyuncertaintyishigh.Thisresultisquiteintuitive.

However, the VIX-index, whichis signiﬁcant in both the univariate model andthe multivariate models, demonstrates negativerelationshipswithbubblesinallpanel models.Thisimpliesthat eventhoughboth EPUandVIXaremeasures of uncertainty,thesemeasurescapturesigniﬁcantlydifferentaspectsofuncertainty.

TheEPUindexisbasedonthenumberofarticles thatcontainatleastonetermfromeachofthreesetsofterms.The firstsetiseconomicoreconomy.Thesecondisuncertainoruncertainty.Thethirdsetislegislationordeficitorregulation orcongressorfederalreserveorwhitehouse.Inother words,theEPUindexreflectsonly sourcesofuncertaintythat are alreadyreflected anddiscussedinthe media.Therefore, theEPU indexmightbe agood proxy foruncertaintyasviewed bythe generalpublic. TheVIXindex, on theother hand, isbasedon optionprices, whichcapturethe marketconsensus andrespondto newinformation almost immediately.The VIXindex thereforemainly capturesuncertainty asviewedby professionalinvestorsinthefinancialmarkets.

OnepossibleexplanationwhyhighEPU isassociatedwitha greaterlikelihoodofbubbleoccurrence,whilehighVIXis associatedwithlower bubble occurrence,is that whenthe generalpublic perceives highuncertainty,some people resort tocryptocurrencies,raisingthelikelihoodofbubbles.However, whenprofessionalinvestorsperceivehighuncertaintythey become morecautious, reducing the likelihood ofbubbles. Thisexplanation is onlyone possible explanation; we donot currentlyhaveempiricalevidencetosupportordisprovethisexplanation.

Consideringthe measures ofﬁt metrics of the panel probit models, the McFaddenR-squared showsthat the models displayvarying abilitytopredictbubbles. ThemodelwiththeVIX-indexasanexplanatoryvariablehasthe highestvalue andthemodelwithTED-spreadasanexplanatoryvariablehasthelowestvalueoftheMcFaddenR-squared.

3.2.2. Timeseriesregressions:individualcryptocurrencies

Theresultsfromthe estimatedprobitregressionsforindividual cryptocurrenciesare showninTable8.⁵ We studythe cryptocurrenciesseparately toexamine whetherthe predictiveeffectsseem tobecryptocurrency-dependentorconsistent acrosscryptocurrencies.

Similartowhat weobservedinthe resultsofthepanelregressions, volatilityandvolumeexhibit positiveassociations withbubblesformostcryptocurrencies.Thismeans thathighvolatilityorvolume correspondwitha higherlikelihoodof bubbles,asdemonstratedinthepanelregressionmodels.Googlesearchesshowsvaryingdirectionofeffectsandpredictive abilitydependingontheparticularcryptocurrencystudied.GooglesearchesarepositivelyassociatedwithbubblesforBTC

5We also estimated linear univariate and multivariate regressions for the individual cryptocurrencies, which are included in the appendix ( Table A.1, Table A.2 and Table A.4 ).

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Table 9

Models’ Predictive Ability. % True Bubble Days Predicted is the share of the bubble days detected by the PSY framework which the respective model is able to predict. % Correct Predictions is the share of model-predicted bubble days that are detected by the PSY framework as bubble days.

BTC ETH XRP LTC XMR DASH XEM DOGE Average

PSY Detected Bubbles Days 193 91 100 118 92 188 79 64

Panel A: Probit regression

Predicted Bubble Days 144 76 69 94 53 169 46 54

% True Bubble Days Predicted 58.6% 65.9% 53.00% 62.7% 46.7% 75.5% 40.51% 70.3% 59.2%

% Correct Predictions 78.5% 79.0% 76.81% 78.7% 81.1% 84.0% 69.57% 83.3% 78.9%

Panel B: Linear regression

Predicted Bubble Days 115 113 86 81 52 79 70 38

% True PSY Bubble Days Predicted 46.63% 78.02% 59.00% 52.54% 34.78% 32.98% 53.16% 48.44% 50.69%

% Correct Predictions 78.26% 62.83% 68.60% 76.54% 61.54% 78.48% 60.00% 81.58% 70.98%

andETH and negatively associated withbubbles forDASH andXMR. This variation ineffects maypossibly be explained by thedifferencesinthevarious cryptocurrencies’totalmarket values.Thetransactions variablegenerallydemonstratesa positiverelationshipswithbubbles,exceptinthecaseofBTC,whereitdisplaysanegativeeffect.Onepossibleexplanation forthisexception isthat BTCisoneofthehighest-rankingcryptocurrenciesintermsoftotalmarketvalue.Anincreasein transactionsforsuchahigh-valuecryptocurrencymightimplyahigherdegreeofuseofthatcurrencyasmeansofexchange.

Thiscould leadtoaweaker associationwithbubblebehavior,asitcould indicatepracticalutility fortheowners.Overall, thecryptocurrency-speciﬁcvariablesmostlydemonstratethesamepositiveassociationswithbubblebehavioraswesawin thepanelregressionmodels.

TheexamineduncertaintyvariablesEPU-index,VIX-indexandTED-spreadshowvaryingrelationshipswithbubblestates whenit comesto thedirectionoftheireffects.As theresultsfromthepanel modelregressionindicate,the EPU-indexis positively associated withbubbles, although thisrelationship is dependent onthe particular cryptocurrencystudied. The VIX-indexisingeneralnegatively associatedwithbubblesacrosscryptocurrencies,aswealsosaw inthepanelregression models.Intheprobitmodels,theVIXvariableisnegativelyassociatedwithbubblesforBTC,DASHandDOGE,whichmight explainwhythepanelmodelsexhibitthesameeffect.TED-spreadshowsapositiverelationshipwithbubblesforBTCinthe timeseriesmodels,butnotinthepanelmodels,wherethereareonlyweakindicationsofaneffect.Notethat TED-spread doesnotshowanysigniﬁcanteffectsfortheothercryptocurrencies.

Themeasuresofﬁtmetrics,R-squaredandMcFaddenR-squaredarerelativelyhigh,whichdemonstratesthatthemodels haveaconsiderableabilitytopredictbubbles.

3.2.3. Summaryofregressionresults

Ingeneral,thecryptocurrency-speciﬁcvariablesvolatilityandtradingvolumedemonstratesimilarandconsistentresults inboththepanelregressionsandtimeseriesregressions.Inthepanelregressionmodels,Googlesearchesandtransactions are generally positively associated withbubbles. In the time series regression models, Google searches and transactions demonstratevaryingeffectsforthevariouscryptocurrenciesstudied.

TheuncertaintyvariablesEPU-index,VIX-indexandTED-spreadexhibitdifferingassociationswithbubblebehaviorinthe panelregressionmodels.TheEPU-indexshowspositiverelationshipsintheprobitpanelmodels,theVIX-indexdemonstrates negativerelationshipswithbubblesinallpanelmodels,whiletheTED-spreadexhibitsamoreambiguousrelationship.The timeseriesregressionsfortheuncertaintyvariablesrevealvaryingeffectsdependingonthecryptocurrencystudied.

Insummary,we ﬁndthatseveralvariablescanpredictbubbles.Overall,thepanel regressionresultsfortheuncertainty variables areprimarily inlinewiththetime seriesregressionresults.Inparticular,we ﬁndthatvolatility, tradingvolume andtheVIX-indexdemonstrateageneralpotential topredictbubblebehavioracrosscryptocurrencies.Thepredictiveeffect ofother variablesiscontingentonwhetherwelookattheprobitmodelsorthelinearmodels,andwhichcryptocurrency weexamine.

3.2.4. Models’predictiveability

Table 9presents acomparison ofthe time seriesmodels’ abilityto predict thebubble dates estimatedusing thePSY framework. The models utilized to test this predictive ability are the multivariate regressions displayed in Table 8 and Table A.4.The probitmodelspresented inpanel Apredict that a bubbleisexpected forthenext observationifthe esti- matedprobabilityisabovea50%threshold.ThelinearregressionmodelspredictthePSYstatisticforthenextobservation.

A bubble is predictedifthe estimated PSY statistic exceeds the criticalvalue (generated by the PSY framework) forthe respectivecryptocurrency.

TheresultsinTable9indicatethattheprobitmodelsaregenerallysuperiortothelinearregressionmodels.Theseresults contradictouraprioriexpectationthatthelinearmodelswouldperformbetterthantheprobitmodels.Wehadsuspected thattryingtopredicttheunderlyingPSYvalueswouldresultingreaterpredictiveaccuracy.

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The superiorityof the probitmodels to the linear models might be dueto the binary categorization ofthe detected bubbledays.Following thedefinitionusedinthePSYframework, bubbledaysare detectedwhen thePSYvaluesarehigh andabovethegeneratedcriticalvalue.Therefore,itseemsthatextremevaluesfitbetterintothebinarystructure(bubble/no bubble)oftheprobitmodels.Ontheotherhand,thelinearPSYmodelsmightbeabetterfitwiththeunderlyingPSYdata.

4. Conclusion

In this paper, we have examined whethercertain variables can predict bubbles in cryptocurrency prices. The ability topredictbubblespotentiallyrepresentsanimportantcontributiontomarketmonitoringandtotheunderstandingofprice dynamicsforcryptocurrencies.Toourknowledge,thisistheﬁrststudytoexaminepredictorsofbubblesincryptocurrencies.

Ascryptocurrenciesemerged onlyrecently,theyare onlynowbeginningtobeﬁnancially regulated.Wehavetherefore includedeconomic policy uncertainty(EPU), theVIX indexandthe TEDspread amongourtested bubblepredictors.The EPUindexcapturesuncertaintyaboutlegislationandregulations,whiletheVIXindexandTEDspreadcapturegeneralun- certaintyinﬁnancialmarkets.

We havestudied a set ofvariables with potential impacts on cryptocurrencyprices and used thisas a basis for our selectionofpredictorsintheregressionmodels.

Ourresults,basedonthePSYtest,revealmultiplebubbleperiodsinallthestudiedcryptocurrencies,particularlyduring 2017 and2018. Thisis inline withthe resultsof Corbetet al.(2018) andBouriet al.(2018), who alsodetect extensive cryptocurrencybubbles inthesame periods.Furthermore,Bouri etal.(2018) ﬁndthat Bitcoininparticular demonstrates extensivepriceexplosivity,andourﬁndingssupportthis.

Wehavealsolookedintowhichfactorscanpredictthesebubbles.Wherecryptocurrency-speciﬁcvariablesareconcerned, volatilityandvolumearedistinctly associatedwithbubblebehavior acrossallthestudied cryptocurrencies.Googletrends andtransactionsmostlydemonstratepositive relationshipswithbubbles,buttheeffectsare dependent onthecryptocur- rencystudiedandthetypeofregressionmodel.Amongtheuncertaintyvariableswetested,theVIX-indexgenerallyexhibits anegativeassociationwithbubbles,whiletheEPU-indexdemonstratesapositiverelationshipwithbubbles.TheTED-spread exhibitsamoreambiguousrelationshipwithbubbles.Overall,manyofthevariableswehaveinvestigatedexhibitpotential topredict bubbles, andofthese, tradingvolume, volatilityandthe VIX-indexappear tobe particularlystrong predictors.

Theseresultsmayassistauthoritiesindesigningappropriateﬁnancialregulationsforcryptocurrencies.

DeclarationofCompetingInterest Noconﬂictofinterestexists.

AppendixA. AdditionalTables

TheregressionresultsfromtheprobitunivariateregressionsandthePSYstatisticunivariateregressionsareprovidedin TableA.1andA.2,respectively.Theunivariatemodelsemployregressionsbetweenthedependentvariable(PSY-statisticor bubbledatesdummy) withone explanatoryvariableatatime, foreachcryptocurrency.The modelsare estimatedwitha constant,butonlythe parametersofthe explanatoryvariablesandthecorresponding standard errorsare reportedinthe table.Thisimpliesthatweestimate7univariateregressionequationspercryptocurrency.

Table A.1

Probit Regression Results - Univariate Time Series Regressions. The dependent binary variable BUB i,tonly takes the values 1 (explosive dates) and 0 (non- explosive dates). The independent variables are described in the data section. The sample includes all dates for the respective cryptocurrency (see Table 1 for individual time spans). ^∗, ^∗∗and ^∗∗∗ represents signiﬁcance at the 10%, 5% and 1% level, respectively. All the reported estimates are coeﬃcients with corresponding Newey-West standard errors.

Dependent variable: BUB i,t

BTC ETH XRP LTC XMR DASH XEM DOGE

Google _t−1 1.187 ^∗∗∗ 2.075 ^∗∗∗ 1.173 ^∗∗∗ 1.725 ^∗∗∗ 1.866 ^∗∗∗ 0.454 ^∗∗∗ 0.311 ^∗∗∗ 1.742 ^∗∗∗

(0.420) (0.298) (0.416) (0.486) (0.608) (0.137) (0.0799) (0.431)

Volatility _t−1 36.23 ^∗∗∗ 20.25 ^∗∗∗ 17.69 ^∗∗∗ 22.97 ^∗∗∗ 22.65 ^∗∗∗ 15.77 ^∗∗∗ 16.52 ^∗∗∗ 19.07 ^∗∗∗

(4.685) (4.939) (4.364) (4.806) (3.810) (4.515) (3.446) (3.317)

Transactions t−1 −0.213 ^∗∗ 0.700 ^∗∗∗ 0.162 ^∗∗ 0.162 ^∗∗ 0.609 ^∗∗∗ 0.450 0.445 ^∗∗∗ 0.374 ^∗∗∗

(0.0836) (0.174) (0.0691) (0.0691) (0.0909) (0.313) (0.108) (0.0713)

Volume _t−1 1.204 ^∗∗∗ 0.620 ^∗∗∗ 1.070 ^∗∗∗ 1.051 ^∗∗∗ 0.847 ^∗∗∗ 0.954 ^∗∗∗ 0.526 ^∗∗∗ 1.338 ^∗∗∗

(0.160) (0.162) (0.132) (0.140) (0.171) (0.160) (0.0816) (0.186)

EPU t−1 0.464 ^∗∗ 0.489 ^∗ 0.563 ^∗ 0.767 ^∗∗∗ 0.0138 1.003 ^∗∗∗ 0.828 ^∗∗∗ 0.866 ^∗∗∗

(0.208) (0.291) (0.292) (0.234) (0.362) (0.248) (0.289) (0.229)

VIX t−1 −2.117 ^∗∗∗ −2.370 ^∗∗∗ −2.659 ^∗∗ −3.296 ^∗∗∗ −1.936 ^∗∗∗ −4.864 ^∗∗∗ −1.572 ^∗ −4.001 ^∗∗

(0.754) (0.827) (1.132) (1.160) (0.650) (1.129) (0.830) (1.711)

TED t−1 −0.199 −1.020 ^∗∗∗ −0.579 ^∗∗∗ −0.353 ^∗∗ 0.113 −1.064 ^∗∗∗ −1.098 ^∗∗∗ −0.912 ^∗∗∗

(0.193) (0.304) (0.200) (0.160) (0.427) (0.290) (0.311) (0.216)

Observations 1258 1258 1256 1019 998 939 625 707