A “US–China World” capital International markets structure, preferences andpuzzles: Institutions & Money Journal of International FinancialMarkets,

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ContentslistsavailableatScienceDirect

Journal

of

International

Financial

Markets,

Institutions

&

Money

j o u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / i n t f i n

International

capital

markets

structure,

preferences

and

puzzles:

A

“US–China

World”

夽

Guglielmo

Maria

Caporale

a

_,

_Michael

_Donadelli

b,∗

_,

_Alessia

_Varani

c

a_Department_of_Economics_and_Finance,_Brunel_University,_London,_United_Kingdom

b_Research_Center_SAFE,_House_of_Finance,_Goethe_University,_Frankfurt,_Germany

c_{HEC-Montréal,}_Department_of_Applied_Economics,_Canada

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received7October2014

Accepted19December2014

Availableonline29December2014

JELclassiﬁcation: F3 F4 Keywords: Macro-anomalies Financialautarky Completemarkets Long-runinnovations Homebias

a

b

s

t

r

a

c

t

TheUS–Chinadatasuggestthat(i)therealexchangerate(RER)volatilitypuzzle(high RERvolatilityrelativetoconsumptionvolatility),(ii)theBackus–Smithanomaly(negative correlationbetweentheRERandconsumptiondifferentials),(iii)theconsumption corre-lationpuzzle(relativelylowcross-countryconsumptioncorrelation)becamemoresevere intheaftermathofChina’sstockmarketliberalization.Thisindicatesthatinternational macro-anomaliesdonotshowupexclusivelyamongpairsofadvancedeconomies.Inan internationalendowmenteconomycontext,weshowthatthecombinationofrecursive preferencesandlong-runriskallowsforthesimultaneousresolutionoftheseanomalies.In contrasttostandardmacromodels,thisholdseveninthepresenceoffullﬁnancial integra-tion,segmentedgoodsmarketsandnon-negligiblechangesinseveralparametervalues. ©2014ElsevierB.V.Allrightsreserved.

1. Introduction

Theinternationalbusinesscycle(IBC)literatureofthelast20yearspointsoutthattherisk-sharingpredictionsofstandard modelswithinternationalcompletemarketsdonotmatchcross-countrymovementsinconsumption.Earlystudiesshow thatastandardIBCmodelwithcompletemarketsencountersdifﬁcultiesinmatchinginternationalconsumptionandasset pricingdata(Backusetal.,1994,1995).Inparticular,itproduces(i)smoothedassetprices;and(ii)anunrealisticallyhigh levelofinternationalrisk-sharing.AsdiscussedinBackusandSmith(1993),amongothers,thisexcessamountofrisk-sharing givesrisetoaperfectpositiveco-movementbetweenRERandconsumptiondifferentialsaswellasbetweencross-country consumptiongrowthrates.Inaseminalcontribution,Lewis(1996)suggeststhathighdegreesofinternationalrisk-sharing mightbegeneratedbythenon-separabilityoftradableandnon-tradablegoodsintheutilityfunctionemployedinthemodel aswellasbythepresenceofcompletemarkets.Sheconcludesthatcapitalmarketrestrictionsandnon-separabilityareboth requiredtoexplainthelackofinternationalrisk-sharingobservedinthedata.

夽 Thispaperwaspreparedforthe4thEMG-ECBEmergingMarketsGroupConference,CassBusinessSchool(London),May8–9,2014.Wewouldliketo

thankananonymousreferee,PatrickGrüning,andseminarparticipantsatBrunelUniversity,LUISSGuidoCarli,HallInstituteofEconomicResearch,and

the12thINFINITIConferenceonInternationalFinance.Allremainingerrorsareourown.

∗ Correspondingauthorat:ResearchCenterSAFE,GoetheUniversityFrankfurt,Grüneburgplatz1,60323FrankfurtamMain,Germany.

Tel.:+496979833882.

E-mailaddresses:Guglielmo-Maria.Caporale@brunel.ac.uk(G.M.Caporale),michael.donadelli@gmail.com(M.Donadelli),alessia.varani@gmail.com

(A.Varani).

http://dx.doi.org/10.1016/j.intﬁn.2014.12.006

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Overall,theinternationalrisk-sharingmechanismembodiedinstandardIBCmodelsgivesrisetothreehighlydiscussed internationalmacroeconomicpuzzles:(i)thehighvolatilityoftheRERrelativetothevolatilityofconsumption(RERvolatility puzzle);(ii)thenegativecorrelationbetweentheRERandconsumptiondifferentials(Backus–Smithanomaly);(iii)thelow correlationofconsumptiongrowthacrosscountries(consumptioncorrelationpuzzle).1_Further,_traditional_models_with standardpreferencesdonotaddresstwowellknowndomesticassetpricingpuzzles:(i)theequitypremiumpuzzle,EPP, (MehraandPrescott,1985;Mehra,2003);(ii)therisk-freeratepuzzle(Weil,1989).

Financialintegrationanditsimplicationsfortheresolutionofbothmacroeconomicandassetpricinganomalieshave receivedconsiderableattentioninthemostrecentliterature,muchofitaddressingindividualanomalies(Benignoand Thoenissen,2008;Corsettietal.,2008;Kollmann,2012;Hamano,2013,amongothers).Relativelylittleresearch,however, hasfocusedonthejointresolutionofsomeofthesepuzzles(Bodenstein,2008;ColacitoandCroce,2013).Benignoand Thoenissen(2008)developastandardIBCmodelwithnon-tradedgoodsandincompletemarkets.Theyshowthatunder strongcomplementarybetweendomesticandforeigntradablesthemodelreproducestheBackus–Smithcorrelation. Simi-larly,Corsettietal.(2008)arguethatinternationalfinancialmarketsarenotdevelopedenoughtogeneratefullrisk-sharing andshowthatstandardmacromodelswithincompletemarketsmayaccountfortheBackus–Smithcorrelation.Inparticular, ifthereisahighlevelofcomplementarybetweenexportedandimportedgoods,thenthemodelproducessubstantial move-mentsintheRERaswellasanegativecorrelationbetweentheRERandrelativeconsumption,andreducesthecorrelation betweendomesticandforeignconsumption.However,theseresultsarenotrobusttotheintroductionofasecondtrade asset(seeBenignoandKücük-Tuger,2012).2_Kollmann₍₂₀₁₂₎_shows_that_the_{Backus–Smith}_anomaly_can_be_explained_by_a simplemodelwhereonlyafractionofhouseholdscantradeassetsfreelyincompletefinancialmarkets.FollowingCorsetti etal.(2008),Thoenissen(2011)showsthatastandardIBCmodelwithincompletemarketsisabletosolvetheRERvolatility puzzle,theRERpersistencepuzzleandtheBackus–Smithanomaly.However,thesuccessofthemodelheavilydependson thechoiceoftheelasticityofsubstitutionbetweendomesticandforeignproducedgoods.Inparticular,therangeofelasticity valuesthatallowsthemodeltoaddressthemacro-puzzlesisverynarrow,suggestingthatthemodel’sperformanceisnot sufficientlyrobust.Bodenstein(2008)developsaninternationalendowmenteconomywithcompleteassetmarketsand limitedenforcementforinternationalfinancialcontractswheretheabilitytoshareriskdependsonthedegreeofpatience oftheagents.Heshowsthat,ifagentsaresufficientlyimpatient(i.e.marketsareincomplete),themodeljointlysolves theRERvolatilitypuzzle,theBackus–Smithanomalyandtheconsumptioncorrelationpuzzle.Inlinewiththesestudies, Hamano(2013)showsthatmarketincompleteness(i.e.aninefficientinternationalrisk-sharingenvironment)iscrucialfor theresolutionoftheconsumption-realexchangerateanomaly.

However,thedebateonwhetherornota“financialautarky”ora“single-bondeconomy”regimesmayrepresentarealistic financialenvironmentisstillopen.Ontheonehand,numerousinternationalfinancestudiesshowthatbothdeveloped andemerging(inparticularBrazil,ChinaandIndia)capitalmarketshave becomeincreasingly integratedoverthelast twodecades(Cheungetal.,2006;LaneandSchmukler,2007;Donadelli,2013;MaandMcCauley,2013;amongothers). Forexample,Fitzgerald(2012)findsthatfinancialrisk-sharingamongdevelopedcountriesisnearlyoptimal.Jappelliand Pistaferri(2011),showthattheincreasingdegreeoffinancialintegrationacrossinternationalfinancialmarketshaslargely improvedhouseholdsconsumptionsmoothing(i.e.risk-sharing).Thissuggeststhateithera“financialautarky”ora “single-bondeconomy”regimescannotbeemployedtomodelthecurrentinternationalcapitalmarketsstructure.Ontheotherhand, sometheoreticalstudiesdirectlyarguethatthesetworegimesdonotrepresentrealisticfinancialenvironments.Crucini (1999)andSantosMonteiro(2008)pointoutthatstandardincompletemarketsmodelsareproblematicbecausetheyare characterizedbylimitedconsumptionrisk-sharingatboththedomesticandinternationallevel.Kollmann(2012)argues thatinternationalcapitalmarketsallowforanalmostfrictionlesstradingactivityinalargevarietyofsecurities(e.g.equities, futures,options,CDS,bonds).HeathcoteandPerri(2002)stressthatanefficientinternationaltradingactivityisimportant forthecross-countrybusinesscycles.

Theaimofthepresentpaperistocomparethemacroeconomicquantitiesandpricesproducedbytwodifferent inter-nationalendowment economies: (i)one in which agents can tradeassets for consumption smoothing purposes only domestically(i.e.financialautarky);and(ii)onewhereallagentsareallowedtoefficientlysharetheirconsumptionriskby tradingincompletefinancialmarkets.Inotherwords,weaskthequestionwhetheralimitedamountofinternationalrisk sharingisnecessarytosimultaneouslysolvetheabovementionedinternationalmacroeconomicanomaliesaswellastwo wellknownassetpricingpuzzles.Inaddition,weexaminewhetherthesepuzzlesexistinthecaseoftheUSandChina,an issuenotpreviouslyinvestigated.

OuranalysisiscarriedoutbyusingtheinternationalendowmenteconomydevelopedbyColacitoandCroce(2010, 2013).Inthiseconomy,(i)homeandforeignagentsdisplayrecursivepreferences;(ii)endowmentprocessesembodya long-runriskcomponentalàBansalandYaron(2004)andareco-integrated(seealsoTretvoll,2013).Inthissetup, capi-talmarketsarecompletebothdomesticallyandinternationally,andagentshavepreferencefordomesticgoods(i.e.home biasinconsumption).Thechoiceofthismodelismotivatedbyseveralfactors:(i)itreflectsaperiodofincreasing finan-cialintegrationbyassumingcompletemarkets;(ii)itcancaptureboth thefirstandsecondmomentsofassetpricing;

1 _For_additional_details,_see_Bodenstein₍₂₀₀₈₎_.

2 _{Speciﬁcally,}_they_say_“..._the_performance_of_these_models_worsens_considerably_when_we_move_away_from_a_single-bond_{economy...”}₍_Benigno_and

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(iii)itaccountsforconsumptionhomebias(assuggestedbyinternationaltradedata);(iv)itembodiesanovelrisk-sharing mechanismwhichdoesnotrelyonanyﬁnancialmarketimperfections.

Ourpapercontributestotheexistingliteratureinseveraldimensions.First,itfocusesonUS–Chinadataovertwodifferent periods:(i)the“ﬁnancialautarkyregimeera”whichrunsfrom1972to1990(beforeChina’sstockmarketliberalization), and(ii)the“internationalcompletemarketsera”whichrunsfrom1991to2009(afterChina’sstockmarket liberaliza-tion).WeobservethattheRERvolatility–consumptionvolatilityratio,theBackus–Smithcorrelationandthecross-country consumptioncorrelationchangedintheaftermathofChina’sequitymarketliberalization.Inparticular,theRER-volatility puzzleandtheBackus–Smithanomalybecamemoreapparentinthemid-90s.Therefore,internationalmacropuzzlesmay arisealsoamongdevelopedandemergingcountries.Second,asinBodenstein(2008),itisaimedataddressingtheRER volatilitypuzzle,theBackus–Smithpuzzleandthelowconsumptioncorrelationpuzzlesimultaneously.Weshowthatthe employedtwocountry/two-goodmodelwithrecursivepreferences,long-runriskandcompletemarketscanaddressthe puzzlessimultaneously,eveniftherearenoﬁnancialmarketimperfections.3_By_contrast,_a_moderate_amount_of_home_bias inconsumptionisrequired.Third,itexaminestherobustnessofthemodelandshowsthattheresultsholdforarelatively largerangeofparametervalues.Inparticular,realisticchangesintheRRA,IES,consumptionhomebiasparameterand cross-countrylong-runshockscorrelationonlyweaklyaffecttheRER-consumptionvolatilityratio,theBackus–Smithcorrelation andthecross-countryconsumptiongrowthcorrelation.

Therestofthepaperisorganizedasfollows.Section2presentssomestylizedfactsforChinaandtheUS.Section4outlines themodel.Section4discussestheresults.Section5concludes.

2. ThebackgroundoftheUS–Chinarelationship 2.1. WhyUS–China?

Mostinternationalﬁnance,RBCandIBCstudieshavefocusedexclusivelyondevelopedeconomies(orWestern,Educated, Industrialized,Rich,andDemocratic,WEIRD,societies).AssuggestedbyHeinrichetal.(2010),thesepapersimplicitlyassume thatthereisnovariationacrosscountries(i.e.humanpopulations).However,low–middleincomesocietiesaccountformore than80%oftheWorldpopulation.Inparticular,(i)Chinaaccountsfor20%oftheWorldpopulation;(ii)thesumofUSand ChinaGDPsisalmostonethirdoftheWorld’sGDP.4_At_present,_the_literature_on_{macroeconomic}_anomalies_in_emerging economiesisratherthin.Withthisstudy,wealsoaimtoﬁllthisgapatleasttosomeextent.5

TheChinesestockmarketwasclosedfornearlyhalfacenturyandreopenedlessthan25yearsago.Inthelate1980s, Chinatransformedmanystate-owned-enterprisesintostockcompanies.ThefirststockmarketinthehistoryofthePeople’s RepublicofChina,theShanghaiStockExchange,openedonNovember26, 1990.ShenzhenStockExchangeopenedon April11,1991,andinitiallyonlyoneclassofshares(publicAshares)wereallowedtotradeonQualifiedForeignInstitutional Investor(QFII).Thisallowsustoanalyzetwodifferentinternationalcapitalmarketregimes,afinancialautarkyone(i.e.before 1991)andacompletemarketsone(i.e.after1991).Specifically,weestimatetheRERvolatility–consumptionvolatilityratio, correlationbetweenRERandconsumptiondifferentials,andcross-countryconsumptioncorrelationovertwodifferent sub-samples:(i)pre-liberalizationera(i.e.1972–1990);(ii)post-liberalizationera(i.e.1991–2009).Consequently,international macroeconomicquantitiesandpricesarecomputedbyimposingthesetwodifferentregimes.

2.2. US–Chinastylizedfacts

Fig.1suggeststhat thesetwocountrieshavesubstantiallyincreasedtheirdegreeofopennesstowardinternational marketsafter1990,andthatfluctuationsoftheircurrencieshavesignificantlyincreasedaftercapitalmarketliberalizations. ThisisclearfromthedynamicsoftheratiosofthesumofUSandChinatradetoworldtradeandthesumofUS-owned assetsabroadandforeign-ownedassetsintheUStothesumofUSandChina’sGDPs.Bothmeasuresareincreasingover time(Fig.1,top-leftpanel).Wearguethattheincreasingdegreeofintegrationacrossbothequityandgoodsmarketshas alsolargelyinfluencedtheRERvolatility–consumptionvolatilityratioandtheBackus–Smithcorrelation.6_The_former_has increasedsharply(Fig.1,top-rightpanel),whereasthelatterhassignificantlydecreased(Fig.1,bottom-leftpanel).7 _The ratiobetweentheRERandconsumptionvolatilityisconstantlyaboveone.Overthepost-liberalizationperiodtheaverage is5.2,amuchhighervaluethantheoneusuallyproducedbystandardmacromodels.ThecorrelationbetweenRERandreal consumptiongrowthdifferentialsdeclinedsharplyimmediatelyafter1990andstartedtobecomenegativeinthemid-90’s

3_This_is_in_stark_contrast_to_Bodenstein₍₂₀₀₈₎_,_whose_model_requires_an_inefﬁcient_{international}_risk-sharing_environment_to_address_{macroeconomic}

anomalies.

4_Source:_World_Development_Indicators_(World_Bank).

5_In_this_respect,_our_work_is_most_closely_related_to_Jahan-Parvar_et_al.₍₂₀₁₃₎_.

6_Donadelli_and_Paradiso₍₂₀₁₄₎_show_that_full_risk-sharing_(i.e._the_presence_of_perfectly_integrated_markets)_tends_to_produce_a_relatively_high_RER volatility.

7_Two_facts_are_noteworthy_for_the_dynamics_of_the_RER_{volatility–consumption}_volatility_ratio_and_{Backus–Smith}_correlation:_(i)_the_Renminbi_(RMB)

hasappreciatedbyalmost38%since1994evenifChinaadoptedaﬁxedexchangerateregime;(ii)amanagedﬂoatingexchangeratesysteminChinastarted

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G.M. Caporale et al. / Int. Fin. Markets, Inst. and Money 36 (2015) 85–99 0.0 0.5 1.0 1.5 2.0 2.5 3.0 1998 2000 2002 2004 2006 2008 2010

Trade and Financial Openness

Trade Financial 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 1990 1995 2000 2005 2010

RER Volatility-Consumption Volatility Ratio

-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 1990 1995 2000 2005 2010 Backus-Smith Correlation -0.1 0.0 0.1 0.1 0.2 0.2 0.3 0.3 0.4 1990 1995 2000 2005 2010

Cross-Country Consumption Correlation

Fig.1.Financialandtradeopennessvs.puzzles.Notes:tradeopenness(TO)isdeﬁnedasfollows:TO=EI/GDP,whereEIrepresentsthesumofexportsandimportsoftheUSandChina,andGDPisthesumUS andChinaGDPs.Financialopennessisdeﬁnedasfollows:FO=(USOA+FOA)/GDPwhereUSOAdenoteUS-ownedassetsabroad(i.e.inChina),FOAareChina-ownedassetsintheUnitedStates.Theratiobetween theRERvolatilityandconsumptiongrowthvolatility,thecorrelationbetweentheRERandconsumptiondifferentialsandthecross-countryconsumptioncorrelationarecomputedusingarollingwindowof20 years.DetailsondatasourcesaregiveninAppendixA.

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(Fig.1,bottom-leftpanel).Inparticular,itispositiveunderﬁnancialautarky(0.34overtheperiod1972–1990),andnegative aftertheequitymarketliberalization(_−0.56overtheperiod1991–2009).AtoddswiththeresultsofastandardIBCmodel withcompletemarkets,thecorrelationbetweentheUSandChinarealconsumptiongrowthratesiswellbelowone(Fig.1, bottom-rightpanel).However,weobservea sharpincreaseover theperiod1995–2003(i.e.afterliberalization),which appearstobeduetoarapidexpansionofﬁnancialandtradelinkagesacrosstheUSandChina(Fig.1,top-leftpanel).Still, theconsumptioncorrelationpuzzleseemstobemoresevereifemerginganddevelopedeconomiesarejointlyconsidered. 3. Themodel

ThissectiondescribesaninternationalendowmenteconomyalongthelinesofColacitoandCroce(2010,2013).Many elementsofthemodelarestandardinthelong-runriskliterature(seeforexampleBansalandYaron,2004;Bansaletal., 2012;andBeelerandCampbell,2012)aswellasintheIBCliterature(seeforexampleTretvoll,2013andGrüning,2014). Whatisnewisthatpricesandquantitiesarecomputedunderseveralscenarios,which,amongothers,includedifferent degreesofeconomicandﬁnancialintegration,andcross-countrylong-runshockscomovement.Thisallowsustotestthe robustnessofthemodelinaddressingmacroeconomicanomalies.

3.1. Consumptionstructure

Theeconomycomprisestwocountries,home(H)andforeign(F),andtwogoodsGhandGf.Thehome(foreign)countryis

endowedwithgoodGH(GF).Inourworld,thehomecountryistheUS.Theagents’preferencesaredeﬁnedoveraconsumption

aggregateofbothhomeandforeigngoods.Formally, Ch,t=(gh,th ) ˛ (g_f,th)1−˛ (1a) Cf,t=(gh,tf ) 1−˛ (gf f,t) ˛ (1b) whereCh,t(Cf,t)istheconsumptionaggregateinthehome(foreign)country,g_h,th (gf_h,t)andg_f,th (g_f,tf )denotethe

consump-tionofgoodGhandgoodGfinthehome(foreign)countryattimet,and˛∈(0,1)representsthehomebiasparameter.

3.2. Preferences

3.2.1. Standardpreferences

First,asincanonicalstudies,weassumestandardpreferences:

Uh,t= C_h,t1−−1 1₋ (2a) Uf,t= C_f,t1−−1 1− (2b)

wherecapturesrelativeriskaversion(RRA). 3.2.2. Recursivepreferences

Inthesecondpartofouranalysisweturnourattentiontoascenariowherehouseholdsareequippedwithrecursive preferences: Uh,t=[(1−ı)(Ch,t)1−/+ıEt[(Uh,t+1)(1−)] 1/ ] /1− (3a) Uf,t=[(1−ı)(Cf,t)1−/+ıEt[(Uf,t+1)(1−)] 1/ ] /1− (3b) where 0<ı<1isthesubjectivediscount factorand ı−1−1therateoftime preference,=1−/1−1/ ,and is the intertemporalelasticityofsubstitution.Inthissetup,if−1/ >0,householdscareaboutfutureuncertainty.8

8_This_preference_{speciﬁcation}_is_consistent_with_recent_experimental_studies._{Speciﬁcally,}_the_recent_experimental_work_of_Brown_and_Kim₍₂₀₁₄₎_reveals

thatmostsubjectsdisplayrelativeriskaversiongreaterthanthereciprocaloftheelasticityofintertemporalsubstitution,conﬁrmingthattheyexhibit

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3.3. Endowments

AsinTretvoll(2013),endowmentsarecointegratedprocesses.Inaddition,theyembodyalong-runriskcomponent. Formally,

logGh,t=+ωh,t−1+(logGf,t−1−logGh,t−1)+

SRh,t

logGf,t =+ωf,t−1+(logGh,t−1−logGf,t−1)+

SRf,t

ωh,t = hωh,t−1+

LRh,t

ωf,t = fωf,t−1+

LRf,t.

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whereisthelong-runendowmentgrowthrate,∈(0,1)denotestheco-integrationparameter,ωh,tandωf,tarehighly

persistentAR(1)processes,

SR

h,tand

SRf,tareshort-runshocks,and

h,tLR and

LRf,tarelong-runshocks.Shocksaredistributed

asfollows

⎛

⎜

⎝

SR h,t

SR f,t

LR h,t

LR f,t

⎞

⎟

⎠

∼i.i.d.N

⎛

⎜

⎝

⎛

⎜

⎝

0 0 0 0

⎞

⎟

⎠

0 ,

⎛

⎜

⎝

2 SR h SR h, SR f 0 0 SR f , SR h 2 SR f 0 0 0 0 2 LR h LR h, LR f 0 0 LR f , LR h 2 LR f

⎞

⎟

⎠

⎞

⎟

⎠

whereisvectorofshocksandrepresentsthevariance–covariancematrixofthecross-countryshort-andlong-run shocks.

3.4. Capitalmarketstructureandoptimalallocations 3.4.1. Financialautarky

AssuggestedbyColeandObstfeld(1991),inaﬁnancialautarkyregimetradeinthegoodsmarkettakesplaceanditmust bebalancedineveryperiod.Formally,thebudgetconstraintforthehomeandforeigncountry:

gh

h,t+ptgf,th =Gh,t (5a)

g_h,tf +ptg_f,tf =ptGy,t (5b)

whereptisthepriceofgoodGf,tintermsofgoodGh,t.Underﬁnancialautarkyagentscannottradesecuritiesinternationally.

Inpractice,marketsarecompleteonlydomestically.Therefore,thereisnoroomforinternationalconsumptionsmoothing. Thiscapitalmarketstructuregivesrisetothefollowingoptimalallocation

gh

h,t=˛Gh,t,gh,tf =(1−˛)Gh,t (6a)

g_f,th =(1−˛)Gf,t,gff,t=˛Gf,t (6b)

Inthissetup,therealexchangerateissimplyrepresentedbythehome-biasadjustedcurrentrelativesupplyofthehome andforeigngoods.Formally,

et=(2˛−1)(gh,t−gf,t)≡ch−cf (7)

3.4.2. Completemarkets

Inordertoemphasizethattheresolutionofthepuzzlesdoesnotrelyonanyfinancialmarketimperfections,wealso accountforcompleteandfrictionlessmarkets(i.e.fullrisk-sharing).Completemarketsarealmostinvariablyassumedin internationalfinanceandIBCstudies(ColacitoandCroce,2010;Readyetal.,2013,amongothers).Suchenvironmentis supportedbyrecentstudiesshowingthatrisk-sharingviafinancialmarketsisnearlyoptimal,andthattradefrictionsin goodsmarketsarenotnegligible(Fitzgerald,2012).However,thedebateonwhetheremerginganddevelopedfinancial marketsarefullyintegratedisstillopen.OnemayarguethattheUS–Chinacapitalmarketarestillincompleteandembody frictions.Anyhow,similartootherworks(seeBacchettaandvanWincoop,2013;Readyetal.,2013;Tretvoll,2013),the modelaccountsforpartialrisk-sharingbymeansofgoodmarketsfrictions.

Undermarketcompletenessthefollowinghomeandforeignbudgetconstraintshold: g_h,th +ptg_f,th +

s_t+1

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g_h,tf +ptgf_f,t+

st+1

P_t+1(st+1)Af,t+1(st+1)≤ptGf,t+Af,t (8b)

whereAh,t(st)(Af,t(st))denotestheclaimofcountryhome(foreign)totimetconsumption ofgoodGh,t,and Pt+1 isthe

state-contingentprice(i.e.thepriceofoneunitoft+1consumptioncontingentontherealizationofst+1_at_time_t₊_1)._In

equilibrium,thefollowingholds: Ah,t+Af,t=0

∀

t.

Theefﬁcientallocationisthesolutionofaplanner’sproblemchoosingasequenceofallocations{gh

h,t,gh,tf ,gf,th,gf,tf } +∞ t=0to

maximize

Q=WhUh,0+WfUf,0

subjecttothefollowingfeasibilityconstraints: g_h,th +g_h,tf =Gh,t; ghf,t+g

f

f,t=Gf,t

∀

t≥0

whereWhandWfarethedatet=0non-negativeParetoweightsattachedtotheconsumerbytheplanner.Byassuming

St=Wh,t/Wf,t,theﬁrstorderconditionsofthesocialplanningproblemgiverisetothefollowingoptimalallocation9

gh h,t=˛Gh,t

1+(1−˛)(St−1) 1−˛+˛St

, gf h,t=(1−˛)Gh,t

1+ ˛(St−1) 1−˛+˛St

(9a) g_f,th =(1−˛)Gf,t

1+ ˛(St−1) ˛+(1−˛)St

, g_f,tf =˛Gf,t

1+(1−˛)(St−1) ˛+(1−˛)St

(9b) where St=St−1M_Mh,t f,t

ech,t ecf,t

andMh,t(Mf,t)isthehome(foreign)stochasticdiscountfactor.Inthepresenceoffullﬁnancialintegration,theRERgrowth

isequaltothedifferencebetweenthelogoftheforeignanddomesticstochasticdiscountfactors.

e=logMf,t−logMh,t (10)

3.5. Thestochasticdiscountfactor 3.5.1. Standardpreferences

CRRApreferencesimplythefollowingstochasticdiscountfactor M_h,t+1=ı

C_h,t+1 Ch,t

− (11a) Mf,t+1=ı

C_f,t+1 Cf,t

− (11b) forthehomeandforeigncountry,respectively.

3.5.2. Recursivepreferences

AsshowninEpsteinandZin(1989),thestochasticdiscountfactorinthehomeandforeigncountrytakesthefollowing form Mh,t+1=ı

C_h,t+1 Ch,t

−(1/ )

_U1− h,t+1 Et[U_h,t+11− ]

(1/ −)/(1−) (12a) Mf,t+1=ı

C_f,t+1 Cf,t

−(1/ )

_U1− f,t+1 Et[U_f,t+11− ]

(1/ −)/(1−) (12b)

9_The_detailed_solution_of_the_Pareto_problem_associated_with_this_economy_can_be_found_in_Colacito_and_Croce₍₂₀₁₃₎_._For_a_similar_problem,_see_also

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Table1

Benchmarkcalibration.

Parameter Value Parameter Value

Endowmentlong-rungrowthrate 2.00% ˛ Consumptionhome-bias 0.97

SR

Short-runshockvolatility 1.87% Co-integrationparameter 0.055%

LR

Long-runshockvolatility 4.4%SR ı Subjectivediscountfactor 0.9825

h, f Long-runcomponentpersistence 0.985 RRA 8

LR h

LR f

Long-runshockscorrelation 0.90 IES 1.5

SR h

SR f

Short-runshockscorrelation 0.05

4. Calibrationandresults

RecentIBCstudiesarguethatinternationalconsumptionandﬁnancialrisksharingisincomplete(HeathcoteandPerri,

2002;Bodenstein,2008;Corsettietal.,2008;DevereuxandYetman,2010;Kollmann,2012,amongothers).Forthisreason, canonicalmacromodelswithcompletemarketsdonotaddressclassicinternationalmacroeconomicpuzzles.Inaddition, byassumingstandardpreferences,frictionlessandcompletemarkets,thisclassofmodelsinheritsalldomesticassetpricing puzzles.Inthissection,wedemonstratethat,ifagentshaverecursivepreferencesandthereisarelativelyhighpositive cross-countrylong-runshockscorrelationandhomebiasinconsumption,marketincompletenessandﬁnancialfrictionsare notnecessarytoaddresstheaforementionedmacroeconomicpuzzles.Inthissetup,wealsosolvedomesticassetpricing puzzles.However,ifagent’spreferencesarerepresentedbypowerutility,thepresenceofcompletemarketsonlyallowsfor theresolutionoftheRERvolatilitypuzzle.

4.1. Benchmarkcalibration

Wecalibratetheparametersofthelong-runriskcomponents,ωh,tandωf,t,inlinewiththelong-runriskliterature.

Inparticular,weﬁxthepersistenceofωh,tandωf,ttobe h= f=0.985asinColacitoandCroce(2010),andLR tobea

smallpercentageofthestandarddeviationofendowment(i.e.LR

=0.044SR ).Cross-countryshort-andlong-runnewsare

correlatedasinColacitoandCroce(2010).AsinTretvoll(2013)andColacitoandCroce(2013),thecointegrationparameter isassumedtobeverysmall.Weset=0.055%.Theconsumptionhomebiasparameter,˛,isequalto0.97,suggestingthat agentsinthedomesticcountryconsumeonly3%offoreigngoods(i.e.3%oftotalconsumptionisrepresentedbyimported goods).10_Given_the_observed_growth_in_{international}_trade_since_the_80s_this_value_may_appear_unrealistic._However,_the averageratiobetweenUSimportsfromChinaandUStotalconsumptionisaround2%overtheperiod1999–2009(source: bea.gov).Itturnsoutthatthechoiceof˛=0.97ﬁtsourUS–Chinaworld,andislinewiththebenchmarkcalibrationofColacito andCroce(2013).11_This_parameter_choice_is_also_in_line_with_Erceg_et_al.₍₂₀₀₈₎_who_show_that_foreign_consumption_goods accountforonly3–5%oftheUSconsumption.Alltheotherparameters(i.e.,ı,, )arecalibratedfollowingstandard long-runriskstudies(BansalandYaron,2004;Bansaletal.,2012;Pancrazi,2014)(Table1).

4.2. Results:ﬁnancialautarkyvs.marketcompleteness

Toexaminetheroleofthenovelrisk-sharingmechanismembodiedinthemodel,wecomparetheresultsobtainedin aninternationalcompletemarketsregime(i.e.post-liberalization)withthoseobtainedunderﬁnancialautarky(i.e. pre-liberalization).First,wepresenttheresultsofthemodelwithstandardpreferencesandbothlong-runriskandnolong-run risk.Second,weturnourattentiontothemodelwithrecursivepreferences.12

4.2.1. Standardpreferences

Underfinancialautarky,theratioofdomesticandforeignconsumptiondeterminestheRERratebetweentwocountries (seeEq.(7)).ItturnsoutthatthecorrelationbetweenconsumptiondifferentialsandtheRERequalsunity.Becauseofstandard preferences,thisholdseveniftherearecompletemarkets.Ofcourse,fullrisk-sharingtendstoproduceahighdegreeof comovementbetweendomesticandforeignconsumptiongrowthrates.Itisalsowellknownthattraditionalmacromodels withpowerutilitydonotaddressdomesticassetpricingpuzzles.WereviewmostofthesefindingsinTable2,whichreports internationalmacroeconomicquantitiesandpricesestimatedoverthepre-andpost-liberalizationperiodsalongwiththe resultsforthebenchmarkcalibrationfortwodifferentcapitalmarketstructures(i.e.financialautarkyandcompletemarkets), bothinthepresenceandabsenceoflong-runrisk.

10 _A_moderate_amount_of_consumption_home_bias_can_be_found_also_in_Thoenissen₍₂₀₁₁₎_and_Corsetti_et_al.₍₂₀₀₈₎_,_who_introduce_preferences_towards

domesticgoodsinastandardIBCmodelwithincompletemarkets.

11 _For_a_detailed_discussion_on_the_role_of_home-bias_in_consumption_and_equity_in_a_IBC_context,_see_Tretvoll₍₂₀₀₈₎_.

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Table2

Modelvs.data:macroeconomicquantitiesandprices.Notes:thistablereportstheaverageequitypremium,ERP,risk-freerate,E(Rf_),_real_exchange_rate

volatility–consumptiongrowthvolatilitypuzzle,(e)/(c),thecross-countryconsumptiongrowthcorrelation,Corr(ch,cf),andtheBackus–Smith

correlation,Corr(ch−cf,e),simulatedunderdifferentinternationalcapitalmarketstructures.Theriskpremiumisnotlevered.Allparametersare

calibratedtothevaluesreportedinTable1.Withno-LRRthelong-runshockvolatilityandthecross-countrylong-runshockcorrelationsarere-calibrated,

LR

=0and SR h

SR f

=0.35.Momentsareobtainedfromrepetitionsofsmall-samplesimulations.TheERPandE(Rf₎_are_annualized_and_expressed_in

percentagepoints.Thepre-liberalizationperiodrunsfrom1972to1990.Thepost-liberalizationperiodrunsfrom1991to2009.Detailsondatasources

aregiveninAppendixA.

Model Data (1) (2) Data (3) (4)

CRRA US–China (Pre-Lib) Financialautarky (noLRR) Financialautarky (withLRR) US–China (Post-Lib) Completemarkets (noLRR) Completemarkets (withLRR) Macroquantities (e)/(c) 4.869 1.115 1.128 5.259 5.276 5.094 Corr(ch,cf) 0.112 0.404 0.392 0.016 0.784 0.799 Corr(ch−cf,e) 0.338 1.000 1.000 −0.557 1.000 1.000 Assetprices ERP 4.357 0.248 −0.207 7.542 0.190 −0.281 E(Rf₎ _1.458 _16.686 _15.921 _0.999 _16.850 _16.078

InlinewiththedynamicsreportedinFig.1,weobservethat(i)theRERvolatilityinthepost-liberalizationeraishigherthan

inthepre-liberalizationera(i.e.5.259vs.4.869);(ii)thecorrelationbetweentheRERandconsumptiongrowthdifferentials ispositiveovertheperiod1972–1990(i.e.0.338)andnegativeovertheperiod1991–2009(i.e.−0.557).

Asexpected,ifbothdomesticandforeignagentsarenotallowedtoefficientlysharetheirconsumptionriskbytradingin completefinancialmarkets,themodeldoesnotproducearealisticRERvolatility.Specifically,underfinancialautarky,the RERvolatility–consumptionvolatilityratioproducedbythemodelisjustaboveone(i.e.1.115and1.128inthemodelwith nolong-runriskandwithlong-runrisk,respectively).Ofcourse,financialautarkygivesrisealsotoarelativelylow cross-countryconsumptioncorrelation.Inotherwords,specifications(1)and(2)inTable2canonlyaccountfortherelativelylow cross-countryconsumptiongrowthcorrelationinthedata.

Differently,ifallagentscanefficientlysharetheirconsumptionriskbytradingincompletefinancialmarkets,themodel producesamuchhigherRERvolatility.Thelatterisfivetimehigherthanconsumptionvolatility,allowingthemodelto addresstheRERvolatilitypuzzle(seespecifications(3)and(4)inTable2).Theresultisinstarkcontrasttothefindings ofHeathcoteandPerri(2002)andBodenstein(2008).Undercompletemarketstheinternationalproductioneconomyof HeathcoteandPerri(2002)generatesextremelylowRERvolatility.13_Similarly,_the_endowment_economy_of_Bodenstein (2008)withcompletemarketsproducesaclosetounityRERvolatility–consumptionvolatilityratio.14_However,_the_presence offullrisk-sharingtendstogenerateastrongerpositivecross-countryconsumptioncomovement(i.e.0.784and0.799in themodelwithnolong-runriskandwithlong-runrisk,respectively).Thissuggeststhatthemodelcannotaccountforthe lowcross-countryconsumptioncorrelationintheUS–Chinamacroeconomicdata.15_Because_of_standard_preferences,_the modeldoesnotaddresstheBackus–Smithanomalyanddomesticassetpricingpuzzles.Inotherwords,forallspecifications, itproduces(i)aperfectpositivecorrelationbetweenRERandconsumptiondifferentials;(ii)anunrealisticallyhighrisk-free rate;(iii)analmostzeroERP.16

4.2.2. Recursivepreferences

Table3reportsdataontheUSandChinaforthepre-andpost-liberalizationperiodsalongwiththemacroquantities andpricesproducedbythemodelwithrecursivepreferencesforthebenchmarkcalibrationfortwodifferentcapitalmarket structures(i.e.ﬁnancialautarkyandcompletemarkets),bothwithandwithoutlong-runrisk.

On the one hand, similarly to the economy with standard preferences, under financial autarky, the RER volatility–consumptionvolatilityratioisclosetoone(i.e.1.115and1.128intheeconomywithnolong-runriskand long-runrisk,respectively)whereasinthedataitisclosetofive(i.e.4.869).17_In_addition,_the_correlation_between_the_RER_and consumptiondifferentialequalsunitybothinthemodelwithandwithoutlong-runrisk.Inthisregimeresourcesdonotflow

13_They_obtain_a_RER_{volatility–consumption}_volatility_ratio_equal_to_0.86,_three_times_lower_than_the_value_suggested_by_their_empirical_moments_(i.e.

2.76).WestressthattheydonotmatchtheRERvolatilitypuzzleevenifthereisaninefﬁcientinternationalrisk-sharingenvironment(i.e.ﬁnancialautarky

regimeorsingle-bondeconomy).TheyobtainaRERvolatility–consumptionvolatilityratioequalto1.97and0.94,respectively.Bothvaluesarestilllower

thanthe2.76theyobservedinthedata.

14_When_markets_are_complete_(i.e._agents_are_patient_⇒_subjective_discount_factor_approaches_one)_the_{international}_endowment_economy_of_Bodenstein

(2008)producesaratioequalto1.2.However,theinternationalmacro-datasuggestavaluearound5.

15_We_stress_that_in_both_capital_markets_regimes_the_results_produced_by_the_model_with_and_without_long-run_risk,_{respectively,}_are_very_similar._Loosely

speaking,long-runriskplaysakeyroleonlyifagentshavepreferencesforearlyresolutionofuncertainty.

16_Notice_that_the_pre-_and_{post-liberalization}_US_ERP_is_equal_to_4.36%_and_7.54%,_{respectively.}_This_gap_reﬂects_both_the_great_moderation_and_the_dot-com

bubbleyears,andconﬁrmsthattheUSERPembodiesastrongtime-varyingcomponent.

17_Kollmann₍₂₀₁₅₎_shows_that_this_result_holds_even_if_a_single_bond_is_traded_{internationally.}_He_argues_that_the_combination_of_long-run_productivity

shocksandrecursivepreferencesgivesrisetoarealisticRERvolatility,onlyifthereisasufﬁcientamountofinternationalrisk-sharing.Therefore,amodel

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Table3

Modelvs.data:macroeconomicquantitiesandprices.Notes:thistablereportstheaverageequitypremium,ERP,risk-freerate,Rf_,_real_exchange_rate

volatility–consumptiongrowthvolatilitypuzzle,(e)/(c),thecross-countryconsumptiongrowthcorrelation,Corr(ch,cf),andtheBackus–Smith

correlation,Corr(ch−cf,e),simulatedunderdifferentinternationalcapitalmarketstructures.Theriskpremiumisnotlevered.Allparametersare

calibratedtothevaluesreportedinTable1.Withno-LRRthelong-runshockvolatilityandthecross-countrylong-runshockcorrelationsarere-calibrated,

LR

=0and SR h

SR f

=0.35.Momentsareobtainedfromrepetitionsofsmall-samplesimulations.TheERPandE(Rf₎_are_annualized_and_expressed_in

percentagepoints.Thepre-liberalizationperiodrunsfrom1972to1990.Thepost-liberalizationperiodrunsfrom1991to2009.Detailsondatasources

aregiveninAppendixA.

Model Data (1) (2) Data (3) (4)

EZ US–China (Pre-Lib) Financialautarky (noLRR) Financialautarky (withLRR) US–China (Post-Lib) Completemarkets (noLRR) Completemarkets (withLRR) Macroquantities (e)/(c) 4.869 1.115 1.128 5.259 5.112 7.595 Corr(ch,cf) 0.112 0.404 0.392 0.016 0.768 0.578 Corr(ch−cf,e) 0.338 1.000 1.000 −0.557 1.000 −0.145 Assetprices ERP 4.357 0.237 2.610 7.542 0.189 2.470 E(Rf₎ _1.458 _2.892 _1.646 _0.999 _2.926 _1.747 0 2 4 6 8 10 12 14 16 18 20 −2 0 2 x 10−3 Endowment 0 2 4 6 8 10 12 14 16 18 20 −2 0 2 x 10−3 RER 0 2 4 6 8 10 12 14 16 18 20 −2 0 2 x 10−3

Consumption United States China

Fig.2.Impulseresponsefunctions:ﬁnancialautarky.Notes:thisﬁgureshowstheimpulseresponsefunctionsofendowment,exchangerateanddomestic (blackline)andforeign(pinkline)consumptiontoalong-runpositivenewstothesupplyoftheUSgood.(Forinterpretationofthereferencestocolorin thistext,thereaderisreferredtothewebversionofthearticle.)

fromthelow-marginalutilitycountrytothehigh-marginalutilityoneforconsumptionsmoothingpurposes.Inpractice,

followingpositivelong-runnewsregardingthesupplyofthedomesticgoods,agentsinthehomecountryhavenoaccessto

internationalﬁnancialmarketsinordertobuyinsuranceassets,and,therefore,giveuppartoftheirresources.Thisimplies

that,underﬁnancialautarky,foreignconsumptiondoesnotmovefromt+1onwardanddomesticconsumptionmoves

symmetricallywiththeRER(seemiddleandbottompanelsofFig.2).

Asiswellknown,recursivepreferencesallowtoseparatetheRRAparameterfromtheIES.Suchseparabilityisanecessary conditiontomatchassetpricingdata(BansalandYaron,2004;Bansaletal.,2012;BeelerandCampbell,2012;Pancrazi,2014). Therefore,incontrasttotheeconomywithstandardpreferences,speciﬁcation(2)inTable3producesasizableERPanda relativelylowrisk-freerate(consistentwithassetpricingdata).18

Thepresence offullrisk-sharing in themodelwithoutlong-run risk onlyaffects theRER volatilitywhich is more thanﬁvetimestheconsumptionvolatility (consistentwithUS–Chinapost-liberalizationdata).Therefore, speciﬁcation (3)inTable3addressesonlytheRERvolatilitypuzzle.Thisbecausethenovelrisksharingmechanismembodiedinthe

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0 2 4 6 8 10 12 14 16 18 20 0 1 2 3 x 10−3 Endowment 0 2 4 6 8 10 12 14 16 18 20 −0.1 0 0.1 SWC 0 2 4 6 8 10 12 14 16 18 20 −0.02 0 0.02 Consumption 0 2 4 6 8 10 12 14 16 18 20 −0.05 0 0.05 RER

United States China

Fig.3.Impulseresponsefunctions:completemarkets.Notes:thisﬁgureshowstheimpulseresponsefunctionsofendowment,shareofworldconsumption,

exchangerateanddomestic(blackline)andforeign(pinkline)consumptiontoalong-runpositivenewstothesupplyoftheUSgood.(Forinterpretation

ofthereferencestocolorinthistext,thereaderisreferredtothewebversionofthearticle.)

two-country/two-goodmodelwithrecursivepreferencesandcompletemarketsproducesendogenoustimevariationinthe distributionofconsumptionandcurrencyriskacrosscountries.Itturnsoutthatthecombinationofrecursivepreferences, completeandfrictionlessmarkets,andlong-runriskcansimultaneouslyaddressthethreeinternationalmacroeconomic anomaliesaswellasthedomesticassetpricingpuzzles(seespecification(4)inTable3).Inthisenvironment,risk-sharing takesplacethroughimportsandexports(i.e.endowmentsflowfromthelow-marginalutilitycountrytothehigh-marginal utilityone).Forexample,followingpositivelong-runnewsonthesupplyofthedomesticgood,thereisalong-lastingimpact onthedomesticmarginalutility.Thisimpliesthatdomesticagentswillsteadilydecreasetheirshareofworldconsumption (viaexports)fromtimet+1onward(aslong-runnewsdoesnotaffectcurrentconsumption).Itturnsoutthatdomestic consumptiondecreasesandforeignconsumptionincreases.Becauseoftheexcesssupplyofthedomesticgood,theRER depreciates.ThelasttwoeffectsarekeytoreplicatetheBackus–Smithanomaly.ThisisclearfromFig.3,whichshows theimpulseresponsefunctionsofendowment,shareofworldconsumption,RERanddomesticandforeignconsumption followinglong-runnewsonthesupplyofthehomegood.Westressthatinthisinternationalendowmenteconomyagents areaversetobothconsumptionandutilityrisk.Thismeansthattheyarewillingtoexchangepartoftheircurrentresourcesin ordertoinsurethemselvesagainstvariationsinfutureutility.Therefore,inthepresenceoflong-runnews,domesticagents willreducetheirshareofworldconsumptiontobuyinsuranceassetsinthefinancialmarkets.Thismechanismgeneratesa substantialamountofpressureonthecurrencyandsignificantlyaffectsassetprices.Consequently,themodelwithrecursive preferences,completemarketsandlong-runriskproducesamuchhigherRERvolatility(seealsoDonadelliandParadiso, 2014).19_In_fact,_the_RER_{volatility–consumption}_volatility_ratio_jumps_to_a_value_of_7.595_(see_{specification}₍₄₎_in_Table₃_).20 4.3. Asensitivityanalysis

Table4reportsquantitiesandpricesproducedbythemodelfordifferentvaluesoftheRRA(seespecification(2)),,the IES(seespecification(3)), ,consumptionhomebias(seespecification(4)),˛,cross-countrylong-runshockscorrelation (seespecification(5)), LR

h LR f

,andthesubjectivediscountfactor(seespecification(6)),ı.Thefirstcolumn(i.e.specification (1))reportstheresultsforthebenchmarkcalibration(asinthelastcolumnofTable3).ThelastcolumnofTable4reports theempiricalmomentsforthepost-liberalizationperiod(consistentwithaninternationalcompletemarketsregime).The

19_This_results_is_in_line_with_Kollmann₍₂₀₁₅₎_who_shows_that_a_long-run_risk,_{recursive-preferences}_model_can_reproduce_a_realistic_RER_volatility_even

ifonlyafractionofhouseholdsisallowedtotradeincompletemarkets.

20_Notice_that_the_model_produces_also_a_non-close_to_unity_{cross-country}_equity_market_returns_correlation_(see_Donadelli_and_Paradiso,₂₀₁₄_)._This

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Table4

Modelvs.data:asensitivityanalysisonmacroeconomicquantitiesandprices.Notes:thistablereportstheequitypremium,ERP,therisk-freerate,E(Rf_),

realexchangeratevolatility–consumptiongrowthratevolatilitypuzzle,(e)/(c),thecross-countryconsumptiongrowthcorrelation,Corr(ch,cf),

andtheBackus–Smithcorrelation,Corr(ch−cf,e).TheERPandE(Rf₎_are_annualized_and_expressed_in_percentage_points._The_risk_premium_is_not

levered.CM≡CompleteMarkets.EZ≡RecursivePreferences.SV≡modelwithStochasticVolatility.Momentsareobtainedfromrepetitionsofsmall-sample

simulations.DetailsondatasourcesaregiveninAppendixA.

Model(LRR) (1) (2) (3) (4) (5) (6) (7) (8) Data CM(EZ) BM RRA↑ =10 IES↑ =2 ˛↓ ˛=0.9 CORR↓ LR h LR f = 0.75 ı↓ ı=0.96 ↓ =0 SV (Post-Lib) Macroquantities (e)/(c) 7.595 9.428 9.525 3.053 9.381 2.62 7.17 9.707 5.259 Corr(ch,cf) 0.578 0.510 0.631 0.484 −0.012 0.69 0.60 0.196 0.016 Corr(ch−cf,e) −0.145 −0.418 −0.304 −0.517 −0.639 −0.12 −0.15 −0.583 −0.557 Assetprices ERP 2.470 3.153 4.760 2.434 2.305 0.76 2.47 3.099 7.542 E(Rf₎ _1.747 _1.408 _0.700 _1.773 _1.843 _4.91 _1.75 _0.081 _0.999

RERvolatility,thecross-countryconsumptiongrowthcorrelationandtheBackus–Smithanomalyareweaklyaffectedby

differentRRAandIESvalues.Thesubjectivediscountfactor,thecoefﬁcientofriskaversionandtheintertemporalelasticityof

substitutionrepresentrisk-sharingbasedparameters.Inpractice,theycontrolagent’swillingnesstosharerisk.Thisimplies

thatchangesintheseparameterstendtoaffectmainlytheagents’utilityfunctionbutleavethesetoffeasibleallocations

unchanged.Inotherwords,differentvaluesofı,and altermainlytheERPandtherisk-freerate.Asisstandardinthe

long-runriskliterature(BansalandYaron,2004;Pancrazi,2014),ahigherRRAorIESproducesahigherERPaswellasa

higherRERvolatility–consumptionvolatilityratio.Theexplanationisstraightforward.WithhigherRRAorIESvalues,agents becomemoreriskaversetoconsumptionandutilityriskandtheirwillingnesstobuyinsuranceassetsininternational capitalmarkets(forconsumptionsmoothing)increases.Therefore,assetpriceschangeandthecurrencybecomesmuch morevolatile.

Byassumingsufficientlyimpatientagents(i.e.ı=0.96),themodelisstillabletoproduceahighRERvolatility,anegative correlationbetweenRERandconsumptiondifferentials,andarelativelylowcross-countryconsumptioncorrelation.More myopicagentstendtoplacelessweightonthedistantfuture.Doingso,theycarelessaboutuncertaintyonfutureutility.As aresult,tradingactivitydecreases(i.e.(e)↓)andtheyaskforalowerequitypremium(i.e.ERP↓).Theseresultsareinline withthoseofBodenstein(2008).However,inthismodelthereisfullfinancialrisk-sharingwhereasintheBodenstein(2008)’s endowmenteconomyfinancialmarketsarecompletebuttheenforcementofinternationalfinancialcontractsislimited(i.e. agentscannotshareriskefficiently).Bycontrast,ifcontractenforcementisnotlimitedandagentsarenotimpatient,the modelbehavesasastandardIBCmodelwithcompletemarkets,thatis,itproducesaRERvolatility–consumptionvolatility ratioclosetoone,ahighercross-countryconsumptioncorrelation,andthecorrelationbetweenRERandrelativeconsumption isequaltoone.AsinBodenstein(2008),wefindthatahigherdegreeofeconomicintegration(i.elowerconsumptionhome bias–˛closerto0.5),leadstoadecreaseintheRERvolatility,andtoahigher(negative)correlationbetweentheRERand consumptiondifferentialscomparedtothebenchmarkcalibration.

Overall,theentriesinTable4suggestthattheparameterspaceof, ,˛, LR h

LR f

andıallowingthemodeltosolvethethree classicinternationalmacroeconomicpuzzlesisrelativelylarge.Notealsothatthemodel’sperformanceispreservedevenif theendowmentprocessesarenotcointegrated(i.e.=0).Themodelfailsifthecorrelationbetweendomesticandforeign long-runinnovationsissigniﬁcantlylowerthaninthebenchmarkcalibration.Inthiscase,itproducesanegativecorrelation betweenconsumptiongrowthrates,butstilladdressestheRERvolatilityandtheBackus–Smithpuzzleaswellasthedomestic assetpricingpuzzles.Itisnoteworthythatitproducesanegativecorrelationratherthanacorrelationclosetounity(asin standardmacromodels).Therefore,inouropinion,it“partiallyfails”.21_We_stress_that_if_the_correlation_between_domestic andforeignlong-runshocksrangesfrom0.9(benchmarkcalibration)to0.76,theperformanceofthemodelisnotaffected, thatis,itstillsolvestheﬁvepuzzlessimultaneously.ThisisclearfromFig.4,whichplotstheRERvolatility–consumption volatilityratio,(e)/(c),thecorrelationbetweentheRERandconsumptiondifferentials,Corr(ch−cf,e),the

cross-countryconsumptiongrowthcorrelation,Corr(ch,cf),forvariousvaluesofthecross-countrylong-runshockscorrelation

(onthehorizontalaxes), LR h

LR f

,byassuming˛=0.97(Panela)and˛=0.9(Panelb).22

Finally,speciﬁcation(8)inTable4suggeststhatstochasticvolatilitydoesnotaffectmuchthemodel’sperformance.23 Tworesultsarenoteworthy.First,andnotsurprisingly,themodelwithstochasticvolatilityproducesahigherERPaswellas ahigherRERvolatility.Second,itallowsforamuchlowercross-countryconsumptioncorrelation.Thecorrelationisalmost threetimeslowerthantheoneproducedinthebenchmarkmodel(i.e.0.196vs.0.578).However,thisismoreconsistentwith

21 _This_is_in_line_with_US–China_consumption_data_over_speciﬁc_periods_(see_Fig.₁_,_bottom-right_panel).

22 _Notice_that_the_model_produces_a_{cross-country}_consumption_correlation_lower_than_an_empirical_{cross-country}_GDP_correlation_(see_dotted_blue_line

inFig.4).Thisholdsiftheparameterspaceof LR

h LR f

isquitenarrow.

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Caporale et al. / Int. Fin. Markets, Inst. and Money 36 (2015) 85–99 97

Fig.4.Puzzlesvs.cross-countrycorrelationinthelong-runinnovations:alpha=0.97(Panela)andalpha=0.90(Paneb).Notes:Thisﬁgurereportstherealexchangeratevolatility–consumptionvolatilityratio, (e)/(c),thecorrelationbetweentherealexchangerateandconsumptiondifferentials,Corr(ch−cf,e),thecross-countryconsumptiongrowthcorrelation,Corr(ch,cf),forvariousvaluesofthe correlationbetweenlong-runendowmentshocks, LR

h LR f

,from0.62to0.9(Panela),andfrom0.74to0.9(Panelb).ThedottedbluelinerepresentsthecorrelationbetweentheUSandChinaGDPgrowthrates (post-liberalizationsample:1991–2009).Momentsareobtainedfromrepetitionsofsmall-samplesimulations.

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US–Chinapost-liberalizationdata,whichsuggestacorrelationof0.016.Overall,stochasticvolatilityimprovesrisk-sharing. Asaresults,itbringsusclosertothecorrelationbetweentheRERandconsumptiondifferentialsobservedintheUS–China dataovertheperiod1991–2009.

5. Concludingremarks

EarlyIBCstudiesshowthatastandardmodelwithinternationalcompletemarketsdoesnotaccountfortherelativelyhigh RERvolatility,thenegativecorrelationbetweenRERandconsumptiondifferentialsandthelowcross-countryconsumption correlationinthedata.Theyarguethatsuchfailureisduetothefactthatmarketcompletenessproducesanunrealistically highlevelofrisk-sharing.Therefore,morerecentIBCstudiesarguethatalowerdegreeofinternationalrisk-sharingseems tobeanecessaryconditiontosolveinternationalmacroeconomicpuzzles.Theyrelyoninternationalincompletemarket regimes(e.g.“ﬁnancialautarky”and“single-bondeconomy”)orﬁnancialmarketimperfections(e.g.“borrowingcontraints” and“limitedenforcement”).

Thispapercomparestheinternationalquantitiesandpricesgeneratedunderﬁnancialautarky(withstandardand recur-sivepreferences)withthoseunderinternationalcompletemarkets(withstandardandrecursivepreferences).For this purposeitusesaninternationalendowmenteconomywithfrictionlessmarkets,highlycorrelatedlong-runinnovations andpreferencestowardsdomesticgoods,andreliesonUS–Chinamacroeconomicdata.Theanalysissuggeststhatthe RER-volatilitypuzzle,theBackus–Smithanomalyandtheconsumptioncorrelationpuzzlecanbemoreorlesspronouncedunder differentcapitalmarketregimes.Inparticular,weobservethat(i)theRER-volatilitypuzzleandtheBackus–Smithanomaly havebecomemoreapparentintheaftermathofChina’sstockmarketliberalization(i.e.after1991);(ii)theconsumption correlationpuzzle(onaverage)isevenstrongerifadevelopedeconomyandanemergingoneareconsidered.Therefore, internationalmacroeconomicpuzzlesdonotariseexclusivelyamongpairsofdevelopedcountries(e.g.USvs.Canada,US vs.UK).

IncontrasttorecentIBCstudies,wepointoutthataninefﬁcientinternationalrisk-sharingenvironmentdoesnot rep-resentanecessaryconditiontoaddressinternationalmacroeconomicpuzzles.Instead,amoderateamountofhomebiasin consumptionisrequired.Speciﬁcally,weshowthat,inthepresenceofcompleteandfrictionlessmarkets,thecombinationof recursivepreferencesandcorrelatedlong-runinnovationsallowsforthesimultaneousresolutionofthreeimportant inter-nationalmacroeconomicpuzzles(i.e.RERvolatilitypuzzle,Backus–Smithanomaly,consumptioncorrelationpuzzle)and twoassetpricingpuzzles(i.e.EPPandrisk-freeratepuzzle).Thisholdseveniftherearenon-negligiblechangesinseveral parametervalues,suggestingthatthemodel’sperformanceisrobust.

AppendixA. Data

We base our analysis on US–China data over the period 1972–2009. Real consumption data are from the Robert Barro’s website (Barro-Ursua Macroeconomic Data, 2010, freely available at http://rbarro.com/data-sets/).The annual average China/US nominal exchange rate, and the US and China GDP deﬂator are collected from the St. Louis FED (FRED ECONOMIC DATA, freely available at http://research.stlouisfed.org/fred2/). The US annual average equity risk premium and risk-free rate are from Kenneth French Data Library (freely available at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/datalibrary.html).TheGrossDomesticProduct(GDP)oftheUS, China,UK,andGermany(atcurrentUS$prices)arefromtheIMFWorldEconomicOutlookDatabases(WEO).

DataoninternationaltransactionsarefromBureauofEconomicAnalysis(Table12,U.S.InternationalTransactions,byArea –China,freelyavailableathttp://www.bea.gov/international/index.htm).Wecollectthefollowingseries:Exportsofgoods andservicesandincomereceipts(line1),importsofgoodsandservicesandincomepayments(line18),U.S.–ownedassets abroad,excludingﬁnancialderivatives(line40),Foreign-ownedassetsintheUnitedStates,excludingﬁnancialderivatives (line55).Allseriesareavailablefrom1999.

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