Risk management in life insurance companies: Evidence from Taiwan

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NorthAmericanJournalofEconomicsandFinance29(2014)185–199

ContentslistsavailableatScienceDirect

North

American

Journal

of

Economics

and

Finance

Risk

management

in

life

insurance

companies:

Evidence

from

Taiwan

Jin-Li

Hu

∗,1

,

Hsueh-E

Yu

InstituteofBusinessandManagement,NationalChiaoTungUniversity,Taiwan

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received11January2014

Receivedinrevisedform20June2014 Accepted23June2014 JELclassiﬁcation: G22 G32 Keywords: Investingrisk Underwritingrisk

Two-stagequantileregression Risked-basedcapital

a

b

s

t

r

a

c

t

Thesolvencyissueoflifeinsurancecompanieshasbecomemore

important in recent years as business risks turn increasingly

greater.Thisstudyexaminestherelationshipamonginvestingrisk,

underwritingrisk,andthecapitalratioduringthepostrisk-based

capitalregulationperiodof2004–2009inTaiwan.Inadditionto

thetwo-stageleastsquareregression(2SLS),wealso adoptthe

two-stagequantileregression(2SQR)tocapturetheeffectsoflow

capital(orrisk)levelsand highcapital(orrisk)levels.2SLSdo

notfullyexplainthecapital-riskrelation.Contrarytoprevious

evi-dencereportedintheU.S.,ourﬁndingsin2SQRmodelindicatethat

therelationshipbetweencapitalandunderwritingriskispositive,

whiletherelationshipbetweeninvestingriskandcapitalshowsa

reversepattern.Overall,the2SQRprovidesstrongerevidencethan

the2SLS.

1. Introduction

Thisistheﬁrststudytoexaminetheinterrelationshipsamongcapital,investingrisk,and under-writingriskinthelifeinsuranceindustrybyusingthetwo-stagequantileregression(2SQR)method. Fortheinsurancesector,theoreticalliteratureandacademicstudiesinthisareahavefocusedmostlyon

∗ Correspondingauthorat:InstituteofBusinessandManagement,NationalChiaoTungUniversity,118,Chung-HsiaoWest Rd.,Sec.1,TaipeiCity100,Taiwan.Fax:+886223494922.

E-mailaddresses:jinlihu@yahoo.com,jinlihu@gmail.com(J.-L.Hu). 1 _{http://jinlihu.tripod.com}_.

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theinfluenceoftherisk-basedcapital(RBC)regulatoryinstrument.Thetheoreticalliteraturewidely examinesavarietyofhypothesespredictinginsurers’capitalandrisk-takingbehavior,suchasrisk subsidies,transactioncostsandregulatorycosts.Thefirstistherisksubsidyhypothesisthatassumes anegativerelationbetweenriskandcapital.Thishypothesisimpliesthatfinancialfirmsareproneto havemoreincentivestoincreaserisksthroughexploitingthebenefitsofguarantyfunds(Lee,Mayers, &Smith,1997)sincetheguarantychargesareflatonpremiumsratherthanbeingrisk-based.The secondiscalledtheregulatorycosthypothesisandsuggestsapositiverelationbetweenriskand cap-ital(Shrieves&Dahl,1992).Thishypothesispredictsthatiftheregulatorycapitalcostishigh,then thefinancialfirmsmaytendtotakeonmorerisktobalancetheexplicitandimplicitcostsof regula-tion.ThethirdisrepresentedasthetransactioncosthypothesisandfirstintroducedbyCoase(1937) andfurtherexpandedbyWilliamson(1988),whocontendsthattheleveloftransactioncostsmostly determinesthedegreeofverticalintegrationandcapitalstructure.

BaranoffandSager(2002)usetheviewoftransactioncoststopredicttherelationbetweenproduct riskandcapitalinthelifeinsuranceindustry.Theyrecognizethathealthinsuranceisthekernelof transactioncosts,becauseitinvolvesmorecontractualuncertaintythanotherproductlines.When lifeinsurerssellriskierproductssuchashealthinsurance,theymayincreasetheirequity,ratherthan debt.Hence,thetransactioncosthypothesisimpliesthatriskandcapitalarepositivelyrelated.

Similartothetheoreticalliterature,theempiricalliteraturealsoproducescontradictory conclu-sions,sinceeachstudymayoutlinecapitalandriskdecisionsinitssmallsetoffinancialfirms,risk measures,andmethods,dependingonthestudy’scharacteristics.Table1showsseveralrepresentative studiesregardingrisk-capitalrelationships.Amonginsurancestudies,CumminsandSommer(1996) addressthattheinsurersincreasetheirriskpositionsascapitallevelsincreaseintheproperty/casualty insurancemarket.BaranoffandSager(2002,2003)andBaranoff,Papadopoulos,andSager(2007)show apositiverelationshipbetweencapitalandregulatoryassetrisk(oropportunityassetrisk),supporting theregulatorycosthypothesisandthebankruptcyavoidancehypothesis.Theyalsofindanegative relationshipbetweenproductriskandthecapitalratio.Inbankingstudies,ShrievesandDahl(1992) findapositiverelationshipbetweencapitalandassetrisk,revealingthatbanksthathaveincreased theircapitallevelhavealsoraisedtheirrisklevel.Theirresultssupportseveralhypotheses, includ-ingtheunintendedeffectofminimumcapitalregulation,regulatorycosts,aswellasbankruptcycost avoidance.

TheoppositefindingsareencounteredbyJacquesandNigro(1997),whopostanegativerelation betweenportfolioriskandcapitalamonga largenumberofU.S.commercialbanks.Severalbank studiesreportthatbanksmaytakeonmoreorlessriskdependingontheirdifferentcapitalpositions. CalemandRob(1999)arguethatseverelyundercapitalizedbanksmaybeargreaterrisksthan medium-sizedcapitalbanksaswellaswell-capitalizedbanks.Heid,Porath,andStolz(2003),Jeitschkoand Jeung(2007)andJokipiiandMilne(2011)notethat,forwell-capitalizedbanks,riskandcapitallevel arepositivelyrelated,whileforundercapitalizedbanks,thereisanegativerelationbetweenthetwo. BoththeoreticalandempiricalargumentsraisesomequestionsintermsofRBCrequirements. Forinstance,howdolifeinsurersreacttocapitalrequirements?Dotheyraiseorreducetheir risk-takingbehavior?Howdotheyreacttodifferenttypesofrisk?Asweknow,thelifeinsurancesector isahighlyregulatedindustry,becauseinsurers’insolvencybringsaboutanegativeimpactuponthe soundnessandstabilityofthefinancialsystem.AsLee,Huang,andYin(2013)note,thelifeinsurance market,particularlythelifeinsurancepremium,playsasignificantroleinfinancialmarkets.Whenthe regulatorsimplementfinancialoreconomicpolicies,theymusttakeaccountoftheimpactsofthese policiesontheinsurancemarket.daSilvaandDivino(2013)alsowarnthatfinancialinstitutions’credit risksarepro-cyclicalanddefaultrisksdependonstructuralfeatures,andthustheregulatorshould setupapolicytopromotefinancialstabilityandefficientlyreducefluctuations.

LifeinsurersinTaiwanhaverecentlybeenincreasinglyexposedtogreaterrisks,becauseofmore competitors,expandinginsuranceinterestlosses,andtherecentglobalﬁnancialcrisis.Tomitigate lifeinsurers’excessiveriskseeking,TaiwanhasimplementedtheRBCrequirementsinitsdomestic insurancesystemsince2003.Thismechanismmaybringasubstantiallyimportantimpactonlife insurers’capitaldecisionandrisk-takingbehaviors.Sinceriskmanagementintheinsuranceindustry hasbecomeanimportantissue,investigatingtherelationshipsamonginvestingrisk,underwriting risk,andcapitaliscrucialforregulatorsandlifeinsurersinTaiwan.

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J.-L. Hu, H.-E. Yu / North American Journal of Economics and Finance 29 (2014) 185–199 187 Table1

Summaryofrepresentativestudiesexaminingrisk-capitalrelationships.

Country Authors Riskmeasure Sample Method Findings

U.S. ShrievesandDahl

(1992)

1.Assetrisk

2.Non-performingloansrisk

1800FDIC-insured andholding company commercialbanks (1983–1984) Simultaneous equations approach(2SLS)

Apositiverelationbetweenassetriskandcapitalsupports theregulatorybankruptcycostavoidanceandmanagerial risk-aversetheory

U.S. Cumminsand

Sommer(1996)

StandarddeviationofROAand lossratio Property–liability insurers (1979–1990) Simultaneous equations approach(2SLS)

Positiverelation(agency-costtheory)

U.S. Aggarwaland

Jacques(1998, 2001)

1.Riskweightedasset(RWA) 2.Non-performingloansrisk

Banks(1991,1992, 1993–1996)

Three-stage simultaneous equations(3SL)

Mixed:Negativerelationsin1991–1992,butpositive relationin1993(RWA)

U.S. JacquesandNigro

(1997)

Risk-weightedasset 2570U.S. FDIC-insured commercialbanks (1990–1991) Simultaneous equations approach(2SLS) Negativerelation

U.S. BeattyandGron

(2001)

1.Riskadjustedassets 2.Assetgrowth

438holding companybanks (1990–1995)

OLSand2SLS Riskispositivelyrelatedtoequitycapitalﬁnancing, particularlyforbankswithlowcapital

U.S. BaranoffandSager

(2002)

1.Regulatoryassetrisk 2.Productrisk 1022lifeinsurers (1993–1997) Simultaneous equations approach(2SLS)

Thereexistsapositiverelationbetweenassetriskand capital,butanegativerelationbetweenproductriskand capital(transactioncosttheory).

U.S. BaranoffandSager

(2003)

1.Regulatoryassetrisk 2.Productassetrisk

789lifeinsurers (1993–1999)

Simultaneous equations approach(2SLS)

Thereisapositiverelationbetweenassetriskandcapital

U.S. Baranoffetal.

(2007)

1.Regulatoryassetrisk 2.Opportunityassetrisk

719lifeinsurers (1994–2000)

Structuralequation model(SEM)

BothRARandOARhavepositiveeffectsoncapitalfor largerinsurers

U.S. JokipiiandMilne

(2011)

1.Riskweightedassets 2.NPLrisk U.S.holding companiesand commercialbank (1986–2008) 1.Singleequation 2.GMMequations

Forwell-capitalizedbanks,RWAandbuffercapitalare positivelyrelated,butforundercapitalizedbanks,RWA andbuffercapitalarenegativelyrelated

Swiss BichselandBlum (2004) 1.S.D.ofrateofreturnon assets 2.S.D.ofstockindex 19Publiclytraded banks(1990–2002) Two-stepFGLS procedure

Positiverelation(regulatorycosttheory)

Germany Heidetal.(2003) Riskweightedassets 550savingbanks (1994–2002)

2SLSand3SLS Thereexistsapositiverelationforbankswithhighcapital buffersandanegativerelationforlowcapitalbanks Japan Deelchandand

Padgett(2009)

Marketrisk(S.D.ofstock return)

263cooperative banks(2003–2006)

2SLS 1.Negativerelations(buffereffect)

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Ourresearchisofinterestforseveralreasons.First,lifeinsurersmayshowdifferentmanagerial discretionwhenconsideringtwotypesofriskunderincreasedcapitalrequirements.Duetoagradual relaxationofportfoliorestrictionsinrecentyearsinTaiwan,insurersmayhavemoreincentivesto pursuegreaterinvestingriskforthemaximizationofprofitswhiletheincentiveforunderwritingis notobvious,becauseinsurerssufferfromagreatdealofinsuranceinterestlosses,promptingthemto adoptrelativelyconservativestrategies.Second,thecapitalrequirementsofTaiwanmaydifferfrom thoseoftheU.S.andothercountriesduetodifferentregulatorycultures,economicdevelopment, andmanagers’riskpreferences.Forinstance,Taiwan’sportfoliorestrictionsmaybemorestringent suchasonregulatingoverseasinvestment,whiletheauthoritycapitalrequirementseemslooser, whencomparedtotheU.S.ThismaycausedifferentpolicyeffectsbetweenTaiwanandtheU.S.Third, theabilityofTaiwan’slifeinsurerstoadjusttheircapitalandriskmaydifferfromthatoftheU.S. SuchadjustmentabilitiesmaybemarginalinTaiwanforlowerliquidityamongthestocksharesof smallfirmsanda fledglingmarketforasset-backed securities.MostofTaiwan’ssmallcompanies finditdifficulttoraisecapitalinalessdevelopedcapitalmarketduetotheirlimitedresourcesand asymmetricinformation.Moreover,Taiwanhasnothadmuchexperienceinassetsecuritizationlike intheU.S.Such adifficultyinadjustingcapitaland riskmayimpactTaiwaninsurers’risk-taking behaviors.

Onecontributionofourstudyistoprovideempiricalfindingsofriskmanagementinadeveloping economyoutsidetheU.S.andEuropeanfinancialinstitutions.Asecondcontributionistopushforward theliteraturenotonlybyusingthetwo-stageleastsquares(2SLS)method,butalsobyadoptinganew methodofthetwo-stagequantileregression(2SQR).Whilemanyempiricaleconomistspreferthe traditionaltwo-stagesleastsquares(2SLS)duetoitsadvantageinloweringestimationbiasescaused byendogeneity,thetwo-stagequantileregression(2SQR)approachprovidesmoreinformation,other thanthemean,whenresearchersareinterestedinaspecificpartofthedistributionofthevariables (Kim&Muller,2004;Fattouh,Scaramozzino,&Harris,2005).Third,thispapersimultaneouslytakes intoaccounttwotypesofrisks:investingrisk2_and_underwriting_risk.3_We_believe_this_paper_offers

someinsightsfortheempiricalliteratureonthelifeinsuranceindustry. 2. AnalysisofTaiwan’slifeinsurancesectorandthehypothesis

Taiwan’slifeinsuranceindustryhasexperiencedtremendousgrowthsinceitwasderegulatedin 1992byallowingnewentrantsintothemarketunderthegloballiberalizationtrend.Lifeinsurance inthecountryisanintegralﬁnancialserviceindustrywithNT$2006(US$60.70)billioninpremium incomeandNT$10,782(US$326.24)billioninassetsin2009.

Mostprofitsinthelifeinsuranceindustrycomefromfinancialinvestment.Astheimportanceof financialinvestmentforinsurers’profitabilityisincreasing,Taiwan’sregulatorhasexpandedthescope ofinvestmenttargets,likerelaxingcorporatebondrestrictionsandallowinginvestmentstoacquireup to25%ofthesharesofaninsurancecompanyinChina.Theregulatoriscurrentlyconsideringtofurther lifttheoverseasinvestmentceilingfrom40%to50%.Undertherelaxationofportfoliorestrictions,life insurersmayhavemoreincentivestoengageininvestingratherthanunderwriting.Theymayhold thelowestcapitallevelaspossibleinordertopursuemoreoverseasinvestments,whichmayleadto amoralhazardproblem.Moreover,Taiwan’sguarantyfundsystemforinsolvencyprotectionisnot executedonthebasisofrisk.Lifeinsurersarenotpenalizedfortheirrisk-takingbehaviors,because anyshortfallofcapitalisexpectedtobecoveredbytheguarantyfundmechanism.Undersuchaflat guarantyfundmechanism,lifeinsurersmaychoosetotakeonmoreinvestingrisk,becausetheywant toobtainmoreprofitsfrominvesting,whichistheirmainsourceofprofitability.Accordingtothe

2_Investing_risks:_Life_insurers_may_have_different_levels_of_risks_when_they_invest_in_many_types_of_assets_such_as_loans,_bonds, stocksecurities,realestate,orforeigninvestment.Forexample,overseasﬁnancialinvestmentsareviewedashighriskassets whencomparedtoloansandbonds,inwhichtheriskfromthelatterfacedbyinsurersisrelativelylow.

3_Underwriting_risks:_For_insurers,_different_types_of_insurance_products_may_face_different_levels_of_risks._When_life_insurers writemorehealthinsuranceproducts,whichusuallyinvolvemorecontractualuncertainty,theymaytakeonmorerisks.In contrast,lifeinsurerstakeonlessrisktohandlelifeinsuranceandannuities.

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J.-L.Hu,H.-E.Yu/NorthAmericanJournalofEconomicsandFinance29(2014)185–199 189 moralhazardhypothesis,wepredictthatlifeinsurersmayincreasetheirinvestingriskwhencapital declinesasstatedbelow.

H1. Thereisanegativerelationbetweencapitalandinvestingriskaftercontrollingunderwriting risk.

Intheinsurers’productmarkets,intensecompetitionhaseruptedintoapricewar,leavingalmost nomarginforunderwritingprofitability.Inordertoupholdmarketsharetosurvive,lifeinsurerstry toadoptariskyproductstrategy,buttheystillhavetobecarefulasexcessiveexposuremaydeepen theexistinginsuranceinterestlosses.Healthinsuranceisconsideredasariskierproductstrategythan lifeinsuranceorannuities(Baranoff&Sager,2002,2003).Iflifeinsurerswriteriskierproductslike healthinsurance,thentheymaytrytoholdmorebuffercapitaltorespondtothehigherrisks,because theymaybeburdenedwithhightransactioncostsanderodingcapitalmayresultingreater under-writinginefficiency.Ontheotherhand,highlycapitalizedinsurersmayhavemorefinancialcapital orsocialcapitaltoprovidedifferentiatedservicestoattractpolicyholdersandalsocarrysuperior bargainingpowertowriteriskierproducts.Thisisbecausetheymayhaveagreaterrisktoleranceto dealwithincreasingdisputesamongthestake-holdersortocopewithanydramaticchangeinthe competitiveenvironment.Inaddition,theregulatorycostofheathinsuranceishigh,sincethe regu-latorimposeshigherpenaltyweightsonhealthinsurancecomparedtolifeinsuranceandannuities accordingtoTaiwan’scapitalrequirements.Insurersmaybeforcedtowritemorehealthinsuranceto compensateforregulatorycapitalcosts.Accordingtothetransactioncosthypothesisandregulatory costhypothesis,wepredictthatthecapitallevelmaybepositivelyrelatedtounderwritingrisk. H2. Thereisapositiverelationbetweencapitalandunderwritingriskaftercontrollinginvestingrisk. 3. Investingrisk,underwritingrisk,capital,andrelevantvariables

3.1. Investingrisk(INR)

Inadditionaltosellinginsuranceproducts,life insurersinvestthefundsthat areentrustedto them,thusmakingthemapartofthefinancialinstitutionindustry.Regulatorsassessinsurers’credit ordefaultriskmostly bymeansoftheassetrisk componentintheRBCformula.Our paperuses regulatoryassetsasaproxyforinvestingriskbasedontworeasons.First,thismeasureessentially echoestheregulators’objectiveofminimizingbusinessriskandreflectsinsurers’solvency.Second,it canreflectfirms’risk-takingdecisioninatimelymanner(Rime,2001)asaresultofbeinganexante indicator.Similartopriorstudies(Jacques&Nigro,1997;Baranoff&Sager,2003),wedefineinvesting riskbytheratioofrisk-weightedassetstototalassets.

3.2. Underwritingrisk(UNR)

Thelifeinsuranceindustryisinthebusinessofsellinginsurancecoverageandannuities(Baranoff &Sager,2002).Forlifeinsurers,eachproductsoldtopolicy-holderisacontractbasically.Thus, under-writingriskderivesfromincompleteness,uncertainty,andcomplexitiesofinsurancecontractswithin theprocessoftradingriskyproductssuchashealthinsurance.BaranoffandSager(2002)notethat healthinsuranceisriskierthanlifeinsuranceandannuities.PottierandSommer(1997)alsoholdthe sameview.Inlifeinsuranceandannuities,lifeinsurerslargelycountonmortalitytablestopredict longevityandtoreducetheirrisks,butasuddenincreaseinthecostofhealthinsuranceis unpre-dictable,becauserelevantinformationisnotavailable.Moreover,fraudeventsofaccidentinsurance haveraisedlitigationcostsandrisksduetomoreconﬂictsofinterestamonginsurersand policy-holders.FollowingBaranoffandSager(2002),4_we_measure_the_ratio_of_health_writings_plus_accident

writingstototalwritingsbyalifeinsurerasaproxyforunderwritingrisk.

4_They_use_the_health_writings_ratio_to_total_writings_as_a_proxy_for_underwriting_product_risk._In_our_case,_we_differ_by_adding accidentwritings.Thereisaslightdifferencebetweenthetwo.

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3.3. Capitalratio(CAR)

Somestudiesadopttheratiooftotalequitytototalrisk-weightedassetsaftertheintroductionof risk-basedcapitalregulation,whileothers(Baranoff&Sager,2002;Deelchand&Padgett,2009)prefer usingtheratiooftotalequitytototalassets.FollowingBaranoffandSager(2002)andDeelchandand Padgett(2009),wedeﬁnethecapitalratiousedinourstudyasaratioofequitycapitaltototalassets. Marketdataarepreferabletobookvaluedata,butnotreadilyavailable,becausemostlifeinsurersare notpubliclytradedcompaniesinTaiwan.

3.4. Relevantvariables

Inadditiontosize,ROA,andtherecentglobalfinancialcrisis,wealsoincorporateownership struc-turevariablesthatmayaffectthecapital-riskrelationshipbasedonagencyissues.Thesizefeature isacriticaldeterminantofafirm’scapitalizationaccordingtotheeconomiesofscalehypothesis. Firmsize(SIZE)ismeasuredbythenaturallogoftotalassets.Returnonassets(ROA),representing theprofitabilityofinsurers,mayplayanimportantroleindeterminingcapital(orrisk)level.The recentglobalfinancialcrisis(GFC)isconsideredinthispaper,becausemarketconditionmayrelateto insurers’capitaldecisionandrisktaking.AsMcAleer,Jimenez-Martin,andPerez-Amaral(2013)note, firmsmayhaveexecuteddifferentriskmanagementstrategies(conservativeoraggressive)during the2008–2009globalfinancialcrises.AsLiao,Chou,andChiu(2013)statethatforeignownership investorsaremomentumtradersinfinancialmarketandhaveenjoyedremarkablereturnsontheir investments,foreigninsurers(FOR)maybedifferentfromlocalinsurersincapitaldecisionsandrisk managementstyles.Apubliclyheldcompany(PUB)cantesttherelationshipsbetweentheseparation ofownershipfrommanagementandrisk-takingbehavior(Cole,He,McCullough,&Sommer,2011; Cummins&Sommer,1996).Wealsoaddanindicatorforwhethertheinsurerisamemberofa finan-cialholdinggroup(FHG).Ifinsurersarepartofalargerfinancialholdinggroup,thentheywillhave superioraccesstocapitalandinvestmentopportunities,becauseoftheirdifferentmechanismsfor controllingperformance(Shrieves&Dahl,1992).Afamily-controlledcompany(FAM)mayperform differently(Huang,Hsiao,&Lai,2007),orhaveadifferentriskandcapitallevel,becauseofits undi-versifiedownershipstructurebasedontheagencycosttheory.FOR,PUB,FHG,FAM,andGFCare representedasdummyvariables.IfaninsurerisaFOR(orPUB,orFHG,orFAM,orGFC),thenthevalue isone,whileitiszerootherwise.

4. Dataandmethodology

Althoughquantileregressionhasnotbeenaswidelyusedastheleastsquares,theformermaybe moredesiredifconditionalquantilefunctionsareofinterest.Relativetotheordinaryleastsquares regression,oneadvantageofquantileregressionisthatthequantileregressionestimatesaremore robust,particularformisspeciﬁcationerrorsrelatedtonon-normalityandtothepresenceofoutliers (Kim&Muller,2004).However,themajorattractionofquantileregressionsmaygobeyondthat.In practice,economicresearchersoftenpreferusingdifferentmeasuresofcentraltendencyandstatistical dispersiontoobtainamorecomprehensiveanalysisoftherelationshipbetweenvariables.Therefore, weusetwo-stageleastsquaresandtwo-stagequantileregressionstoinvestigatetherelationbetween riskandcapital.

4.1. Datacollection

ThesampleusedinthisresearchincludeslifeinsurancecompaniesinTaiwanduringtheperiod of2004–2009,collectedfromtheTaiwanInsuranceInstitutewebsitedatabase,5_Taiwan_Economic

Journal,6_and_the_Annual_Statistics_Report_of_Taiwan_Life_Insurance_Companies_published_by_the_Life

5_Taiwan_Insurance_Institute_website:_{http://pivot.tii.org.tw}_. 6_Taiwan_Economic_Journal_website:_{http://www.ﬁnasia.biz}_.

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J.-L.Hu,H.-E.Yu/NorthAmericanJournalofEconomicsandFinance29(2014)185–199 191 InsuranceAssociation.Thereareabout30lifeinsurancecompaniesinTaiwan.Duetomissingdatain someyears,thisdatasetisunbalanced.Exceptfornewentrantswhosedataarenotcompleteinthe ﬁrstyearoftheirbusiness,wechoose28(or27)insurancecompaniesavailableeachyear,7_presenting

thewholepopulation. 4.2. Two-stageleastsquares

Accordingtothepriorliterature,capitalandriskaredeterminedsimultaneously.Ifweuse ordi-nalleastsquares,theestimatorsoftheparameterswillbeinconsistent.Thetraditional2SLSmaybe agoodchoicetoreducetheendogeneitybiasandobtainconsistentestimations.AsCumminsand Sommer(1996)note,thetwo-stageprocedureisdesignedtodealwiththeestimationof simulta-neousequationswithlaggedendogenousvariables.BaranoffandSager(2002)alsoaddressthatthe autoregressive2SLSprocedureprovidesacorrectionforautocorrelationinsimultaneousequations bymeansofinstrumentalvariables.Foroursixyearsofdata,autocorrelationmaybepredictable.As inBaranoffandSager(2002)andCumminsandSommer(1996),wemodelthedisturbancethrougha ﬁrst-orderautoregressiveprocess,whichgeneratesadiagonalstructureforthecovariancematrixof thedisturbance.Byusingautoregressive2SLS,wespecifyasimultaneousequationsystemthatallows ustotestfortherelationshipbetweencapitalandrisklevelsasfollows.

CARit=˛0+˛1INRit+˛2UNRit+˛3CAR(−1)it+˛4SIZEit+˛5ROAit+˛6GFCit+˛7FORit

+˛8PUBit+˛9FHGit+˛10FAMit+e1 (1)

INRit =ˇ0+ˇ1CARit+ˇ2UNRit+ˇ3INR(−1)it+ˇ4SIZEit+ˇ5ROAit+ˇ6GFCit+ˇ7FORit

+ˇ8PUBit+ˇ9FHGit+ˇ10FAMit+e2 (2)

UNRit =0+1CARit+2INRit+3UNR(−1)it+4SIZEit+5ROAit+6GFCit+7FORit

+8PUBit+9FHGit+10FAMit+e3 (3)

whereINR–risk-weightedassetstototalassetsofinsureriinyeart;UNR–healthwritingsplus accidentwritingstototalwritingsofinsureriinyeart;CAR–ratiooftotalequitytototalassetsof insureriinyeart;ROA–returnonthetotalassetsofinsureriinyeart;SIZE–totalassetsofinsureriin yeart;FOR–oneforforeigncompany–andzerootherwise–forinsureriinthetyear;GFC–onefor theperiodofthe2008globalfinancialcrisis,andzerootherwise,forinsureriinthetyear;PUB–one forapubliclyheldcompany,andzerootherwise,forinsureriinthetyear;FHG–oneforafinancial holdingcompany,andzerootherwise,forinsureriinthetyear;FAM–oneforaTaiwan-foreignjoint company,andzerootherwise,forinsureriinthetyear;and˛,ˇ,–coefficientstobeestimated, whereεrepresentserrorterms.

Investingrisk(INR),underwritingrisk(UNR),andcapitalratio(CAR)aredependentvariables,while firmsize(SIZE),returnonassets(ROA),globalfinancialcrisis(GFC),foreigncompany(FOR),financial holdinggroup(FHG),andfamilycompany(FAM)areindependentvariables.Eq.(1)representsthe insurers’capitalratio(CAR),whichisdeterminedbyendogenousvariableslikeinvestingrisk(INR), underwritingrisk(UNR),andotherexogenousfactors.Eq.(2)hasunderwritingrisk(UNR)asthe dependentvariable.Eq.(3)explainsthedeterminantsoftheinvestingrisk(INR).

4.3. Two-stagequantileregression

Comparedtothetraditional2SLSmethod,the2SQRmethodtakesintoaccounttheheterogeneity ofthecapital(orrisk)structureofinsurersorthelargevariationacrosstheinsurers.KimandMuller

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(2004)proposetwo-stagequantileregression,wheretheﬁrststageisbasedonquantileregressions withthesamequantileasinthesecondstage.Theypresenttheasymptoticpropertiesof2SQRwith randomregressors,ensuringrobustnessoftheestimation.Sincethechangeinthemeanofcapitalfor Taiwaninsurersisdeterminedbyafewobservationsintheupperpartsofthedistribution,classical methodsbasedontheestimationoftheconditionalmeanmaynotfullyexplainthecapital(orrisk) structureofTaiwan.Therefore,wealsoadoptthe2SQRapproachtocapturetheeffectofdifferent levelsofcapital(risk).FollowingthesymbolsusedbyAmemiya(1982),Powell(1983),andKimand Muller(2004),werewritetheequationsasbelow.

y=Yo+X1o+ε, (4)

whereyshowsthedependentvariableslikethecapitallevel(orrisklevel);Yrepresentsother endoge-nousvariablesliketherisklevel(orcapitallevel);X1representsexogenousvariablesthatrelatetoy; andεrepresentstheresidual.Moreover,[y,Y]isaI×(G+1)matrixofendogenousvariables,X1isa I×K1matrixofexogenousvariables,andεisaI×1vector.TheendogeneityofYinEq.(4)mightcause Q(ε|Y) /= Q(ε),whereQ(·)isthequantilefunctionoforder,andQ(·|Y)isthequantilefunctionof orderconditionalonY.

Inthiscontextabove,theestimationofthetraditionalone-stagequantileregressionmayresultin endogeneitybias.Hence,usingtwo-stagequantileregressionisnecessaryforreducingendogeneity problem.Here,weassumethatYhasthereducedformasbelow:

Y=X˘+, (5)

whereX=[X1,X2]representsaI×Kmatrix, ¯˘ representsaK×Gmatrixofunknownparameters,and

v

isaI×Gmatrixoferrorterms.Theﬁrst-stagequantileregressionisrepresentedasfollows.

Min

j n

i=1 ˇ(Yij−Xi

j), (6)

whereYijisthe(i,j)thelementofY.ViaEq.(6),weestimatetheﬁttedvalueofthejthendogenous variable( ˆYj=X ˆ˘j)andsubstituteitintoYinEq.(4):y=Yo+X1o+ε.Inthesecondstage,weagain conductthequantileregressionsasthefollowing.

Min oo

ˇ(y− ∧ Yo−X1o). (7)

Theparameters(0and0)areconsequentlyestimatedbytwo-stagequantileregressions.Kim andMuller(2004)provethattheestimateoftheparameterin2SQRhasasymptoticnormality(see AppendixAandAssumption3inKimandMuller(2004)).AlthoughKimandMuller(2004)present thattheparametersestimatedbythe2SQRcarryasymptoticnormality,wealsouseabootstrapping set,andtheresultsshownosigniﬁcantdifferencesascomparedwiththeoriginalresults.

Therelativesizeofaninsurancecompanydoesnotsuddenlychangeovertime.However,paneldata quantileregressionmainlydealswiththecross-sectionheterogeneityproblem.Becausethesample sizeofeachquantileineachyearistoosmall,paneldataquantileregressionisbetterthan cross-sectionquantileregressionbyincorporatingintertemporalobservationsofthesamequantileinone regression.8

5. Empiricalresultsanddiscussion 5.1. DatafeaturesofTaiwanandtheU.S.

Table2liststhemeanvaluesofallvariables.Aswecansee,themeanvalueoffirms’totalassets increasesannuallywiththepassageoftime.ThemeanvalueofROAisgenerallypoor,butfluctuates heavilyduring2008–2009.LowprofitabilityimpliesthatlifeinsurersinTaiwanoperateinasaturated

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J.-L.Hu,H.-E.Yu/NorthAmericanJournalofEconomicsandFinance29(2014)185–199 193 Table2 Meanofvariables. Variable Year 2004|2009 2004 2005 2006 2007 2008 2009 Capitalratio 0.050 0.059 0.055 0.084 0.058 0.013 0.032 Investingrisk 0.056 0.051 0.054 0.0554 0.0583 0.054 0.062 Underwritingrisk 0.181 0.182 0.181 0.175 0.180 0.179 0.191 Returnonassets −2.388 −1.908 −2.248 −3.700 −0.995 −4.246 −1.158

Totalassets(NT$billion) 277.402 189.719 225.095 257.703 300.468 302.780 384.469

Totalassets(US$billion) 8.512 5.676 6.997 7.921 9.149 9.606 11.633

Globalcrisis 0.169 0 0 0 0 1 0 Foreigncomp. 0.236 0.222 0.222 0.25 0.222 0.25 0.25 Publiclyheld 0.400 0.407 0.407 0.392 0.407 0.392 0.392 Holdingcomp. 0.145 0.148 0.148 0.143 0.148 0.143 0.143 Familycomp. 0.299 0.296 0.296 0.286 0.296 0.286 0.286 Sample 165 27 27 28 27 28 28 Notes:

Forafewsampleinsurers,someannualobservationsarelost,becauseproxydataareincompleteand/orinsurerswithinthe grouphavemerged.

US$1isapproximatelyequaltoNT$33.422in2004;NT$32.617in2005;NT$32.531in2006;NT$32.842in2007;NT$31.517in 2008;NT$33.049in2009. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 underwring risk invesng risk capital rao Taiwan US

Fig.1. Capitalratio,investingrisk,andunderwritingriskinTaiwanandtheU.S.

andhighlycompetitivemarket.Overall,themeancapitalratioincreasesfrom5.901%in2004toapeak of8.849%in2006.However,inﬂuencedbytheglobalﬁnancialcrisis,itsharplydropstothelowest pointof1.256%in2008,andthenrapidlyrisesto3.242%in2009.Investingriskgraduallyincreases from5.119%to6.253%exceptfor2008.Underwritingriskapproachesthehighestpointof19.15%in 2009,implyingthatthereisaslightrecoveryfromtheglobalrecession.

ItisinterestingtocomparethedifferencesbetweenthedataofTaiwanandtheU.S.asnotedby BaranoffandSager(2002),becausetheirstudyandoursexaminelifeinsurers’capital-riskrelationship overtherespectivetimeperiodsof2004–2009and1993–1997.AlthoughTaiwan’scapital require-mentsprincipallyrefertothoseoftheU.S.,botheconomiesstillpresentsomedivergences,whichmay arisefromdifferentstrictdegreesofcapitalregulationsbasedondifferentculturalbackgroundsand operatingexperiences(i.e.,TaiwanimplementedRBCin2003,laterthantheU.S.byabout10years).

Fig.1demonstratesinvestingrisk,underwritingrisk,andcapitalratioforTaiwanandtheU.S.9_The

capitalratio(5.02%)inTaiwanisprominentlysmallerthanintheU.S.(32.21%).Ontheotherhand,the averageinvestingrisk(5.60%)inTaiwanisrelativelyhigherthanintheU.S.(2.40%).Thedatashow thatlifeinsurersinTaiwantendtoholdafarlowercapitalratioandinvestinariskierassetportfolio

9_In_Fig.₁_the_U.S._data_refer_to_the_study_of_Baranoff_and_Sager_(2002,_p.₁₁₉₂₎_who_report_the_relation_among_asset_risk, productrisk,andcapitalintheU.Slifeinsurancesector.Exceptfortheresearchtime,investingrisk,underwritingrisk,and capitalratioinourstudyaresimilartotheirmeasures.

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comparedtolifeinsurersintheU.S.Apossibleexplanationisthat,beinginthelargestfinancialmarket intheworld,U.S.insurersmaybewillingtoholdahighercapitallevelformorediversifiedinvestment opportunities.Incontrast,lookingforappropriateinvestmentchannelsisnoteasyforinsurersina smallfinancialmarketsuchasTaiwan.Underwritingriskis27.27%intheU.S.,whichisgreaterthan 18.20%inTaiwan.Itseemspredictableundergreatdemandforlong-termmedicalcareindeveloped countriesliketheU.S.thattherewillbeanincreaseinwritingriskierproducts(e.g.,healthinsurance) withclaimsdisputes.

5.2. Interrelationshipamonginvestingrisk,underwritingrisk,andcapital

Table3showstheestimationsofthe2SLSand2SQRinregressionequations.PanelsA,B,andC cor-respondtotheequationsforthecapitalratio,investingrisk,andunderwritingrisk,respectively.Inthe 2SQRmodel,ourpaperanalyzestherelationshipamonginvestingrisk,underwritingrisk,andcapital levelatthe10th,50th,and90thconditionalquantiledistributions,representingthelow,median,and highcapital(orrisk)levelsofinsurers,respectively,accordingtothesuggestionsbyKimandMuller (2004).10_In_the_investing_risk_equation,_the_R-square_in_the_2SLS_model_is_0.55,_and_the_Pseudo

R-squares11_in_the_2SQR_models_are_about_0.57._In_the_capital_equation,_the_R-square_in_the_2SLS_model

is0.45,andthePseudoR-squaresinthe2SQRmodelareabout0.71.Intheunderwritingriskequation, theR-squareinthe2SLSmodelis0.24,andthePseudoR-squaresinthe2SQRmodelareabout0.64. Overall,thePseudoR-squaresinthe2SQRmodelsappeartobehigherthanR-squaresinthe2SLS models,indicatingthattheexplanatorypowerinthe2SQRmodelsisbettertothatinthe2SLSmodels. InPanelAtheestimationresultsofthe2SLSmodelshowthatthelevelofinvestingriskhasno impactonthecapitallevel,whilethelevelofunderwritingriskpostsasignificantandpositiveeffect onthecapitallevel.Theestimationsresultsofthe2SQRmodelsshowthattheinvestingrisk→capital relationissignificantlynegativeatthelowandmedianquantiles,indicatingthatinsurersholdinglower levelsofcapitaltendtoreducetheircapitallevelsasinvestingriskincreases.Thissupportsthemoral hazardhypothesis.Nevertheless,theunderwritingrisk→capitalrelationissignificantlypositiveatthe medianquantileandhighquantile,implyingthat,comparedtopoorlycapitalizedinsurers, median-capitalizedandwell-capitalizedinsurersaresignificantlywillingtoraisetheircapitalpositionwhen theyfacegreaterunderwritingrisk.Thislendssupporttothetransaction-costhypothesis.

InPanelBtheestimationresultofthe2SLSmodelreportsthatthecapitallevelisnotrelatedto thelevelofinvestingrisk,andtherelationbetweeninvestingriskandunderwritingriskispositive, butinsigniﬁcant.Inthe2SQRmodelthereisanegativerelationbetweencapitalandinvestingrisk atalowerconditionalquantiledistribution,implyingthatinsurers’investingriskmayincreaseas theircapitaldeclines.Moreover,underwritingriskandinvestingriskarepositivelyrelatedathigher conditionalquantiles,butarenegativelyrelatedatlowerconditionalquantiles.

InPanelCtheestimationofthe2SLSmodelillustratesthattherelationbetweenthecapitalleveland underwritingrisklevelispositive,butinsignificant.Wealsofindthatinvestingriskispositivelyrelated totheunderwritingrisk.Inthe2SQRmodelthecapital_→underwritingriskrelationissignificantly positivelyrelatedatmedianandhighquantiledistributions.Apossibleexplanationisthatinsurers withhigherunderwritingriskmaytendtoholdhigherlevelsofcapitalinresponsetohigherrisksthan insurerswithlowerunderwritingrisk.

Generallyspeaking,whencomparedtothe2SLSmodel,the2SQRmodelseemstofullycapturethe effectofdifferenttypesofrisk.In2SLS,mostresultsareinsigniﬁcantinthecapital-riskrelation.Weﬁnd strongerevidencein2SQRthatinvestingriskandcapitalarenegativelyrelated,whileunderwritingrisk

10_They_conduct_Monte_Carlo_simulation_experiments_to_investigate_the_{ﬁnite-sample}_properties_of_the_2SQR._For_all_types oferrorterms,the2SQRhasgoodﬁnitesampleproperties,althoughasizethatistoosmallorwhentherearetooextreme quantiles(=0.05,0.95)maydegradeitsperformance.Therefore,underthe2SQRapproach,the10th,50th,and90thquantiles areadequateforourmodel.

11_In_linear_regression_models_(i.e.,_ordinary_least_squares),_R2_is_a_statistic,_which_is_often_used_as_a_{goodness-of-ﬁt}_measure. Sincequantileregressionisnotalinearregressionmodel,PseudoR2_is_used_to_calculate_the_explanatory_power_of_quantile regression.PseudoR2₌₁₋_(Estimated_likelihood_of_unrestricted_{model/Estimated}_likelihood_of_restricted_model)._The_reader mayrefertoGujarati(2003,pp.605–606,chap.3).

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J.-L. Hu, H.-E. Yu / North American Journal of Economics and Finance 29 (2014) 185–199 195 Table3

Estimatedresultsofthe2SLSand2SQR.

INR UNR CAR(−1) SIZE ROA GFC FOR PUB FHG FAM

PanelA.Capitalequations

2SLS −0.102 0.135*** −0.356 −2.382* −0.210* −5.933** −0.122 −6.149* 12.490*** −0.753 (−0.324) (3.682) (−1.872) (−2.642) (−2.476) (−3.365) (−0.044) (−2.271) (3.610) (−0.712) Q=0.1 −18.44*** 0.772 0.095 −0.407 −0.392*** −0.399 −25.25** 4.180*** 18.932*** 19.383*** low (−31.45) (0.776) (0.985) (−0.594) (−6.902) (−0.269) (−13.130) (10.730) (6.781) (21.246) Q=0.5 −2.369** 0.793*** −0.003 −0.195 0.648*** −2.844*** −12.38*** −3.655** 5.552*** 4.476*** med (−3.241) (16.555) (−0.176) (−0.572) (8.893) (−4.395) (−4.898) (−2.815) (7.241) (3.634) Q=0.9 −1.004 1.265* 0.063 1.817* 0.484 −2.970* −41.421 2.591 32.351* −3.108 high (−1.612) (2.408) (0.054) (2.581) (0.315) (−2.180) (−1.598) (0.607) (2.326) (−0.810)

PanelB.Investingriskequations

CAR UNR INR(−1) SIZE ROA GFC FOR PUB FHG FAM

2SLS −0.216 0.054 −0.401 0.606 −0.124 −14.523 −1.906 1.636 0.465 1.148 (−1.865) (1.709) (−1.901) (1.06) (−1.02) (−1.706) (−0.925) (1.239) (0.265) (0.818) Q=0.1 −0.827*** −0.714* −0.005 −1.98*** 0.915*** −2.186** −3.468** 3.250** 6.558*** −0.589 low (−4.169) (−2.041) (−0.076) (−3.658) (4.064) (−2.801) (−4.159) (2.887) (3.877) (−0.610) Q=0.5 −0.084 0.005 −0.093 0.180 −0.031 −0.255 −3.906*** 0.828 0.412 1.557* med (−1.301) (0.218) (−1.121) (0.739) (−0.650) (−0.511) (−3.498) (1.167) (0.641) (2.346) Q=0.9 0.125 0.427*** −0.334** 1.382** 0.280 0.162 −18.45** 0.078 −8.382*** −5.16*** high (1.651) (3.692) (−2.757) (3.121) (1.407) (0.127) (−4.946) (0.069) (−4.480) (−4.480)

PanelC.Underwritingriskequations

CAR INR UNR(−1) SIZE ROA GFC FOR PUB FHG FAM

2SL 0.321 1.975** −0.601* −5.15** −0.022 2.238 7.579 −6.902 17.318 −0.176 (1.355) (2.645) (−2.532) (−3.167) (−0.094) (0.546) (1.213) (−1.493) (1.652) (−0.034) Q=0.1 1.292 0.291 0.012 3.125* −1.422* 0.665 3.526 6.868 −15.688* 5.932 low (1.901) (0.056) (1.824) (2.122) (−1.985) (0.265) (0.429) (0.379) (−2.095) (0.493) Q=0.5 5.864*** 1.271 0.045** 1.274** 2.411*** 9.885*** −3.454 13.639*** −18.28*** −11.51** med (73.974) (1.732) (2.924) (2.833) (62.980) (15.976) (−1.054) (12.581) (−17.828) (−11.05) Q=0.9 3.287*** −0.167 −0.015 4.689** 2.027*** 7.875*** 6.784*** 16.409*** −9.789** −11.94** high (83.497) (−0.704) (−0.918) (19.744) (27.151) (17.685) (13.142) (20.003) (−14.356) (−14.132) Notes:

1.Thenumbersinparenthesesaretvalues.

2.*,**,and***indicatesigniﬁcanceatthe5%,1%,and0.1%levels,respectively.

3.CAR=capitalratio;INR=investingrisk;UNR=underwritingrisk;CAR(−1)=lagofcapital;INR(−1)=lagofinvestingrisk;UNR(−1)=lagofunderwritingrisk;SIZE=totalassets; ROA=returnonassets;theothersaredummyvariablesinwhichGFC=globalﬁnancialcrisis,FOR=foreignbranch,PUB=publiclyheld,FAM=family-controlled,andFHG=ﬁnancial holdinggroup.

4.MostPseudoR2_in_the_2SQR_are_between_0.57_and_0.71,_and_R2_in_2SLS_are_between_0.24_and_0.55.

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andcapitalarepositivelyrelatedatmostquantiledistributions.Anegativerelationbetweeninvesting riskandcapitalsupportsthemoralhazardhypothesis.Apositiverelationbetweenunderwritingrisk andcapitalsupportsthetransaction-costhypothesisorregulatorycosthypothesis.

This paper also examines the relation between underwriting risk and capital in the period 2000–2002beforetheadoptionofRBCregulationinTaiwan.Contrarytothepositiverelationinthe periodofpost-RBC,weﬁndthatthecapitalratiohasanegativeimpactonunderwritingriskatthe mediumquantileandissigniﬁcantat10%level,althoughtherelationbetweenthetwodoesnotexist atthelowquantileorhighquantiledistribution.12_In_other_words,_life_insurers_tend_to_take_greater

underwritingriskintheperiodofpost-RBC,whencomparedtotheperiodofpre-RBC.Thismaybe attributedtoinsurers’increasedregulatorycost.Suchcontrastingresultsbetweenthetwoperiods sug-gesttheimportanceofcapitalregulation,andthismechanismpartiallychangeslifeinsurers’capital positionsandrisk-takingbehaviors.

5.3. Impactofexplanatoryvariablesincapital-riskrelations

Comparedtothe2SLSmethod,the2SQRcananalyzetheeffectsofexplanatoryvariablesindetail. Inthe2SQRmodel,firmsizehasmixedeffectsoncapitalandrisk.ROAhasapositiveeffectoncapitalat themediumquantile,whilethereisareverserelationatthelowquantile.Theinsurers’profitabilityhas apositiveeffectoninvestingriskatthelowquantileandshowsconflictingeffectsonunderwriting riskacrossthreequantiles.Theglobalfinancialcrisisisfoundtobenegativelyassociatedwiththe insurers’capitallevelatthelowandthemediumquantiles,suggestingthattheinsurerstendedto holdalowcapitallevelofcapitalwhentheglobalcrisishit.Theglobalfinancialcrisisisalsofoundto haveapositiveimpactonunderwritingriskatthemediumquantileandhighquantile,whileareverse relationbetweentheglobalfinancialcrisisandinvestingriskisfoundatthelowlevelofquantile.This resultmaybeexplainedbywhenfacingthecrisis,lifeinsurerspreferredtoadoptconservativefinancial investmentstrategiestoavoidlosses.Ontheotherhand,theytendtopursuemoreunderwritingrisks tosurviveintheinsuranceindustry.

Foreigncompaniesoveralltendtoholdlowercapitalandhavelessinvestingriskthandomestic localinsurersatdifferentquantiledistributions.Notsurprisingly,thismaybeduetobetterexperiences inriskmanagementderivedfromtheirparentcompanies,eventhoughmostofthemaremuchsmaller companies.Asexpected,financialholdingcompaniesarefoundtoholdmuchmorecapitalthan inde-pendentcompanies,whichmaybeattributedtotheirbetterfinancialstrength.Interestingly,theyalso tendtopursuegreaterinvestingriskatalowquantileandareriskadverseatahighquantile,while significantlytakingonlessunderwritingriskthannon-holdinginsurers.Publiclyheldinsurerstend toholdahighlevelofcapitalatalowquantileandhavealowlevelofcapitalatamediumquantile. Theyarealsofoundtotakehigherunderwritingriskandinvestingriskthancloselyheldinsurers. Family-controlledinsurersseemtomaintainalargeramountofcapitalthannon-familyinsurersand alsohavealowerlevelofinvestingriskandunderwritingriskathighquantiledistributions. 5.4. AcomparisonofTaiwanandtheU.S.

ItmightbemoreusefultoexplaintheobservedresultsbetweenTaiwanandtheU.S.,becauseof thedifferencesinspeciﬁcationsoftheRBCregulationsandmanagerialdiscretionowingtodifferent economicdevelopmentstagesorregulatoryculture.Suchacomparisonalsohelpsusunderstandthe policyeffectsbetweenthetwoandprovidesevidencetolearnaboutriskmanagementpractices.

AmongmostU.S.studies,theﬁndingsofBaranoffandSager(2002)areregardedasthemost rep-resentativework,becausethisistheﬁrstempiricalstudytoobservetherelationbetweenriskand capitalinthelifeinsuranceindustry.WecompareTaiwanandtheU.S.throughthefollowingtwo

12_We_only_use_the_underwriting_risk_measure,_because_investing_risk_is_measured_by_life_insurers’_{risk-weighted}_assets,_which arenotavailablebeforetheimplementationofRBCrequirements.Thedetailedresultsoftheotherindependentvariablesare notreportedhereduetolimitedspace.

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J.-L.Hu,H.-E.Yu/NorthAmericanJournalofEconomicsandFinance29(2014)185–199 197 steps:First,weusesimilarvariablesasusedbyBaranoffandSager(2002)13_to_run_data_using_the

same2SLSmethod.Second,newvariablesaresubsequentlyaddedtoourmodelsandtheresultsare quicklyobtained.Throughthetwo-stepprocess,wedonotﬁndanegativerelationbetweeninvesting riskandcapitalalthoughthereisapositiverelationbetweenunderwritingriskandcapital.In2SQR, ourresultsshowanegativerelationbetweeninvestingriskandcapitalandapositiverelationbetween underwritingriskandcapital.Itisworthnotingthattheresultsarecontrarytotheevidenceofthe U.S.inBaranoffandSager(2002),whoreportapositiverelationbetweenassetriskandcapitalanda negativerelationbetweenproductriskandcapital.

ItisnotsurprisingthatTaiwan’sinsurersholdarelativelylowerlevelofcapitalandahigherlevelof regulatoryassetsthaninsurersintheU.S.asFig.1shows.Inpractice,Taiwan’sinsurersareincreasing theirriskyﬁnancialinvestmentswiththerelaxationofportfoliorestrictionsandproﬁtincentives.It seemsthatTaiwan’sinsurersmayhavethemoralhazardofpursuinginvestingriskcomparedtoU.S. insurers.Ontheotherhand,apositiverelationbetweenunderwritingriskandcapitalimpliesthat therapidgrowthofTaiwan’slong-termmedicalcareinrecentyearshasresultedinanincreasein holdingcapitalinresponsetomoreunderwritingriskswhencomparedtoevidenceintheU.S.Such contrastingresultsbetweenTaiwanandtheU.S.maybeattributedtodifferentmanagerialdiscretion fortwotypesofriskordifferentregulatorycultures.

6. Conclusionsandsuggestion

Viatheuseofthe2SLSand2SQRmethods,thispaperexaminestherelationshipsamonginvesting risk,underwritingrisk,andcapitalundertheframeworkofsimultaneousequationsduringthe post-RBCtimeperiodinTaiwan.In2SLS,wedonotfindarelationbetweeninvestingriskandcapital, butfindunderwritingriskhasapositiveimpactonthecapitallevel.The2SQRmethodanalyzesthe capital-riskrelationingreaterdetailandprovidesstrongerevidencethan2SLS.Inthe10th,50thand 90thconditionalquantiles,ourempiricalresultsindicatethatthecapitallevelisnegativelyrelated toinvestingrisklevelasthemoralhazardhypothesispredicts,whilethecapitallevelispositively relatedtotheunderwritingrisklevel,lendingsupporttothetransactioncosthypothesisandregulatory costhypothesis.Suchcontrastingfindingsemphasizetheimportanceofsimultaneouslytakinginto accounttwokindsofrisksgiventheassumptionthatinsurersmayreactdifferentlywhenencountering differentfacetedrisks.

Inthe2SQRmodelwealsoexaminetheeffectsofthe30thand70thconditionalquantile distri-butions,andmostoftheestimationsaresimilartotheresultsmentionedabove.14_Our_ﬁndings_are

contrarytopreviousevidenceintheU.S.Thismaybeduetodifferentregulatorypolicyeffects, depend-ingonastringentoraﬂatcapitalrequirement,market-basedincentive,andmanagers’riskpreference basedondifferentculturefactors.

Ouroverallresultshaveimportantimplicationsforlifeinsurerexaminationandsurveillance.It isquiteinterestingtodiscussanegativetrade-offeffectbetweencapitalandinvestingriskdueto theexistenceofmoralhazardininvestingactivities.Ifinsurersholdtoomuchcapitaloverthe reg-ulatoryminimum,thentheinvestingriskmaybereduced,buttheyhavetogiveupsomepotential opportunitiesthathavehighexpectedreturns.AsDickinson(1997)notes,toolittlecapitalisunable tofullyabsorbthebusinessrisksinfinancingfuturegrowth.LeeandChih(2013)alsowarnthat,for financialinstitutions,stricterregulationmaybegoodfortheirstability,butnotforefficiency.Life insurersshouldcontrolinvestingriskaccordingtotheirtoleranceforriskortheirsensitivitiestothe costofcapitalsoastopreventtheirfailure.Regulatorsalsorecognizethat,eventhoughincreased capitalrequirementsmaydiminishlifeinsurers’riskandenhancesafety,regulatoryconstraintsalso holdthembackfrominvestinginpotentialopportunitiesorpushthemtoshifttowardinefficient activities.

13_They_use_the_capital_ratio,_asset_risk,_product_risk,_total_assets,_return_on_capital,_the_RBC_rate,_a_group_member,_a_stock company(oramutualcompany),etc.Weemploymostvariablesexceptforastockcompanyvariable,becausealltheinsurers arestockcompaniesinTaiwan.

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InTaiwanthepresenceofaregulatorycapitalpolicymayeitheraccentuateormitigatelife insur-ers’risk-takingbehaviors,hingingondistinguishingbetweentwotypesofrisk:investingriskand underwritingrisk.Therefore,bothregulatorsandinsurersshouldstrengthentheirawarenessofthe relationbetweencapitalandrisk,particularlyinthemanagementofdifferentkindsofrisk.In addi-tion,insurers’ownershipstructuresplayacrucialroleincapital-riskrelations,andthusafirm’stype ofownershipstructurecouldbeusedasaflagfordeterminingexaminationfrequency.Lastly,the recentglobalfinancialcrisishasnegativelyimpactedinsurers’capitalratio,limitingtheirfinancial investmentbehavior.Forthehealthandstabilityoftheinsuranceindustry,theregulatorshould tem-porarilyrelaxtheRBCregulation,whileatthesametimeinsurerslearntobeinapositiontoskirt marketvolatilitywhenfacingadversemarketconditions.

Acknowledgments

Wewouldliketothankvaluablecommentsprovidedbyaneditorandtwoanonymousreviewers ofthisjournalandseminarparticipantsatSoochowUniversity.TheﬁnancialgrantfromTaiwan’s MinistryofScienceandTechnology(NSC101-2410-H-009-044)isgratefullyacknowledged.

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