Regressivity in Public Natural Hazard Insurance: A Quantitative Analysis … · 2018. 7. 10. · 1...

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RegressivityinPublicNaturalHazardInsurance:AQuantitativeAnalysisoftheNewZealandCaseSallyOwen(MotuEconomicandPublicPolicyResearch)IlanNoy(VictoriaUniversityofWellington)

Abstract:Naturalhazardinsuranceisalmostalwaysprovidedbythepublicsector(directly,or

indirectlythroughpublic-privatepartnerships).Giventhisdominantroleofthepublicsectorin

hazardinsurance,andtheimportanceofshocksineconomicdynamics,itissurprisingthatequity

issueshavenotfacedmorescrutinywithrespecttothedesignofhazardinsurance.Thenatureof

theregressivitywequantifyhasnotbeenpreviouslyidentified.Weprovideadetailedquantification

ofthedegreeofregressivityoftheNewZealandearthquakeinsuranceprogram–asystemthatwas

designedwithanegalitarianpurpose.Wemeasurethisregressivityasitmanifestedinthehalfa

millioninsuranceclaimsthatresultedfromtheCanterburyearthquakesof2011.Wesuggesthow

thisregressivitycanberemediedwithmodificationstotheprograms’structure,andpointtohow

otherinsuranceschemesinternationallyarelikelytoalsoberegressive.

WethankQuakeCoreandtheResilienceNationalScienceChallengeforsupportingthiswork.Noy’sresearchispartiallyfundedbytheEarthquakeCommission(EQC),whichisanalysedinthiswork.

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1.Introduction

Privatenaturalhazardinsurancemarketsseldomsucceedinprovidingwidespreadcoverage

(KunreutherandPauly,2009;Noy,Cuong,andKusuma,2017).1Therearemultipleexamples

offailedattemptstoprovidefinancialnaturalhazardrisktransfer(insurance)through

privatemarkets,floodandearthquakeinsuranceintheUnitedStatesbeingtwoprominent

cases.Infact,nocountryhasaprivatemarketforfloodinsurancethatprovidesaffordable

andaccessiblecoverforhigh-riskhouseholdswithoutsomeformofgovernment

involvement(ABI2011).

Agoodinsurancesystemincentivizesriskreductionandenablestheinsuredpartytotake

onbeneficialandprofitablebusinessrisksandinvestexante;expost,itallowstheinsured

partytoevadeatleastsomeofthefinancialloss,avoiddestitution,andrecovermore

quicklyandmorefully.O’Neill&O’Neill(2012)furtherarguethatinsuranceshould

guaranteethesecurityofrequiredbasicgoods,accordingtosocialjusticecriteria,

independentlyoftherisksinvolvedandtherisk-takingbyindividuals—housingbeinga

primeexamplefora‘basicgood’.

Fromacommunitarianratherthananindividualistperspective,theinabilityofsome

householdstorebuildtheirpre-disasterlivesinflictsadditionalharmontherestofthe

community.But,evenfromanindividualistperspective,ifthereisnoprovisionofnatural

hazardinsurancebytheprivatemarket,governmentsfindapolitical-electoralrationalefor

interventiontofacilitateinsurancecoverageforall.Governmentscanchoosetopursuethis

aimbyeitherinsuringdirectlyorsubsidizingtheprivateinsurancesector,andhavechosen

1Naturalhazardinsuranceisalsoknownascatastropheinsurance,disasterinsurance,ornaturaldisasterinsurance,dependingonthecontext.Weusenaturalhazardinsuranceforspecificity.

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todosoinmanycountries.2Giventhecomplexityofinsuringextremerisks,private-sector

insurersandgovernmentstendtocooperateinpublic-private-partnership(PPP)schemes.3

Mostdisastereconomistsalsoarguethatinsurancepremiumsshouldberiskbased(e.g.,

Bin,Bishop&Kousky,2010andKunreuther,2015).Risk-basedinsurancepremiumssignalto

residentsandbusinessesthehazardstheyfaceandenableinsurerstolowerpremiumsfor

propertiesforwhichstepshavebeentakentoreducerisk.Risk-basedpremiums,however,

doraiseequityconcerns,andthereissomerecognitionthatafullyrisk-sensitiveinsurance

regimemaybesociallyorpoliticallyunacceptableifitimposesveryhighcostsonsome

groups(Houstonetal.,2011).4

Giventhedominantroleofthepublicsectorintheprovisionofnaturalhazardinsurance,

andtheevidentconcernworldwideaboutgrowingincomeandwealthinequality,itis

surprisingthatequityissueshavenotfacedmorescrutinywithrespecttopubliclyprovided

naturalhazardinsurance.Forexample,thisaspectoftherecentlylaunchedUKgovernment

FloodReprogramhasreceivedalmostnoattention,inspiteofthepotentiallyvery

regressivestructureofthatprogram.

Inthispaper,weprovide—possiblyforthefirsttime—adetailedquantificationofthe

degreeofregressivityofapublicnaturalhazardinsuranceschemeandthechannelthrough

whichitisgenerated.WechosetofocusontheNewZealand(NZ)earthquakeinsurance

schemeforfourmainreasons:(1)Theavailabilityofclaimsrecordsafteralargeevent(the

2Belgium,France,Japan,NewZealand,Spain,Switzerland,Turkey,UK,andtheUSAtonameonlyafew.3Paudel(2012)providesninerecommendationsfordesigningsuchPPPschemes.Hisrecommendationsinclude:mandatoryparticipation;adequateenforcementtoensurecompliance;publicresponsibilityfortheextremerisk(thecatastrophicend)oftheinsuredrisk,privatesectoradministeringofpolicies;publicprovisionofsubsidiesthrough,forexample,taxexemptions;publicinvestmentinriskmitigation;a(publiclyprovided)detailedassessmentandmappingofrisk;andtheprovisionoffinancialincentivesforpolicyholderstotakeriskmitigationmeasures.4Kunreuther(2015)suggeststhattoaddressissuesofequityandfairness,homeownerswhocannotaffordinsurancecouldbegivenvoucherstiedtoloansforinvestinginlossreductionmeasures,butthiskindofvoucherprogramisyettobeimplementedanywhere.

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seriesofCanterburyearthquakesin2010–2011thatledtoaverylargenumberofclaims);

(2)Thewell-establishedsuccessofthisprograminachievingwide-spreadcoverage–the

Canterburyearthquakeswerethemostinsuredlarge-scaleseriesofeventsever5;(3)The

egalitarianaimofthisscheme(alldwellingspayidenticalpremiumsandreceivethesame

amountofcover);and(4)Thecomparativelyegalitariandistributionalpolicyofpastand

presentNZgovernments.

Inspiteofboth(3)and(4),wefindthatthecurrentNZschemeisstronglyregressive,and

wereportontheexactextentofthisregressivityasitmanifestedinthehalfamillion

insuranceclaimsthatresultedfromtheCanterburyearthquakes.

2.RegressivityandNaturalhazardinsurance

Fairnesshaslongbeendiscussedintheevaluationoftaxation(e.g.,Simons,1938;Goode,

1980).Economistshavegenerallyrecognisedtwoprincipalconceptsoffairtaxation:benefit,

andtheabilitytopay.Fromabenefitperspective,taxesshouldbeleviedsuchthatbenefits

receivedbythepayersareproportionaltotheirtaxburden.Underthisconceptoffairness,

thereislittlescopeforredistribution.Anexampleismotorfuelexcisetax,whichisusedto

payforroadwayconstructionandmaintenance.Theabilitytopayprinciplefocusesonlyon

thecostside,whileignoringthedistributionofbenefits.Itviewstaxationasimposingacost

thatshouldbeallocatedinsuchawaythatittaxesthosewithequalabilitytopayequally

5ThethreehighestcostearthquakesintheCanterburysequenceareamongthetop10costliestearthquakesfor1980–2015(byinsuredlosses).Relativetodamages,theseeventswereatleasttwiceaswellinsuredasanyoftheothersonthelist(MunichRe,2016).

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(horizontalequity),andimposesagreaterburdenonthosewithgreaterabilitytopay

(verticalequity).6

Theconceptofregressivitywasoriginallyappliedtoincometaxsystems.Asdefinedin

Kakwani(1977),ifT(x)isthetaxpaidbyanindividualwithincomex,thetaxsystemis

proportionalwhentheelasticityofTwithrespecttoxisequaltooneforallx,thetax

systemisprogressivewhentheelasticityexceedsone,andregressivewhentheelasticityis

lessthanone.Thisisequivalenttosayingthatataxsystemisprogressive,proportional,and

regressivewhenthemarginaltaxrateisgreater,equal,andlessthantheaveragetaxrate,

respectively.7

MusgraveandThin(1948)createdamoreuniversalmeasureofprogressivitybycomparing

theinequalityofincomedistributionspre-taxandpost-tax.Aprogressivetaxsystemwill

thencreateadecreaseinincomeinequality,whileregressivetaxrateswillbereflectedby

increasesinincomeinequality.TheauthorswereabletoconcludethatiftheGiniindexis

usedtomeasureinequality,theratiooftheGiniindicesofthebefore-taxandafter-tax

incomesprovidesasinglemeasureoftaxprogressivity.8

Previousworkhaslookedattheregressivityofexplicittaxschemes;examplesinclude“sin”

taxes9andcarbontaxes.10Thistypeofmeasurementofprogressivityhasalsobeenusedto

studyimplicittaxesandsubsidies.Forexample,DavisandKnittel(2016)investigatewhether

6Abilitytopayisgenerallymeasuredbyannualincome.Thereisnoagreeduponstandardtodeterminewhatverticaldifferentiationintaxliabilitiesismostfair(JointCommitteeonTaxation,2015).7Slitor(1948)usedthistypeofdefinitiontoproposeameasureofprogression:dt(x)/dx=[m(x)-t(X)]/x;wheret(x)istheaveragetaxrateattheincomelevelxandm(x)isthemarginaltaxrateatthatlevelofincome.8Kakwani(1977),however,pointedoutthatbydoublingthetaxratesatallincomelevels,thetaxprogressivitywouldmechanicallyincreasewhenusingtheMusgrave-Thinratio.Thisisproblematicbecauseprogressivity(orregressivity)issupposedtomeasurethedeviationofataxsystemfromproportionality.KakwaniproposestousetheGiniindexonlytomeasurethedistributionaleffectsoftaxation,andpresentsanalternativemeasureusingtheLorenzCurvetocreateameasurethataccountsforboththedistributionalandproportionalelementsofataxsystem.9Poterba(1991a),Lyon&Schwab(1991),Bentoetal.(2012),andBorren&Sutton(1992).10Wieretal(2005),andPoterba(1991b).

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fuelefficiencystandardsareregressive,andJohnson(2006)looksatpublicspendingon

highereducation.

Whilethepotentialdistributionalaspectofpublicnaturalhazardinsurancehasbeennoted

intheliterature,thepracticalimplicationsintermsofbenefits(expectedpaymentofclaims)

relativetocosts(premiumspaid)havenotpreviouslybeenquantified.

Ben-ShaharandLogue(2015)examineFlorida’sstate-ownedCitizens'PropertyInsurance

Corporation(“Citizens”)anditscoverageforwind-damage(hurricanes).Theirworkrelieson

Citizens’owncalculationsoftheactualriskittakesonwhenprovidinginsurance,andonthe

premiumsitcharges.Theyfindthatthehighersubsidiesareprovidedforareasincurring

morerisk,andthattheseareasaregenerally(statistically)wealthier,mostlikelybecause

theyarelocatedclosertothecoast.Asecondpaperthatinvestigatesasimilarprogram,by

Bin,Bishop,andKousky(2012),studiestheU.S.NationalFloodInsuranceProgram(NFIP).It

focusesonthedeparturefromtheproportionalitymeasureofprogressivity.Aprogressive

departurefromproportionalityrequiresthateverypremiumdecilebenolargerthanthe

correspondingincomedecile.Theauthorsshowthatthedeparture-from-proportionality

indexisnotsignificantlydifferentfromzeroforpremiums,implyingtheyareproportionalto

income.Theyconsiderpremiumsandpaymentsseparately,andnotethatneithereffectis

extremeandthattheseeffectsaresmoothedovertime.

Howard(2016)examinesthenetsocialbenefitsoftheNFIP,usingdataonpremiums,

claims,policies,andgrantsfrom1996–2010.Inhismorecomprehensiveanalysis(thanBin

etal.,2012)hefindsthatthissystemis“moderatelyregressive.”Accordingtothesethree

analysesofthenaturalhazardinsuranceintheU.S.,itisplausiblethatthedistributional

aspectarisessolelyfromthedifferentiatedexposureofwealthierhouseholds,duetotheir

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locationonthecoastsandthefocusonhurricanedamage,asmanyoftheNFIPclaimsarise

fromstorm-generatedwavesurges.Inmanycases,andinmostcountries,however,itis

generallythepoorerhouseholdsthataremoreexposed(KarimandNoy,2016).

Surminski(2016)andDavey(2015)discussvariousdistributionalaspectsofFloodRe,the

UK’snewfloodreinsuranceprogrammethatisdesignedtomaintainaffordablypricedflood

insurance.BothpapersidentifyseveralwaysinwhichFloodRemayhavedistributional

consequences,butdonotquantifythem.O’Neill&O’Neill(2012)discussfloodinsurancein

theUK(beforethelaunchofFloodRe)andargueforasolidarity-basedschemeonfairness

grounds,acknowledgingthatriskbasedpremiumswouldunfairlypenalisehouseholdswho

couldnotreasonablybefoundtohavechosentoliveinfloodproneareasoftheirownwill.

Theynotethat“choiceisvoluntaryonlyifitcanbereasonablyforeseenandtheagentshave

realandacceptablealternativestoit.”Thisstatementraisesinterestingequityquestions,as

itislikelythatthosehouseholdsfacinghigherrisksarewealthier,inwhichcasethefairness

principletheyadvocatemayleadtotheinsurancetransferringriskfromrichtopoor

households,andtherebythepoorsubsidisingtherich.11

Here,wequantifythedistributionaleffectofpublicnaturalhazardinsuranceinaNZcase,

andidentifytheunfortunateregressivityofoneofthetheoreticallymostequitablydesigned

publicnaturalhazardinsurancesystemsglobally.Itiseasytoarguethatmanyoftheother

publicnaturalhazardinsurancesystemsestablishedglobally(seeTable1)arelikelytobeat

leastasregressive.Thenextsectiondescribesthedataweuseforourquantitativeanalysis.

11Thequestionoffairnessbecomesevenmorecomplicatedifthehazardbeinginsuredisclimate-relatedanditsfrequencyorintensityischangingbecauseofclimatechange.Inthiscase,insurancesystemsprovideacertaindegreeofcollectiveprotectionwithsomedistributionalconsequences,buttheinsuredeventwasoutcomeofactionsforwhichthereisanuneven,sharedresponsibility.Forflooding,itistheoutcomeofactionsforwhichthosewhoaremostvulnerableoftenareatleasthypotheticallytheleastresponsible.Thereisadoubleinjusticeifthosewithlowincomeswhoareleastresponsibleforanthropogenicglobalwarmingarefacedwiththelargestburdensofdamages(Thumimetal.,2011,Lindleyetal.,2011).

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Section3explainsthemethodology,inSection4weexplainourresults,andSection5

concludes.

3.Data

InNZ,publicnaturalhazardinsuranceisprovidedtoresidentialhomeownersbythe

EarthquakeCommission(EQC).Inordertoaccessthisinsurance,homeownersneedonly

haveprivatefireinsurance(whichover90%do).ThepublicEQCpremiumsarecollected

throughprivatefireinsurers,andareidenticalforbuildingcoverofalldwellingsinsuredfor

morethanNZ$100,000(asalmostallare).

TofullyappreciatetheroleEQCplays,wemustconsiderhowitdeveloped.In1906San

Franciscowashitbyadevastatingearthquake,hittingGermaninsurersespeciallyhard.In

thewakeofthisevent,muchoftheglobalinsuranceindustryrespondedbyexcluding

earthquakeandrelatedfiredamagefromtheirpolicies(Henderson,2010).In1931,NZwas

struckbyanearthquakecenteredonNapier.Atthistime,privateearthquakeinsurancewas

availableinNZ,butwasvoluntary(NZNSEE,1993).Then,in1937,withWorldWarII

looming,wardamagewasexcludedfrommostprivateinsurancecontracts.Again,in1942,

NZwashitbyanotherdamagingearthquakenotfarfromthecapital,andin1944,the

EarthquakeandWarDamageCommissionwasestablished;itisthehistoricalprecursorto

theEQC.12

12Partofthemotivationforthiswastheslowratesofrepairfollowingthe1931and1942events(NZTreasury2015).IntheyearsthatfollowedNZwashitbyanumberofdisastersincludinganearthquaketriggeredtsunamiin1944,anearthquakein1968andamajorlandslipin1979.TheEarthquakeCommissionActof1993redesignedthescheme.Amajordevelopmentwasthephase-outofcommercialproperties.ItalsoamalgamatedtheWarDamageandEarthquakeFundandtheDisasterandLandslipFundastheNaturalDisasterFund.ThisisthefundEQCdrawsfromtopayoutonclaims.

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TheEQCcurrentlyprovidesthreeformsofinsurancecovertoresidentialpropertyowners:

structure,land,andcontents.Theseareinsuredtoreplacementvalueagainstnatural

hazardssuchasearthquake/tsunami,volcaniceruption,andlandslip.Since1980,outof

543,531claims,94.9%havebeenrelatedtoearthquakes.Thecoverforresidentialbuildings

providesthefirstNZ$100,000ofreplacementvalueforeachinsureddwelling.13Ifthelossis

greater,theprivateinsurerisresponsibleforanyover-caprepaircosts.Aswewillfocusthe

analysisbelowexclusivelyonstructuraldamageclaims(andnotoncontentsorland),we

onlydescribethisaspectofEQCpolicy.14ForeachNZ$100ofpropertyinsuredbytheEQC,

alevyischargedbytheprivateinsurerandsenttoEQC.Thesepremiumshadbeensetat

0.0005%oftheamountinsuredin1993,andweretripledaftertheCanterburyearthquakes

of2010–11to0.0015%.Morethan99%ofhomesarevaluedatmorethanNZ$100,000,so

thatineffectallpaythesameamounttoEQCforthebuildinginsuranceitprovides(NZ$150

perannum).15

InordertoquantifytheregressivityoftheEQCbuildingcover,werequiredameasureofthe

benefitdeliveredbytheEQCscheme.Thereisvalueinthecertaintyofknowingoneis

insuredregardlessofwhetherthatinsuranceiseverrequired,andsomevalueinthe

indirectfacilitationoftheover-capprivatenaturalhazardinsurancemarket.Ouranalysis

assumesthatthisvalueisequalforallparticipantsintheschemeandwethereforeignoreit.

Forthepurposesofthisanalysis,thebenefitisdefinedasactualpayouttotheownerfor

disasterdamage.ThisisaplausiblemeasuresincevirtuallyallhomesinChristchurchwere

damagedintheCanterburyearthquakesequence,andifanything,homeownersofweaker

13Amulti-unitresidentialbuildingcoveredforfiredamagewouldbeinsuredthroughEQCforthefirstNZ$100,000timesthenumberofdwellingsinthebuilding.14Thedetailsaboutlandcover,uniquelycoveredinNZ,aresignificantlymorecomplicated.15RecallthebuildingcoverfromEQCiscappedatNZ$100,000perdwelling.

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socioeconomicbackgroundswerelocatedclosertotheepicentreoftheearthquake.Thus,

theredistributivequestionis:HavewealthierhomeownersreceivedmoremoneyfromEQC

forbuildingrepairthantheirlesswell-offcounterparts.Toanswerthisquestion,we

combinedtwodatasets:EQCinsuranceclaimdatafromtheCanterburyEarthquakeseriesof

2010–2011,16andcensusdatafromStatisticsNZ.Table2reportsthesummarystatisticsof

thedwelling-leveldatasetweusedinouranalysis.

Table2:SummaryStatistics-PropertyleveldatafortheCanterburyEQSeriesDataset (1) (2) (3) (4)VARIABLES mean sd min max TotalDwellingPayout 45,774 58,207 0 358,381DwellingPayout/#ofClaims 26,254 31,503 0 344,101AssessedBldgRepairCosts 63,370 139,215 0 1.498e+07#claimsmadeonthataddress 1.538 0.734 1 7#dwellingsclaimedforonthataddress 1.066 1.014 1 102BuildingValue10 319,991 240,102 43,844 2.091e+07DwellingadjustedBuildingValue2010 303,682 150,233 1,120 1.752e+07Note:Thistablecontainssummarystatisticsforthe94,687propertiesforwhichwehaveinsuranceclaimdatarelatingtotheCanterburyEarthquakeSeries.Therewerefiveearthquakesassociatedwithasignificantnumberofpayments(04/09/2010,26/12/2010,22/02/2011,13/06/2011,23/12/2011).Mostareassociatedwiththefirstandthirdevents.7.2%ofdwellingsareintheruralmeshblocks.AllmonetaryamountsinNZ$.WealsomadeuseofStatisticsNewZealanddata—itprovidedmeshblocklevelinformation

fromtheNewZealandCensus,conductedin2001,2006and2013.17Theaveragenumberof

peopleresidinginameshblockinCanterburywasabout105.Wewereabletomatcheach

propertytoameshblock,whichallowedustomatchtheproperty-leveldatatothe

meshblock-levelsocioeconomicdataavailablefromtheCensus.Forourinitialanalysis,we

includedanumberofexplanatoryvariablesgeneratedfromthe2006Census(sinceit

precededtheearthquakes).Weuseddatapertainingtothepersonalandhousehold

sectionsofthecensus,specifically;theproportionofthemeshblockwhoidentifiedasMāori

(theindigenouspeopleofNZ)orPacifika(PacificIslanders),ofindividualswhoself-reportas

16OnSeptember4th,2010,Canterburywashitbyamagnitude7.1earthquake.Thiswasfollowedbyaseriesofaftershocks,themostdevastatingofwhichwasa6.3earthquakeonFebruary22nd,2011,whichtook185lives.17AmeshblockisthesmallestunitforwhichStatisticsNewZealandcollectsdata,withboundariesrelatedtopopulation.Censusesareconductedevery5years.The2011censuswaspostponedto2013becauseoftheearthquakes.

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havingbeenbornoverseas,andwhoself-reportashavingcompletedtertiarylevel

education;themedianhouseholdincomepermeshblock;18thechangeinthemedian

householdincomebetween2001and2006,themeannumberofhouseholdmembers,and

theproportionofthemeshblockresidentswhichself-reportasnotowningtheirhouse.

ThesedataaresummarizedinTable3.InCanterbury,4,516meshblockshaveatleastone

valuedpropertywithfullyrecordedclaimsrelatingtothe2010–2011sequenceof

earthquakes,aswellasthecorrespondingcensusinformation.

AsafirststepininvestigatingthedistributionalimplicationsoftheEQCcover,infigure1,we

graphedthepayoutdatabypropertydecileandincomedecileforalltheclaimsarisingout

oftheCanterburyEarthquakeSeriesdataset.Inthefigure,weseethatastheproperty

decileincreases,theaveragetotalbuildingpayoutforthedecileincreasesaswell,witha

sharpestincreaseforthetenthdecile.Thispatternisrepeatedinthepanelontheright

whereweusemedianhouseholdincomedeciles.

18Thetopincomeiscensoredat$100,000.In2006,therewere0.03%ofmeshblockswheretheMedHHIncometopcensoredat$100,000,andin20010.01%.

Figure 1: Distribution of Adjusted Building Payouts by Property Value and Income deciles. Canterbury dataset only, excludes zero value payouts. Distribution of payouts per property adjusted by number of dwellings insured by deciles of either dwelling adjusted modelled building value as at mid-2010, or meshblock level median household income as at 2006. Whiskers indicate 0.5 times the IQR, to better show the median values (version with standard whiskers in appendix).

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Intheboxplots,themiddlelineindicatesthemedian,theshadedboxindicatesthe

interquartilerange(IQR),and“whiskers"indicate0.5timestheIQR.Anotableobservation

istheincreaseinthespreadofthetotalpayoutperdwellingasthedecilesincrease.This

reflectshigher-valuepropertiesrequirehighercostofrepairs.Itisworthremindingthe

readerherethatthesepayoutsonlytakeintoaccountthepayoutsfromthepublicinsurer,

andsignificantlydamagedhomeswouldverylikelyhavealsoreceivedrepairpayoutsfrom

theirprivateinsurancecompany.

3.Methodology

GiventheidenticalpremiumspaidforEQCcoverbyhomeowners,weexpectedsome

redistributiontooccur.Wehypothesizedtwodifferentmechanismsfortheregressivityin

thisscheme:

1. Wealthierhouseholdsmayliveinriskierareas(suchasonhillsidesorbythewater),

leadingtoahigherlikelihoodofnaturalhazardexposure,andthustoahigherlikelihood

ofdamage.

2. The100Kcaponbuildingpaymentspereventislikelytobemoredrawnonforwealthier

homessincethesehomeshavethecapacitytoincurmoredamage.Giventhehigher

valueofeachcomponentofthehome,allelseconstant,highvaluehomeswillincur

moredamage.

Thefirstmechanismisfrequentlymentionedasaplausibleonefordamagesfromfloods,

bothfromstormsurgesthathitcoastalpropertiesandfromriverinefloodsthathit

propertiesonriverbanks.Thisreasonhasbeensuggestedascausingsignificantregressivity

intheU.S.andUKfloodinsuranceprograms.Whileadmittedlythishasnotyetbeen

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quantifiedineitherofthesefloodinsuranceprograms,itislessinterestingfromour

perspective.Itislessrelevantforearthquakes,whoseexactlocationandseismic-wave

propagationaremorerandomandlessorientedwithobviousexternalcharacteristics

determiningthespatialdistributionofhousing.InthecaseoftheCanterburyearthquakes,

the22/2/2011earthquake’sepicentrewaslocatedtothesoutheastofthecity;ingeneral

theeasternsuburbsarelesswealthywhilethenorth-westernsuburbs,furtherawayfrom

theepicentreoftheearthquake,havethehighervaluepropertiesandhigher-income

households.

ThefocusofouranalysisoftheCanterburyexperiencewashencethesecondmechanism.

Thehypothesisweexaminedwasthatwealthierhomeownersownpropertiesthatarelikely

tobecostliertorepairthantheirlesswell-offcounterparts.Forexample,alargerhouse

usuallyhasmoreinteriorfloorsthatmaycrack,andthesefloorsmaybemadefrommore

expensivematerials.Naturally,therearealsopossiblemechanismsthatcanleadtothe

oppositeoutcome:perhapsnewerorbetter-maintainedhousesarelessvulnerableto

earthquakesastheywerebuilttohigherseismicstandards.

Toidentifytheeffectofthe100Kcap,wefirstlookedatwhetherhigher-valuehomesin

CanterburysustainedhigherdamagesfromtheCanterburyEarthquakeSeries.Inthiscase,

wealthierhomeownerswereidentifiedeitherbythevalueofthehomeorbytheaverage

socioeconomicstatusoftheresidentsintherespectivemeshblock.19Weregressedthe

19Duetothenatureoftheavailabledata,wecouldnotidentifywhetherasinglehomeownerownedmultipleproperties.Giventhismissingindicatoroftheparticularlywealthy,ourresultsarelikelytobeconservative.Theidentificationbasedonaproxyforwealth(thevalueofthehome)ispotentiallymoreinformativethanthedistinctionbasedonaverageincome(permeshblock).Thelattersuffers,potentially,fromtheEcologicialFallacy(Robinson,1950)–thatthestatisticalcorrelationbetweentwovariableswhentheyaregroupedmightbedifferentfromthestatisticalcorrelationoftheindividualmembersofthesegroups.Furthermore,althoughthepropertyvaluationspokesomewhatdirectlytothewealthofthehomeowner,thecensusincomedatarelatedtotheresidentsofthesemeshblocksratherthanthehomeowners.Thus,forexample,a“slumlord”whoownedanumberofcheaperpropertiesinlowsocioeconomicareascouldnotbeidentifiedcleary.However,theseareunlikelytobeveryimportantconsiderationsasthemajorityofhouseswereowneroccupied(67%ofthe2006Censusstatedoccupiedprivatedwellingswereowneroccupied).

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assessedrepaircostonthemostrecentvaluationoftheproperty,aswellasanumberof

indicatorsofthesocioeconomiclevelofresidents,asindicatedbelow:

!" = $ + &'()*+,)-./012," + &34,566789*:," + ;<" + =" (1)

where!" = >*-01?,+0@)"isthesumofallassessedrepaircostsmadeforpropertywefor

claimsrelatedtoearthquakeeventsduringthespecifiedlocation(Canterbury)andtime

period(2010–2011).Theerrorterm,=",isclusteredatthemeshblockleveltoaccountfor

someofourexplanatoryvariablesonlyvaryingatthisaggregatelevel.20Inasecond

specification,whichbettercapturestheregressivityoftheEQCschemeasitiscurrently

structured,thedependent(LHS)variableisthetotalpayoutonapropertyagainstthesame

covariates,includingthemostrecentvaluationofthepropertyandanumberofcontrol

variablesatthemeshblocklevel(!" = >*-01BCD+0.*2-").Weestimatedseveralalternative

specificationstotesttherobustnessofourresultsandtoattempttoidentifyareasof

variationthatmightrequirefurtheranalysis.

GivenourfocusonthedistributionalimpactofEQCover,wealsoperformquantile

regressionontheCanterburydataset,asbelow:

!" = $ + &'()*+,)-./012," + &34,566789*:," + ;<" + =" (2)

4.ResultsandDiscussion

ResultsareshowninTable3.Incolumns1–3,weusedTotalActualAssessedRepairCostsas

thedependentvariable,andincolumns4–6weusedAdjustedTotalDwellingPayout.

20Weestimatethiswithheteroscedasticandclusterrobuststandarderrors(Cameron&Miller,2015).Wealsoperformedthisanalysisattheclaimlevel(ratherthansummingallclaimsforasingleproperty).Theresultswereverysimilar,andareavailableuponrequest.

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Columns1and4showourcomprehensivespecifications.Thefirstclearresultisthatthe

coefficientsofinterest(thoseonpropertyvalueormedianhouseholdincome)arealways

positiveandstatisticallysignificantatthe1%level.Theirmagnitudeissuchthatforevery

NZ$1,000ofhigherdwellingvalue,wefoundapproximatelyaNZ$62.70increaseinTotal

ActualAssessedRepaircost,holdingotherfactorsconstant,includingmedianhousehold

incomeinthemeshblock.Further,foreveryNZ$1,000ofhigherbuildingvalue,wefound

approximately$28.30moretohavebeenpaidoutfromEQCtothehomeowner.The

associationofhighervaluesinthesewealth/incomeindicatorswasmorethantwiceaslarge

forassessedrepaircoststhanfortheactualEQCpayouts.

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Table4:RegressionResults-CanterburyEarthquakeSeries

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

VARIABLES TotalAssessedRepairCosts TotalDwellingPayout

DwellingadjustedBuildingValue'10 0.0577*** 0.0671*** 0.0257*** 0.0304***

(0.0145) (0.0163) (0.00653) (0.00747)

MedianHouseholdIncome‘06 1.297*** 1.404*** 0.662*** 0.710***

(0.149) (0.147) (0.0713) (0.0707)

Dif.inMedHHIncome‘01-‘06 -0.839*** -0.0790 -0.896*** -0.364*** 0.0235 -0.390***

(0.161) (0.132) (0.161) (0.0775) (0.0655) (0.0776)

ProportionTertiaryEducated‘06 93,461*** 178,205*** 95,614*** 77,588*** 120,855*** 78,459***

(18,081) (17,336) (18,144) (9,370) (8,856) (9,388)

ProportionNotHomeowners‘06 -23,626** -55,219*** -25,703*** -14,901*** -31,031*** -15,852***

(9,344) (9,579) (9,316) (4,835) (4,824) (4,810)

MeanNumberofHouseholdMembers‘06 -32,364*** -12,728*** -31,872*** -15,895*** -5,869*** -15,671***

(4,100) (3,599) (4,101) (2,084) (1,915) (2,083)

ProportionMāori‘06 102,156*** 65,041** 92,382*** 84,528*** 65,579*** 80,172***

(27,231) (27,339) (27,055) (15,261) (15,275) (15,194)

ProportionPasifika‘06 110,083*** 81,959** 105,593*** 79,400*** 65,041*** 77,281***

(37,144) (37,533) (37,110) (20,728) (20,948) (20,705)

ProportionBornOverseas‘06 -22,657 -46,174*** -22,376 -19,178** -31,185*** -19,023**

(16,017) (16,277) (15,999) (8,899) (9,037) (8,879)

RuralMeshblock -46,007*** -45,428*** -44,539*** -28,920*** -28,624*** -28,259***

(2,733) (2,721) (2,699) (1,394) (1,392) (1,384)

Constant 61,067*** 70,917*** 72,808*** 38,727*** 43,757*** 43,941***

(10,575) (10,855) (10,137) (5,427) (5,536) (5,243)

Observations 94,723 94,723 94,799 94,723 94,723 94,799

R-squared 0.040 0.032 0.036 0.079 0.066 0.074

Robuststandarderrorsinparentheses.***p<0.01,**p<0.05,*p<0.1.

ThistablecontainsresultsfromOLSregressionswithmeshblocklevelclusteredstandarderrors.ThedatasetincludesinformationonallclaimsmadetotheNZEQCrelatedtoinsured

damagesfollowingtheearthquakesintheCanterburyregionforeventsfrom2010-09-04to2012-02-11.Thedatasetisatthepropertylevelandexcludeszerovalueclaims(thosewhichdid

notreceiveEQCfundedrepairs).Therawclaimsandportfoliodataisconfidentialbecauseofprivacyconcerns.Theotherexplanatoryvariablesareallgatheredfrompubliclyavailable

CensustabulationfromStatisticsNZ.Thesearemeshblocklevelvariablesascollectedfromthe2006(andforMedianHouseholdIncome,2001)Census.21

21ThereaderwillnotelowR-squaredvalues.However,thisresearchdidnotsetouttoaccuratelypredictdamagesorpayouts,buttoidentifyvariationscorrelatedwithsocioeconomiccharacteristics.AlowR-

squaredisthereforenotofconcerninthiscontext.

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Theeffectsofthemeshblock-levelexplanatoryvariableswerequalitativelythesamefor

bothdependentvariables,andconsistentlyaffectedthedependentvariablesinthe

expecteddirections.ThegrowthinmedianHHincome(2001to2006)hadanegativeeffect

whenstatisticallysignificant;sothatthe“newer”thewealthinthearea,thelowerthe

assesseddamageandEQCpayout.Ithasbeensuggestedinnumerousmediareportsthat

becauseofthebureaucraticcomplexityoftheinsurancesystem,moreeducatedclaimants

finditeasiertonavigatethesystemandsuccessfullyclaimforhigherdamages.This

hypothesisjustifiesthetertiaryeducationmeasureweincludedasanexplanatoryvariable.

Ashypothesized,thecoefficientwaspositiveandstatisticallysignificant.Ithasalsobeen

suggestedthathomeownerthatliveinthehousearemorelikelytonegotiatewiththe

insurertoexpeditetheprocess(thusputtingrenterswhosepropertywasdamagedata

disadvantage).Thisvariablewasstatisticallysignificantandnegativeashypothesized.

Anotherpossiblefactorwasthenumberofhouseholdmembers.Ashypothesizedlarger

householdsize,anotherimperfectproxyforsocioeconomicstatus,wasalsonegativeand

statisticallysignificant.

Wealsoincludedanumberofethnicityvariablesatthemeshblocklevel.TheProportion

MaoriandProportionPasifikaareincludedtocheckiftheschemeishavinganadverse

effectontheseminorities,whichareofparticularimportancetoNewZealand.InNZ,both

ethnicitiesareidentifiedwithlowerincome,onaverage,thoughthePasifikapopulation

(thoseoriginatingfromotherPacificIslands)aregenerallymoredisadvantaged,witha

significantproportionusingEnglishasasecondlanguage.However,aftercontrollingfor

income,education,andfamilysize,whichalsoproxyforsocioeconomics,theseethnicities

arestatisticallyidentifiedwithpositiveeffectsonbothdamagesandpayouts.Finally,we

alsoincludedtheproportionofthepopulationbornoverseas,astabulatedinthe2006

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census,incasetheclaimprocessismoredifficultforthisgrouptonavigatebecauseof

languagebarriers,fewerlocalsocialties,lackofcommunicationwithassessorsabout

deadlines,etc.Theassessedrepaircostsarenotsignificantlyaffectedbythismeasure.

However,theredoesappeartobeanegativeeffectontotaldwellingpayouts.Finally,ifthe

propertyisinaruralmeshblock,weseenegativeeffectsonbothdamagesandtotal

payouts;likelybecausemostruralmeshblockswerefurtherawayfromthequake’s

epicentre.

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Table5:Regressionspecificationtesting-CanterburyEarthquakeSeries (1) (2) (3) (4) (5) (6)VARIABLES TotalDwellingPayout DwellingadjustedBuildingValue‘10 0.0257*** 0.0269*** 0.0269*** 0.0282*** 0.0264*** 0.0264*** (0.00653) (0.00678) (0.00678) (0.00700) (0.00647) (0.00644)MedianHouseholdIncome‘06 0.662*** 0.473*** 0.491*** 0.729*** 0.507*** 0.504*** (0.0713) (0.0591) (0.0582) (0.0553) (0.0502) (0.0450)Dif.inMedHHIncome‘01-‘06 -0.364*** (0.0775) ProportionTertiaryEducated‘06 77,588*** 85,462*** 77,979*** (9,370) (9,353) (8,549) ProportionNotHomeowners‘06 -14,901*** -18,594*** -21,511*** -8,876** 512.2 (4,835) (4,858) (4,540) (4,428) (4,317) MeanNumberofHouseholdMembers‘06 -15,895*** -14,299*** -15,102*** -17,301*** (2,084) (2,087) (2,041) (2,066) ProportionBornOverseas‘06 -19,178** -20,625** (8,899) (8,933)

ProportionMāori‘06 84,528*** 80,825*** 89,274*** 60,879***

(15,261) (15,262) (14,413) (14,018) ProportionPasifika‘06 79,400*** 75,247*** 71,703*** 52,096** (20,728) (20,814) (20,799) (20,778) RuralMeshblock -28,920*** -28,863*** -28,077*** -31,257*** -34,118*** -34,147*** (1,394) (1,399) (1,379) (1,350) (1,329) (1,249)Constant 38,727*** 40,524*** 39,145*** 42,908*** 13,849*** 14,133*** (5,427) (5,455) (5,467) (5,514) (3,847) (2,555) Observations 94,723 94,723 94,723 94,723 94,725 94,725R-squared 0.079 0.076 0.075 0.064 0.053 0.053Robuststandarderrorsinparentheses.***p<0.01,**p<0.05,*p<0.1.ThistablecontainsresultsfromOLSregressionswithmeshblocklevelclusteredstandarderrors.ThedatasetincludesinformationonclaimsmadetotheNewZealandEarthquakeCommissionrelatedtoEarthquakesorFiresfollowingEarthquakesintheCanterburyregionofNewZealandforeventsfrom2010-09-04to2012-02-11.Thedatasetisatthepropertylevelandexcludesunfundedclaims.Rawdataconfidential.Datasource:EQC.Totaldwellingpayoutisanaggregatevariableincludingbothanycashsettlementmadetothepropertyandanypayoutformanagedrepairs,dividedbythenumberofdwellingsinsuredonthatproperty.AdjustedBuildingValue10isthebuildingvaluefortheportfolio,dividedbythenumberofdwellingsinsuredontheproperty.TheotherexplanatoryvariablesareallgatheredfrompubliclyavailableCensusdatafromStatisticsNewZealand.Thesearemeshblocklevelvariablesascollectedinthe2006(andforMedianHouseholdIncome,2001)Census.

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InTable5,theconsequencesofprogressivelyremovingsomeoftheexplanatoryvariables

arepresented.Incolumn(1)(identicaltocolumn(4)inTable4)weseethatallthe

explanatoryvariablesarestatisticallysignificantlydifferentfromzeroatthe1%level,with

theexceptionofthepopulationbornoverseas.Wefirstremovedthegrowthinmedian

householdincomefrom2001to2006,asthishadamoretenuoustheoreticaleffecton

payouts;aspresentedincolumn(2).Thisresultedinadecreaseintheeffectof2006

MedianHouseholdIncome,andhadasmallpositiveeffectonthecoefficientforBuilding

Value.Incolumn(3)weremovedtheleaststatisticallysignificantvariable:theproportionof

themeshblockbornoverseas.Thecoefficientonmedianhouseholdincomeincreased

slightlyandbecamemarginallymoreprecise,whiletheeffectofbuildingvalueremained

unchanged.Droppingtheproportionofthetertiaryincolumn(4)ledtoasharpincreasein

theeffectofmedianhouseholdincome,corroboratingthewidelyestablishedobservation

thateducationandincomearepositivelycorrelated,andshowingthatwithoutcontrolling

foreducation,wemightoverestimatetheincomeeffect.

Table6:QuantileRegressionResults (1) (2) (3) (4) QuantileRegressions OLSRegression 0.25 0.5 0.75 TotalDwellingPayout TotalDwellingPayoutVARIABLES AdjustedBuildingValue‘10 0.000322*** 0.0107*** 0.0739*** 0.0245*** (1.83e-06) (0.00182) (0.0106) (0.00613)MedianHHIncome'06 0.106*** 0.370*** 1.433*** 0.802*** (0.00289) (0.0453) (0.0688) (0.0586)Dif.MedHHIncome‘01-'06 -0.0555*** -0.198*** -0.610*** -0.408*** (0.00402) (0.0367) (0.109) (0.0766)Mean#ofHHMembers‘06 -936.2*** -5,380*** -29,969*** -14,667*** (45.35) (527.0) (2,533) (1,951)RuralMeshblockIndicator -2,482*** -7,981*** -59,810*** -32,875*** (72.28) (348.8) (3,249) (1,227)Constant 3,899 9,871*** 72,701*** 41,002*** (0) (2,850) (7,791) (4,473) Observations 94,725 94,725 94,725 94,725R-squared 0.064

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Robuststandarderrorsinparentheses.***p<0.01,**p<0.05,*p<0.1.Thistablecontainsresultsfromquantileregressionswithmeshblocklevelclusteredstandarderrors.ThedatasetincludesinformationonallclaimsmadetotheNZEQCrelatedtoinsureddamagesfollowingtheearthquakesintheCanterburyregionforeventsfrom2010-09-04to2012-02-11.Thedatasetisatthepropertylevelandexcludeszerovalueclaims(thosewhichdidnotreceiveEQCfundedrepairs).Therawclaimsandportfoliodataisconfidentialbecauseofprivacyconcerns.TheotherexplanatoryvariablesareallgatheredfrompubliclyavailableCensustabulationfromStatisticsNZ.Thesearemeshblocklevelvariablesascollectedinthe2006(andforMedianHouseholdIncome,2001)Census.

Thisalsoledtoaslightincreaseintheeffectofbuildingvalue,andinterestingly,also

decreasedtheabsolutevaluesofthecoefficientsontheethnicitymeasures.Incolumn(5)

weremovedethnicityandhouseholdmembercontrols,bringingbuildingvaluedown

marginally,median2006householdincomedownsharply,andremovingallstatistical

significancefortheproportionnothomeowners.Removingthislastproportionincolumn

(6)completedourrobustnesschecks,withnegligibleeffectsonthecoefficientsofinterest.

Ourprimaryresultsremainedrobustthroughoutthesechecks.Tertiaryeducationand

changesinhouseholdincomeappearedthemostcloselycorrelatedwithmedianhousehold

income.Theproportionnothomeownersappearedtoaffectthedependentvariableonly

throughourothercontrols.Therewasclearlysomeculturaleffectatworkaswell,since

controllingforincomeandeducationincreasedtheabsolutevalueofthecoefficientson

ethnicitycontrols.

Columns1-3ofTable6containcoefficientsfromregressionsatdifferentquantiles.In

Column1arethosepertainingtothe25thpercentile.Asthereadercansee,thecoefficients

ofinterestarerathersmallbutsignificant.Onaverage,withathousand-dollarincreasein

AdjustedBuildingValue,wewouldexpectthe25thpercentileofTotalDwellingPayoutto

increasebyonly30c,allelseequal.However,withathousand-dollarincreaseinMedian

HouseholdIncometherewouldbeonaveragea$100increaseinthe25thpercentileofTotal

DwellingPayout.InColumn2seetheeffectonthemedianofTotalDwellingPayout,which

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aresignificantlyhigherthanthoseforthe25thpercentile,andinColumn3theeffectonthe

75thpercentile,whicharehigheragain.InterestinglythecoefficientsofinterestbyOLS

regressionsitbetweenthemedianand75thquantileresults.22

5.Aneasysolutiontotheregressivityproblem

Unfortunately,wecannotdefineanactuariallyfairpremiumstructuregivenwedonot

knowthedistributionoftherisk.However,nonethelesswecandefinepossibleremediesto

theregressivityissue.OnepotentialfixtotheunfortunateregressivityoftheNZdisaster

insurancesystemisremarkablysimple;ratherthanpayingaflatpremiumperyear,

homeownerscouldberequiredtopayasetpercentageoftotalprivatesuminsured.This

wouldreflectthathomeswithalargersuminsuredaremorelikelytoclaimlargeramounts,

evenofthe$100,000perdwelling,asshownintheanalysisthusfar.Thismodification

wouldcorrecttheregressivityissue.

Totestthissuggestion,weperformanumericalsimulationontheCanterburydataset.We

simulatethepremiumsusingthepercentagesadoptedbyEQC,butappliedtotheDwelling-

adjustedbuildingvalueasopposedtothefirst$100,000ofthese.Thiswouldmovethe

schemetowardsamorerisk-based(asopposedtoflat)premiumstructure.

Firstthesuggestedpremiumsforeachproperty(byEQCPropertyGroup)arecreatedas

0.0005x(Dwelling-adjustedbuildingvalueasatmid-2010).Then,thesameprocessisused

butsubstituting0.0005forfirst0.0015andthen0.002.Toexplorewhatthiswouldhave

meantforCanterburybuildingclaimants,webuildthedistributionofthesesuggested

22weshouldnoteherethatquantilecoefficientstellusabouteffectsonthedistribution,notonindividuals.

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premiumswithineachdecileofdwelling-adjustedbuildingvalues.AsshowninFigure2

below,annualpremiumswouldhavebeenslightlyhigherforthosehomeownerslivingin

wealthierareas.However,theyarebynomeansunaffordable.

Usingthe0.0005%measure,forthefirstsixdecilesofpropertiesbyDwelling-adjusted

PropertyValues,suggestedpremiumsperyearwouldactuallylikelybelowerthanthe

current$150perannum,andfornoonedoesthesuggestedpremiumgoabove$400per

annum.Ahomeownerwhosehomewasvaluedat$300,000(andinsuredtothatlevel)

wouldpay$150peryear,whereasahomeownerwhosehomewasvaluedat$1,000,000

wouldpay$500peryear.Withthe0.0015%or0.002%measures,thevastmajorityof

homeownerswouldstillpaylessthan$1000peryear.

Withthese94722homes,undertheoriginalpremiumstructureEQCwouldhaveraised

4,736,100inoneyearifallweresingledwellinghomes.Withthesuggestedpremiums,EQC

wouldhaveraised14,100,000withthe5%measure,42,200,000withthe15%or56,200,000

withthe20%.Thus,thepremiumchangewouldlikelyalsohavefinancialbenefitsforEQC.

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Figure2:Distributionofsuggestedpremiums.This figure shows the distribution of suggested premiums. The first is the distribution ofpremiumsas0.0005timesthedwelling-adjustedbuildingvalue,thesecondusing0.0015andthethirdusing0.002.Thebuildingvaluesareasatmid-2010,andadjustedbythenumberofdwellingsrecorded.ThisfigurealsousesonlythebuildingclaimantsfromtheCanterbury2010-2011earthquakeseries.DatasuppliedbyEQC,andconfidential.DollarsareNZ$.

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Figure3:PremiumtoPayoutRatioforsuggestedpremiums,byBuildingValueDecileThisfigureshowsthedistributionofSuggestedPremium/TotalPayout,whereinpanel1thesuggestedpremium iscalculatedas0.0005times thedwelling-adjustedbuildingvalue(prequake),thesecondusing0.0015andthethirdusing0.002.Thebuildingvaluesareasatmid-2010. This figure also uses only the building claimants from the Canterbury 2010-2011earthquakeseries.DatasuppliedbyEQC,andconfidential.DollarsareNZ$.

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ThehopewiththisprogressivepremiumstructureisthattheratioofpremiumtoEQC

payoutbecomesconstantacrossdeciles.InFigure3below,theseratiosofsuggested

premiumsagainstactualpayouts(perdwelling),aregraphedinstandardboxandwhisker

plotsbybuildingvaluedecile.Themedianratioforeachisrelativelyflatacrossdeciles,

supportingthisasapossiblefixtotheregressivityissue.Thesuggestedpremiumstructure

couldbeadjustedtomakeitmoreconstant.AlternategraphsbyMedianHouseholdIncome

decileareincludedintheAppendix,asarethoseshowingtheflatstructureasitoperates

currently.

AnyofthethreesuggestedoptionsofpremiumstructurewouldmakeEQC’sresidential

buildingcoverschemesignificantlylessregressive.Thechoiceofpremiumstructure(using

0.0005,0.0015or0.002)woulddependontherequirementsforincomeraisedperyearand

thecapabilityofhomeownersatthelowerendofthespectrumtoaffordincreased

premiums.The0.0005measurereducesregressivity,increasesEQCrevenueperyear,and

doesnotincreaseannualpremiumsforhomeownersofthelowestdecileofvaluedhomes.

Thismeasureisthereforepreferredbytheauthors.

6.Conclusions

Inalmostallcaseswherehomeownersareexposedtoasignificantriskofsudden-onset

naturalhazards,theprivateinsurancesectorelectsnottoinsureagainstthesehazards.23

Directpublicprovisionorsubsidizationofinsurancearethereforenecessaryifsuchcoveris

perceivedtobesociallydesirable.Unfortunately,publicnaturalhazardinsurancehas

23 The many reasons why this is the case are discussed in Kusuma et al. (2017).

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adversedistributionalconsequencesinalmostallcases.Thispaper’saimisnotonlyto

describethesocioeconomicdirectioninwhichtheseinsurance-relatedfinancialtransfers

areflowing,buttoquantifythem.Themechanismforwealthtransferinpublicearthquake

insuranceanalyzedinthispaperfacilitatesupwardtransfers—thepooraresubsidizingthe

rich.

OuranalysisoftheCanterburyEarthquakeseries,andthefunctioningofNewZealand’s

publicinsurer,offerstwoinsights.First,itclearlysupportsthehypothesisthatmore

expensivehomesreceivehigherpayoutsirrespectiveoftheirexposuretothehazard;i.e.,

highersumsthatareadirectconsequenceofthehighervalueoftheaffectedproperties.

Secondly,itsuggeststhatcappingcoverageandhavingflatpremiums,bothofwhichaimto

deliveramoreequitablescheme,arenotsufficient;eventhesekindsofprogramsendup

transferringriskfromhomeownersofexpensivehomestohomeownersoflower-value

homes(andinsomeothercasestonon-homeowners).OurfindingintheNewZealandcase,

suggeststhatmanyotherseeminglymoreegalitariannaturalhazardinsurancesystemsare

regressiveaswell.

Withthiswork,weaimtoimprovethefunctionalityofpublicnaturalhazardinsurance,by

drawingattentiontothedistributionalfunctionoftheseschemes.IntheNewZealandcase,

theregressiveeffectcanbecounteractedbyasimpleshiftfromeffectivelyflatpremiumsto

asetpercentageofthetotalprivatesuminsured(whilemaintainingthecoveragecap).

Futureresearchshouldextendthistypeofanalysistootherpublicnaturalhazardinsurance

schemesinothercountries,sothattheadversedistributionalcharacteristicofthese

programsisavoided.

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Appendix1:SuggestedPremiumtoTotalPayoutratiosbyalternatedeciles

Figure4:PremiumtoPayoutRatioforsuggestedpremiums,byMedianHouseholdIncomeDeciles.Inpanel1thesuggestedpremiumiscalculatedas0.0005timesthedwelling-adjustedbuildingvalue(prequake),thesecond

using0.0015andthethirdusing0.002.TheMedianHoueholdIncomevaluesareatthemeshblocklevel,andasat2006.Thisfigurealsousesonlythe

propertiesofbuildingclaimantsfromtheCanterbury2010-2011earthquakeseries.PropertyandpayoutdatasuppliedbyEQCandconfidential,incomedatacollectedbyStatisticsNewZealandinthe2006Census.DollarsareNZ$.

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Appendix2:$150/TotalPayoutratios,bypropertyvalueandincomedeciles

Figure5:$150/TotalBuildingPayoutbyBuildingValueDecilethenMedianHouseholdIncomeDecile

Inpanel1thesuggestedpremiumiscalculatedas0.0005timesthedwelling-adjustedbuildingvalue(prequake),thesecondusing0.0015andthethirdusing0.002.Thebuildingvaluesareasatmid-2010.TheMedianHouseholdIncomevaluesareatthemeshblocklevel,andasat2006.ThisfigurealsousesonlythepropertiesofbuildingclaimantsfromtheCanterbury2010-2011earthquakeseries.PropertyandpayoutdatasuppliedbyEQCandconfidential,incomedatacollectedbyStatisticsNewZealandinthe2006Census.DollarsareNZ$.“Excludesoutsidevalues"

referstotheoutliersoftheboxandwhiskerplotsbeingomitted.

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Appendix3

Figure6:DistributionofAdjustedBuildingPayoutsbyPropertyValueandIncomedeciles–version2StandardBoxandWhiskerPlots-Canterburydatasetonly,excludeszerovaluepayouts.Distributionofpayoutsperpropertyadjustedbynumberofdwellingsinsuredbydecilesofeitherdwellingadjustedmodelled

buildingvalueasatmid-2010,ormeshblocklevelmedianhouseholdincomeasat2006.