Journal of Economic Perspectives—Volume 25, Number 1—Winter 2011—Pages 115–138

Selection in Insurance Markets: Theory and Empirics in Pictures

Liran Einav and Amy Finkelstein

rromom tthehe llarge-scalearge-scale ssocialocial iinsurancensurance pprogramsrograms ooff SSocialocial SSecurityecurity aandnd MMedi-edi- ccareare ttoo tthehe hheavilyeavily rregulatedegulated pprivaterivate mmarketsarkets fforor ppropertyroperty aandnd ccasualtyasualty F iinsurance,nsurance, ggovernmentovernment iinterventionntervention iinn iinsurancensurance mmarketsarkets iiss uubiquitous.biquitous. TThehe ffundamentalundamental ttheoreticalheoretical rreasoneason fforor ssuchuch iintervention,ntervention, bbasedased oonn cclassiclassic wworkork ffromrom tthehe 11970s,970s, iiss tthehe pproblemroblem ooff aadversedverse sselection.election. BButut ddespiteespite tthehe aagege aandnd iinflnfl uuenceence ooff thethe theory,theory, systematicsystematic empiricalempirical examinationexamination ofof selectionselection inin actualactual insuranceinsurance mmarketsarkets isis a relativelyrelatively recentrecent development.development. Indeed,Indeed, inin awardingawarding thethe 20012001 NobelNobel PPrizerize forfor thethe pioneeringpioneering theoreticaltheoretical workwork onon asymmetricasymmetric informationinformation toto GeorgeGeorge AAkerlof,kerlof, MichaelMichael Spence,Spence, andand JosephJoseph Stiglitz,Stiglitz, thethe NobelNobel committeecommittee notednoted thisthis ppaucityaucity ofof empiricalempirical workwork (Nobelprize.org,(Nobelprize.org, 2001).2001). OOverver tthehe llastast ddecade,ecade, hhowever,owever, eempiricalmpirical wworkork oonn sselectionelection iinn iinsurancensurance mmarketsarkets hhasas ggainedained cconsiderableonsiderable mmomentum,omentum, aandnd a ffairlyairly eextensivextensive ((andand sstilltill ggrowing)rowing) eempiricalmpirical lliteratureiterature oonn tthehe ttopicopic hhasas eemerged.merged. TThishis rresearchesearch hhasas ffoundound tthathat aadversedverse sselectionelection eexistsxists iinn ssomeome iinsurancensurance mmarketsarkets bbutut nnotot iinn oothers.thers. IItt hhasas aalsolso uuncoveredncovered eexamplesxamples ooff mmarketsarkets tthathat eexhibitxhibit ““advantageousadvantageous sselection”—aelection”—a pphenomenonhenomenon nnotot cconsideredonsidered bbyy tthehe ooriginalriginal ttheory,heory, aandnd oonene tthathat hhasas ddifferentifferent cconsequencesonsequences fforor eequilibriumquilibrium iinsurancensurance aallocationllocation aandnd ooptimalptimal ppublicublic ppolicyolicy tthanhan tthehe cclassicallassical ccasease ooff aadversedverse sselection.election. RResearchersesearchers hhaveave aalsolso ttakenaken sstepsteps ttowardoward eestimatingstimating tthehe wwelfareelfare cconsequencesonsequences ooff ddetectedetected sselectionelection aandnd ooff ppotentialotential ppublicublic ppolicyolicy iinterventions.nterventions.

■ LLiraniran EinavEinav isis AAssociatessociate ProfessorProfessor ofof Economics,Economics, StanfordStanford University,University, Stanford,Stanford, California.California. AAmymy FinkelsteinFinkelstein isis ProfessorProfessor ofof Economics,Economics, MassachusettsMassachusetts InstituteInstitute ofof Technology,Technology, Cambridge,Cambridge, MMassachusetts.assachusetts. BothBoth authorsauthors areare alsoalso ResearchResearch Associates,Associates, NationalNational BureauBureau ofof EconomicEconomic RResearch,esearch, CCambridge,ambridge, Massachusetts.Massachusetts. TheirTheir e-maile-mail addressesaddresses areare 〈[email protected]@stanford.edu〉 aandnd 〈aafifi [email protected]@mit.edu〉. doi=10.1257/jep.25.1.115 116 Journal of Economic Perspectives

IInn thisthis essay,essay, wewe presentpresent a graphicalgraphical frameworkframework forfor analyzinganalyzing bothboth theoreticaltheoretical aandnd eempiricalmpirical wworkork oonn selectionselection inin insuranceinsurance markets.markets. ThisThis graphicalgraphical approach,approach, wwhichhich drawsdraws heavilyheavily onon a paperpaper wewe wrotewrote withwith MarkMark CullenCullen (Einav,(Einav, Finkelstein,Finkelstein, andand CCullen,ullen, 2010),2010), providesprovides bothboth a usefuluseful andand intuitiveintuitive depictiondepiction ofof thethe basicbasic theorytheory ofof sselectionelection andand itsits implicationsimplications forfor welfarewelfare andand publicpublic policy,policy, asas wellwell asas a lenslens throughthrough wwhichhich oneone cancan understandunderstand thethe ideasideas andand limitationslimitations ofof existingexisting empiricalempirical workwork onon tthishis ttopic.opic. WWee bbeginegin byby usingusing thisthis frameworkframework toto reviewreview thethe “textbook”“textbook” adverseadverse selectionselection eenvironmentnvironment andand iitsts iimplicationsmplications fforor iinsurancensurance aallocation,llocation, ssocialocial wwelfare,elfare, aandnd ppublicublic ppolicy.olicy. WWee tthenhen discussdiscuss severalseveral importantimportant extensionsextensions toto thisthis classicclassic treatmenttreatment thatthat areare nnecessitatedecessitated byby iimportantmportant rreal-worldeal-world featuresfeatures ofof iinsurancensurance marketsmarkets aandnd wwhichhich ccanan bbee easilyeasily incorporatedincorporated inin thethe basicbasic framework.framework. Finally,Finally, wewe useuse thethe samesame graphicalgraphical aapproachpproach toto ddiscussiscuss tthehe iintuitionntuition bbehindehind rrecentlyecently ddevelopedeveloped eempiricalmpirical mmethodsethods fforor ttestingesting forfor thethe existenceexistence ofof selectionselection andand examiningexamining itsits welfarewelfare consequences.consequences. WWee concludeconclude byby discussingdiscussing somesome importantimportant issuesissues thatthat areare notnot well-handledwell-handled byby thisthis fframeworkramework andand which,which, perhapsperhaps relatedly,relatedly, havehave beenbeen littlelittle addressedaddressed byby thethe existingexisting eempiricalmpirical work;work; wewe considerconsider thesethese fruitfulfruitful areasareas forfor additionaladditional research.research. OurOur essayessay ddoesoes nnotot aaimim aatt rreviewingeviewing tthehe bburgeoningurgeoning eempiricalmpirical lliteratureiterature oonn sselectionelection iinn iinsur-nsur- aancence markets.markets. However,However, atat relevantrelevant pointspoints inin ourour discussiondiscussion wewe pointpoint thethe interestedinterested rreadereader ttoo rrecentecent ppapersapers tthathat rrevieweview oorr ssummarizeummarize rrecentecent fi ndings.ndings.

AAdversedverse aandnd AAdvantageousdvantageous SSelection:election: A GraphicalGraphical FFrameworkramework

TThehe TTextbookextbook EEnvironmentnvironment fforor IInsurancensurance MMarketsarkets WWee sstarttart byby consideringconsidering thethe textbooktextbook casecase ofof insuranceinsurance demanddemand andand cost,cost, inin wwhichhich perfectlyperfectly competitive,competitive, risk-neutralrisk-neutral fi rrmsms offeroffer a singlesingle insuranceinsurance contractcontract tthathat coverscovers somesome probabilisticprobabilistic loss;loss; risk-averserisk-averse individualsindividuals differdiffer onlyonly inin theirtheir ((privately-known)privately-known) probabilityprobability ofof incurringincurring thatthat loss;loss; andand therethere areare nono otherother fric-fric- ttionsions inin providingproviding insurance,insurance, suchsuch asas administrativeadministrative oror claim-processingclaim-processing costs.costs. TThus,hus, moremore inin thethe spiritspirit ofof AkerlofAkerlof (1970)(1970) andand unlikeunlike thethe well-knownwell-known environmentenvironment ooff RothschildRothschild andand StiglitzStiglitz (1976),(1976), fi rrmsms competecompete inin pricesprices butbut dodo notnot competecompete oonn thethe coveragecoverage featuresfeatures ofof thethe insuranceinsurance contract.contract. WeWe returnreturn toto thisthis importantimportant ssimplifyingimplifying assumptionassumption laterlater inin thisthis essay.essay. FFigureigure 1 pprovidesrovides a ggraphicalraphical rrepresentationepresentation ooff tthishis ccasease aandnd iillustratesllustrates tthehe rresultingesulting aadversedverse sselectionelection aass wwellell aass iitsts cconsequencesonsequences fforor iinsurancensurance ccoverageoverage aandnd wwelfare.elfare. TThehe fi ggureure cconsidersonsiders tthehe mmarketarket fforor a sspecifipecifi c insuranceinsurance ccontract.ontract. CConsumersonsumers iinn tthishis mmarketarket mmakeake a bbinaryinary cchoicehoice ooff wwhetherhether oorr nnotot ttoo ppurchaseurchase tthishis ccontract,ontract, aandnd fi rrmsms iinn tthishis mmarketarket ccompeteompete oonlynly ooverver wwhathat ppricerice ttoo cchargeharge fforor tthehe ccontract.ontract. TThehe verticalvertical axisaxis indicatesindicates thethe priceprice (and(and expectedexpected cost)cost) ofof thatthat contract,contract, andand tthehe hhorizontalorizontal axisaxis indicatesindicates thethe quantityquantity ofof insuranceinsurance demand.demand. SinceSince individualsindividuals ffaceace a binarybinary choicechoice ofof whetherwhether oror notnot toto purchasepurchase thethe contract,contract, thethe “quantity”“quantity” ooff iinsurancensurance isis thethe fractionfraction ofof insuredinsured individuals.individuals. WithWith risk-neutralrisk-neutral insuranceinsurance pprovidersroviders andand nono additionaladditional frictions,frictions, thethe socialsocial (and(and fi rms’)rms’) costscosts associatedassociated withwith Liran Einav and Amy Finkelstein 117

Figure 1 Adverse Selection in the Textbook Setting

B

Demand curve

A Price AC curve

C Peqm J G MC curve E D F

Q eqm Q max Quantity

pprovidingroviding insuranceinsurance areare thethe expectedexpected insuranceinsurance claims—thatclaims—that is,is, thethe expectedexpected ppayoutsayouts oonn ppolicies.olicies. FFigureigure 1 showsshows thethe marketmarket demanddemand curvecurve forfor thethe insuranceinsurance contract.contract. BecauseBecause iindividualsndividuals inin thisthis settingsetting cancan onlyonly choosechoose thethe contractcontract oror not,not, thethe marketmarket demanddemand ccurveurve ssimplyimply rreflefl ectsects thethe cumulativecumulative distributiondistribution ofof individuals’individuals’ willingnesswillingness toto paypay fforor thethe contract.contract. WhileWhile thisthis isis a standardstandard unitunit demanddemand modelmodel thatthat couldcould applyapply toto mmanyany ttraditionalraditional productproduct markets,markets, thethe textbooktextbook insuranceinsurance contextcontext allowsallows usus toto linklink wwillingnessillingness toto paypay toto cost.cost. InIn particular,particular, a risk-averserisk-averse individual’sindividual’s willingnesswillingness toto paypay fforor iinsurancensurance iiss tthehe ssumum ooff tthehe eexpectedxpected ccostost aandnd rriskisk ppremiumremium fforor tthathat iindividual.ndividual. IInn tthehe ttextbookextbook eenvironment,nvironment, iindividualsndividuals aarere hhomogeneousomogeneous iinn ttheirheir rriskisk aaver-ver- ssionion (and(and allall otherother featuresfeatures ofof theirtheir utilityutility function).function). Therefore,Therefore, theirtheir willingnesswillingness toto ppayay forfor insuranceinsurance isis increasingincreasing inin theirtheir riskrisk type—thattype—that is,is, theirtheir probabilityprobability ofof loss,loss, oror eexpectedxpected cost—whichcost—which isis privatelyprivately known.known. ThisThis isis illustratedillustrated inin FigureFigure 1 byby plottingplotting tthehe marginalmarginal costcost (MC)(MC) curvecurve asas downwarddownward sloping:sloping: thosethose individualsindividuals whowho areare willingwilling ttoo paypay thethe mostmost forfor coveragecoverage areare thosethose thatthat havehave thethe highesthighest expectedexpected cost.cost. ThisThis ddownward-slopingownward-sloping MMCC curvecurve representsrepresents thethe well-knownwell-known adverseadverse selectionselection propertyproperty ofof iinsurancensurance mmarkets:arkets: tthehe iindividualsndividuals wwhoho hhaveave tthehe hhighestighest wwillingnessillingness ttoo ppayay fforor insur-insur- aancence aarere tthosehose wwhoho aarere eexpectedxpected ttoo bbee tthehe mmostost ccostlyostly fforor tthehe fi rrmm ttoo ccover.over. TThehe linklink betweenbetween thethe demanddemand andand ccostost ccurveurve iiss aarguablyrguably tthehe mmostost iimportantmportant ddistinctionistinction ooff iinsurancensurance mmarketsarkets ((oror sselectionelection mmarketsarkets mmoreore ggenerally)enerally) ffromrom ttraditionalraditional 118 Journal of Economic Perspectives

pproductroduct mmarkets.arkets. TThehe sshapehape ooff tthehe ccostost ccurveurve iiss ddrivenriven bbyy tthehe ddemand-sideemand-side ccustomerustomer sselection.election. IInn mmostost ootherther ccontexts,ontexts, tthehe ddemandemand ccurveurve aandnd ccostost ccurveurve aarere iindependentndependent oobjects;bjects; ddemandemand iiss ddeterminedetermined bbyy ppreferencesreferences aandnd ccostsosts bbyy tthehe pproductionroduction ttechnology.echnology. TThehe ddistinguishingistinguishing ffeatureeature ooff sselectionelection mmarketsarkets iiss tthathat tthehe ddemandemand aandnd ccostost curvescurves aarere tightlytightly linked,linked, becausebecause thethe individual’sindividual’s riskrisk typetype notnot onlyonly affectsaffects demanddemand butbut alsoalso ddirectlyirectly ddeterminesetermines ccost.ost. TThehe riskrisk premiumpremium iiss sshownhown ggraphicallyraphically inin thethe fi guregure asas thethe verticalvertical distancedistance bbetweenetween expectedexpected costcost (the(the MCMC curve)curve) andand thethe willingnesswillingness toto paypay forfor insuranceinsurance ((thethe ddemandemand ccurve).urve). IInn tthehe ttextbookextbook ccase,ase, tthehe rriskisk ppremiumremium iiss aalwayslways ppositive,ositive, ssinceince aallll iindividualsndividuals areare riskrisk averseaverse andand therethere areare nono otherother marketmarket frictions.frictions. AsAs a result,result, tthehe demanddemand curvecurve isis alwaysalways aboveabove thethe MCMC curve,curve, andand itit isis thereforetherefore effieffi cientcient forfor allall iindividualsndividuals toto bebe iinsurednsured (Q eeffff = Q mmaxax)).. AAbsentbsent iincomencome eeffects,ffects, tthehe wwelfareelfare llossoss ffromrom nnotot iinsuringnsuring a ggiveniven iindividualndividual iiss tthehe rriskisk ppremiumremium ooff tthathat iindividual,ndividual, oorr tthehe vverticalertical ddifferenceifference bbetweenetween tthehe ddemandemand aandnd MMCC ccurves.urves. WWhenhen tthehe iindividual-specifindividual-specifi c lossloss probabilityprobability (or(or expectedexpected cost)cost) isis privateprivate infor-infor- mmationation ttoo tthehe iindividual,ndividual, fi rmsrms mustmust offeroffer a singlesingle priceprice forfor poolspools ofof observationallyobservationally iidenticaldentical bbutut iinn ffactact hheterogeneouseterogeneous individuals.individuals. OfOf course,course, inin practicepractice fi rmsrms maymay vvaryary thethe priceprice basedbased onon somesome observableobservable individualindividual characteristicscharacteristics (such(such asas ageage oror zzipip code).code). Thus,Thus, FigureFigure 1 cancan bebe thoughtthought ofof asas depictingdepicting thethe marketmarket forfor coveragecoverage aamongmong iindividualsndividuals wwhoho aarere ttreatedreated iidenticallydentically bbyy tthehe fi rm.rm. TThehe competitivecompetitive equilibriumequilibrium priceprice willwill bebe equalequal toto thethe fi rms’rms’ averageaverage costcost atat tthathat price.price. ThisThis isis a zero-profizero-profi t condition;condition; offeringoffering a lowerlower priceprice willwill resultresult inin nega-nega- ttiveive profiprofi ts,ts, andand offeringoffering higherhigher pricesprices thanthan competitorscompetitors willwill notnot attractattract anyany buyers.buyers. TThehe relevantrelevant costcost curvecurve thethe fi rmrm facesfaces isis thereforetherefore thethe averageaverage costcost (AC)(AC) curve,curve, wwhichhich iiss aalsolso sshownhown iinn FFigureigure 11.. TThehe ((competitive)competitive) eequilibriumquilibrium ppricerice aandnd qquantityuantity iiss ggiveniven bbyy tthehe iintersectionntersection ooff tthehe ddemandemand ccurveurve aandnd tthehe AACC ccurveurve ((pointpoint C )).. TThehe ffundamentalundamental iineffineffi ciencyciency createdcreated byby adverseadverse selectionselection arisesarises becausebecause tthehe eeffiffi cientcient allocationallocation isis determineddetermined byby thethe relationshiprelationship betweenbetween marginal ccostost aandnd ddemand,emand, bbutut tthehe eequilibriumquilibrium allocationallocation isis determineddetermined byby thethe relationshiprelationship bbetweenetween average ccostost aandnd ddemand.emand. BBecauseecause ooff aadversedverse sselectionelection ((downwarddownward sslopingloping MMCC ccurve),urve), tthehe mmarginalarginal bbuyeruyer isis alwaysalways associatedassociated withwith a lowerlower expectedexpected costcost thanthan tthathat ooff iinfra-marginalnfra-marginal buyers.buyers. Therefore,Therefore, asas drawndrawn inin FigureFigure 1,1, thethe ACAC curvecurve alwaysalways lliesies aboveabove thethe MCMC curvecurve andand intersectsintersects thethe demanddemand curvecurve atat a quantityquantity lowerlower thanthan

Q mmaxax. AsAs a rresult,esult, thethe equilibriumequilibrium quantityquantity ofof insuranceinsurance willwill bebe lessless thanthan thethe effieffi cientcient qquantityuantity (Q mmaxax) aandnd thethe equilibriumequilibrium priceprice (Peeqmqm) wwillill bebe aboveabove thethe effieffi ccientient price,price, iillustratingllustrating thethe classicalclassical resultresult ofof under-insuranceunder-insurance inin thethe presencepresence ofof adverseadverse selec-selec- ttionion ((Akerlof,Akerlof, 11970;970; RothschildRothschild andand Stiglitz,Stiglitz, 1976).1976). ThatThat is,is, itit isis effieffi cientcient toto insureinsure eeveryvery iindividualndividual (MC(MC isis aalwayslways belowbelow demand)demand) butbut inin equilibriumequilibrium thethe Q mmaxax – Q eeqmqm iindividualsndividuals whowho havehave thethe lowestlowest expectedexpected costscosts remainremain uninsureduninsured becausebecause thethe AACC ccurveurve isis nnotot alwaysalways belowbelow thethe demanddemand curve.curve. TheseThese individualsindividuals valuevalue thethe insur-insur- aancence atat moremore thanthan theirtheir expectedexpected costs,costs, butbut fi rmsrms cannotcannot insureinsure thesethese individualsindividuals aandnd sstilltill bbreakreak eeven.ven. TThehe wwelfareelfare costcost ofof thisthis under-insuranceunder-insurance dependsdepends onon thethe lostlost surplussurplus (the(the rriskisk premium)premium) ofof thosethose individualsindividuals whowho remainremain ineffiineffi cientlyciently uninsureduninsured inin thethe Selection in Insurance Markets: Theory and Empirics in Pictures 119

Figure 2 Specifi c Examples of Extreme Cases

A: Adverse Selection with No Efficiency Cost

Demand curve

AC curve Price

Peqm C MC curve

Q max Quantity

(continued on next page)

ccompetitiveompetitive eequilibrium.quilibrium. IInn FFigureigure 11,, tthesehese aarere tthehe iindividualsndividuals wwhosehose wwillingnessillingness ttoo ppayay isis lessless thanthan thethe equilibriumequilibrium price,price, Peeqmqm. IIntegratingntegrating overover allall thesethese individuals’individuals’ rriskisk ppremia,remia, tthehe wwelfareelfare llossoss ffromrom aadversedverse sselectionelection iinn tthishis ssimpleimple fframeworkramework iiss ggiveniven bbyy tthehe aarearea ooff tthehe ddeadweighteadweight llossoss ttrapezoidrapezoid DCEF . EEvenven inin thethe textbooktextbook environment,environment, thethe amountamount ofof under-insuranceunder-insurance generatedgenerated bbyy aadversedverse selection,selection, andand itsits associatedassociated welfarewelfare loss,loss, cancan varyvary greatly.greatly. FigureFigure 2 illus-illus- ttratesrates tthishis ppointoint bbyy ddepictingepicting ttwowo sspecifipecifi c examplesexamples ofof thethe textbooktextbook adverseadverse selectionselection eenvironment,nvironment, oneone thatthat producesproduces thethe effieffi cientcient insuranceinsurance allocationallocation andand oneone thatthat pproducesroduces completecomplete unravelingunraveling ofof insuranceinsurance coverage.coverage. TheThe effieffi cientcient outcomeoutcome isis ddepictedepicted inin panelpanel A.A. WhileWhile thethe marketmarket isis adverselyadversely selectedselected (that(that is,is, thethe MCMC curvecurve iiss downwarddownward sloping),sloping), thethe ACAC curvecurve alwaysalways lieslies belowbelow thethe demanddemand curve.curve. ThisThis leadsleads ttoo aann eequilibriumquilibrium ppricerice Peeqmqm , that,that, althoughalthough itit isis higherhigher thanthan marginalmarginal cost,cost, stillstill pproducesroduces thethe effieffi cientcient allocationallocation (Q eeqmqm = Q eeffff = Q mmaxax)).. TThishis ssituationituation ccanan aarise,rise, fforor eexample,xample, whenwhen individualsindividuals dodo notnot varyvary tootoo muchmuch inin theirtheir unobservedunobserved riskrisk (that(that is,is, tthehe MCMC andand consequentlyconsequently ACAC curvecurve isis relativelyrelatively fl aat)t) aand/ornd/or individuals’individuals’ riskrisk aver-aver- ssionion iiss hhighigh ((thatthat iis,s, tthehe ddemandemand ccurveurve lliesies wwellell aabovebove tthehe MMCC ccurve).urve). 120 Journal of Economic Perspectives

Figure 2 (continued)

B: Adverse Selection with Complete Unraveling

AC curve

Demand curve Price

MC curve

Q max Quantity

TThehe casecase ofof ccompleteomplete uunravelingnraveling isis iillustratedllustrated inin panelpanel B ofof FigureFigure 2.2. HHere,ere, tthehe AACC curvecurve alwaysalways lieslies aboveabove thethe demanddemand curvecurve eveneven thoughthough thethe MCMC curvecurve isis alwaysalways bbelowelow it.it.1 AsAs a result,result, thethe competitivecompetitive equilibriumequilibrium isis thatthat nono individualindividual inin thethe marketmarket iiss iinsured,nsured, whilewhile tthehe eeffiffi cientcient outcomeoutcome isis forfor everyoneeveryone toto havehave insurance.insurance. OneOne couldcould aalsolso useuse panelpanel B toto illustrateillustrate thethe potentialpotential deathdeath spiralspiral dynamicsdynamics thatthat maymay leadlead toto ssuchuch uunraveling.nraveling. ForFor example,example, iiff iinsurancensurance ppricingricing iiss nnaivelyaively ssetet bbutut ddynamicallyynamically aadjusteddjusted toto reflrefl ectect thethe averageaverage costcost fromfrom thethe previousprevious periodperiod (which(which is,is, inin fact,fact, a ffairlyairly commoncommon practicepractice inin manymany healthhealth insuranceinsurance settings),settings), thethe marketmarket willwill gradu-gradu- aallylly sshrinkhrink uuntilntil itit ccompletelyompletely disappears.disappears. ThisThis convergentconvergent adjustmentadjustment processprocess isis iillustratedllustrated byby thethe arrowsarrows inin panelpanel B.B. CutlerCutler andand ReberReber (1998)(1998) provideprovide anan empiricalempirical ccasease studystudy ofof a ddeatheath spiralspiral ofof thisthis naturenature inin thethe contextcontext ofof a healthhealth insuranceinsurance planplan oofferedffered ttoo HHarvardarvard UniversityUniversity employees.employees.

PPublicublic PPolicyolicy iinn tthehe TTextbookextbook CCasease OOurur graphicalgraphical frameworkframework cancan alsoalso bbee uusedsed ttoo iillustratellustrate tthehe cconsequencesonsequences ofof ccommonommon ppublicublic ppolicyolicy iinterventionsnterventions iinn iinsurancensurance markets.markets. TThehe ccanonicalanonical solutionsolution ttoo tthehe iineffineffi ciencyciency createdcreated byby adverseadverse selectionselection isis toto mandatemandate thatthat everyoneeveryone purchasepurchase iinsurance.nsurance. InIn thethe textbooktextbook setting,setting, thisthis producesproduces thethe effieffi cientcient outcomeoutcome inin whichwhich eeveryoneveryone hashas insurance.insurance. However,However, thethe magnitudemagnitude ofof thethe welfarewelfare benefibenefi t producedproduced

1 This can happen even within the textbook example if the individuals with the greatest risk are certain to incur a loss, so their risk premium is zero and their willingness to pay is the same as their expected costs. Liran Einav and Amy Finkelstein 121

bbyy aann iinsurancensurance purchasepurchase requirementrequirement cancan varyvary dramaticallydramatically dependingdepending onon thethe sspecifipecifi cscs ofof thethe market.market. TheThe twotwo extremeextreme examplesexamples presentedpresented inin FigureFigure 2 illustrateillustrate tthishis point,point, butbut eveneven inin intermediateintermediate casescases capturedcaptured byby FigureFigure 1,1, thethe magnitudemagnitude ofof tthehe wwelfareelfare llossoss ((areaarea CDEF ) iiss hhighlyighly sensitivesensitive toto thethe shapeshape andand locationlocation ofof thethe costcost aandnd ddemandemand ccurvesurves aandnd iiss tthereforeherefore uultimatelyltimately aann eempiricalmpirical qquestion.uestion.2 AAnothernother commonlycommonly discusseddiscussed policypolicy remedyremedy forfor adverseadverse selectionselection isis toto subsi-subsi- ddizeize insuranceinsurance coverage.coverage. WeWe cancan useuse FigureFigure 1 toto illustrate.illustrate. Consider,Consider, forfor example,example, a lumplump sumsum subsidysubsidy towardtoward thethe priceprice ofof coverage.coverage. ThisThis wouldwould shiftshift demanddemand out,out, lleadingeading toto a hhigherigher eequilibriumquilibrium qquantityuantity andand llessess uunder-insurance.nder-insurance. TheThe welfarewelfare lossloss wwouldould stillstill bebe associatedassociated withwith thethe areaarea betweenbetween thethe originaloriginal (pre-subsidy)(pre-subsidy) demanddemand ccurveurve aandnd tthehe MMCC ccurve,urve, aandnd wwouldould tthereforeherefore uunambiguouslynambiguously ddeclineecline wwithith aanyny pposi-osi- ttiveive ssubsidy.ubsidy. A llargearge eenoughnough ssubsidyubsidy (greater(greater thanthan thethe lineline segmentsegment GE iinn FigureFigure 1)1) wwouldould lleadead ttoo tthehe eeffiffi cientcient outcome,outcome, withwith everybodyeverybody insured.insured. A fi nnalal ccommonommon fformorm ooff ppublicublic ppolicyolicy iinterventionntervention iiss regulationregulation thatthat imposesimposes rrestrictionsestrictions onon tthehe ccharacteristicsharacteristics ooff cconsumersonsumers ooverver wwhichhich fi rmsrms cancan priceprice discrimi-discrimi- nnate.ate. SomeSome rregulationsegulations requirerequire “community“community rates”rates” thatthat areare uniformuniform acrossacross allall iindividuals,ndividuals, whilewhile oothersthers pprohibitrohibit iinsurancensurance companiescompanies ffromrom mmakingaking ppricesrices ccontin-ontin- ggentent oonn certaincertain observableobservable riskrisk factors,factors, suchsuch asas racerace oror gender.gender. ForFor concreteness,concreteness, cconsideronsider thethe casecase ofof a regulationregulation thatthat prohibitsprohibits pricingpricing onon thethe basisbasis ofof gender.gender. RecallRecall tthathat FigureFigure 1 cancan bebe interpretedinterpreted asas applyingapplying toto a groupgroup ofof individualsindividuals whowho mustmust bbee treatedtreated thethe samesame byby thethe insuranceinsurance company.company. WhenWhen pricingpricing basedbased onon gendergender isis pprohibited,rohibited, malesmales andand femalesfemales aarere ppooledooled intointo thethe samesame mmarket,arket, wwithith a vvariantariant ooff FFigureigure 1 ddescribingescribing thatthat mmarket.arket. WWhenhen ppricingricing oonn ggenderender iiss aallowed,llowed, ttherehere aarere nnowow ttwowo ddistinctistinct iinsurancensurance mmarkets—describedarkets—described bbyy ttwowo ddistinctistinct vvariantsariants ooff FFigureigure 11—one—one fforor wwomenomen aandnd oonene fforor mmen,en, eeachach ooff wwhichhich ccanan bbee analyzedanalyzed separately.separately. A ccentralentral iissuessue forfor wwelfareelfare analysisanalysis isis whether,whether, wwhenhen iinsurancensurance companiescompanies areare allowedallowed toto priceprice oonn gender,gender, consumersconsumers stillstill havehave residualresidual privateprivate informationinformation aboutabout theirtheir expectedexpected ccosts.osts. IIff ttheyhey ddoo nnot,ot, tthenhen tthehe iinsurancensurance mmarketarket wwithinithin eeachach ggender-specifiender-specifi c segmentsegment ooff thethe marketmarket willwill exhibitexhibit a constantconstant (fl(fl at)at) MCMC curvecurve andand thethe equilibriumequilibrium inin eacheach mmarketarket willwill bebe effieffi cient.cient. InIn thisthis case,case, policiespolicies thatthat restrictrestrict pricingpricing onon gendergender areare uunambiguouslynambiguously wwelfareelfare decreasingdecreasing sincesince theythey ccreatereate aadversedverse sselectionelection wwherehere nnoneone eexistedxisted before.before. However,However, inin thethe moremore likelylikely casecase thatthat individualsindividuals havehave somesome rresidualesidual privateprivate informationinformation aboutabout theirtheir riskrisk thatthat isis notnot capturedcaptured byby theirtheir gender,gender, eeachach ggender-specifiender-specifi c marketmarket segmentsegment wouldwould looklook qualitativelyqualitatively thethe samesame asas FigureFigure 1 ((withwith downwarddownward slopingsloping MCMC andand ACAC curves).curves). InIn suchsuch cases,cases, thethe welfarewelfare implica-implica- ttionsions ofof restrictingrestricting pricingpricing onon gendergender couldcould gogo inin eithereither direction;direction; dependingdepending onon tthehe sshapehape aandnd ppositionosition ooff tthehe ggender-specifiender-specifi c demanddemand andand costcost curvescurves relativerelative toto tthehe gender-pooledgender-pooled ones,ones, thethe sumsum ooff tthehe aareasreas ooff tthehe ddeadweighteadweight lossloss trapezoidstrapezoids inin

2 Although in the specifi c examples in Figure 2, the welfare cost of adverse selection is increasing with the amount of under-insurance it creates, this does not have to be the case in general. 122 Journal of Economic Perspectives

tthehe ggender-specifiender-specifi c marketsmarkets couldcould bebe largerlarger oror smallersmaller thanthan thethe areaarea ofof thethe singlesingle ddeadweighteadweight llossoss ttrapezoidrapezoid inin thethe gender-pooledgender-pooled market.market.3

DDeparturesepartures ffromrom tthehe TTextbookextbook EEnvironmentnvironment AAlthoughlthough thethe ttextbookextbook ttreatmentreatment ooff iinsurancensurance mmarketsarkets mmayay ggiveive rriseise ttoo ddramat-ramat- iicallycally ddifferentifferent magnitudesmagnitudes ofof thethe welfarewelfare costscosts arisingarising fromfrom aadversedverse selection,selection, thethe qqualitativeualitative fi ndingsndings areare robust.robust. UnderUnder thethe textbooktextbook assumptions,assumptions, privateprivate informa-informa- ttionion aaboutbout rriskisk nneverever producesproduces over-insuranceover-insurance relativerelative toto thethe effieffi cientcient outcome,outcome, aandnd mandatorymandatory insuranceinsurance coveragecoverage isis alwaysalways a (weakly)(weakly) welfare-improvingwelfare-improving policypolicy iintervention.ntervention. However,However, thesethese robustrobust qualitativequalitative resultsresults onlyonly holdhold inin thisthis textbooktextbook ccase.ase. TTheyhey mmayay bbee rreversedeversed wwithith tthehe iintroductionntroduction ooff ttwowo iimportantmportant ffeatureseatures ooff aactualctual iinsurancensurance markets:markets: 11)) iinsurancensurance ““loads”loads” oorr aadministrativedministrative ccostsosts ooff pprovidingroviding iinsur-nsur- aance,nce, aandnd 22)) ppreferencereference hheterogeneity.eterogeneity. CConsideronsider fi rstrst a loadingloading factorfactor onon insurance,insurance, forfor exampleexample inin thethe formform ofof addi-addi- ttionalional administrativeadministrative costcost associatedassociated withwith sellingselling andand servicingservicing insurance,insurance, perhapsperhaps ddueue toto costscosts associatedassociated withwith advertisingadvertising andand marketing,marketing, oror withwith verifyingverifying andand pprocessingrocessing claims.claims. ManyMany iinsurancensurance marketsmarkets ddisplayisplay eevidencevidence ofof nontrivialnontrivial loadingloading ffactors,actors, includingincluding marketsmarkets forfor long-termlong-term carecare insuranceinsurance (Brown(Brown andand Finkelstein,Finkelstein, 22007),007), annuitiesannuities (Friedman(Friedman andand Warshawsky,Warshawsky, 1990;1990; Mitchell,Mitchell, Poterba,Poterba, Warshawsky,Warshawsky, aandnd BBrown,rown, 1999;1999; FFinkelsteininkelstein aandnd PPoterba,oterba, 22002),002), hhealthealth iinsurancensurance (Newhouse,(Newhouse, 22002),002), aandnd aautomobileutomobile iinsurancensurance ((Chiappori,Chiappori, JJullien,ullien, SSalanié,alanié, aandnd SSalanié,alanié, 22006).006).4 TThehe kkeyey implicationimplication ofof suchsuch loadsloads isis thatthat itit iiss nnowow nnotot nnecessarilyecessarily effieffi cientcient toto aallocatellocate insuranceinsurance coveragecoverage toto allall individuals.individuals. EvenEven ifif allall individualsindividuals areare riskrisk averse,averse, tthehe additionaladditional costcost ofof providingproviding anan individualindividual withwith insuranceinsurance maymay bebe greatergreater thanthan tthehe rriskisk ppremiumremium fforor ccertainertain iindividuals,ndividuals, mmakingaking iitt ssociallyocially eeffiffi cientcient toto leaveleave suchsuch iindividualsndividuals uninsured.uninsured. ThisThis ccasease iiss iillustratedllustrated iinn FFigureigure 33,, wwhichhich iiss ssimilarimilar ttoo FFigureigure 11,, eexceptxcept thatthat tthehe ccostost ccurvesurves aarere sshiftedhifted uupwardpward rreflefl ectingecting thethe additionaladditional costcost ofof insur-insur- aancence pprovision.rovision.5 FFigureigure 3 isis ddrawnrawn inin a wayway thatthat thethe MCMC curvecurve crossescrosses thethe demanddemand curvecurve “inter-“inter- nnally”ally” (that(that is,is, atat a quantityquantity lowerlower thanthan Qmmaxax)),, aatt ppointoint E , wwhichhich depictsdepicts thethe sociallysocially eeffiffi ccientient insuranceinsurance allocation.allocation. ItIt isis effieffi cientcient toto insureinsure everyoneeveryone toto thethe leftleft ofof pointpoint E ((becausebecause theirtheir willingnesswillingness toto paypay forfor insuranceinsurance exceedsexceeds theirtheir expectedexpected cost),cost), butbut

3 An example illustrates how pricing on gender can increase deadweight loss. Consider three types of individuals. Type 1 individuals (representing 10 percent of the population) have expected cost of 20 and willingness to pay for insurance of 30. Type 2 individuals (60 percent) have expected cost of 5 and willingness to pay of 20, and type 3 (30 percent) have expected cost of 4 and willingness to pay of 7.5. The competitive (zero-profi t) price in this market is 6.2, leading to an effi cient allocation in which everyone is insured (this case is similar to that of panel A in Figure 2). Suppose now that type 2 individuals are all females and type 1 and 3 individuals are all males, and gender can be priced. In this case, the competitive price for women is 5 and they are all insured. However, the competitive price for men is 8, leaving all type 3 individuals ineffi ciently uninsured. 4 Admittedly, most of these papers lack the data to distinguish between loading factors arising from administrative costs to the insurance company and those arising from market power (insurance company profi ts). Still, it seems a reasonable assumption that it is not costless to run an insurance company. 5 We note that Figure 3 could also describe a market with no frictions, but in which a fraction of the individuals are risk loving. Selection in Insurance Markets: Theory and Empirics in Pictures 123

Figure 3 Adverse Selection with Additional Cost of Providing Insurance

A

Demand curve

B AC curve

C Peqm Price MC curve F D E Peff

G H

Q eqm Q eff Q max Quantity

Source: Einav, Finkelstein, and Cullen (2010), fi gure 1. ssociallyocially ineffiineffi cientcient toto insureinsure anyoneanyone toto thethe rightright ofof pointpoint E ((becausebecause theirtheir willing-willing- nnessess toto paypay isis lessless thanthan theirtheir expectedexpected cost).cost). InIn thisthis situation,situation, itit isis effieffi ccientient toto keepkeep

Q mmaxax – Q eeffff iindividualsndividuals uninsured.uninsured. TThehe introductionintroduction ofof loadsloads doesdoes notnot affectaffect thethe basicbasic analysisanalysis ofof adverseadverse selection,selection, bbutut itit doesdoes havehave importantimportant implicationsimplications forfor itsits standardstandard publicpublic policypolicy remedies.remedies. TThehe competitivecompetitive equilibriumequilibrium isis stillstill determineddetermined byby thethe zerozero profiprofi t condition,condition, oror thethe iintersectionntersection ooff tthehe ddemandemand ccurveurve aandnd tthehe AACC ccurveurve ((pointpoint C iinn FigureFigure 3),3), andand inin tthehe presencepresence ofof adverseadverse selectionselection (and(and thusthus a downwarddownward slopingsloping MCMC curve),curve), thisthis lleadseads ttoo uunder-insurancender-insurance rrelativeelative ttoo tthehe ssocialocial ooptimumptimum (Q eeqmqm < Q eeffff)),, andand toto a ffamiliaramiliar deadweightdeadweight llossoss ttriangleriangle CDE . HHowever,owever, withwith insuranceinsurance loads,loads, thethe textbooktextbook resultresult ofof anan unambiguousunambiguous welfarewelfare ggainain fromfrom mmandatoryandatory ccoverageoverage nnoo llongeronger oobtains.btains. AsAs FigureFigure 3 shows,shows, whilewhile a mandatemandate tthathat everyoneeveryone bebe insuredinsured “regains”“regains” thethe welfarewelfare lossloss associatedassociated withwith under-insuranceunder-insurance ((triangletriangle CDE )),, iitt aalsolso lleadseads ttoo oover-insurancever-insurance byby coveringcovering individualsindividuals whomwhom itit isis ssociallyocially ineffiineffi cientcient toto insureinsure (that(that is,is, whosewhose expectedexpected costscosts areare aboveabove ttheirheir wwillingnessillingness ttoo pay).pay). ThisThis latterlatter effecteffect leadsleads toto a welfarewelfare lossloss givengiven byby thethe areaarea EGH iinn FigureFigure 3.3. TThereforeherefore whetherwhether a mandatemandate improvesimproves welfarewelfare overover thethe competitivecompetitive allocationallocation ddependsepends onon thethe rrelativeelative sizessizes ooff ttrianglesriangles CDE aandnd EGH ; thisthis inin turnturn dependsdepends onon thethe sspecifipecifi c market’smarket’s demanddemand aandnd ccostost ccurvesurves andand isis thereforetherefore anan empiricalempirical question.question. 124 Journal of Economic Perspectives

A secondsecond importantimportant featurefeature ofof real-worldreal-world insuranceinsurance marketsmarkets notnot capturedcaptured byby tthehe textbooktextbook treatmenttreatment isis preferencepreference heterogeneity:heterogeneity: thatthat is,is, thethe possibilitypossibility thatthat iindividualsndividuals maymay differdiffer notnot onlyonly inin theirtheir riskrisk butbut alsoalso inin theirtheir preferences,preferences, suchsuch asas ttheirheir willingnesswillingness toto bearbear riskrisk (risk(risk aaversion).version). TheThe classicalclassical modelsmodels (like(like RothschildRothschild aandnd SStiglitz,tiglitz, 11976)976) mmakeake tthehe ssimplifyingimplifying aandnd ttheoreticallyheoretically aattractivettractive aassumptionssumption tthathat iindividualsndividuals havehave thethe samesame preferencespreferences andand maymay varyvary onlyonly inin theirtheir (privately(privately known)known) eexpectedxpected costs.costs. AsAs a rresult,esult, willingnesswillingness toto paypay forfor insuranceinsurance isis anan increasingincreasing functionfunction ooff eexpectedxpected ccosts.osts. IInn ppractice,ractice, ofof ccourse,ourse, iindividualsndividuals maymay ddifferiffer nnotot oonlynly iinn ttheirheir eexpectedxpected ccostost bbutut aalsolso inin theirtheir preferences.preferences. Indeed,Indeed, recentrecent empiricalempirical workwork hashas documenteddocumented substan-substan- ttialial ppreferencereference hheterogeneityeterogeneity iinn ddifferentifferent iinsurancensurance mmarkets,arkets, iincludingncluding aautomobileutomobile iinsurancensurance (Cohen(Cohen andand Einav,Einav, 2007),2007), reversereverse mortgagesmortgages (Davidoff(Davidoff andand Welke,Welke, 2007),2007), hhealthealth iinsurancensurance ((Fang,Fang, KKeane,eane, aandnd SSilverman,ilverman, 22008),008), aandnd llong-termong-term ccareare iinsur-nsur- aancence (Finkelstein(Finkelstein andand McGarry,McGarry, 2006).2006). TheThe existenceexistence ofof unobservedunobserved preferencepreference hheterogeneityeterogeneity opensopens upup thethe ppossibilityossibility ooff advantageous selection,selection, whichwhich producesproduces ooppositepposite rresultsesults ttoo tthehe adverse sselectionelection rresultsesults jjustust discussed.discussed.6 CConsideronsider forfor eexamplexample hheterogeneityeterogeneity iinn rriskisk aaversionversion iinn aadditionddition ttoo tthehe ooriginalriginal hheterogeneityeterogeneity inin riskrisk ((expectedexpected ccost).ost). AAllll eelselse eequal,qual, wwillingnessillingness ttoo ppayay fforor iinsurancensurance iiss increasingincreasing inin riskrisk aversionaversion andand inin risk.risk. IfIf heterogeneityheterogeneity inin riskrisk aversionaversion isis small,small, oorr iiff tthosehose iindividualsndividuals whowho aarere hhighigh rriskisk aarere aalsolso mmoreore rriskisk aaverse,verse, tthehe mmainain iinsightsnsights ffromrom thethe textbooktextbook analysisanalysis remain.remain. ButBut ifif high-riskhigh-risk individualsindividuals areare lessless riskrisk averseaverse aandnd thethe heterogeneityheterogeneity inin riskrisk aversionaversion isis suffisuffi cientlyciently large,large, advantageousadvantageous selectionselection mmayay emerge.emerge. Namely,Namely, tthehe individualsindividuals whowho areare willingwilling toto paypay thethe mostmost forfor insuranceinsurance aarere thosethose whowho areare thethe mostmost rriskisk aaverse,verse, andand inin thethe casecase described,described, thesethese areare alsoalso tthosehose iindividualsndividuals associatedassociated withwith thethe lowestlowest (rather(rather thanthan tthehe hhighest)ighest) eexpectedxpected ccost.ost. IIndeed,ndeed, itit iiss nnaturalatural ttoo tthinkhink tthathat iinn mmanyany iinstancesnstances iindividualsndividuals wwhoho vvaluealue iinsurancensurance mmoreore mmayay aalsolso ttakeake aactionction ttoo llowerower ttheirheir eexpectedxpected ccosts:osts: ddriverive mmoreore ccarefully,arefully, iinvestnvest iinn ppreventivereventive hhealthealth ccare,are, aandnd soso on.on. FFigureigure 4 pprovidesrovides oourur graphicalgraphical illustrationillustration ooff suchsuch advantageousadvantageous sselectionelection aandnd iitsts cconsequencesonsequences fforor iinsurancensurance ccoverageoverage aandnd wwelfare.elfare. IInn ccontrastontrast ttoo aadversedverse sselection,election, aadvantageousdvantageous sselectionelection iiss ddefiefi nedned byby anan upward slopingsloping MMCC ((andand AAC)C) ccurve.urve.7 AsAs ppricerice iiss lloweredowered aandnd mmoreore iindividualsndividuals ooptpt iintonto tthehe mmarket,arket, tthehe mmarginalarginal iindividualndividual ooptingpting iinn hashas higherhigher expectedexpected ccostost tthanhan iinfra-marginalnfra-marginal iindividuals.ndividuals. SSinceince tthehe MMCC ccurveurve iiss

6 Another important (and more nuanced) aspect of preference heterogeneity is that it complicates the notion of effi ciency. With preference heterogeneity, the mapping from expected cost to willingness to pay need no longer be unique. That is, two individuals with the same expected cost may have different valuations for the same coverage, or two individual with the same willingness to pay for the coverage may have different underlying expected costs. This possibility does not affect our earlier and subsequent analysis, except that one needs to recognize that it requires a weaker sense of effi ciency. Specifi cally, it requires us to think of a constrained effi cient allocation that maximizes welfare subject to a uniform price. In such cases, the (constrained) effi cient allocation need not coincide with the fi rst-best allocation. Bundorf, Levin, and Mahoney (2010) discuss and empirically analyze this issue in more detail. 7 More generally, once we allow for preference heterogeneity, the marginal cost curve needs not be monotone. However, for simplicity and clarity we focus our discussion on the polar cases of monotone cost curves. Liran Einav and Amy Finkelstein 125

Figure 4 Advantageous Selection

A Demand curve

G

Price D MC curve E Peff C F Peqm

H B AC curve

Q eff Q eqm Q max

Quantity

Source: Einav, Finkelstein, and Cullen (2010), fi gure 2. uupwardpward ssloping,loping, tthehe AACC ccurveurve wwillill llieie eeverywhereverywhere bbelowelow iit.t. IIff ttherehere wwereere nnoo iinsurancensurance lloadsoads ((asas iinn tthehe ttextbookextbook ssituation),ituation), aadvantageousdvantageous sselectionelection wwouldould nnotot lleadead ttoo aanyny iineffineffi cciency;iency; tthehe MMCC aandnd AACC ccurvesurves wwouldould aalwayslways llieie bbelowelow tthehe ddemandemand ccurve,urve, aandnd iinn eequilibriumquilibrium aallll iindividualsndividuals iinn tthehe mmarketarket wwouldould bbee ccovered,overed, wwhichhich wwouldould bbee eeffiffi ccient.ient. WWithith iinsurancensurance loads,loads, however,however, advantageousadvantageous selectionselection generatesgenerates thethe mirrormirror iimagemage ooff tthehe aadversedverse sselectionelection ccase,ase, aalsolso lleadingeading ttoo iineffineffi ciency,ciency, butbut thisthis timetime duedue toto oover-insurancever-insurance ratherrather thanthan uunder-insurance.nder-insurance. FFigureigure 4 ddepictsepicts tthishis ccase.ase. TThehe eeffiffi cientcient aallocationllocation callscalls forfor providingproviding insuranceinsurance toto allall individualsindividuals whosewhose expectedexpected costcost isis llowerower thanthan theirtheir willingnesswillingness toto pay—thatpay—that is,is, allall thosethose whowho areare toto thethe leftleft ofof pointpoint E ((wherewhere tthehe MMCC ccurveurve iintersectsntersects tthehe ddemandemand ccurve)urve) iinn FFigureigure 44.. CCompetitiveompetitive eequilib-quilib- rrium,ium, aass bbefore,efore, isis ddeterminedetermined byby thethe intersectionintersection ofof thethe ACAC curvecurve andand thethe demanddemand ccurveurve ((pointpoint C inin FigureFigure 4).4). ButBut sincesince thethe ACAC curvecurve nownow lieslies belowbelow thethe MCMC curve,curve, eequilibriumquilibrium impliesimplies thatthat tootoo manymany individualsindividuals areare providedprovided insurance,insurance, leadingleading toto oover-insurance:ver-insurance: therethere areare Q eeqmqm – Q eeffff iindividualsndividuals whowho areare ineffiineffi cientlyciently providedprovided iinsurancensurance inin eequilibrium.quilibrium. TThesehese individualsindividuals valuevalue thethe iinsurancensurance atat llessess tthanhan ttheirheir eexpectedxpected costs,costs, butbut competitivecompetitive forcesforces makemake fi rmsrms reducereduce thethe price,price, thusthus attractingattracting tthesehese iindividualsndividuals togethertogether withwith moremore profiprofi tabletable infra-marginalinfra-marginal individuals.individuals. Again,Again, tthehe areaarea ofof thethe ddeadweighteadweight lossloss triangletriangle EDC qquantifiuantifi eses thethe extentextent ofof thethe welfarewelfare lossloss ffromrom tthishis oover-insurance.ver-insurance. 126 Journal of Economic Perspectives

FFromrom a ppublicublic ppolicyolicy pperspective,erspective, aadvantageousdvantageous sselectionelection ccallsalls fforor tthehe ooppositepposite ssolutionsolutions relativerelative toto thethe toolstools usedused toto combatcombat adverseadverse selection.selection. ForFor example,example, givengiven tthathat aadvantageousdvantageous sselectionelection pproducesroduces ““tootoo mmuch”uch” iinsurancensurance rrelativeelative ttoo tthehe eeffiffi cientcient ooutcome,utcome, ppublicublic ppoliciesolicies tthathat ttaxax eexistingxisting iinsurancensurance ppoliciesolicies ((andand tthereforeherefore rraiseaise

Peeqmqm ttowardoward Peeffff) oorr ooutlawutlaw insuranceinsurance coveragecoverage (mandate(mandate nono coverage)coverage) couldcould bebe wwelfare-improving.elfare-improving. AlthoughAlthough therethere areare ccertainlyertainly ttaxesaxes lleviedevied oonn iinsurancensurance ppolicies,olicies, ttoo oourur kknowledgenowledge advantageousadvantageous selectionselection hashas notnot yetyet beenbeen invokedinvoked asas a rationalerationale iinn ppublicublic ppolicyolicy ddiscourse,iscourse, pperhapserhaps rreflefl ectingecting thethe relativerelative newnessnewness ofof bothboth thethe theo-theo- rreticaletical workwork andand empiricalempirical evidence.evidence. ToTo ourour knowledge,knowledge, advantageousadvantageous selectionselection waswas fi rstrst discusseddiscussed byby HemenwayHemenway (1990),(1990), whowho termedtermed itit “propitious”“propitious” selection.selection. DeDe MezaMeza aandnd WebbWebb (2001)(2001) provideprovide a theoreticaltheoretical treatmenttreatment ofof advantageousadvantageous selectionselection andand itsits iimplicationsmplications fforor iinsurancensurance ccoverageoverage aandnd ppublicublic ppolicy.olicy. AAdvantageousdvantageous sselectionelection iiss notnot merelymerely a theoreticaltheoretical possibility.possibility. ItIt hashas recentlyrecently bbeeneen ddocumentedocumented iinn sseveraleveral iinsurancensurance mmarkets,arkets, wwithith ddifferentifferent ssourcesources ooff iindividualndividual heterogeneityheterogeneity thatthat givegive riserise toto it.it. FinkelsteinFinkelstein andand McGarryMcGarry (2006)(2006) ddocumentocument advantageousadvantageous selectionselection inin thethe marketmarket forfor long-termlong-term carecare insuranceinsurance andand pproviderovide eevidencevidence tthathat mmoreore ccautiousautious iindividualsndividuals iinvestnvest mmoreore iinn pprecautionaryrecautionary bbehaviorehavior andand areare lessless likelylikely ttoo uusese a nnursingursing hhomeome bbutut aatt tthehe ssameame ttimeime aarere mmoreore llikelyikely toto purchasepurchase long-termlong-term carecare insurance.insurance. Fang,Fang, Keane,Keane, andand SilvermanSilverman (2008)(2008) ddocumentocument advantageousadvantageous sselectionelection iinn tthehe mmarketarket fforor MMedigapedigap ccoverage,overage, wwhichhich pprovidesrovides privateprivate healthhealth insuranceinsurance thatthat supplementssupplements MMedicareedicare fforor thethe elderly,elderly, butbut sshowhow thatthat inin tthehe ccasease ooff MMedigap,edigap, ccognitionognition mmayay bbee tthehe ddrivingriving fforce:orce: iindividualsndividuals wwithith higherhigher cognitivecognitive abilityability areare oftenoften ableable toto makemake betterbetter decisions,decisions, whichwhich cancan ttranslateranslate intointo bbothoth ggreaterreater ccoverageoverage aandnd aatt tthehe ssameame ttimeime llowerower hhealthcareealthcare eexpenditures.xpenditures. AAdvantageousdvantageous selectionselection providesprovides a nicenice exampleexample ofof thethe interplayinterplay inin thethe selec-selec- ttionion literatureliterature betweenbetween theorytheory andand empiricalempirical work.work. TheThe originaloriginal adverseadverse selectionselection ttheoryheory mmotivatedotivated empiricalempirical workwork testingtesting forfor thethe existenceexistence ofof adverseadverse selection.selection. ThisThis eempiricalmpirical wworkork iinn tturnurn pprovidedrovided eexamplesxamples ooff aadvantageousdvantageous sselectionelection ((whichwhich tthehe ooriginalriginal theorytheory hadhad precluded),precluded), suggestingsuggesting thethe needneed forfor importantimportant extensionsextensions toto tthehe theory.theory. WWee nnowow tturnurn ttoo a mmoreore ddetailedetailed ddiscussioniscussion ooff hhowow tthehe eexistingxisting eempiricalmpirical wworkork ccanan bbee vviewediewed tthroughhrough tthehe ggraphicalraphical fframeworkramework wwee hhaveave ddeveloped.eveloped.

EEmpiricalmpirical WorkWork onon SelectionSelection

EEmpiricalmpirical researchresearch onon selectionselection inin insuranceinsurance marketsmarkets hashas fl ourishedourished overover thethe llastast decade.decade. ThisThis empiricalempirical literatureliterature began,began, quitequite naturally,naturally, byby askingasking howhow wewe cancan ttestest forfor whetherwhether thethe classicclassic adverseadverse selectionselection modelsmodels applyapply inin real-worldreal-world insuranceinsurance mmarkets.arkets. InIn otherother words,words, whatwhat wouldwould selectionselection looklook likelike inin thethe data,data, whenwhen oror ifif itit eexists?xists? EmpiricalEmpirical researchresearch hashas nownow progressedprogressed fromfrom tryingtrying toto detectdetect thethe existenceexistence ((andand nnature)ature) ofof sselectionelection towardtoward attemptsattempts ttoo qquantifyuantify iitsts wwelfareelfare cconsequencesonsequences andand tthosehose ofof potentialpotential publicpublic policypolicy interventions.interventions. WeWe cancan useuse ourour graphicalgraphical frameworkframework ttoo uunderstandnderstand tthehe iintuitionntuition aandnd llimitationsimitations ooff tthishis rresearchesearch pprogram.rogram. Selection in Insurance Markets: Theory and Empirics in Pictures 127

Figure 5 The “Positive Correlation” Test for Selection

A

Demand curve

B AC insured curve

C Peqm I MC curve Price D

F E Peff

G H AC uninsured curve

Q eqm Q eff Q max Quantity

““PositivePositive CCorrelation”orrelation” TestsTests forfor AdverseAdverse SelectionSelection UUsingsing ourour ggraphicalraphical fframework,ramework, ttestingesting fforor aadversedverse sselectionelection eessentiallyssentially rrequiresequires uuss ttoo ttestest wwhetherhether thethe MCMC curvecurve isis downwarddownward sloping.sloping. MakingMaking inferencesinferences aboutabout mmarginalarginal iindividualsndividuals iiss ddiffiiffi cult,cult, however.however. AsAs a result,result, thethe earlyearly empiricalempirical approachesapproaches ddevelopedeveloped strategiesstrategies thatthat attemptattempt toto getget aroundaround thisthis diffidiffi cultyculty by,by, instead,instead, focusingfocusing oonn ccomparingomparing aaverages.verages. TThehe graphicalgraphical ddepictionsepictions ooff aadversedverse sselectionelection iinn FFigureigure 1 ((oror FFigureigure 33)) ssuggestuggest oonene wayway toto examineexamine whetherwhether adverseadverse selectionselection isis presentpresent inin a particularparticular insuranceinsurance mmarket:arket: comparecompare thethe expectedexpected costcost ofof thosethose withwith insuranceinsurance toto thethe expectedexpected costcost ooff tthosehose wwithoutithout ((oror ccompareompare tthosehose wwithith mmoreore iinsurancensurance ccoverageoverage ttoo tthosehose wwithith llessess coverage).coverage). TToo seesee tthishis iideadea mmoreore cclearly,learly, cconsideronsider FFigureigure 55.. HHereere wwee sstarttart wwithith tthehe aadversedverse sselectionelection situationsituation alreadyalready depicteddepicted inin FigureFigure 3,3, denotingdenoting thethe ACAC curvecurve shownshown inin ppreviousrevious fi guresgures byby ACAC iinsurednsured toto reflrefl ectect thethe factfact thatthat itit averagesaverages overover thosethose individualsindividuals wwithith insurance,insurance, andand addingadding oneone moremore line:line: thethe ACAC uuninsuredninsured curve.curve. TheThe ACAC uuninsuredninsured ccurveurve rrepresentsepresents thethe averageaverage expectedexpected costcost ofof thosethose individualsindividuals whowho dodo notnot havehave iinsurance.nsurance. ThatThat iis,s, tthehe AACC iinsurednsured ccurveurve isis derivedderived byby averagingaveraging overover thethe expectedexpected costscosts ooff thethe insuredinsured (averaging(averaging “from“from thethe left,”left,” startingstarting atat Q = 0)0) whilewhile thethe ACAC uuninsuredninsured ccurveurve iiss pproducedroduced bbyy aaveragingveraging ooverver tthehe eexpectedxpected ccostsosts ooff tthehe uuninsuredninsured ((averagingaveraging

““fromfrom tthehe rright,”ight,” sstartingtarting aatt Q = Q mmaxax)).. A downward-slopingdownward-sloping MCMC curvecurve impliesimplies thatthat 128 Journal of Economic Perspectives

AACC iinsurednsured iiss aalwayslways aboveabove ACAC uuninsuredninsured , wwithith thethe averageaverage costscosts ofof thethe insuredinsured atat Q mmaxax eequalqual toto tthehe aaverageverage costscosts ofof thethe uninsureduninsured atat Q = 0 ((becausebecause bbothoth rrepresentepresent thethe aaverageverage costscosts ofof thethe fullfull population)population) andand withwith thethe marginalmarginal costcost curvecurve intersectingintersecting

AACC iinsurednsured aatt Q = 0 aandnd AACC uuninsuredninsured aatt Q = Qmmaxax. TThus,hus, aatt aanyny ggiveniven iinsurancensurance pprice,rice, aandnd iinn pparticulararticular aatt tthehe eequilibriumquilibrium pprice,rice, aadversedverse sselectionelection iimpliesmplies tthathat tthehe aaverageverage ccostost ooff iinsurednsured iindividualsndividuals iiss hhigherigher tthanhan tthehe aaverageverage ccostost ooff uuninsured,ninsured, aandnd tthehe ddifferenceifference iinn tthesehese aaveragesverages iiss ggiveniven bbyy llineine ssegmentegment CF iinn FFigureigure 5 ((thethe tthickhick aarrowedrrowed llineine iinn tthehe fi gure).gure). TThishis bbasicasic iinsightnsight uunderliesnderlies tthehe wwidelyidely uusedsed ““positivepositive ccorrelation”orrelation” ttestest fforor aasymmetricsymmetric iinformation.nformation. TThishis ppositiveositive ccorrelationorrelation ((betweenbetween iinsurancensurance ccoverageoverage aandnd eexpectedxpected ccosts)osts) iiss aanalogousnalogous ttoo tthehe ddistanceistance bbetweenetween ppointoint C (average(average ccostsosts ooff tthosehose wwhoho iinn eequilibriumquilibrium aarere iinsured)nsured) aandnd ppointoint F (average(average ccostsosts ooff tthosehose wwhoho iinn eequilibriumquilibrium aarere nnotot iinsured).nsured). TThehe rresultsesults aarere cconsistentonsistent wwithith tthehe eexistencexistence ooff aadversedverse sselectionelection iiff tthehe aaverageverage ccostost ooff tthehe iinsurednsured ((pointpoint C ) iiss sstatisticallytatistically ggreaterreater tthanhan tthosehose ooff tthehe uuninsuredninsured ((pointpoint F ).). TThehe ttestest hhasas ttypicallyypically beenbeen implementedimplemented byby comparingcomparing proxiesproxies forfor expectedexpected ccostsosts acrossacross iindividualsndividuals withwith differentdifferent insuranceinsurance coverage,coverage, controllingcontrolling asas neededneeded fforor iimportantmportant cconfoundingonfounding factorsfactors (as(as wewe discussdiscuss below).below). ManyMany ooff tthesehese eempiricalmpirical ppapersapers useuse datadata fromfrom a singlesingle companycompany andand examineexamine averageaverage claimsclaims acrossacross individ-individ- uualsals wwhoho aarere oofferedffered tthehe ssameame ccontractsontracts bbutut wwhoho cchoosehoose mmoreore oorr llessess ccoverage.overage. OOurur ggraphicalraphical frameworkframework naturallynaturally extendsextends toto thethe choicechoice ofof moremore versusversus lessless coveragecoverage ((asas oopposedpposed toto anyany insuranceinsurance versusversus nono insurance).insurance). Indeed,Indeed, thethe recentrecent burgeoningburgeoning ooff empiricalempirical workwork onon selectionselection likelylikely reflrefl ectsects atat leastleast inin partpart researchers’researchers’ increasingincreasing ssuccessuccess iinn oobtainingbtaining accessaccess toto iinsurancensurance companycompany ddata,ata, wwhichhich hhasas ggreatlyreatly iimprovedmproved ttheirheir aabilitybility ttoo eexaminexamine qquestionsuestions ooff pprivaterivate iinformationnformation eempirically.mpirically. PPerhapserhaps ddueue iinn ppartart ttoo iitsts nnot-so-demandingot-so-demanding ddataata rrequirement,equirement, variantsvariants ofof thethe ppositiveositive correlationcorrelation testtest havehave beenbeen quitequite popular;popular; thethe testtest requiresrequires “only”“only” thatthat oneone oobservebserve tthehe aaverageverage eexpectedxpected ccostsosts ooff iindividualsndividuals ((whowho aarere oobservationallybservationally iidenticaldentical ttoo tthehe fi rm)rm) wwithith ddifferentifferent aamountsmounts ooff iinsurancensurance ccoverage.overage. ThereThere isis nownow a llargearge lliter-iter- aatureture studyingstudying howhow averageaverage costscosts varyvary acrossacross differentdifferent coveragecoverage optionsoptions inin a broadbroad rrangeange ofof iinsurancensurance markets,markets, includingincluding health,health, life,life, automobile,automobile, andand homeownerhomeowner iinsurance.nsurance. TheThe resultsresults havehave beenbeen mixed.mixed. InIn somesome markets,markets, researchersresearchers havehave foundfound eevidencevidence consistentconsistent withwith adverseadverse selection—thatselection—that is,is, higherhigher averageaverage costscosts forfor indi-indi- vvidualsiduals withwith greatergreater insuranceinsurance coverage—whilecoverage—while inin othersothers theythey havehave foundfound evidenceevidence ooff aadvantageousdvantageous selection—defiselection—defi nedned byby a negativenegative relationshiprelationship betweenbetween insuranceinsurance ccoverageoverage andand averageaverage costs—orcosts—or havehave beenbeen unableunable toto rejectreject thethe nullnull hypothesishypothesis ooff ssymmetricymmetric iinformation,nformation, mmeaningeaning nnoo ddifferenceifference inin averageaverage costs.costs. CohenCohen andand SSiegelmaniegelman ((2010)2010) pproviderovide a rrecentecent rrevieweview ooff tthishis lliterature.iterature.

CChallengeshallenges iinn AApplyingpplying thethe PPositiveositive CCorrelationorrelation TestTest AAlthoughlthough applyingapplying thethe ssimpleimple ppositiveositive ccorrelationorrelation ttestest iiss rreasonablyeasonably sstraight-traight- fforward,orward, oneone mustmust cconfrontonfront ccertainertain cchallenges.hallenges. ResearchersResearchers havehave generallygenerally beenbeen qquiteuite carefulcareful toto acknowledgeacknowledge thesethese issuesissues andand inin somesome casescases toto fi ndnd creativecreative waysways tthathat getget aroundaround them.them. WeWe mentionmention herehere threethree commoncommon issuesissues thatthat oftenoften comecome upup iinn aapplications.pplications. Liran Einav and Amy Finkelstein 129

Figure 6 The “Positive Correlation” Test for Moral Hazard

A

Demand curve

MCinsured curve

C Peqm Price

F

MCuninsured curve

Q eqm Q eff Q max

Quantity

A fi rstrst importantimportant limitationlimitation ofof thethe positivepositive correlationcorrelation testtest isis thatthat comparingcomparing eexpectedxpected ccostsosts aacrosscross iindividualsndividuals wwithith aandnd wwithoutithout iinsurancensurance mmayay cconfoundonfound aadversedverse sselectionelection aandnd mmoraloral hhazard.azard. BBothoth aadversedverse sselectionelection aandnd mmoraloral hhazardazard ccanan ggenerateenerate a positivepositive correlationcorrelation bbetweenetween iinsurancensurance ccoverageoverage aandnd cclaims,laims, bbutut tthesehese aarere ttwowo vveryery ddifferentifferent fformsorms ooff aasymmetricsymmetric iinformationnformation wwithith vveryery ddifferentifferent iimplicationsmplications fforor publicpublic policy.policy. WithWith adverseadverse selection,selection, individualsindividuals whowho havehave privateprivate informationinformation tthathat ttheyhey aarere aatt hhigherigher rriskisk sself-selectelf-select iintonto tthehe iinsurancensurance mmarket,arket, ggeneratingenerating tthehe ppositiveositive correlationcorrelation betweenbetween insuranceinsurance coveragecoverage andand observedobserved claims.claims. AsAs alreadyalready ddiscussed,iscussed, tthehe ggovernmentovernment hhasas sseveraleveral ppotentialotential wwelfare-improvingelfare-improving ppolicyolicy ttoolsools ttoo possiblypossibly addressaddress suchsuch selection.selection. WithWith moralmoral hazard,hazard, individualsindividuals areare identicalidentical bbeforeefore ttheyhey ppurchaseurchase iinsurance,nsurance, bbutut hhaveave iincentivesncentives ttoo bbehaveehave differentlydifferently aafter.fter. TThosehose wwithith ggreaterreater ccoverageoverage hhaveave llessess iincentivencentive ttoo ttakeake aactionsctions tthathat rreduceeduce ttheirheir eexpectedxpected ccosts,osts, wwhichhich wwillill ggenerateenerate a rrelationshipelationship bbetweenetween iinsurancensurance ccoverageoverage aandnd observedobserved cclaims.laims. UUnlikenlike iinn tthehe ccasease ooff aadversedverse sselection,election, tthehe ggovernmentovernment ttypi-ypi- ccallyally hashas nono advantageadvantage ooverver tthehe pprivaterivate ssectorector aatt rreducingeducing tthehe wwelfareelfare ccostsosts ooff mmoraloral hazard.hazard. FFigureigure 6 showsshows howhow moralmoral hazardhazard cancan produceproduce thethe samesame “positive“positive correlation”correlation” ppropertyroperty asas aadversedverse selectionselection producesproduces inin FigureFigure 5.5. SpecifiSpecifi cally,cally, FigureFigure 6 providesprovides a ggraphicalraphical rrepresentationepresentation ofof anan iinsurancensurance marketmarket wwithith mmoraloral hhazardazard bbutut nnoo sselection.election. TThehe lacklack ofof selectionselection isis capturedcaptured byby thethe fl atat MCMC curves.curves. MoralMoral hazardhazard isis capturedcaptured 130 Journal of Economic Perspectives

bbyy drawingdrawing twotwo differentdifferent MCMC curves,curves, asas opposedopposed toto thethe singlesingle MCMC curvecurve wewe havehave ddrawnrawn inin thethe fi guresgures soso far.far. TheThe MCMC iinsurednsured ccurveurve representsrepresents thethe expectedexpected costcost ofof iinsurednsured iindividuals,ndividuals, andand ccorrespondsorresponds ttoo tthehe MMCC ccurvesurves wwee hhaveave bbeeneen ddrawingrawing iinn aallll ppreviousrevious fi gures.gures. TheThe MCMC uuninsuredninsured ccurveurve representsrepresents thethe expectedexpected costcost ofof thesethese same iindividuals,ndividuals, ifif theythey werewere uninsured.uninsured. MoralMoral hazard,hazard, whichwhich takestakes thethe formform ofof greatergreater eexpectedxpected costscosts wwhenhen a ggiveniven iindividualndividual hhasas iinsurancensurance thanthan whenwhen thethe individualindividual doesdoes nnot,ot, impliesimplies tthathat MMCC iinsurednsured iiss ggreaterreater thanthan MCMC uuninsuredninsured fforor eacheach individualindividual (or,(or, graphi-graphi- 8 ccally,ally, point-by-point).point-by-point). TheThe verticalvertical differencedifference betweenbetween MCMC iinsurednsured andand MCMC uuninsuredninsured isis a ggraphicalraphical wwayay ttoo qquantifyuantify mmoraloral hhazardazard iinn ttermserms ooff eexpectedxpected ccost.ost. FFigureigure 6 isis drawndrawn forfor a casecase inin whichwhich therethere isis nono adverseadverse selection:selection: individualsindividuals hhaveave tthehe ssameame eexpectedxpected ccost,ost, tthehe MMCC ccurvesurves aarere fl at,at, andand thethe demanddemand curvecurve isis down-down- wwardard sslopingloping ddueue ttoo ootherther ffactorsactors ((forfor eexample,xample, hheterogeneityeterogeneity iinn rriskisk aaversion).version). YYet,et, a comparisoncomparison ofof expectedexpected costscosts betweenbetween thethe “insureds”“insureds” andand “uninsureds”“uninsureds” wouldwould leadlead ttoo thethe samesame quantityquantity (line(line segmentsegment CF ) aass inin FigureFigure 5.5. However,However, whilewhile inin FigureFigure 5 tthehe ppositiveositive ccorrelationorrelation aaroserose ddueue ttoo aadversedverse sselection,election, iinn FFigureigure 6 tthishis ssameame ppositiveositive ccorrelationorrelation iiss ggeneratedenerated eentirelyntirely bbyy mmoraloral hhazard.azard.9 TTherefore,herefore, iinn ssituationsituations wwherehere mmoraloral hhazardazard ccouldould bbee aann iimportantmportant ffactor,actor, tthehe ppositiveositive ccorrelationorrelation ttestest iiss a jjointoint ttestest ooff eeitherither aadversedverse sselectionelection oorr mmoraloral hhazard.azard. FFindinginding a ppositiveositive ccorrelationorrelation bbetweenetween iinsurancensurance ccoverageoverage aandnd eexpectedxpected ccostsosts wwouldould fforceorce uuss ttoo rrejecteject tthehe nnullull hhypothesisypothesis ((ofof ssymmetricymmetric iinformation)nformation) eeitherither ddueue ttoo tthehe ppresenceresence ooff aadversedverse sselectionelection oorr mmoraloral hhazardazard ((oror bboth).oth). MMoreover,oreover, a fi nndingding ooff nnoo ccorrelationorrelation ccouldould eeitherither bbee ddueue ttoo nnoo aasymmetricsymmetric iinformationnformation oorr ttoo tthehe eexistencexistence ooff bbothoth mmoraloral hhazardazard aandnd aadvantageousdvantageous sselection,election, wwhichhich ooffsetffset eeachach oother.ther. OOnn tthehe ootherther hhand,and, a cconvincingonvincing fi ndingnding ooff a nnegativeegative ccorrelationorrelation iiss sstilltill iinformative,nformative, aass iitt wwouldould bbee cconsistentonsistent wwithith aadvantageousdvantageous sselection,election, eevenven iinn tthehe ppresenceresence ooff mmoraloral hhazard.azard. A secondsecond importantimportant considerationconsideration inin applyingapplying thethe positivepositive correlationcorrelation testtest isis tthehe ssetet ooff ccovariatesovariates thatthat areare beingbeing conditionedconditioned out.out. AsAs a startingstarting point,point, oneone mustmust cconditionondition oonn tthehe cconsumeronsumer ccharacteristicsharacteristics tthathat ddetermineetermine tthehe ppricesrices oofferedffered ttoo eeachach iindividual.ndividual. ThatThat is,is, a pproperroper implementationimplementation ofof thethe positivepositive correlationcorrelation testtest requiresrequires tthathat wewe examineexamine whether,whether, amongamong a setset ofof individualsindividuals whowho areare offeredoffered coveragecoverage ooptionsptions atat identical prices,prices, thosethose whowho buybuy moremore insuranceinsurance havehave higherhigher expectedexpected ccostsosts tthanhan tthosehose wwhoho ddoo nnot.ot. IInn tthehe aabsencebsence ooff ssuchuch cconditioning,onditioning, iitt iiss iimpossiblempossible ttoo kknownow whetherwhether a correlationcorrelation arisesarises duedue toto demanddemand (different(different individualsindividuals self-selectself-select

8 For simplicity, we have drawn Figure 6 so that the MC uninsured curve is parallel to the MC insured curve, thus assuming that the cost effect associated with moral hazard is homogeneous across individuals. The discussion would be the same for a richer situation, in which the moral hazard effect is heterogeneous (so that the vertical distance between the MC insured and MC uninsured varies). 9 Naturally, one could consider an environment in which both selection and moral hazard were present. The issues and discussion would be similar; we focused on the extreme case to simplify the graphical presentation. In particular, with no selection (fl at MC curves) we do not need to draw the corresponding AC curves since they are identical to the MC curves. In an environment with both selection (as shown by non-fl at MC curves) and moral hazard (MC insured > MC uninsured) each MC curve would have a corre- sponding AC curve. As in Figure 5, AC insured would be constructed by averaging “from the left” over the marginal costs of those with insurance (MC insured), while AC uninsured would be constructed by averaging “from the right” over the marginal costs of those without insurance (MC uninsured). Selection in Insurance Markets: Theory and Empirics in Pictures 131

iintonto ddifferentifferent ccontracts)ontracts) oror ssupplyupply ((differentdifferent individualsindividuals areare offeredoffered thethe contractscontracts aatt ddifferentifferent ppricesrices bbyy tthehe iinsurancensurance company).company). OnlyOnly tthehe fformerormer isis eevidencevidence ooff sselection.election. AsAs a result,result, somesome ofof thethe mostmost convincingconvincing teststests areare thosethose carriedcarried outout usingusing iinsurancensurance companycompany data,data, wherewhere thethe researcherresearcher knowsknows (rather(rather thanthan assumes)assumes) thethe ffullull ssetet ooff characteristicscharacteristics thatthat thethe insuranceinsurance companycompany usesuses forfor pricing.pricing. AbsentAbsent datadata oonn iindividuallyndividually ccustomizedustomized pprices,rices, wwhichhich iiss ssometimesometimes ddiffiiffi cultcult toto obtain,obtain, oneone maymay iinsteadnstead trytry toto controlcontrol inin a fl exibleexible mannermanner forfor allall individualindividual characteristicscharacteristics thatthat aaffectffect ppricingricing ((ChiapporiChiappori andand Salanie,Salanie, 2000).2000). A yet-more-nuancedyet-more-nuanced decisiondecision isis whetherwhether oneone shouldshould controlcontrol forfor a largerlarger setset ofof ccovariatesovariates (when(when available).available). InIn additionaddition toto thethe cconsumeronsumer ccharacteristicsharacteristics thatthat ddeter-eter- mmineine ttheirheir cchoicehoice sset—thatet—that iis,s, tthehe sspecifipecifi c contractscontracts andand theirtheir prices—oneprices—one couldcould aattemptttempt ttoo ccontrolontrol fforor ootherther oobservedbserved vvariablesariables tthathat aarere nnotot uusedsed bbyy tthehe fi rmrm (due(due toto rregulationegulation oror aanyny ootherther rreason),eason), fforor ootherther oobservablebservable vvariablesariables tthathat aarere nnotot oobservedbserved bbyy thethe fi rmrm (some(some maymay bebe observableobservable toto thethe fi rmrm withwith additionaladditional cost,cost, othersothers maymay bbee oobservablebservable oonlynly ttoo tthehe rresearcher),esearcher), aandnd ssoo oon.n. WWhetherhether ssuchuch vvariablesariables sshouldhould bbee uusedsed asas covariatescovariates isis lessless obviousobvious andand isis likelylikely toto dependdepend onon thethe questionquestion thatthat oneone wwouldould likelike toto answer.answer. OneOne needsneeds toto recognizerecognize thatthat thethe interpretationinterpretation ofof a positivepositive ccorrelationorrelation cancan varyvary dependingdepending onon suchsuch decision.decision. ForFor example,example, oneone maymay fi ndnd a posi-posi- ttiveive correlationcorrelation betweenbetween insuranceinsurance coveragecoverage andand expectedexpected costscosts onlyonly becausebecause fi rmsrms aarere notnot allowedallowed toto incorporateincorporate racerace intointo pricing.pricing. IfIf thisthis positivepositive correlationcorrelation disap-disap- ppearsears whenwhen racerace isis includedincluded asas a controlcontrol variable,variable, oneone maymay wantwant toto bebe carefulcareful aboutabout tthehe preciseprecise meaningmeaning ofof thethe termterm “asymmetric“asymmetric information”information” (since(since racerace isis knownknown toto tthehe iinsurancensurance companycompany eveneven ifif nnotot uusedsed iinn pricing)pricing) eveneven thoughthough thethe implicationsimplications fforor mmarketarket eequilibriumquilibrium aandnd iineffineffi ciencyciency maymay bebe thethe same.same. A fi nnalal importantimportant considerationconsideration inin applyingapplying thethe testtest concernsconcerns thethe measurementmeasurement ooff costs.costs. FigureFigure 5 suggestssuggests thatthat thethe theoreticaltheoretical objectobject oneone wouldwould likelike toto observeobserve isis tthathat ooff eexpectedxpected ccost.ost. EExpectationsxpectations aare,re, ooff ccourse,ourse, ddiffiiffi cultcult toto observe,observe, soso researchersresearchers ooftenften uusese pproxies.roxies. TThehe mmostost ddirectirect pproxyroxy wwouldould uusese tthehe aaverageverage rrealizedealized ccosts.osts. WWithith eenoughnough ddata,ata, rrealizedealized costscosts ooff tthehe iinsurednsured cconvergeonverge ttoo tthehe eexpectedxpected ccosts,osts, ppreciselyrecisely ccapturingapturing tthehe ttheoreticalheoretical object.object. InIn practice,practice, however,however, realizedrealized costscosts maymay bebe tricky.tricky. ForFor example,example, wwhenhen ccomparingomparing insuredinsured toto uninsureduninsured individuals,individuals, oneone obviouslyobviously doesdoes notnot observeobserve tthehe ““claims”claims” ooff tthehe uuninsured.ninsured. EEvenven wwhenhen ccomparingomparing cclaimslaims ooff iindividualsndividuals wwhoho cchoosehoose moremore oorr llessess ccoverageoverage withinwithin a ggiveniven ccompany,ompany, ccertainertain rrealizedealized (social)(social) costscosts aarere llessess llikelyikely toto bebe claimedclaimed byby individualsindividuals withwith lessless coverage.coverage. ForFor example,example, therethere isis a rrangeange ofof possiblepossible claimclaim amountsamounts thatthat areare worthworth claimingclaiming underunder lowlow deductible,deductible, bbutut wouldwould notnot provideprovide anyany benefibenefi tsts forfor (and(and areare unlikelyunlikely toto bebe fi ledled by)by) individualsindividuals ccoveredovered bbyy a hhigherigher ddeductible.eductible. TTherehere areare severalseveral potentialpotential strategiesstrategies forfor tryingtrying toto detectdetect differencesdifferences inin realreal bbehaviorehavior asas opposedopposed toto differencesdifferences inin claimingclaiming behavior.behavior. OneOne optionoption isis toto focusfocus onon a ssubsetubset ofof realizedrealized claimsclaims thatthat areare lessless proneprone toto insuranceinsurance coveragecoverage inflinfl uencinguencing ddecisionsecisions ttoo fi lele a cclaim:laim: fforor eexample,xample, oonene ccouldould ffocusocus oonn mmultiple-carultiple-car aaccidentsccidents iinn tthehe ccontextontext ofof automobileautomobile insurance.insurance. Alternatively,Alternatively, oneone mightmight useuse datadata externalexternal toto tthehe fi rm:rm: forfor example,example, byby examiningexamining mortalitymortality certificertifi catescates inin thethe contextcontext ofof annuitiesannuities 132 Journal of Economic Perspectives

oorr lifelife insurance.insurance. TheThe latterlatter hashas thethe ancillaryancillary benefibenefi t thatthat suchsuch “external”“external” datadata areare oobservedbserved fforor tthehe uuninsuredninsured populationpopulation asas well.well. AAnothernother approachapproach isis toto identifyidentify individualindividual characteristicscharacteristics thatthat areare notnot pricedpriced bbyy insuranceinsurance companiescompanies butbut areare knownknown toto bebe associatedassociated withwith expectedexpected cost,cost, suchsuch asas aagege oorr ggenderender inin thethe contextcontext ofof employer-providedemployer-provided healthhealth insurance.insurance. AnAn ancillaryancillary bbenefienefi t ooff thisthis approachapproach isis thatthat itit alsoalso getsgets aroundaround thethe issueissue ofof moralmoral hazard.hazard. A llimitationimitation ofof thisthis approach,approach, however,however, isis thatthat itit cancan onlyonly bebe appliedapplied inin situationssituations inin wwhich—inhich—in cconflonfl ictict withwith textbooktextbook economics—pricingeconomics—pricing isis notnot affectedaffected byby anan impor-impor- ttantant rriskisk ffactor.actor. IInn ssuchuch ssettings,ettings, oonene mmightight rreasonablyeasonably wwonderonder wwhetherhether tthehe ooriginalriginal cconcernsoncerns aboutabout thethe effieffi ciencyciency lossloss fromfrom adverseadverse selectionselection andand thethe potentialpotential publicpublic ppolicyolicy rremediesemedies aarere aallll tthathat rrelevant.elevant.

BBeyondeyond TTesting:esting: QQuantifyinguantifying SSelectionelection EEffectsffects TThehe importanceimportance andand inflinfl uenceuence ofof thethe seminalseminal theoreticaltheoretical workwork onon selectionselection iinn insuranceinsurance marketsmarkets stemmedstemmed iinn llargearge ppartart ffromrom iitsts fi ndingsndings thatthat selectionselection couldcould iimpairmpair thethe effieffi cientcient operationoperation ofof competitivecompetitive insuranceinsurance marketsmarkets andand potentiallypotentially oopenpen uupp sscopecope fforor wwelfare-improvingelfare-improving ggovernmentovernment iintervention.ntervention. DDetectingetecting sselectionelection iiss tthereforeherefore onlyonly a fi rstrst step.step. IfIf selectionselection isis empiricallyempirically detected,detected, itit isis naturalnatural toto askask wwhetherhether thethe welfarewelfare costscosts itit generatesgenerates areare largelarge oror small,small, andand whatwhat mightmight bebe thethe wwelfareelfare cconsequencesonsequences ofof specifispecifi c governmentgovernment policies.policies. TheseThese areare fundamentallyfundamentally eempiricalmpirical qquestions,uestions, andand ourour graphicalgraphical frameworkframework isis uusefulseful forfor guidingguiding attemptsattempts ttoo qquantifyuantify tthesehese wwelfareelfare cconstructs.onstructs. WWee bbeginegin byby debunkingdebunking a commoncommon (mis)perception(mis)perception thatthat thethe veryvery samesame eempiricalmpirical objectsobjects thatthat areare usedused forfor tthehe ppositiveositive ccorrelationorrelation testtest (described(described earlier)earlier) ccanan aalsolso bebe informativeinformative aboutabout thethe welfarewelfare costscosts associatedassociated withwith selection.selection. ItIt maymay bebe aappealingppealing toto imagineimagine tthathat mmarketsarkets tthathat aappearppear ““moremore aadverselydversely sselected”—thatelected”—that iis,s, oonesnes iinn wwhichhich therethere isis a llargerarger differencedifference betweenbetween thethe expectedexpected costscosts ofof thethe insuredsinsureds aandnd uuninsureds—experienceninsureds—experience greatergreater welfarewelfare lossloss associatedassociated withwith thatthat selection.selection. UUnfortunately,nfortunately, FigureFigure 7 illustratesillustrates thatthat withoutwithout additionaladditional assumptions,assumptions, compari-compari- ssonsons ooff eexpectedxpected ccostsosts aarere nnotot tthathat iinformativenformative aaboutbout uunderlyingnderlying eeffiffi ciencyciency costs.costs. FFigureigure 7 startsstarts withwith thethe situationsituation depicteddepicted inin FigureFigure 3.3. OnceOnce again,again, thethe equilibriumequilibrium ddifferenceifference inin expectedexpected costscosts betweenbetween thethe insuredsinsureds andand uninsuredsuninsureds isis givengiven byby thethe ddistanceistance betweenbetween pointspoints C aandnd F , aandnd thethe welfarewelfare lossloss fromfrom adverseadverse selectionselection isis ggiveniven bbyy tthehe aarearea ooff tthehe ddeadweighteadweight llossoss ttriangleriangle CDE . However,However, herehere wewe havehave drawndrawn ttwowo ppossibleossible demanddemand curves,curves, eacheach ofof whichwhich givegive riserise toto thethe samesame equilibriumequilibrium pointpoint ((pointpoint C )),, wwhilehile kkeepingeeping thethe MCMC andand ACAC curvescurves unchanged.unchanged.1100 BByy design,design, thethe twotwo ddemandemand curvescurves generategenerate thethe samesame equilibriumequilibrium point,point, therebythereby producingproducing thethe samesame ddifferenceifference inin eexpectedxpected ccostsosts bbetweenetween tthehe iinsuredsnsureds aandnd uuninsuredsninsureds ((lineline ssegmentegment CF

10 Linear demand curves (as in Figure 7) allow us to rotate the demand curve without altering the rela- tionship between the MC curve and the AC curve. If demand was nonlinear, changes to demand would have triggered shifts in the AC curve (holding the MC curve constant). The basic point that the welfare cost of adverse selection can vary across markets with the same difference in expected costs between the uninsured and insured would still apply in cases with a nonlinear demand curve, but the fi gure would be messier to draw. Liran Einav and Amy Finkelstein 133

Figure 7 The “Positive Correlation” and Its (Non)relation to Welfare Costs of Selection

A

Possible demand curves

B AC insured curve

C Peqm Price

D MC curve E1 F E2

AC uninsured curve

Q eqm Q max Quantity

iinn FigureFigure 7).7). However,However, thesethese demanddemand curvescurves generategenerate differentdifferent effieffi cientcient outcomes,outcomes, mmeaningeaning differentdifferent pointspoints atat whichwhich thethe twotwo demanddemand curvescurves intersectintersect thethe MCMC curve,curve, 1111 ddenotedenoted inin thethe fi guregure byby pointspoints E1 andand E2. AsAs a result,result, theythey produceproduce different-sizeddifferent-sized wwelfareelfare losses,losses, givengiven bbyy tthehe ccorrespondingorresponding trianglestriangles CDE 1 andand CDE 2. ThisThis exampleexample tthushus illustratesillustrates howhow deadweightdeadweight lossloss trianglestriangles ofof differentdifferent sizessizes cancan bebe generatedgenerated eevenven tthoughhough tthehe ““extentextent ofof adverseadverse selection”selection” asas measuredmeasured byby thethe differencedifference inin aaverageverage ccostsosts iiss tthehe ssame.ame. OOnene wwayay ttoo mmakeake ssomeome pprogressrogress iinn qquantifyinguantifying tthehe wwelfareelfare cconsequencesonsequences ofof sselectionelection oror ofof potentialpotential publicpublic policypolicy isis toto useuse boundsbounds thatthat areare basedbased onon easilyeasily oobservablebservable objects.objects. ForFor example,example, supposesuppose wewe wouldwould likelike toto boundbound thethe welfarewelfare costcost ooff sselection.election. WeWe useuse FigureFigure 1 (adverse(adverse selection)selection) forfor thisthis discussion,discussion, butbut itit isis easyeasy toto iimaginemagine aann aanalogousnalogous ddiscussioniscussion fforor tthehe aadvantageousdvantageous selectionselection shownshown inin FigureFigure 4.4. SSupposeuppose fi rstrst thatthat wewe oobservebserve onlyonly tthehe ppricerice ooff tthehe iinsurancensurance ssoldold iinn tthehe mmarket.arket. IIff wwee aarere wwillingilling ttoo aassumessume tthathat wwee oobservebserve tthehe ccompetitiveompetitive eequilibriumquilibrium ppricerice (Peeqmqm)),, wwee ccanan oobtainbtain a (presumably(presumably notnot veryvery tight)tight) upperupper boundbound ofof thethe welfarewelfare costcost ofof

11 As we emphasize throughout, the demand and cost curves are tightly linked. Thus, many changes in primitives will shift both demand and cost curves at the same time. It is still possible, however, to think of changes in the environment that could change demand without affecting the cost curves. For example, in the textbook case such changes would require preferences (but not loss probabilities) to change while preserving the ranking of willingness to pay for insurance across individuals. 134 Journal of Economic Perspectives

sselection,election, givengiven bbyy Peeqmqm × Q mmaxax. Intuitively,Intuitively, becausebecause adverseadverse selectionselection leadsleads toto under-under- iinsurance,nsurance, thethe worstworst possiblepossible scenarioscenario isis whenwhen nobodynobody isis insuredinsured butbut everybodyeverybody sshouldhould bebe insured.insured. SinceSince thethe equilibriumequilibrium priceprice mustmust exceedexceed thethe willingnesswillingness toto paypay fforor insuranceinsurance byby thethe uninsuredsuninsureds (otherwise(otherwise theythey wouldwould havehave purchasedpurchased insurance),insurance), tthehe ppricerice pprovidesrovides aann uupperpper boundbound onon thethe per-individualper-individual wwelfareelfare lloss.oss. AAdditionaldditional ddataata mmayay hhelpelp ttightenighten tthehe bbound.ound. IIff wwee aalsolso oobservebserve tthehe ((equilib-equilib- rrium)ium) shareshare ofof uninsureduninsured iindividualsndividuals ((thatthat iis,s, Q mmaxax – Q eeqmqm)),, thethe upperupper boundbound forfor tthehe welfarewelfare lossloss cancan bebe tightenedtightened ttoo Peeqmqm(Q mmaxax – Q eeqmqm)).. Finally,Finally, ifif wewe alsoalso havehave allall tthehe datadata elementselements neededneeded forfor thethe positivepositive correlationcorrelation test—sotest—so thatthat wewe alsoalso observeobserve tthehe expectedexpected costscosts ofof thethe uninsuredsuninsureds andand denotedenote itit byby X—weX—we cancan furtherfurther tightentighten tthishis upperupper boundbound toto (Peeqmqm – X ))((Q mmaxax – Q eeqmqm) (which(which isis equalequal toto areaarea CDFJ inin FFigureigure 1.)1.)1122 SSubstantiallyubstantially moremore progressprogress cancan bebe mademade inin estimatingestimating thethe welfarewelfare conse-conse- qquenceuence ofof selectionselection (or(or ofof potentialpotential publicpublic policypolicy interventions)interventions) ifif wewe hhaveave oonene aadditionaldditional datadata elementelement beyondbeyond whatwhat isis requiredrequired forfor thethe positivepositive correlationcorrelation test.test. TThishis additionaladditional element,element, whichwhich isis soso heavilyheavily usedused inin otherother subfisubfi eldselds ofof appliedapplied mmicroeconomics,icroeconomics, iiss iidentifyingdentifying vvariationariation iinn iinsurancensurance pprices.rices. TToo sseeee howhow usefuluseful priceprice variationvariation maymay bebe forfor welfarewelfare analysis,analysis, oneone cancan imagineimagine tthehe idealideal experimentexperiment ofof randomlyrandomly varyingvarying thethe priceprice atat whichwhich insuranceinsurance isis offeredoffered ttoo largelarge poolspools ofof otherwiseotherwise identicalidentical individuals.individuals. ForFor eacheach pool,pool, wewe wouldwould thenthen oobservebserve thethe fractionfraction ofof individualsindividuals whowho boughtbought insuranceinsurance andand thethe averageaverage realizedrealized ccostsosts ofof insuredinsured individuals.individuals. InIn suchsuch anan idealideal situation,situation, wewe cancan useuse thethe datadata gener-gener- aatedted toto “trace“trace out”out” thethe demanddemand curvecurve andand thethe ACAC curvecurve inin ourour graphicalgraphical analysis,analysis, aandnd toto derivederive thethe MCMC curve,curve, thusthus producingproducing thethe threethree essentialessential curvescurves behindbehind allall ofof tthehe welfarewelfare analysisanalysis inin ourour graphicalgraphical framework.framework.1133 OObservingbserving tthehe MMCC ccurveurve aarguablyrguably aaddressesddresses thethe keykey challengechallenge forfor empiricallyempirically aanalyzingnalyzing insuranceinsurance marketsmarkets which,which, asas notednoted earlier,earlier, isis toto identifyidentify thethe marginalmarginal indi-indi- vviduals.iduals. Indeed,Indeed, withwith kknowledgenowledge ofof tthehe MMCC ccurve,urve, AACC ccurve,urve, aandnd ddemandemand ccurve,urve, iitt iiss sstraightforwardtraightforward ttoo ccomputeompute tthehe wwelfareelfare llossoss ooff aadversedverse sselectionelection oorr aanyny ootherther oobjectbject ooff iinterestnterest withinwithin thethe graphicalgraphical frameworkframework wewe propose,propose, suchsuch asas thethe welfarewelfare effectseffects ooff tthehe vvariousarious ppublicublic ppolicyolicy iinterventionsnterventions wwee aanalyzednalyzed eearlier.arlier. TThishis iiss tthehe bbasicasic ppointoint wwee aadvancedvance iinn EEinav,inav, FFinkelstein,inkelstein, aandnd CCullenullen ((2010),2010), wwherehere wwee eempiricallympirically iillustratellustrate tthishis ideaidea inin thethe contextcontext ofof employer-providedemployer-provided healthhealth insurance.insurance. WeWe alsoalso provideprovide ssomeome ddiscussioniscussion ooff ppossibleossible ssourcesources ooff ssuchuch iidentifyingdentifying ppricingricing vvariation,ariation, iincludingncluding fi eeldld experiments,experiments, experimentationexperimentation byby fi rms,rms, andand pricingpricing variationvariation drivendriven byby variousvarious ccommonommon fformsorms ooff iinsurancensurance rregulation.egulation. SSuchuch pricingpricing variationvariation hashas twotwo relatedrelated ancillaryancillary benefibenefi ts.ts. First,First, itit providesprovides a ddirectirect testtest ofof bothboth thethe existenceexistence andand naturenature ofof selectionselection basedbased onon thethe slopeslope ofof thethe

12 To see this, note that Peqm(Q max – Q eqm) is equal to the area below line CJ, while X (Q max – Q eqm) is equal to the area below line DF because X is the average value of the MC curve between Q eqm and Q max. 13 Note that the AC curve and the MC curve are linked through the demand curve, so that knowledge of two of the three curves allows us to obtain the third. To see this, note that marginal costs at point p, MC( p), can be computed by evaluating the difference in total costs TC( p) – TC(p′ ) for p′ just above p, where TC( p) is simply the product of average cost AC( p) and demand Q( p). Selection in Insurance Markets: Theory and Empirics in Pictures 135

eestimatedstimated MCMC curve.curve. WeWe cancan rejectreject thethe nullnull hypothesishypothesis ofof symmetricsymmetric informationinformation iiff wwee cancan rejectreject thethe nullnull hypothesishypothesis ofof a constantconstant MCMC curve.curve. Moreover,Moreover, a fi ndingnding tthathat tthehe MCMC ccurveurve iiss ddownwardownward slopingsloping suggestssuggests thethe existenceexistence ofof adverseadverse selection;selection; cconversely,onversely, a fi ndingnding thatthat thethe MCMC curvecurve isis upwardupward slopingsloping suggestssuggests thethe existenceexistence ofof aadvantageousdvantageous selection.selection. UnlikeUnlike thethe “positive“positive correlation”correlation” test,test, thisthis “cost“cost curve”curve” testtest ooff selectionselection isis notnot affectedaffected byby thethe existenceexistence (or(or lacklack thereof)thereof) ofof moralmoral hazard.hazard. ToTo sseeee whywhy thisthis isis true,true, recallrecall thatthat thethe ACAC curvecurve fromfrom whichwhich thethe MCMC curvecurve isis derivedderived iiss defidefi nedned asas thethe averageaverage costscosts ofof allall thosethose individualsindividuals whowho buybuy a specifispecifi c insuranceinsurance ccontract.ontract. BecauseBecause thethe costcost curvescurves areare defidefi nedned overover a samplesample ofof individualsindividuals whowho allall hhaveave tthehe same insuranceinsurance contract,contract, differencesdifferences inin thethe shapeshape ofof thethe costcost curvecurve areare notnot ddirectlyirectly aaffectedffected bbyy mmoraloral hhazard.azard.1144 TThishis iinsightnsight ssuggestsuggests a sstep-by-steptep-by-step aapproachpproach toto aanalysisnalysis ooff sselectionelection iinn iinsurancensurance mmarketsarkets ifif oonene hhasas aaccessccess ttoo iidentifyingdentifying pricingpricing variationvariation inin additionaddition toto thethe datadata onon aaverageverage costscosts ooff tthosehose wwithith ddifferentifferent iinsurancensurance ccoverage.overage. IInn tthehe fi rstrst step,step, thethe simplesimple ccorrelationorrelation testtest cancan bebe usedused toto seesee ifif oneone cancan rejectreject thethe nullnull ofof symmetricsymmetric informa-informa- ttionion (in(in ffavoravor ooff eeitherither a ppositiveositive oorr nnegativeegative correlation).correlation). InIn thethe secondsecond step,step, ifif tthehe nnullull ooff ssymmetricymmetric iinformationnformation iiss rrejected,ejected, tthehe iidentifyingdentifying ppricingricing vvariationariation ccanan tthenhen bbee usedused toto estimateestimate thethe costcost curvescurves andand thusthus detectdetect whetherwhether selection—asselection—as distinctdistinct ffromrom mmoraloral hhazard—existsazard—exists andand wwhetherhether itit iiss aadversedverse oorr aadvantageous.dvantageous. Finally,Finally, iiff sselectionelection isis ddetected,etected, thenthen itsits welfarewelfare costcost cancan bebe estimated,estimated, andand thethe welfarewelfare conse-conse- qquencesuences ofof ppotentialotential ppublicublic ppolicyolicy iinterventionsnterventions wweighed,eighed, bbyy bbringingringing tthehe eestimatedstimated ddemandemand ccurveurve iintonto tthehe aanalysisnalysis aass wwell.ell. TTherehere isis yetyet anotheranother importantimportant benefibenefi t fromfrom identifyingidentifying pricingpricing variationvariation ((althoughalthough itit isis notnot thethe focusfocus ofof thisthis essay),essay), whichwhich isis thatthat itit allowsallows oneone toto testtest forfor andand qquantifyuantify mmoraloral hhazard.azard. TToo sseeee tthis,his, wwee ccanan aagaingain cconsideronsider wwhathat tthehe iidealdeal eexperimentxperiment mmightight be.be. ToTo aanalyzenalyze moralmoral hazard,hazard, oneone wouldwould randomlyrandomly allocateallocate insuranceinsurance toto somesome iindividualsndividuals andand aallocatellocate nnoo iinsurancensurance ttoo oothers.thers. BButut tthishis iiss eessentiallyssentially tthehe eexperimentxperiment ggeneratedenerated byby identifyingidentifying pricingpricing variation:variation: thosethose individualsindividuals whowho areare assignedassigned highhigh ppricesrices areare lessless likelylikely toto havehave insurance,insurance, whilewhile thosethose whowho areare assignedassigned lowlow pricesprices areare mmoreore llikelyikely ttoo bbee iinsured.nsured. OOnene ccanan tthenhen ttestest aandnd qquantifyuantify tthehe mmoraloral hhazardazard eeffectffect ooff iinsurancensurance byby regressingregressing anyany observedobserved bbehaviorehavior ooff iinterestnterest oonn wwhetherhether aann iindividualndividual iiss iinsurednsured oror nnot,ot, uusingsing tthehe iidentifyingdentifying ssourceource ooff ppricerice vvariationariation aass aann iinstrumentnstrument fforor iinsurancensurance coverage.coverage. Moreover,Moreover, oneone cancan gogo furtherfurther and,and, insteadinstead ofof onlyonly quantifyingquantifying tthehe aaverageverage moralmoral hazardhazard effect,effect, useuse thethe estimatedestimated demanddemand curvecurve forfor insuranceinsurance toto qquantifyuantify thethe heterogeneityheterogeneity ofof moralmoral hazardhazard asas a functionfunction ofof thethe individual’sindividual’s willing-willing- nnessess ttoo ppayay forfor insurance.insurance. SuchSuch analysisanalysis maymay addressaddress importantimportant questionsquestions thatthat gogo wwellell beyondbeyond thethe ccurrenturrent statestate ooff tthehe eempiricalmpirical lliteratureiterature oonn aaverageverage mmoraloral hhazardazard eeffectsffects inin insuranceinsurance marketsmarkets toto examineexamine whetherwhether high-riskhigh-risk individualsindividuals areare suchsuch bbecauseecause theirtheir underlyingunderlying riskrisk isis higher—forhigher—for example,example, becausebecause theythey areare chronicallychronically

14 Of course, it is possible that the moral hazard effect of insurance is greater for some individuals than others and that, anticipating this, individuals whose behavior is more responsive to insurance may be more likely to buy insurance. We would still view this as selection, however, in the sense that individuals are selecting insurance on the basis of their anticipated behavioral response to it. 136 Journal of Economic Perspectives

iill—orll—or bbecauseecause ttheirheir bbehavioralehavioral rresponseesponse ttoo iinsurancensurance iiss ggreater—forreater—for eexample,xample, ttheyhey aarere deterreddeterred fromfrom seeingseeing a doctordoctor unlessunless theirtheir out-of-pocketout-of-pocket costcost isis suffisuffi cientlyciently low.low. IIndeed,ndeed, wewe iinvestigatenvestigate thisthis qquestionuestion eempiricallympirically iinn ssomeome ooff oourur ccurrenturrent wworkork ((Einav,Einav, FFinkelstein,inkelstein, RRyan,yan, SSchrimpf,chrimpf, aandnd CCullen,ullen, 22010).010). FFinally,inally, wewe notenote thatthat anan attractiveattractive featurefeature ofof ourour graphicalgraphical frameworkframework isis thatthat itit pprovidesrovides a transparenttransparent wayway toto assessassess thethe relativerelative contributioncontribution ofof thethe datadata andand ofof anyany uunderlyingnderlying theoreticaltheoretical oror statisticalstatistical assumptionsassumptions inin givinggiving riserise toto thethe empiricalempirical esti-esti- mmates.ates. AAnn eexamplexample mmayay bbee uuseful.seful. CConsideronsider FFigureigure 33,, aandnd ssupposeuppose wwee aarere iinterestednterested iinn eestimatingstimating tthehe aarearea ooff tthehe ddeadweighteadweight llossoss ttriangleriangle CDE . ForFor thisthis particularparticular objectobject ooff iinterest,nterest, wewe requirerequire estimatesestimates ofof thethe demanddemand curvecurve andand costcost curvescurves atat thethe rangerange tthathat isis betweenbetween Q eeqmqm andand Q eeffff , whilewhile otherother partsparts ofof thethe curvescurves areare lessless important.important. A researcherresearcher whowho hashas excellentexcellent priceprice variationvariation thatthat identifiidentifi eses thethe curvescurves forfor infra-infra- mmarginalarginal buyersbuyers (to(to thethe leftleft ofof Q eeqmqm) wouldwould needneed toto relyrely heavilyheavily onon theoreticaltheoretical oror sstatisticaltatistical aassumptionsssumptions toto extrapolateextrapolate thethe curvescurves toto thethe relevantrelevant regionregion andand wouldwould nneedeed toto pperformerform rrobustnessobustness ccheckshecks toto evaluateevaluate alternativealternative modelsmodels thatthat maymay implyimply ddifferentifferent eextrapolations.xtrapolations. IInn ccontrast,ontrast, iiff tthehe ppricerice vvariationariation sspanspans tthehe rrelevantelevant rregion,egion, ssensitivityensitivity ttoo mmodelingodeling aassumptionsssumptions mmayay bbee llessess ooff a cconcern.oncern. TToo tthehe extentextent thatthat moremore limitedlimited (or(or nonexistent)nonexistent) pricingpricing variationvariation requiresrequires ggreaterreater modelingmodeling assumptionsassumptions forfor thethe wwelfareelfare analysis,analysis, oneone nicenice ffeatureeature ofof insur-insur- aancence mmarketsarkets iiss tthathat tthehe ttheoryheory uunderlyingnderlying iindividualndividual cchoiceshoices ofof insuranceinsurance coveragecoverage iiss wwellell ddevelopedeveloped andand muchmuch testedtested (in(in thethe laboratorylaboratory andand inin thethe fi eld).eld). Thus,Thus, thisthis iiss a contextcontext wherewhere perhapsperhaps moremore thanthan others,others, relyingrelying onon theoreticaltheoretical restrictionsrestrictions mmayay bbee quitequite credible.credible. InIn Einav,Einav, Finkelstein,Finkelstein, andand LevinLevin (2010),(2010), wewe provideprovide a reviewreview ooff mmodelingodeling aapproachespproaches toto welfarewelfare analysisanalysis inin insuranceinsurance marketsmarkets andand somesome ofof thethe rrecentecent fi ndings.ndings.

CConcludingoncluding CCommentsomments

TThehe graphicalgraphical frameworkframework wewe havehave presentedpresented providesprovides a unifiunifi eded approachapproach forfor uunderstandingnderstanding bothboth thethe conceptualconceptual welfarewelfare issuesissues posedposed byby selectionselection inin insuranceinsurance mmarketsarkets aandnd ppotentialotential governmentgovernment intervention,intervention, asas wellwell asas thethe existingexisting empiricalempirical eeffortsfforts toto detectdetect selectionselection andand measuremeasure itsits welfarewelfare consequences.consequences. However,However, thisthis fframeworkramework hashas abstractedabstracted fromfrom severalseveral constructsconstructs thatthat areare potentiallypotentially ofof interest.interest. SSomeome aarere vveryery eeasilyasily hhandledandled bbyy ssimpleimple eextensionsxtensions ooff tthehe fframework,ramework, oothersthers llessess sso.o. WWee startstart wwithith tthehe eeasierasier iissues.ssues. AAlthoughlthough fforor eexpositionalxpositional ssimplicityimplicity wwee ffocusedocused oonn tthehe bbinaryinary cchoicehoice ooff ““whetherwhether oorr nnotot ttoo bbuyuy iinsurance,”nsurance,” tthehe ssameame ggraphicalraphical aanalysisnalysis ccanan eeasilyasily bbee aappliedpplied ttoo a cchoicehoice bbetweenetween mmoreore oorr llessess ccoverage.overage. IItt ccanan aalsolso bbee uusedsed ttoo aanalyzenalyze cchoiceshoices aacrosscross mmoreore thanthan twotwo contracts,contracts, althoughalthough a multidimensionalmultidimensional graph-graph- iicalcal aapproachpproach iiss llessess aappealing.ppealing. FFinally,inally, iitt iiss sstraightforwardtraightforward ttoo rrelaxelax oourur mmaintainedaintained aassumptionssumption ooff pperfectlyerfectly ccompetitiveompetitive iinsurancensurance mmarkets—whicharkets—which iinn mmanyany mmarketsarkets mmayay nnotot bbearear mmuchuch rresemblanceesemblance ttoo rreality.eality. OOnene ccouldould ccarryarry ooutut a ssimilarimilar aanalysisnalysis uusingsing aalternativelternative ppricingricing aassumptionsssumptions wwhichhich lleadead ttoo a differentdifferent equilibriumequilibrium ppointoint (instead(instead ooff thethe averageaverage costcost pricingpricing arisingarising fromfrom perfectperfect competition).competition). WelfareWelfare couldcould thenthen Liran Einav and Amy Finkelstein 137

bbee analyzedanalyzed byby comparingcomparing thethe newnew equilibriumequilibrium pointpoint withwith thethe effieffi ccientient aallocation,llocation, aalthoughlthough ooff ccourseourse nnowow iitt mmustust bbee rrecognizedecognized tthathat aanyny wwelfareelfare ccostost cconflonfl atesates bbothoth tthosehose ccostsosts ccreatedreated bbyy sselectionelection aandnd tthosehose ccreatedreated bbyy iimperfectmperfect ccompetition.ompetition. A mmoreore sseriouserious iissuessue iiss tthathat wwee hhaveave ffocusedocused oonn ppricingricing ddistortionsistortions aarisingrising ffromrom sselectionelection whilewhile abstractingabstracting fromfrom thethe possibilitypossibility thatthat selectionselection cancan distortdistort thethe setset ofof iinsurancensurance ccontractsontracts tthathat aarere ooffered.ffered. IInn ootherther wwords,ords, wwee havehave assumedassumed thatthat insuranceinsurance ccompaniesompanies ccompeteompete ooverver tthehe ppricerice ooff a givengiven setset ofof insuranceinsurance contracts.contracts. InIn practice,practice, iinsurancensurance ccompaniesompanies aalsolso ssetet tthehe ccoverageoverage ffeatureseatures ooff tthehe iinsurancensurance ccontractontract ((likelike ddeductibles,eductibles, ccoveredovered eevents,vents, aandnd ssoo oon)n) aandnd sselectionelection ppressuresressures mmayay wwellell aaffectffect tthehe ssetet ooff ccontractontract ffeatureseatures oofferedffered iinn eequilibrium.quilibrium. AAdmittedly,dmittedly, aabstractingbstracting ffromrom tthishis ppotentialotential cconsequenceonsequence ooff sselectionelection mmayay mmississ a ssubstantialubstantial ccomponentomponent ooff iitsts wwelfareelfare iimplicationsmplications aandnd mmayay eexplainxplain wwhyhy mmostost ooff tthehe eempiricalmpirical wworkork ttoo ddateate oonn tthehe wwelfareelfare ccostsosts ooff sselec-elec- ttionion hashas tendedtended toto fi ndnd relativelyrelatively modestmodest welfarewelfare effects.effects. InIn Einav,Einav, Finkelstein,Finkelstein, andand LLevinevin ((2010),2010), wwee pproviderovide mmoreore ddiscussioniscussion aandnd ddescriptionescription ooff tthishis ppoint.oint. AAllowingllowing tthehe ccontractontract sspacepace ttoo bbee ddeterminedetermined eendogenouslyndogenously iinn a sselectionelection mmarketarket rraisesaises cchallengeshallenges oonn bbothoth tthehe ttheoreticalheoretical aandnd eempiricalmpirical ffront.ront. OOnn tthehe ttheo-heo- rreticaletical ffront,ront, wwee ccurrentlyurrently llackack cclearlear ccharacterizationsharacterizations ooff tthehe eequilibriumquilibrium iinn a mmarketarket iinn wwhichhich fi rrmsms ccompeteompete ooverver ccontractontract ddimensionsimensions aass wwellell aass pprice,rice, aandnd iinn wwhichhich cconsumersonsumers mmayay hhaveave mmultipleultiple ddimensionsimensions ooff pprivaterivate iinformationnformation ((likelike eexpectedxpected ccostost aandnd rriskisk ppreferences).references). FFromrom aann eempiricalmpirical sstandpoint,tandpoint, tthehe cchallengehallenge iiss tthathat iiff aadversedverse sselectionelection ggreatlyreatly rreduceseduces tthehe ssetet ooff oofferedffered ccontracts,ontracts, eestimatingstimating tthehe wwelfareelfare llossoss ffromrom tthehe ccontractsontracts nnotot oofferedffered mmayay rrequireequire tthehe rresearcheresearcher ttoo ggoo qquiteuite ffarar ooutut ooff ssample.ample. WWhilehile tthesehese cchallengeshallenges aarere ffarar ffromrom ttrivialrivial aandnd mmayay eexplainxplain wwhyhy ttherehere hhasas bbeeneen rrelativelyelatively llittleittle wworkork ooff eeitherither ttypeype oonn tthishis ttopicopic ttoo ddate,ate, wwee vviewiew tthishis ddirectionirection aass aann eextremelyxtremely iimportant—andmportant—and llikelyikely ffruitful—topicruitful—topic fforor ffurtherurther rresearch.esearch. AAss wwithith tthehe rresearchesearch ttoo ddateate oonn sselectionelection iinn iinsurancensurance mmarkets,arkets, wwee eexpectxpect tthathat ttherehere wwillill bbee a uusefulseful ccomplementarityomplementarity bbetweenetween ttheoreticalheoretical aandnd eempiricalmpirical pprogressrogress mmovingoving fforward.orward.

■ We are grateful to David Autor, Seema Jayachandran, Chad Jones, Casey Rothschild, Dan Silverman, and Timothy Taylor for helpful comments, and to the National Institute of Aging (Grant No. R01 AG032449) for fi nancial support.

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