Journal of Economic Perspectives—Volume 27, Number 1—Winter 2013—Pages 197–222

The RAND Health Insurance Experiment, Three Decades Later†

Aviva Aron-Dine, Liran Einav, and Amy Finkelstein

n thethe voluminousvoluminous academicacademic lliteratureiterature aandnd publicpublic policypolicy discoursediscourse onon howhow healthhealth iinsurancensurance aaffectsffects mmedicaledical sspending,pending, tthehe ffamousamous RRANDAND HHealthealth IInsurancensurance EExperi-xperi- Immentent sstandstands aapart.part. BBetweenetween 11974974 aandnd 11981,981, tthehe RRANDAND eexperimentxperiment pprovidedrovided hhealthealth iinsurancensurance ttoo mmoreore tthanhan 55,800,800 iindividualsndividuals ffromrom aaboutbout 22,000,000 hhouseholdsouseholds iinn ssixix ddifferentifferent llocationsocations aacrosscross tthehe UUnitednited SStates,tates, a ssampleample ddesignedesigned ttoo bbee rrepresentativeepresentative ooff ffamiliesamilies wwithith aadultsdults uundernder tthehe aagege ooff 662.2. TThehe eexperimentxperiment rrandomlyandomly aassignedssigned tthehe ffamiliesamilies ttoo hhealthealth iinsurancensurance pplanslans wwithith ddifferentifferent llevelsevels ooff ccostost ssharing,haring, rranginganging ffromrom ffullull ccoverageoverage ((“free“free ccare”)are”) ttoo pplanslans tthathat pprovidedrovided aalmostlmost nnoo ccoverageoverage fforor tthehe fi rstrst aapproximatelypproximately $$4,0004,000 ((inin 22011011 ddollars)ollars) tthathat wwereere iincurredncurred dduringuring tthehe yyear.ear. TThehe RRANDAND iinvestigatorsnvestigators wwereere ppioneersioneers iinn wwhathat wwasas tthenhen rrelativelyelatively nnovelovel tterritoryerritory fforor tthehe ssocialocial ssciences,ciences, bbothoth iinn tthehe cconductonduct aandnd aanalysisnalysis ooff rrandomizedandomized eexperimentsxperiments aandnd iinn tthehe eeconomicconomic aanalysisnalysis ooff mmoraloral hhazardazard iinn tthehe ccontextontext ooff hhealthealth iinsurance.nsurance. MMoreore thanthan tthreehree ddecadesecades llater,ater, tthehe RRANDAND rresultsesults aarere sstilltill wwidelyidely hheldeld ttoo bbee tthehe ““goldgold sstandard”tandard” ooff eevidencevidence fforor ppredictingredicting tthehe llikelyikely iimpactmpact ooff hhealthealth iinsurancensurance rreformseforms oonn mmedicaledical sspending,pending, aass wwellell aass fforor ddesigningesigning aactualctual iinsurancensurance ppolicies.olicies. IInn tthehe llightight ooff rrapidapid ggrowthrowth iinn hhealthealth sspendingpending aandnd tthehe ppressureressure tthishis pplaceslaces oonn ppublicublic ssectorector bbudgets,udgets, ssuchuch eestimatesstimates hhaveave eenormousnormous iinflnfl uenceuence asas federalfederal andand statestate policymakerspolicymakers cconsideronsider potentialpotential policypolicy interventionsinterventions toto reducereduce publicpublic spendingspending onon healthhealth care.care.

■ Aviva Aron-Dine received her Ph.D. in Economics in June 2012 from the Massachusetts Insti- tute of Technology, Cambridge, Massachusetts. Liran Einav is Professor of Economics, Stanford University, Stanford, California. Amy Finkelstein is Ford Professor of Economics, Massachusetts Institute of Technology, Cambridge, Massachusetts. Einav and Finkelstein are also Research Associates, National Bureau of Economic Research, Cambridge, Massachusetts. Their email addresses are [email protected], [email protected], and afi [email protected]. † To access the Appendix, visit http://dx.doi.org/10.1257/jep.27.1.197. doi=10.1257/jep.27.1.197 198 Journal of Economic Perspectives

OOnn ccostost ggroundsrounds aalone,lone, wwee aarere uunlikelynlikely ttoo sseeee ssomethingomething llikeike tthehe RRANDAND eexperimentxperiment aagain:gain: tthehe ooverallverall ccostost ooff tthehe eexperiment—fundedxperiment—funded bbyy tthehe UUSS DDepartmentepartment ooff HHealth,ealth, EEducation,ducation, andand WelfareWelfare (now(now thethe DepartmentDepartment ofof HealthHealth andand HumanHuman Services)—wasServices)—was rroughlyoughly $$295295 mmillionillion iinn 22011011 ddollarsollars ((GreenbergGreenberg aandnd SShroderhroder 22004).004).1 IInn thisthis essay,essay, wewe reexaminereexamine thethe corecore fi ndingsndings ofof thethe RANDRAND healthhealth insuranceinsurance eexperimentxperiment iinn llightight ooff tthehe ssubsequentubsequent threethree decadesdecades ofof workwork onon thethe analysisanalysis ofof rrandomizedandomized experimentsexperiments andand thethe economicseconomics ofof moralmoral hazard.hazard. ForFor ourour abilityability toto dodo sso,o, wewe oweowe a heavyheavy debtdebt ofof gratitudegratitude toto thethe originaloriginal RANDRAND investigatorsinvestigators forfor puttingputting ttheirheir ddataata iinn tthehe ppublicublic ddomainomain aandnd ccarefullyarefully ddocumentingocumenting tthehe ddesignesign aandnd cconductonduct ooff tthehe eexperiment.xperiment. TToo oourur kknowledge,nowledge, ttherehere hhasas nnotot bbeeneen aanyny ssystematicystematic rreexamina-eexamina- ttionion ooff tthehe ooriginalriginal ddataata andand corecore fi ndingsndings fromfrom thethe RANDRAND experiment.experiment.2 WWee hhaveave threethree mainmain goals.goals. First,First, wewe re-presentre-present thethe mainmain fi ndingsndings ofof thethe RANDRAND eexperimentxperiment inin a mannermanner moremore similarsimilar toto thethe wayway theythey wouldwould bebe presentedpresented today,today, wwithith tthehe aaimim ooff mmakingaking tthehe ccoreore eexperimentalxperimental resultsresults moremore accessibleaccessible toto currentcurrent rreaders.eaders. SSecond,econd, wwee rreexamineeexamine tthehe vvalidityalidity ooff tthehe eexperimentalxperimental ttreatmentreatment eeffects.ffects. AAllll rreal-worldeal-world experimentsexperiments mustmust aaddressddress tthehe ppotentialotential iissuesssues ooff ddifferentialifferential sstudytudy ppartic-artic- iipationpation andand ddifferentialifferential reportingreporting ofof outcomesoutcomes aacrosscross eexperimentalxperimental treatments:treatments: fforor eexample,xample, iiff tthosehose wwhoho eexpectedxpected toto bebe sickersicker werewere moremore likelylikely toto participateparticipate inin thethe eexperimentxperiment whenwhen thethe insuranceinsurance offeredoffered moremore generousgenerous coverage,coverage, thisthis couldcould biasbias tthehe estimatedestimated impactimpact ofof moremore ggenerousenerous ccoverage.overage. Finally,Finally, wwee rreconsidereconsider thethe famousfamous RRANDAND eestimatestimate tthathat tthehe eelasticitylasticity ooff mmedicaledical sspendingpending wwithith rrespectespect toto itsits out-of-out-of- ppocketocket priceprice isis – 0.2.0.2. WeWe drawdraw a contrastcontrast betweenbetween howhow thisthis elasticityelasticity waswas originallyoriginally eestimatedstimated aandnd hhowow iitt hhasas bbeeneen ssubsequentlyubsequently aapplied,pplied, aandnd mmoreore ggenerallyenerally wwee ccautionaution aagainstgainst tryingtrying toto summarizesummarize thethe experimentalexperimental treatmenttreatment effectseffects fromfrom nonlinearnonlinear hhealthealth iinsurancensurance ccontractsontracts uusingsing a ssingleingle ppricerice eelasticity.lasticity.

The Key Economic Object of Interest

TThroughouthroughout thethe discussion,discussion, wewe focusfocus onon oneone ofof RAND’sRAND’s twotwo enduringenduring lega-lega- ccies—itsies—its eestimatesstimates ooff thethe impactimpact ofof differentdifferent healthhealth insuranceinsurance contractscontracts onon medicalmedical

1 Indeed, since the RAND Health Insurance Experiment, there have been, to our knowledge, only two other randomized health insurance experiments in the United States, both using randomized varia- tions in eligibility to examine the effect of providing public health insurance to uninsured populations: the Finkelstein et al. (2012) analysis of Oregon’s recent use of a lottery to expand Medicaid access to 10,000 additional low-income adults, and the Michalopoulos et al. (2011) study funded by the Social Security Administration to see the impact of providing health insurance to new recipients of disability insurance during the two-year waiting period before they were eligible for Medicare. 2 For many other early and infl uential social science experiments, researchers have gone back and reexamined the original data from the experiments in light of subsequent advances. For example, researchers have reexamined the Negative Income Tax Experiments (Greenberg and Hasley 1983; Ashenfelter and Plant 1990), the Perry preschool and other early childhood interventions experiments (Anderson 2008; Heckman, Moon, Pinto, Savelyev, and Yavitz 2010; Heckman, Pinto, Shaikh, and Yavitz 2011), the Hawthorne effect (Levitt and List 2011), Project STAR on class size (Krueger 1999; Krueger and Whitmore 2001), and the welfare-to-work experiments (Bitler, Gelbach, and Hoynes 2006). Aviva Aron-Dine, Liran Einav, and Amy Finkelstein 199

Figure 1 The Price Elasticity of Healthcare Utilization: A Hypothetical Example

2,000

1,800

1,600

1,400

1,200 Greater utility

1,000

800 Out-of-pocket cost ($) 600

400

200

0 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 Total medical expenditure ($)

Notes: The fi gure presents two different budget sets arising from two different hypothetical insurance contracts: the solid line represents the budget set of an individual who has an insurance contract in which the individual has a constant 20 percent coinsurance rate, while the dashed line represents the budget set under a more generous insurance plan with a 10 percent coinsurance. The arcs are indifference curves. In this example, individuals would increase their total healthcare spending from $3,000 to $5,000 in response to a 50 percent reduction in the out-of-pocket price—that is, an elasticity of – 1.33. sspending—andpending—and dodo notnot examineexamine itsits inflinfl uentialuential fi ndingsndings regardingregarding thethe healthhealth effectseffects ooff ggreaterreater insuranceinsurance coverage.coverage. WeWe mademade thisthis choicechoice inin partpart becausebecause thethe publiclypublicly aavailablevailable healthhealth datadata areare notnot completecomplete (and(and thereforetherefore dodo notnot permitpermit replicationreplication ofof tthehe ooriginalriginal RRANDAND rresults),esults), aandnd iinn ppartart bbecauseecause tthehe ooriginalriginal hhealthealth iimpactmpact eestimatesstimates wwereere alreadyalready lessless preciseprecise thanthan thosethose forfor healthhealth spending,spending, andand ourour exercisesexercises belowbelow eexaminingxamining ppotentialotential tthreatshreats ttoo vvalidityalidity wwouldould oonlynly aadddd aadditionaldditional uuncertainty.ncertainty. FFigureigure 1 iillustratesllustrates tthehe kkeyey oobjectbject ooff iinterest.nterest. HHealthcareealthcare uutilizationtilization iiss ssumma-umma- rrizedized oonn tthehe hhorizontalorizontal aaxisxis bbyy tthehe ttotalotal ddollarollar aamountmount sspentpent oonn hhealthcareealthcare sserviceservices ((regardlessregardless ooff wwhetherhether iitt iiss ppaidaid bbyy tthehe iinsurernsurer oorr ooutut ooff ppocket).ocket). TThehe aamountmount ooff iinsurancensurance ccoverageoverage iiss rrepresentedepresented bbyy hhowow tthishis ttotalotal aamountmount ttranslatesranslates ttoo out-of-pocketout-of-pocket sspendingpending oonn tthehe vverticalertical aaxis.xis. TThehe fi guregure presentspresents twotwo differentdifferent bbudgetudget ssetsets aarisingrising ffromrom ttwowo ddifferentifferent hhypotheticalypothetical iinsurancensurance ccontracts:ontracts: tthehe ssolidolid llineine representsrepresents tthehe bbudgetudget ssetet ooff aann iindividualndividual wwhoho hhasas aann iinsurancensurance ccontractontract iinn wwhichhich thethe iindividualndividual payspays 2020 centscents forfor anyany dollardollar ofof healthcarehealthcare utilization—thatutilization—that 200 Journal of Economic Perspectives

iiss a pplanlan withwith a constantconstant 2020 percentpercent coinsurancecoinsurance rrate—whileate—while tthehe ddashedashed llineine rrepresentsepresents tthehe bbudgetudget ssetet uundernder a mmoreore ggenerousenerous iinsurancensurance pplanlan iinn wwhichhich tthehe iindividualndividual ppaysays oonlynly 1100 ccentsents fforor aanyny ddollarollar ooff hhealthcareealthcare sspending—thatpending—that iis,s, a 1010 percentpercent ccoinsurance.oinsurance. OOurur ffocusocus iinn tthishis eessayssay iiss oonn tthehe eeffectffect ooff tthehe hhealthealth iinsurancensurance ccoverageoverage oonn hhealthcareealthcare utilization.utilization. IfIf utilityutility increasesincreases inin healthcarehealthcare utilizationutilization andand inin incomeincome nnetet ofof out-of-pocketout-of-pocket medicalmedical spending,spending, thethe optimaloptimal spendingspending forfor anan individualindividual ccanan bebe representedrepresented bbyy tthehe ttangencyangency ppointoint bbetweenetween ttheirheir iindifferencendifference ccurveurve aandnd tthehe budgetbudget set,set, asas sshownhown iinn FFigureigure 11.. TThehe wwayay tthehe fi guregure isis drawn,drawn, individualsindividuals wwouldould increaseincrease ttheirheir ttotalotal hhealthcareealthcare sspendingpending ffromrom $$3,0003,000 ttoo $$5,0005,000 iinn rresponseesponse ttoo a 5500 ppercentercent rreductioneduction iinn tthehe oout-of-pocketut-of-pocket pprice—thatrice—that iis,s, aann eelasticitylasticity ooff ––1.33.1.33.3 A focusfocus ooff tthehe RRANDAND eexperimentxperiment wwasas ttoo oobtainbtain eestimatesstimates ooff tthishis eelasticitylasticity ffromrom anan experimentexperiment thatthat randomizedrandomized whichwhich budgetbudget setset consumersconsumers faced.faced. ThisThis eelasticitylasticity isis generallygenerally knownknown asas thethe “moral“moral hazard”hazard” effecteffect ofof healthhealth insurance.insurance. TThishis ttermerm wwasas ((toto oourur kknowledge)nowledge) fi rrstst iintroducedntroduced iintonto tthehe mmodernodern aacademiccademic lliteratureiterature byby ArrowArrow ((1963)1963) wwhoho ddefiefi nedned moralmoral hazardhazard iinn hhealthealth iinsurancensurance aass tthehe nnotionotion thatthat “medical“medical iinsurancensurance iincreasesncreases tthehe ddemandemand fforor mmedicaledical ccare”;are”; iitt hhasas ssinceince comecome toto bebe usedused mmoreore sspecifipecifi callycally toto referrefer toto thethe priceprice sensitivitysensitivity ooff ddemandemand fforor healthhealth care,care, conditionalconditional oonn uunderlyingnderlying hhealthealth sstatustatus ((PaulyPauly 11968;968; CCutlerutler aandnd ZZeckhausereckhauser 22000).000). FFigureigure 1 abstracts,abstracts, ooff ccourse,ourse, ffromrom mmanyany iimportantmportant aaspectsspects ooff aactualctual hhealthealth iinsurancensurance contractscontracts andand healthcarehealthcare consumptionconsumption cchoiceshoices tthathat aarere facedfaced inin thethe rrealeal wworldorld andand inin thethe RANDRAND HealthHealth InsuranceInsurance Experiment.Experiment. First,First, summarizingsummarizing hhealthcareealthcare uutilizationtilization bbyy iitsts ooverallverall ddollarollar ccostost ddoesoes nnotot ttakeake iintonto aaccountccount tthehe hheterogeneityeterogeneity iinn hhealthcareealthcare nneeds.eeds. OneOne commoncommon distinctiondistinction isis oftenoften drawndrawn bbetweenetween inpatientinpatient andand outpatientoutpatient spending.spending. TheThe formerformer isis associatedassociated withwith hospi-hospi- ttalizations,alizations, whilewhile thethe latterlatter isis associatedassociated withwith visitsvisits toto thethe doctor’sdoctor’s offioffi ce,ce, lablab tests,tests, oorr proceduresprocedures tthathat ddoo nnotot rrequireequire aann oovernightvernight sstay.tay. IItt sseemseems pplausiblelausible tthathat tthehe rrateate atat whichwhich iindividualsndividuals ttraderade ooffff hhealthcareealthcare sspendingpending aandnd rresidualesidual iincomencome ccouldould ddifferiffer acrossacross ssuchuch vveryery ddifferentifferent ttypesypes ooff uutilizationtilization aand,nd, ttherefore,herefore, tthathat tthesehese ddifferentifferent typestypes ofof sspendingpending wouldwould respondrespond veryvery differentlydifferently toto a priceprice reductionreduction tthroughhrough insurance.insurance. A secondsecond simplifisimplifi cationcation isis thatthat FigureFigure 1 considersconsiders twotwo linearlinear contracts,contracts, forfor whichwhich tthehe conceptconcept ofof price,price, andand priceprice elasticity,elasticity, isis clearlyclearly defidefi ned.ned. However,However, mostmost healthhealth iinsurancensurance contractscontracts iinn tthehe wworld,orld, aass wwellell aass tthosehose oofferedffered bbyy tthehe RRANDAND eexperiment,xperiment, aarere nonlinear,nonlinear, andand annualannual healthcarehealthcare utilizationutilization consistsconsists ofof manymany smallsmall andand uncer-uncer- ttainain episodesepisodes thatthat accumulate.accumulate. TheThe conceptconcept ofof a singlesingle elasticity,elasticity, oror eveneven ofof a singlesingle pprice,rice, iiss tthereforeherefore nnotot aass sstraightforwardtraightforward aass mmayay bbee ssuggesteduggested bbyy FFigureigure 11.. WWee rreturneturn ttoo tthishis ppointoint llaterater iinn tthishis eessay.ssay.

3 ((P2 – P1)/P1)/((Q 2 – Q 1)/Q 1) = ((5,000 – 3,000)/3,000)/((.1 – .2)/.2) = –1.33. Later we will use arc elasticities, which are slightly different. The RAND Health Insurance Experiment, Three Decades Later 201

A Brief Summary of the RAND Health Insurance Experiment

IInn tthehe RRANDAND eexperiment,xperiment, ffamiliesamilies wwereere aassignedssigned ttoo pplanslans wwithith oonene ooff ssixix cconsumeronsumer ccoinsuranceoinsurance rrates—thatates—that iis,s, tthehe ssharehare ooff mmedicaledical eexpendituresxpenditures ppaidaid bbyy tthehe eenrollee—andnrollee—and wwereere ccoveredovered bbyy tthehe aassignedssigned pplanlan fforor tthreehree ttoo fi veve yyears.ears. FFourour ooff tthehe ssixix pplanslans ssimplyimply ssetet ddifferentifferent ooverallverall ccoinsuranceoinsurance rratesates ooff 995,5, 550,0, 225,5, oorr 0 ppercentercent ((thethe llastast kknownnown aass ““freefree ccare”).are”). A fi fthfth pplanlan hhadad a ““mixedmixed ccoinsuranceoinsurance rrate”ate” ooff 2255 ppercentercent fforor mmostost sserviceservices bbutut 5500 ppercentercent fforor ddentalental aandnd ooutpatientutpatient mmentalental hhealthealth sservices,ervices, aandnd a ssixthixth pplanlan hhadad a ccoinsuranceoinsurance rrateate ooff 9955 ppercentercent fforor ooutpatientutpatient sserviceservices bbutut 0 ppercentercent fforor iinpatientnpatient sserviceservices ((followingfollowing tthehe RRANDAND iinvestigators,nvestigators, wwee rreferefer ttoo tthishis llastast pplanlan aass tthehe ““individualindividual ddeductibleeductible pplan”).lan”). TThehe mmostost ccommonommon pplanlan aassign-ssign- mmentent wwasas ffreeree ccareare ((3232 ppercentercent ooff ffamilies),amilies), ffollowedollowed bbyy tthehe iindividualndividual ddeductibleeductible pplanlan ((2222 ppercent),ercent), tthehe 9955 ppercentercent ccoinsuranceoinsurance rrateate ((1919 ppercent),ercent), aandnd tthehe 2255 ppercentercent ccoinsuranceoinsurance rrateate ((1111 ppercent).ercent).4 TToo limitlimit thethe fi nancialnancial exposureexposure ofof participants,participants, familiesfamilies werewere alsoalso randomlyrandomly aassigned,ssigned, wwithinithin eeachach ooff tthehe ssixix pplans,lans, ttoo ddifferentifferent oout-of-pocketut-of-pocket mmaximums,aximums, rreferredeferred ttoo aass tthehe ““MaximumMaximum DDollarollar EExpenditure.”xpenditure.” TThehe ppossibleossible MMaximumaximum DDollarollar EExpendi-xpendi- ttureure limitslimits werewere 5,5, 10,10, oror 1515 percentpercent ofof familyfamily income,income, upup toto a maximummaximum ofof $750$750 oror $$1,0001,000 (roughly(roughly $3,000$3,000 oror $4,000$4,000 inin 20112011 dollars).dollars). OnOn average,average, aboutabout one-thirdone-third ofof tthehe individualsindividuals whowho werewere subjectsubject toto a MaximumMaximum DollarDollar ExpenditureExpenditure hithit itit duringduring thethe yyear,ear, aalthoughlthough tthishis ooff ccourseourse wwasas mmoreore llikelyikely fforor pplanslans wwithith hhighigh ccoinsuranceoinsurance rrates.ates. TThehe fi rstrst threethree columnscolumns ofof TableTable 1 showshow thethe sixsix plans,plans, thethe numbernumber ofof individualsindividuals aandnd ffamiliesamilies iinn each,each, andand thethe averageaverage shareshare ofof medicalmedical expensesexpenses thatthat theythey paidpaid out-out- oof-pocket.f-pocket. NewhouseNewhouse etet al.al. (1993,(1993, chapterchapter 2 andand appendixappendix B)B) provideprovide considerablyconsiderably mmoreore ddetailetail oonn tthishis aandnd aallll aaspectsspects ooff tthehe eexperiment.xperiment. FFamiliesamilies werewere notnot assignedassigned toto plansplans byby simplesimple randomrandom assignment.assignment. Instead,Instead, wwithinithin a sitesite andand enrollmentenrollment month,month, thethe RANDRAND investigatorsinvestigators selectedselected theirtheir samplesample aandnd assignedassigned familiesfamilies toto plansplans usingusing thethe “fi“fi nitenite selectionselection model”model” (Morris(Morris 1979;1979; NNewhouseewhouse etet aal.l. 11993,993, aappendixppendix BB),), wwhichhich sseekseeks ttoo 11)) mmaximizeaximize tthehe ssampleample vvariationariation iinn bbaselineaseline ccovariatesovariates whilewhile ssatisfyingatisfying tthehe bbudgetudget cconstraintonstraint fforor tthehe eexperiment;xperiment; aandnd 22)) useuse a formform ofof stratifistratifi eded randomrandom assignmentassignment toto achieveachieve betterbetter balancebalance acrossacross a setset ooff bbaselineaseline characteristicscharacteristics thanthan wouldwould likelylikely bebe achievedachieved (given(given thethe fi nitenite sample)sample) bbyy cchancehance aalone.lone. TThehe datadata comecome fromfrom severalseveral sources.sources. PPriorrior ttoo planplan assignment,assignment, a screeningscreening qquestionnaireuestionnaire ccollectedollected bbasicasic ddemographicemographic iinformationnformation aandnd ssomeome iinformationnformation oonn hhealth,ealth, iinsurancensurance sstatus,tatus, aandnd ppastast hhealthcareealthcare uutilizationtilization ffromrom aallll ppotentialotential eenrollees.nrollees. DDuringuring thethe three-to-fithree-to-fi veve yearyear durationduration ofof thethe experiment,experiment, participantsparticipants signedsigned overover aallll ppaymentsayments ffromrom ttheirheir ppreviousrevious iinsurancensurance ppolicyolicy ((ifif aany)ny) ttoo tthehe RANDRAND experimentexperiment

4 Our analysis omits 400 additional families (1,200 individuals) who participated in the experiment but were assigned to coverage by a health maintenance organization. Due to the very different nature of this plan, it is typically excluded from analyses of the impact of cost sharing on medical spending using the RAND data (Keeler and Rolph 1988; Manning, Newhouse, Duan, Keeler, Leibowitz, and Marquis 1987; Newhouse et al. 1993). 202 Journal of Economic Perspectives

Table 1 Plan Summary Statistics and Refusal and Attrition Rates

Average Share Individuals out-of-pocket refusing Share Share refusing Plan ( families) share c enrollment attriting or attriting

Free Care 1,894 (626) 0% 6% 5% 12% 25% Coinsurance 647 (224) 23% 20% 6% 26% Mixed Coinsurance a 490 (172) 28% 19% 9% 26% 50% Coinsurance 383 (130) 44% 17% 4% 21% Individual Deductible b 1,276 (451) 59% 18% 13% 28% 95% Coinsurance 1,121 (382) 76% 24% 17% 37%

All plans 5,811 (1,985) 34% 16% 10% 24% p-value, all plans equal < 0.0001 < 0.0001 < 0.0001 p-value, Free Care vs. 95% < 0.0001 < 0.0001 < 0.0001 p-value, Free Care vs. 25% 0.0001 0.5590 0.0001 p-value, 25% vs. 95% 0.4100 0.0003 0.0136

Notes: “Coinsurance rate” refers to the share of the cost that is paid by the individual. In the 25 percent, mixed, 50 percent, and 95 percent coinsurance rate plans, families were assigned out-of-pocket maximums of 5 percent, 10 percent, or 15 percent of family income, up to a limit of $750 or $1,000. In the individual deductible plan, the out-of-pocket maximum was $150 per-person up to a maximum of $450 per family. The sample counts for the 95 percent coinsurance rate plans include 371 individuals who faced a 100 percent coinsurance rate in the fi rst year of the experiment. Refusal and attrition rates are regression-adjusted for site and contact month fi xed effects and interactions, because plan assignment was random only conditional on site and month of enrollment (see Newhouse et al. 1993, appendix B). “Contact month” refers to the month in which the family was fi rst contacted by the experiment and is used in lieu of month of enrollment because month of enrollment is available only for individuals who agreed to enroll. Refusal and attrition rates exclude the experiment’s Dayton site (which accounted for 1,137 enrollees) because data on Dayton refusers were lost. An individual is categorized as having attrited if he leaves the experiment at any time prior to completion. a The “Mixed Coinsurance” plan had a coinsurance rate of 50 percent for dental and outpatient mental health services, and a coinsurance rate of 25 percent for all other services. b The “Individual Deductible” plan had a coinsurance rate of 95 percent for outpatient services and 0 percent for inpatient services. c To compute the average out-of-pocket share we compute the ratio of out-of-pocket expenses to total medical expenditure for each enrollee, and report the average ratio for each plan. aandnd fi lleded cclaimslaims wwithith tthehe eexperimentxperiment aass iiff iitt wwasas ttheirheir iinsurer;nsurer; ttoo bbee rreimbursedeimbursed fforor iincurredncurred expenditures,expenditures, pparticipantsarticipants hhadad ttoo fi lele claimsclaims withwith thethe experimenters.experimenters. TheseThese cclaimlaim fi lings,lings, whichwhich pproviderovide ddetailedetailed ddataata oonn hhealthealth eexpendituresxpenditures iincurredncurred dduringuring tthehe eexperiment,xperiment, mmakeake uupp tthehe ddataata oonn hhealthcareealthcare sspendingpending aandnd uutilizationtilization ooutcomes.utcomes. TThehe RRANDAND iinvestigatorsnvestigators hhaveave vveryery hhelpfullyelpfully mmadeade aallll tthesehese ddataata aandnd ddetailedetailed ddocumen-ocumen- ttationation aavailablevailable oonline,nline, aallowingllowing uuss ttoo rreplicateeplicate ttheirheir rresultsesults ((almost)almost) pperfectlyerfectly ((seesee TTableable AA11 ooff tthehe oonlinenline AAppendix)ppendix) aandnd ttoo cconductonduct oourur oownwn aanalysisnalysis ooff tthehe ddata.ata.5

5 We accessed the RAND data via the Inter-University Consortium for Political and Social Research; the data can be downloaded at http://www.icpsr.umich.edu/icpsrweb/ICPSR/studies/6439?q=Rand+Health+Insurance +Experiment. The online Appendix and code for reproducing our results can be found at http://e-jep.org. Aviva Aron-Dine, Liran Einav, and Amy Finkelstein 203

Experimental Analysis

AAss inin allall modernmodern presentationspresentations ofof randomizedrandomized experiments,experiments, wewe beginbegin byby rreportingeporting estimatesestimates ofof experimentalexperimental treatmenttreatment effects.effects. WeWe thenthen continuecontinue byby inves-inves- ttigatingigating potentialpotential threatsthreats toto thethe validityvalidity ofof interpretinginterpreting thesethese treatmenttreatment effectseffects asas ccausalausal eestimates.stimates.

Empirical Framework IInn oourur aanalysis,nalysis, wwee ffollowollow tthehe RRANDAND iinvestigatorsnvestigators aandnd uusese tthehe iindividual-yearndividual-year aass tthehe primaryprimary unitunit ofof analysis.analysis. WeWe denotedenote anan individualindividual byby i, thethe planplan thethe individual’sindividual’s ffamilyamily wwasas aassignedssigned ttoo bbyy p, thethe calendarcalendar yearyear byby t, andand thethe locationlocation andand startstart monthmonth bbyy l aandnd m, rrespectively.espectively. TThehe bbaselineaseline regressionregression takestakes thethe formform ooff

yi,t = λp + τt + αl,m + εi,t where an outcome yi,t (for example, medical expenditure) is used as the dependent variable, and the explanatory variables are plan, year, and location-by-start-month fi xed effects. The key coeffi cients of interest are the six plan fi xed effects, λp . Because, as described earlier, there was an additional randomization of Maximum Dollar Expenditure limits, the estimated coeffi cients represent the average effect of each plan, averaging over the different limits that families were assigned to within the plan. Because plan assignment was only random conditional on location and start (that is, enrollment) month, we include a full set of location by start month interactions, αl,m . We also include year fi xed effects, τt , to account for any under- lying time trend in the cost of medical care. Because plans were assigned at the family rather than individual level, all regression results cluster the standard errors on the family.

Treatment Effects TTableable 2 rreportseports thethe treatmenttreatment effectseffects ofof thethe differentdifferent plansplans basedbased onon estimatingestimating tthehe basicbasic regressionregression forfor variousvarious measuresmeasures ofof healthcarehealthcare utilization.utilization. TheThe reportedreported ccoeffioeffi cientscients (the(the λp’’ss ffromrom tthehe aabovebove regression)regression) indicateindicate thethe effecteffect ofof thethe variousvarious pplanslans oonn tthathat mmeasureeasure ooff utilizationutilization relativerelative toto thethe freefree carecare planplan (whose(whose meanmean isis ggiveniven byby thethe constantconstant term).term). ColumnColumn 1 rreportseports rresultsesults fforor a llinearinear pprobabilityrobability modelmodel iinn wwhichhich tthehe ddependentependent variablevariable takestakes thethe valuevalue ofof oneone whenwhen spendingspending isis positivepositive aandnd zzeroero ootherwise.therwise. IInn ccolumnolumn 22,, tthehe ddependentependent variablevariable isis thethe amountamount ofof annualannual mmedicaledical sspendingpending ((inin 22011011 ddollars).ollars). TThehe ppointoint eestimatesstimates ooff bbothoth sspecifipecifi cationscations indicateindicate a consistentconsistent patternpattern ofof lowerlower sspendingpending inin higherhigher cost-sharingcost-sharing plans.plans. ForFor example,example, comparingcomparing thethe highesthighest cost-cost- ssharingharing planplan (the(the 9595 percentpercent coinsurancecoinsurance plan)plan) withwith thethe freefree carecare plan,plan, thethe resultsresults iindicatendicate a 1717 percentagepercentage pointpoint (18(18 percent)percent) declinedecline inin thethe fractionfraction ofof individualsindividuals wwithith zerozero annualannual medicalmedical spendingspending andand a $845$845 (39(39 percent)percent) declinedecline inin averageaverage aannualnnual medicalmedical sspending.pending. AsAs thethe lastlast rrowow sshows,hows, wewe cancan rrejecteject tthehe nnullull hhypothesisypothesis tthathat sspendingpending iinn tthehe ppositiveositive ccost-sharingost-sharing pplanslans iiss eequalqual ttoo tthathat iinn tthehe ffreeree ccareare pplan.lan. 204 Journal of Economic Perspectives

Table 2 Plans’ Effects on Utilization

Total spending a Inpatient spending Outpatient spending

Share Spending Share Spending Share Spending with any in $ with any in $ with any in $ (1) (2) (3) (4) (5) (6)

Constant (Free Care Plan, 0.931 2,170 0.103 827 0.930 1,343 N = 6,840) (0.006) (78) (0.004) (60) (0.006) (35) 25% Coinsurance – 0.079 – 648 – 0.022 –229 – 0.078 – 420 (N = 2,361) (0.015) (152) (0.009) (116) (0.015) (62) Mixed Coinsurance – 0.053 – 377 – 0.018 21 – 0.053 –398 (N = 1,702) (0.015) (178) (0.009) (141) (0.016) (70) 50% Coinsurance – 0.100 – 535 – 0.031 4 – 0.100 – 539 (N = 1,401) (0.019) (283) (0.009) (265) (0.019) (77) Individual Deductible – 0.124 – 473 – 0.006 – 67 – 0.125 – 406 (N = 4,175) (0.012) (121) (0.007) (98) (0.012) (52) 95% Coinsurance – 0.170 – 845 – 0.024 –217 – 0.171 –629 (N = 3,724) (0.015) (119) (0.007) (91) (0.016) (50) p-value: all differences < 0.0001 < 0.0001 0.0008 0.1540 < 0.0001 < 0.0001 from Free Care = 0

Notes: Table 2 reports the treatment effects of the different plans based on estimating the basic regression for various measures of healthcare utilization. The reported coeffi cients are from an ordinary least squares regression and indicate the effect of the various plans on that measure of utilization relative to the free care plan (whose mean is given by the constant term). Column 1 reports results for a linear probability model in which the dependent variable takes the value of one when spending is positive, and zero otherwise. In column 2, the dependent variable is the amount of annual medical spending (in 2011 dollars). The other columns of Table 2 break out results separately for inpatient spending and outpatient spending. Standard errors, clustered on family, are in parentheses below the coeffi cients. Because assignment to plans was random only conditional on site and start month (Newhouse et al. 1993), all regressions include site by start month dummy variables, as well as year fi xed effects. All spending variables are infl ation adjusted to 2011 dollars (adjusted using the CPI‐U). Site by start month and year dummy variables are de-meaned so that the coeffi cients refl ect estimates for the “average” site‐month‐year mix. a Total spending is the sum of inpatient and outpatient spending (where outpatient spending includes dental and outpatient mental health spending).

TThehe ootherther ccolumnsolumns ooff TTableable 2 bbreakreak ooutut rresultsesults sseparatelyeparately fforor iinpatientnpatient sspending,pending, wwhichhich aaccountedccounted forfor 4242 ppercentercent ofof totaltotal sspending,pending, andand outpatientoutpatient spending,spending, whichwhich aaccountedccounted forfor thethe otherother 5858 percent.percent. OnceOnce againagain thethe patternspatterns suggestsuggest lessless spendingspending iinn plansplans withwith higherhigher cost-sharing.cost-sharing. WeWe areare ableable toto rejectreject thethe nullnull ofof nono differencesdifferences iinn spendingspending acrossacross plansplans forfor “any“any inpatient”inpatient” andand forfor bothboth measuresmeasures ofof outpatientoutpatient sspending.pending. TheThe eeffectffect ooff ccostost ssharingharing oonn tthehe llevelevel ooff iinpatientnpatient sspendingpending iiss cconsistentlyonsistently ssmallmall aandnd ggenerallyenerally insignifiinsignifi cant,cant, suggestingsuggesting thatthat moremore seriousserious medicalmedical episodesepisodes mmayay bbee llessess ppricerice ssensitive,ensitive, wwhichhich sseemseems pplausible.lausible. AAnothernother wayway toto approachapproach thethe datadata isis toto looklook atat thethe extentextent toto whichwhich thethe effecteffect ooff costcost sharingsharing mightmight varyvary forfor thosethose withwith higherhigher levelslevels ofof medicalmedical spending.spending. ToTo The RAND Health Insurance Experiment, Three Decades Later 205

eexplorexplore this,this, wewe useuse quantilequantile regressionsregressions toto estimateestimate thethe aboveabove equation,equation, andand tthenhen assessassess thethe wayway byby whichwhich thethe estimatedestimated planplan effectseffects varyvary acrossacross thethe quantilesquantiles ooff medicalmedical spending.spending. DetailedDetailed resultsresults forfor thesethese specifispecifi ccationsations areare availableavailable inin TTableable A2A2 ofof thethe onlineonline AppendixAppendix availableavailable withwith thisthis articlearticle atat http://e-jep.org.http://e-jep.org. TheThe rresultsesults areare consistentconsistent withwith a lowerlower percentagepercentage treatmenttreatment effecteffect forfor higher-spendinghigher-spending iindividuals.ndividuals. ThisThis patternpattern isis likelylikely toto arisearise fromfrom a combinationcombination ofof twotwo effects.effects. First,First, cconsistentonsistent withwith thethe resultsresults forfor inpatientinpatient spending,spending, moremore seriousserious andand costlycostly medicalmedical eepisodespisodes maymay bebe lessless responsiveresponsive toto price.price. Second,Second, individualsindividuals withwith highhigh utilizationutilization ttypicallyypically hithit thethe MaximumMaximum DollarDollar ExpenditureExpenditure limitlimit earlyearly inin thethe coveragecoverage year,year, andand ssoo forfor muchmuch ofof theirtheir coveragecoverage periodperiod theythey faceface a coinsurancecoinsurance raterate ofof zerozero percentpercent rregardlessegardless ofof planplan assignment.assignment.

Threats to Validity TThehe ggreatreat sstrengthtrength ooff a rrandomizedandomized eexperimentalxperimental aapproach,pproach, ooff ccourse,ourse, iiss tthathat a sstraighttraight ccomparisonomparison ooff tthosehose rreceivingeceiving tthehe ttreatmentreatment aandnd tthosehose nnotot rreceivingeceiving tthehe ttreatment,reatment, llikeike tthehe rregressionegression ccoeffioeffi cientscients rreportedeported iinn TTableable 22,, ccanan pplausiblylausibly bbee iinterpretednterpreted aass a ccausalausal eeffectffect ooff tthehe ttreatment.reatment. HHowever,owever, tthishis iinterpretationnterpretation rrequiresequires tthathat nnoo ssystematicystematic ddifferencesifferences eexistxist aacrosscross iindividualsndividuals wwhoho pparticipatearticipate iinn tthehe ddifferentifferent pplanslans tthathat ccouldould bbee ccorrelatedorrelated wwithith mmeasuredeasured uutilization.tilization. IInn tthishis ssection,ection, wwee cconsideronsider iinn tturnurn tthreehree ppossibleossible ssourcesources ooff ssystematicystematic ddifferencesifferences tthathat nneedeed ttoo bbee cconsideredonsidered iinn aanyny rreal-worldeal-world eexperimentalxperimental ccontext:ontext: 11)) nnonrandomonrandom aassignmentssignment ttoo pplans,lans, 22)) ddiffer-iffer- eentialntial pparticipationarticipation iinn tthehe eexperimentxperiment aacrosscross ttreatmentreatment aarms,rms, aandnd 33)) ddifferentialifferential rreportingeporting ((inin tthishis ccase,ase, ooff mmedicaledical ccareare uutilization)tilization) aacrosscross ttreatmentreatment aarms.rms. TThehe fi rrstst ppotentialotential tthreathreat ttoo validityvalidity concernsconcerns wwhetherhether thethe stratifistratifi eded randomrandom aassignmentssignment ttoo pplans,lans, ddescribedescribed eearlier,arlier, wwasas ssuccessfullyuccessfully iimplemented.mplemented. TToo iinves-nves- ttigate,igate, wwee eestimatedstimated a vversionersion ooff tthehe eearlierarlier eequationquation bbut,ut, iinsteadnstead ooff uusingsing hhealthcareealthcare sspendingpending asas thethe dependentdependent variable,variable, wewe usedused asas outcomesoutcomes variousvarious ppersonalersonal ccharacteristics,haracteristics, ssuchuch aass aagege oorr eeducation,ducation, ooff ppeopleeople aassignedssigned ttoo ddifferentifferent pplans.lans. IInn eeffect,ffect, ssuchuch rregressionsegressions sshowhow wwhetherhether ttherehere iiss a statisticallystatistically signifisignifi cantcant ccorrelationorrelation bbetweenetween aanyny pparticulararticular ccharacteristicharacteristic ooff a ppersonerson aandnd tthehe pplanlan ttoo wwhichhich tthathat ppersonerson wwasas aassigned—whichssigned—which wwouldould bbee a wwarningarning ssignign fforor cconcernoncern aaboutbout tthehe rrandomizationandomization pprocess.rocess. WWee fi rstrst focusedfocused onon characteristicscharacteristics uusedsed bbyy tthehe investiga-investiga- ttorsors iinn tthehe fi nniteite sselectionelection mmodelodel tthathat ddeterminedetermined tthehe rrandomization,andomization, iincluding,ncluding, fforor example,example, variablesvariables forfor sizesize ofof family,family, ageage categories,categories, educationeducation level,level, income,income, sself-reportedelf-reported hhealthealth sstatus,tatus, aandnd uusese ooff mmedicaledical ccareare iinn tthehe yyearear ppriorrior ttoo tthehe sstarttart ooff tthehe eexperiment.xperiment. UUnsurprisingly,nsurprisingly, ggiveniven tthathat tthehe aassignmentssignment aalgorithmlgorithm wwasas eexplic-xplic- iitlytly ddesignedesigned ttoo achieveachieve balancesbalances acrossacross planplan assignmentassignment onon thesethese characteristics,characteristics, oourur sstatisticaltatistical ttestsests aarere uunablenable ttoo rrejecteject tthehe nnullull tthathat tthehe ccharacteristicsharacteristics uusedsed iinn sstratifitratifi ccationation aarere bbalancedalanced aacrosscross pplans.lans. ((MoreMore sspecifipecifi ccally,ally, wwee uusedsed a jjointoint F--test,test, aass rreportedeported iinn ppanelanel A ooff TTableable AA33 ooff tthehe onlineonline AppendixAppendix aavailablevailable wwithith tthishis ppaperaper aatt hhttp://e-jep.org.)ttp://e-jep.org.) WWee nnextext eestimatedstimated thesethese samesame typestypes ofof regressions,regressions, butbut nownow usingusing asas thethe depen-depen- ddentent vvariableariable iindividualndividual characteristicscharacteristics notnot usedused byby thethe ooriginalriginal researchersresearchers inin planplan aassignment.ssignment. TThesehese include,include, forfor example,example, thethe kindkind ofof iinsurancensurance (if(if any)any) thethe personperson 206 Journal of Economic Perspectives

hhadad ppriorrior toto thethe experiment,experiment, whetherwhether familyfamily membersmembers grewgrew upup inin a city,city, suburb,suburb, oror ttown,own, aandnd sspendingpending oonn mmedicaledical ccareare aandnd ddentalental ccareare ppriorrior ttoo tthehe eexperiment.xperiment. UUsingsing tthesehese statistics,statistics, people’speople’s characteristicscharacteristics diddid notnot appearappear toto bebe randomlyrandomly distributeddistributed aacrosscross thethe plansplans (as(as shownshown byby thethe jointjoint F--testtest resultsresults inin panelpanel B ofof TableTable A3A3 ofof thethe oonlinenline Appendix).Appendix). However,However, asas wewe lookedlooked moremore closely,closely, thisthis resultresult appearedappeared toto bebe ddrivenriven onlyonly byby assignmentassignment inin thethe 5050 percentpercent coinsurancecoinsurance plan,plan, whichwhich hashas relativelyrelatively ffewew ppeopleeople assignedassigned toto it.it. WhileWhile thesethese imbalancesimbalances maymay havehave beenbeen duedue toto samplingsampling vvariation,ariation, therethere maymay aalsolso hhaveave bbeeneen somesome pproblemroblem wwithith tthehe aassignmentssignment ooff ffamiliesamilies ttoo tthehe 5500 ppercentercent pplan;lan; iindeed,ndeed, midwaymidway tthroughhrough thethe assignmentassignment processprocess thethe RANDRAND iinvestigatorsnvestigators stoppedstopped assigningassigning familiesfamilies toto thisthis plan.plan. WithWith thisthis (small)(small) planplan deleted,deleted, oourur statisticalstatistical teststests areare unableunable toto rejectreject thethe nullnull hypothesishypothesis thatthat covariatescovariates thatthat werewere nnotot usedused inin stratifistratifi ccationation aarere aalsolso bbalancedalanced aacrosscross pplans.lans. WeWe proceedproceed belowbelow onon thethe aassumptionssumption thatthat thethe initialinitial randomizationrandomization waswas inin factfact valid—atvalid—at leastleast forfor allall plansplans eexceptxcept forfor thethe 5050 percentpercent coinsurancecoinsurance plan.plan. However,However, wewe alsoalso assessassess thethe sensitivitysensitivity ooff tthehe rresultsesults ttoo tthehe iinclusionnclusion ooff bbaselineaseline ccovariatesovariates asas controls.controls. TToo examineexamine thethe secondsecond threatthreat toto validity—thevalidity—the concernconcern thatthat differentialdifferential partici-partici- ppationation acrossacross plansplans mightmight affectaffect thethe fi ndings—wendings—we beginbegin withwith thethe observationobservation thatthat iindividualsndividuals assignedassigned toto moremore comprehensivecomprehensive insuranceinsurance willwill havehave greatergreater incentiveincentive ttoo participateparticipate inin thethe experiment.experiment. Indeed,Indeed, thethe RANDRAND investigatorsinvestigators anticipatedanticipated thisthis iissue,ssue, andand attemptedattempted toto offsetoffset thesethese differentialdifferential incentivesincentives byby offeringoffering a higherhigher llumpump ssumum ppaymentayment fforor tthosehose rrandomizedandomized iintonto lless-comprehensiveess-comprehensive pplans.lans. WWhilehile tthishis ddifferentialifferential paymentpayment maymay mmakeake pparticipationarticipation iincentivesncentives mmoreore ssimilarimilar aacrosscross pplans,lans, iitt ccanan ddoo ssoo onlyonly onon average.average. UnlessUnless thethe participationparticipation incentiveincentive variesvaries withwith a family’sfamily’s ppre-experimentre-experiment expectationexpectation ofof medicalmedical spendingspending (and(and itit diddid not),not), thethe incrementalincremental bbenefienefi t fromfrom moremore comprehensivecomprehensive coveragecoverage remainsremains greatergreater forfor individualsindividuals whowho aanticipatenticipate ggreaterreater mmedicaledical sspending.pending. TThus,hus, differentialdifferential participationparticipation (or(or attrition)attrition) couldcould biasbias thethe estimatesestimates ofof thethe sspendingpending rresponseesponse toto coverage.coverage. ForFor example,example, ifif individualsindividuals incurincur a fi xedxed costcost ofof pparticipatingarticipating iinn tthehe eexperiment,xperiment, hhigh-expected-spendingigh-expected-spending iindividualsndividuals mmightight ppartici-artici- ppateate rregardlessegardless ofof planplan assignment,assignment, butbut lower-expected-spendinglower-expected-spending individualsindividuals mightmight bbee iinclinednclined toto dropdrop outout ifif notnot randomizedrandomized intointo a comprehensivecomprehensive plan,plan, whichwhich couldcould bbiasias ddownwardownward thethe estimatedestimated effecteffect ofof insuranceinsurance coveragecoverage onon medicalmedical utilization.utilization. AAlternatively,lternatively, iiff hhigh-expected-spendingigh-expected-spending andand low-expected-spendinglow-expected-spending familiesfamilies werewere aaboutbout equallyequally likelylikely toto participateparticipate inin thethe experimentexperiment whenwhen assignedassigned toto thethe freefree ccareare plan,plan, butbut high-expected-spendinghigh-expected-spending familiesfamilies werewere lessless likelylikely thanthan low-expected-low-expected- sspendingpending ffamiliesamilies ttoo pparticipatearticipate wwhenhen aassignedssigned ttoo lless-comprehensiveess-comprehensive pplans,lans, tthishis ddifferentialifferential selectionselection wouldwould biasbias upwardupward thethe estimatedestimated effecteffect ofof insuranceinsurance coveragecoverage oonn mmedicaledical uutilization.tilization. CColumnsolumns 4 – 6 ofof TableTable 1 presentedpresented earlierearlier suggestsuggest scopescope forfor biasbias fromfrom differ-differ- eentialntial participationparticipation acrossacross plans.plans. Overall,Overall, 7676 percentpercent ofof thethe individualsindividuals offeredoffered eenrollmentnrollment endedended upup completingcompleting thethe experiment.experiment. CompletionCompletion ratesrates werewere substan-substan- ttiallyially andand systematicallysystematically higherhigher inin more-comprehensivemore-comprehensive insuranceinsurance plans,plans, rangingranging ffromrom 8888 ppercentercent iinn tthehe ((mostmost ccomprehensive)omprehensive) freefree carecare planplan toto 6363 percentpercent inin thethe ((leastleast comprehensive)comprehensive) 9595 percentpercent coinsurancecoinsurance plan.plan. MostMost ofof thethe differencedifference inin Aviva Aron-Dine, Liran Einav, and Amy Finkelstein 207

ccompletionompletion ratesrates acrossacross plansplans waswas duedue toto differencesdifferences inin initialinitial enrollmentenrollment rates—rates— tthathat is,is, tthehe shareshare ofof familiesfamilies refusingrefusing coveragecoverage fromfrom thethe experiment—althoughexperiment—although ssubsequentubsequent attritionattrition fromfrom thethe experimentexperiment alsoalso playsplays a nontrivialnontrivial role.role. AsAs shownshown inin tthehe bottombottom rowsrows ofof TableTable 1,1, neitherneither thethe initialinitial refusalrefusal nornor thethe subsequentsubsequent attritionattrition ddifferentialsifferentials ccanan bbee aattributedttributed ttoo ssamplingampling vvariationariation aalone.lone. TThehe ddifferentialifferential participationparticipation byby planplan assignmentassignment waswas notednoted andand investigatedinvestigated bbyy tthehe ooriginalriginal RANDRAND investigatorsinvestigators (Newhouse(Newhouse etet al.al. 1993,1993, ChapterChapter 2).2). TheThe RANDRAND iinvestigatorsnvestigators primarilyprimarily investigatedinvestigated attritionattrition (rather(rather thanthan refusal),refusal), andand focusedfocused onon ttestingesting particularparticular mechanismsmechanisms byby whichwhich biasbias mightmight havehave arisen.arisen. WeWe tooktook a moremore aagnosticgnostic vviewiew aandnd iimplementedmplemented aann oomnibusmnibus ttestest fforor ddifferencesifferences inin availableavailable observ-observ- aableble pre-randomizationpre-randomization characteristicscharacteristics amongamong thosethose completingcompleting thethe experimentexperiment iinn tthehe differentdifferent plans—andplans—and wewe reachreach somewhatsomewhat differentdifferent conclusions.conclusions. First,First, wewe ddividedivided upup allall thethe pre-randomizationpre-randomization measuresmeasures intointo twotwo groups:groups: thosethose thatthat directlydirectly mmeasureeasure ppriorrior hhealthcareealthcare utilization—whichutilization—which areare closelyclosely relatedrelated toto thethe primaryprimary ppost-randomizationost-randomization ooutcomes—andutcomes—and aallll ootherther bbaselineaseline ddemographicemographic iinformation.nformation. FForor eithereither setset ofof covariatescovariates (or(or forfor bothboth combined)combined) wewe areare ableable toto rejectreject atat thethe 1 percentpercent levellevel thatthat tthesehese ppre-randomizationre-randomization covariatescovariates areare balancedbalanced acrossacross plansplans fforor tthosehose ccompletingompleting tthehe eexperimentxperiment ((usingusing a jjointoint F--test;test; sseeee TTableable A4A4 inin thethe onlineonline AAppendixppendix forfor additionaladditional details).details). TheseThese differentialsdifferentials mostlymostly reflrefl ectect imbalancesimbalances thatthat aariserise aafterfter aassignment.ssignment.6 OfOf pparticulararticular nnote,ote, bbyy tthehe eendnd ooff tthehe eexperiment,xperiment, ttherehere aarere iimbalancesmbalances acrossacross plansplans inin pparticipants’articipants’ averageaverage numbernumber ofof ddoctors’octors’ visitsvisits iinn tthehe yyearear bbeforeefore thethe experimentexperiment andand inin thethe shareshare ofof participantsparticipants whowho hadhad a medicalmedical examexam inin tthehe yyearear bbeforeefore tthehe eexperiment.xperiment. TThehe potentialpotential biasbias fromfrom differentialdifferential nonresponsenonresponse oror attritionattrition acrossacross experi-experi- mmentalental treatmentstreatments isis nownow a well-knownwell-known concernconcern forfor analysisanalysis ofof randomizedrandomized socialsocial eexperiments.xperiments. FForor eexample,xample, AAshenfeltershenfelter aandnd PPlantlant ((1990)1990) ddocumentocument tthehe ccontamina-ontamina- ttionion toto estimatesestimates arisingarising fromfrom nonrandomnonrandom attritionattrition inin thethe NegativeNegative IncomeIncome TaxTax eexperimentsxperiments ffromrom tthehe 11970s,970s, wwhichhich wwereere iimplementedmplemented aaroundround tthehe ssameame ttime.ime. WWee ddiscussiscuss bbelowelow ppossibleossible wwaysays ooff ttryingrying ttoo aaccountccount forfor thisthis potentialpotential bias.bias. FFinally,inally, thethe thirdthird potentialpotential threatthreat toto validityvalidity isis thethe extentextent toto whichwhich participantsparticipants iinn moremore comprehensivecomprehensive plansplans hadhad differentialdifferential incentivesincentives toto reportreport theirtheir medicalmedical sspending.pending. DataData onon medicalmedical utilizationutilization andand expendituresexpenditures fromfrom experimentalexperimental partici-partici- ppantsants werewere obtainedobtained fromfrom MedicalMedical ExpenseExpense ReportReport (“claims”)(“claims”) formsforms whichwhich requiredrequired a provider’sprovider’s signaturesignature andand whichwhich thethe participantparticipant (or(or thethe healthcarehealthcare provider)provider) hhadad toto fi lele withwith thethe experimentexperiment inin orderorder toto bebe reimbursedreimbursed forfor thethe expenditure.expenditure. TThehe incentiveincentive forfor fi lingling claimsclaims waswas toto getget reimbursed,reimbursed, andand soso thethe fi llinging incentiveincentive wwasas weakerweaker forfor participantsparticipants enrolledenrolled inin higherhigher coinsurancecoinsurance raterate plansplans (or(or theirtheir pproviders)roviders) thanthan forfor thosethose enrolledenrolled inin lowerlower coinsurancecoinsurance raterate plansplans oror thethe freefree carecare pplan.lan. ForFor example,example, a participantparticipant assignedassigned toto thethe 9595 percentpercent coinsurancecoinsurance plan,plan, whowho hhadad yetyet toto satisfysatisfy thethe MaximumMaximum DollarDollar Expenditure,Expenditure, wouldwould havehave hadhad littlelittle toto gaingain ffromrom fi lingling a claimclaim towardtoward thethe endend ofof thethe coveragecoverage year.year. ThisThis differentialdifferential reportingreporting

6 This can be seen by comparing the balance at completion rates in Table A4 to the balance at assignment results in Table A3; both tables are in the online Appendix. 208 Journal of Economic Perspectives

wwouldould thereforetherefore bebe expectedexpected toto biasbias thethe estimatesestimates inin thethe directiondirection ofof overstatingoverstating tthehe spendingspending responseresponse toto coverage.coverage.7 AAgain,gain, tthehe ooriginalriginal RRANDAND iinvestigatorsnvestigators aanticipatednticipated thisthis ppotentialotential pproblemroblem aandnd cconductedonducted a contemporaneouscontemporaneous surveysurvey toto trytry toto determinedetermine thethe extentextent ofof thethe rreportingeporting biasbias (Rogers(Rogers andand NewhouseNewhouse 1985).1985). InIn thisthis studystudy ofof roughlyroughly one-thirdone-third ofof aallll eenrollees,nrollees, thethe investigatorsinvestigators contactedcontacted thethe providersproviders forfor whomwhom claimsclaims werewere fi ledled bbyy tthehe pparticipantarticipant oror hishis familyfamily members,members, asas wellwell asas a randomrandom subsetsubset ofof providersproviders mmentionedentioned byby otherother participants.participants. FromFrom thesethese providers,providers, theythey requestedrequested allall outpa-outpa- ttientient bbillingilling rrecordsecords fforor tthehe pparticipantsarticipants aandnd ffamilyamily mmembers.embers. FForor tthehe 5577 ppercentercent ooff pprovidersroviders whowho responded,responded, thethe investigatorsinvestigators matchedmatched thethe outpatientoutpatient billingbilling recordsrecords ttoo tthehe eexperiments’xperiments’ outpatientoutpatient claimsclaims datadata andand computedcomputed thethe amountsamounts corre-corre- sspondingponding toto matchedmatched andand unmatchedunmatched billingbilling records.records. TheThe resultsresults indicateindicate that,that, onon aaverage,verage, participantsparticipants inin thethe freefree carecare planplan failedfailed toto fi lele claimsclaims forfor 4 percentpercent ofof theirtheir ttotalotal ooutpatientutpatient spending,spending, whilewhile thosethose inin tthehe 9955 ppercentercent ccoinsuranceoinsurance planplan ffailedailed ttoo fi lele claimsclaims forfor 1212 percentpercent ofof theirtheir totaltotal outpatientoutpatient spending.spending. UnderreportingUnderreporting bbyy pparticipantsarticipants inin thethe otherother plansplans fellfell inin betweenbetween thesethese twotwo extremesextremes (Rogers(Rogers andand NNewhouseewhouse 1985,1985, TableTable 7.3).7.3). OnceOnce again,again, inin whatwhat followsfollows wewe willwill attemptattempt toto adjustadjust tthehe eestimatesstimates ttoo aaddressddress tthehe bbiasias tthathat mmayay aariserise ffromrom tthishis ggreaterreater uunderreportingnderreporting ooff eexpendituresxpenditures iinn tthehe hhigherigher ccost-sharingost-sharing pplans.lans.

Robustness of Treatment Effects TThehe potentialpotential forfor biasbias inin thethe RANDRAND experimentexperiment hashas beenbeen a sourcesource ofof somesome rrecentecent controversy:controversy: forfor example,example, NymanNyman (2007,(2007, 2008)2008) raisesraises concernsconcerns aboutabout biasbias sstemmingtemming ffromrom ddifferentialifferential pparticipationarticipation aacrosscross pplans,lans, aandnd tthehe RRANDAND iinvestigatorsnvestigators oofferffer a rebuttalrebuttal inin NewhouseNewhouse etet al.al. (2008).(2008). ToTo ourour knowledge,knowledge, however,however, therethere hashas bbeeneen nnoo aattemptttempt ttoo qquantifyuantify tthehe ppotentialotential mmagnitudeagnitude ooff tthehe bbias.ias. NNor,or, ttoo oourur kknowl-nowl- eedge,dge, hashas therethere beenbeen a formalformal attemptattempt toto quantifyquantify thethe potentialpotential biasbias arisingarising fromfrom thethe ddifferentialifferential rreportingeporting ddocumentedocumented bbyy RRogersogers aandnd NNewhouseewhouse ((1985).1985). TTableable 3 rreportseports ourour resultsresults fromfrom suchsuch attempts.attempts. TheThe differentdifferent columnscolumns reportreport rresultsesults fforor ddifferentifferent mmeasureseasures ooff sspending,pending, whilewhile thethe differentdifferent panelspanels showshow resultsresults fforor ddifferentifferent pairwisepairwise planplan combinations:combinations: freefree carecare versusversus 9595 percentpercent coinsurance;coinsurance; ffreeree ccareare vversusersus 2255 ppercentercent coinsurance;coinsurance; andand 2525 percentpercent versusversus 9595 percentpercent coinsur-coinsur- aance.nce. ForFor each,each, wewe reportreport resultsresults fromfrom fourfour differentdifferent specifispecifi cations.cations. RowRow 1 ofof eacheach ppanelanel rreplicateseplicates thethe baselinebaseline resultsresults fromfrom TTableable 22,, wwherehere hhereere wwee aalsolso sshowhow eestimatesstimates ffromrom llogog sspecifipecifi cationscations duedue toto thethe eextremextreme ssensitivityensitivity ooff tthehe llevelsevels eestimatesstimates ttoo ssomeome ooff oourur aadjustments.djustments. WWee beginbegin inin rowrow 2,2, byby tryingtrying toto adjustadjust thethe estimatesestimates forfor thethe differentialdifferential fi lingling ofof cclaimslaims bbyy pplanlan ddetectedetected byby RogersRogers andand NewhouseNewhouse (1985).(1985). SpecifiSpecifi cally,cally, wewe propor-propor- ttionallyionally scalescale upup ooutpatientutpatient spendingspending forfor participantsparticipants inin eacheach planplan basedbased onon thethe pplan-specifilan-specifi c underreportingunderreporting percentagespercentages theythey reportreport (Rogers(Rogers andand NewhouseNewhouse 1985,1985,

7 Once again, this issue of differential reporting incentives by experimental assignment also plagued the Negative Income Tax experiments in the 1970s (Greenberg and Hasley 1983). The RAND Health Insurance Experiment, Three Decades Later 209

Table 3 Sensitivity of Results to Additional Covariates and Bounding Exercises

Total spending Inpatient spending Outpatient spending

Share Share Share with Spending Spending with Spending with Spending Spending any (in $) (in logs) any (in $) any (in $) (in logs) (1) (2) (3) (4) (5) (6) (7) (8)

Panel A: 95% Coinsurance plan vs. Free Care (N = 10,564) (1) Baseline specifi cation (from – 0.170 – 845 –1.381 – 0.024 – 217 – 0.171 – 629 –1.361 Table 2) (0.015) (119) (0.096) (0.007) (91) (0.016) (50) (0.093) (2) Adjusted for underreporting – 0.100 –786 –1.313 – 0.024 – 217 – 0.102 – 582 –1.299 (0.017) (123) (0.097) (0.007) (91) (0.018) (55) (0.095) (3) Adjusted for underreporting – 0.095 –728 –1.276 – 0.023 –183 – 0.096 – 558 –1.261 + controlling for (0.016) (111) (0.087) (0.007) (85) (0.016) (50) (0.084) pre-randomization covariates

(4) Lee bounds + adjusted – 0.080 745 –0.672 0.079 592 – 0.081 151 – 0.751 for underreporting (0.018) (96) (0.098) (0.005) (71) (0.018) (38) (0.095)

Panel B: 25% Coinsurance plan vs. Free Care (N = 9,201) (1) Baseline specifi cation (from – 0.079 – 648 – 0.747 – 0.022 – 229 – 0.078 – 420 – 0.719 Table 2) (0.015) (152) (0.095) (0.009) (116) (0.015) (62) (0.093) (2) Adjusted for underreporting – 0.065 – 645 – 0.734 – 0.022 – 229 – 0.065 – 418 – 0.706 (0.016) (155) (0.096) (0.009) (116) (0.016) (65) (0.094) (3) Adjusted for underreporting – 0.069 – 585 – 0.748 – 0.022 –181 – 0.068 – 405 – 0.718 + controlling for (0.014) (137) (0.084) (0.008) (107) (0.014) (59) (0.082) pre-randomization covariates

(4) Lee bounds + adjusted – 0.055 639 – 0.335 0.081 581 – 0.054 205 – 0.369 for underreporting (0.016) (133) (0.096) (0.008) (99) (0.016) (52) (0.093)

Panel C: 95% Coinsurance plan vs. 25% Coinsurance plan (N = 6,085) (1) Baseline specifi cation (from – 0.091 –197 – 0.633 – 0.002 12 – 0.093 –209 – 0.641 Table 2) (0.020) (160) (0.120) (0.009) (122) (0.020) (61) (0.117) (2) Adjusted for underreporting – 0.035 –141 – 0.579 – 0.002 12 – 0.037 –164 – 0.592 (0.022) (164) (0.122) (0.009) (122) (0.022) (66) (0.118) (3) Adjusted for underreporting – 0.026 –143 – 0.529 – 0.001 – 2 – 0.028 –153 – 0.543 + controlling for (0.019) (141) (0.106) (0.009) (108) (0.019) (60) (0.103) pre-randomization covariates (4) Lee bounds + adjusted for – 0.020 764 – 0.248 0.078 657 – 0.021 185 – 0.313 underreporting (0.022) (105) (0.120) (0.006) (78) (0.023) (42) (0.117)

Notes: The table reports coeffi cients on plan dummies from an ordinary least squares regression; the ommitted category is the free care plan. The dependent variable is given in the column headings. Standard errors are in parentheses below the coeffi cients. Standard errors are clustered on familiy. Because assignment to plans was random only conditional on site and start month (Newhouse et al. 1993), all regressions include site by start month dummy variables, as well as year fi xed effects to adjust for infl ation; level regressions use infl ation-adjusted spending variables (in 2011 dollars, adjusted using the CPI-U). Log variables are defi ned as log(var + 1) to accommodate zero values. The regressions adding pre-randomization covariates as controls (row 3) include the full set of covariates shown in Table A4 of the online Appendix. Adjustment for underreporting and bounding procedures are explained in the main text. 210 Journal of Economic Perspectives

TTableable 7.3).7.3).8 WWee ddoo notnot makemake anyany adjustmentadjustment toto inpatientinpatient spendingspending becausebecause therethere isis nnoo sstudytudy onon underreportingunderreporting ofof inpatientinpatient spendingspending andand becausebecause wewe thinkthink inpatientinpatient sspendingpending isis llessess likelylikely toto bebe subjectsubject toto reportingreporting bias.bias. MostMost inpatientinpatient episodesepisodes werewere ccostlyostly eenoughnough tthathat eevenven pparticipantsarticipants inin thethe 9595 percentpercent coinsurancecoinsurance planplan shouldshould hhaveave hadhad strongstrong incentivesincentives toto fi lele claims,claims, becausebecause doingdoing soso wouldwould putput themthem closeclose ttoo oror overover theirtheir MaximumMaximum DollarDollar ExpenditureExpenditure limit.limit. Moreover,Moreover, claimsclaims forfor inpatientinpatient eepisodespisodes werewere generallygenerally fi ledled byby hospitals,hospitals, whichwhich hadhad largelarge billingbilling departmentsdepartments andand ssystematicystematic bbillingilling proceduresprocedures andand soso werewere ppresumablyresumably llessess llikelyikely tthanhan iindividualsndividuals ttoo ffailail toto fi lele claims.claims. AAss sshownhown inin rowrow 2,2, tthehe aadjustmentdjustment rreduceseduces tthehe eestimatedstimated effects,effects, bbutut nnotot bbyy mmuch.uch. TThehe remainingremaining rowsrows highlighthighlight thethe impactimpact ofof differentialdifferential participationparticipation acrossacross pplanslans onon thethe estimatesestimates fromfrom rowrow 2 thatthat accountaccount forfor differentialdifferential fi ling.ling. WeWe fi rstrst cconsideronsider thethe potentialpotential effecteffect ofof observableobservable differencesdifferences acrossacross thosethose whowho choosechoose toto pparticipatearticipate inin differentdifferent plans.plans. RowRow 3 quantifiquantifi eses thethe effecteffect ofof thethe observableobservable differ-differ- eencesnces iinn pparticipantarticipant ccharacteristicsharacteristics acrossacross plansplans bbyy rreestimatingeestimating tthehe rregressionegression ffromrom rrowow 2 butbut nownow controllingcontrolling forfor thethe fullfull setset ofof pre-randomizationpre-randomization covariates.covariates. TheseThese ccontrolsontrols reducereduce furtherfurther thethe estimatedestimated planplan treatmenttreatment effectseffects but,but, again,again, notnot byby mmuch.uch. OOff ccourse,ourse, tthishis iiss oonlynly rreassuringeassuring iinn ssoo ffarar aass wwee bbelieveelieve wwee hhaveave a vveryery rrichich ssetet ooff observablesobservables thatthat capturecapture muchmuch ofof thethe potentialpotential differencesdifferences acrossacross participantsparticipants inin tthehe ddifferentifferent pplans.lans. A ttrickierrickier issueissue isis howhow toto accountaccount forfor potentialpotential unobservableunobservable differencesdifferences acrossacross iindividualsndividuals whowho selectselect iintonto pparticipationarticipation iinn ddifferentifferent eexperimentalxperimental aarms.rms. TTherehere aare,re, bbroadlyroadly speaking,speaking, threethree mainmain aapproachespproaches ttoo tthishis pproblem.roblem. PProbablyrobably tthehe mmostost ddirectirect wwayay ttoo aaddressddress ppotentialotential bbiasias sstemmingtemming ffromrom ddifferentialifferential nnonparticipationonparticipation aacrosscross pplanslans wwouldould bbee ttoo ccollectollect ddataata oonn ooutcomesutcomes ((inin tthishis ccase,ase, hhealthcareealthcare uutilization)tilization) fforor aallll iindividuals,ndividuals, includingincluding thosethose whowho failedfailed toto completecomplete thethe experiment.experiment. SuchSuch datadata wwouldould allowallow comparisoncomparison ofof outcomesoutcomes forfor individualsindividuals basedbased onon initialinitial planplan assign-assign- mment,ent, rregardlessegardless ooff participation,participation, andand thenthen couldcould bebe usedused forfor unbiasedunbiased two-stagetwo-stage lleasteast ssquaresquares estimatesestimates ooff thethe effectseffects ofof costcost sharingsharing onon utilization.utilization. Unfortunately,Unfortunately, wwee knowknow ofof nono potentialpotential sourcesource ofof suchsuch data—individual-leveldata—individual-level hospitalhospital dischargedischarge rrecordsecords dodo not,not, toto ourour knowledge,knowledge, existexist fromfrom thisthis timetime period,period, andand eveneven ifif thethe rrecordsecords existed,existed, therethere isis nono legallegal permissionpermission toto matchmatch RANDRAND participantsparticipants (or(or nnonparticipants)onparticipants) ttoo aadministrativedministrative ddata.ata. A secondsecond approachapproach isis toto makemake assumptionsassumptions aboutabout thethe likelylikely economiceconomic modelmodel ofof sselectionelection andand uusese tthesehese ttoo aadjustdjust tthehe ppointoint eestimatesstimates aaccordingly.ccordingly. ((Angrist,Angrist, BBettinger,ettinger, aandnd KremerKremer 2006,2006, formalizeformalize oneone suchsuch approachapproach inin a veryvery differentdifferent experimentalexperimental ssetting.)etting.) TThen,hen, ddependingepending onon tthehe eeconomicconomic mmodelodel aassumed,ssumed, oonene mmightight cconcludeonclude

8 Rogers and Newhouse (1985) have no estimates of underreporting for those individuals with zero claims. In the regressions with binary outcomes (“any spending”) we somewhat arbitrarily scale up the shares of individuals by the same percentage as we scaled up spending among those who have positive spending amounts. When we analyze spending continuously, however, those who report no spending remain at zero. Aviva Aron-Dine, Liran Einav, and Amy Finkelstein 211

tthathat thethe existingexisting pointpoint estimatesestimates areare under-under- oror overestimatesoverestimates ofof thethe truetrue experi-experi- mmentalental ttreatmentreatment eeffects.ffects. A fi nnalal aapproach,pproach, aandnd tthehe oonene wwee ttakeake hhere,ere, iiss ttoo rremainemain aagnosticgnostic aaboutbout tthehe uunderlyingnderlying economiceconomic mechanismmechanism generatinggenerating thethe differentialdifferential selectionselection andand insteadinstead pperformerform a sstatisticaltatistical eexercisexercise ddesignedesigned ttoo fi ndnd a lowerlower boundbound forfor thethe treatmenttreatment eeffect.ffect. InIn otherother words,words, thisthis approachapproach isis designeddesigned toto askask thethe statisticalstatistical questionquestion ofof hhowow bbadad tthehe bbiasias ffromrom ddifferentialifferential pparticipationarticipation ccouldould bbe.e. SSpecifipecifi cally,cally, iinn rrowow 44,, wwee ffollowollow LLee’see’s ((2009)2009) bboundingounding pprocedurerocedure bbyy ddroppingropping tthehe ttopop ggrouproup ooff sspenderspenders iinn tthehe llowerower ccost-sharingost-sharing pplan.lan. TThehe ffractionraction ooff ppeopleeople ddroppedropped iiss cchosenhosen ssoo tthathat wwithith tthesehese iindividualsndividuals ddropped,ropped, pparticipationarticipation rratesates aarere eequalizedqualized bbetweenetween tthehe llowerower ccost-sharingost-sharing pplanlan aandnd tthehe hhigherigher ccost-sharingost-sharing pplanlan ttoo wwhichhich iitt iiss bbeingeing ccompared.ompared. AAss dderivederived bbyy LLee,ee, tthesehese rresultsesults pproviderovide wworst-caseorst-case llowerower bboundsounds fforor tthehe ttreatmentreatment eeffectffect uundernder tthehe aassumptionssumption tthathat aanyny pparticipantarticipant wwhoho rrefusedefused pparticipationarticipation iinn a ggiveniven pplanlan wwouldould aalsolso hhaveave rrefusedefused pparticipationarticipation iinn aanyny pplanlan wwithith a hhigherigher ccoinsuranceoinsurance rrate.ate. FForor eexample,xample, ssinceince 8888 ppercentercent ooff tthosehose aassignedssigned ttoo tthehe ffreeree ccareare pplanlan ccompletedompleted tthehe eexperimentxperiment ccomparedompared ttoo oonlynly 6633 ppercentercent ooff tthosehose aassignedssigned ttoo tthehe 9955 ppercentercent ccoinsuranceoinsurance ((TableTable 11,, ccolumnolumn 66),), fforor a ccomparisonomparison ooff tthesehese ttwowo pplans,lans, wwee ddroprop tthehe hhighestighest 2288 ppercentercent (((88(88 – 663)/88)3)/88) ooff sspenderspenders iinn tthehe ooriginalriginal ffreeree ccareare ssample,ample, tthushus oobtainingbtaining eequalqual pparticipationarticipation rratesates aacrosscross tthehe ttwowo ssamples.amples. OOurur pprimaryrimary cconclusiononclusion ffromrom TTableable 3 iiss tthathat aafterfter ttryingrying ttoo aadjustdjust fforor ddifferen-ifferen- ttialial sselectionelection aandnd ddifferentialifferential rreportingeporting bbyy pplan,lan, tthehe RRANDAND ddataata sstilltill rrejecteject tthehe nnullull hhypothesisypothesis ooff nnoo uutilizationtilization rresponseesponse ttoo ccostost ssharing.haring.9 IInn pparticular,articular, wwhenhen tthehe ooutcomeutcome iiss totaltotal spending,spending, oourur aabilitybility ttoo rrejecteject tthehe nnullull tthathat uutilizationtilization ddoesoes nnotot rrespondespond ttoo cconsumeronsumer ccostost ssharingharing ssurvivesurvives aallll ooff oourur aadjustmentsdjustments iinn ttwowo ooff tthehe tthreehree sspecifipecifi cca-a- ttions:ions: aanyny sspendingpending aandnd llogog sspending.pending.1100 TThehe sensitivitysensitivity analysisanalysis does,does, however,however, revealreveal considerableconsiderable uncertaintyuncertainty aboutabout thethe mmagnitudeagnitude ooff tthehe rresponseesponse ttoo ccostost ssharing.haring. TThehe ccombinationombination ooff aadjustingdjusting fforor ddiffer-iffer- eentialntial rreportingeporting aandnd tthehe LLeeee ((2009)2009) bboundingounding eexercisexercise iinn rrowow 4 oopenspens uupp sscopecope fforor tthehe possibilitypossibility thatthat thethe treatmenttreatment effectseffects couldcould bebe substantiallysubstantially lowerlower thanthan whatwhat isis iimpliedmplied bbyy tthehe uunadjustednadjusted ppointoint eestimates.stimates. FForor eexample,xample, ffocusingocusing oonn ccolumnolumn 33,, oourur ppointoint estimateestimate inin rowrow 1 indicatesindicates thatthat spendingspending underunder thethe 9595 percentpercent coinsurancecoinsurance

9 Perhaps not surprisingly, there are statistical assumptions under which one cannot still reject this null. For example, we show in Table A5 of the online Appendix what we believe are (too) extreme worst-case bounds under which we can no longer reject the null. Specifi cally, following Manski (1990), for each year in which an individual should have been but was not present in the experiment (due to refusal or attrition), we impute the values that would minimize the treatment effect, and then further adjust the data for differential claim fi ling by plan, as before. 10 In all cases, the statistically signifi cant decline in the mean level of spending (column 2) is not robust to the bounding exercises in row 4. We think that this result is driven by the skewness of medical spending, which makes the results extremely sensitive to dropping the top 10–30 percent of spenders. In addition, we note that in some cases, the lower bounds appear to be statistically signifi cant but with the “wrong” sign. Given strong a priori reasons to think that higher cost-sharing will not raise medical utilization, we interpret these results as simply showing that we cannot reject the null. 212 Journal of Economic Perspectives

pplanlan iiss 7755 ppercentercent llowerower tthanhan uundernder tthehe ffreeree ccareare pplan,lan, bbutut tthehe aadjusteddjusted llowerower bboundound eestimatestimate iinn rrowow 4 ssuggestsuggests tthathat sspendingpending mmayay oonlynly bbee 4499 ppercentercent llower.ower.1111 TTableable 3 alsoalso showsshows thatthat wewe cancan continuecontinue toto rejectreject thethe nullnull ofof nono responseresponse ofof ooutpatientutpatient spendingspending fforor eeitherither tthehe ““anyany sspending”pending” sspecifipecifi cationcation oror thethe loglog specifispecifi ca-ca- ttionion bbutut aarere nnoo llongeronger aableble ttoo rrejecteject tthehe nnullull ooff nnoo rresponseesponse ooff inpatient utilizationutilization toto hhigherigher ccostost ssharing.haring. TThehe bboundingounding eexercisexercise iindicatesndicates tthathat tthehe rresponseesponse ooff iinpatientnpatient sspendingpending isis nnotot rrobustobust toto plausibleplausible adjustmentsadjustments forfor nonparticipationnonparticipation bias,bias, andand thusthus tthehe RANDRAND datadata dodo notnot necessarilynecessarily rejectreject (although(although theythey alsoalso dodo notnot conficonfi rm)rm) thethe hhypothesisypothesis ooff nnoo ppricerice rresponsivenessesponsiveness ooff iinpatientnpatient sspending.pending. FFinally,inally, itit iiss wworthorth reemphasizingreemphasizing thatthat thethe resultsresults inin rowrow 4 ofof TableTable 3 representrepresent lower bounds, ratherrather thanthan alternativealternative pointpoint estimates.estimates. WeWe interpretinterpret thethe exerciseexercise asas iindicatingndicating thatthat tthehe uunadjustednadjusted pointpoint eestimatesstimates ccouldould ssubstantiallyubstantially ooverstateverstate tthehe ccausalausal eeffectffect ooff ccostost ssharingharing oonn hhealthcareealthcare uutilization.tilization.

Estimating the Effect of Cost Sharing on Medical Spending

TThehe mmostost eenduringnduring llegacyegacy ooff tthehe RRANDAND eexperimentxperiment iiss nnotot mmerelyerely tthehe rrejectionejection ooff tthehe nnullull hhypothesisypothesis tthathat ppricerice ddoesoes nnotot aaffectffect mmedicaledical uutilization,tilization, bbutut rratherather tthehe uusese ooff tthehe RRANDAND resultsresults toto forecastforecast thethe spendingspending effectseffects ofof otherother healthhealth insuranceinsurance ccontracts.ontracts. InIn eextrapolatingxtrapolating thethe RANDRAND resultsresults outout ofof sample,sample, analystsanalysts havehave ggenerallyenerally rreliedelied oonn tthehe RRANDAND eestimatestimate ooff a ppricerice eelasticitylasticity ooff ddemandemand fforor mmedicaledical sspendingpending ooff – 0.20.2 (for(for whichwhich Manning,Manning, Newhouse,Newhouse, Duan,Duan, Keeler,Keeler, Leibowitz,Leibowitz, andand MarquisMarquis 1987,1987, isis wwidelyidely ccited,ited, bbutut KKeelereeler aandnd RRolpholph 11988,988, iiss tthehe uunderlyingnderlying source).source). TThishis – 00.2.2 elasticityelasticity estimateestimate isis usuallyusually treatedtreated asas ifif itit emergedemerged directlydirectly fromfrom thethe rrandomizedandomized experiment,experiment, andand isis oftenoften ascribedascribed thethe kindkind ofof reverencereverence thatthat mightmight bebe mmoreore appropriatelyappropriately reservedreserved forfor universaluniversal constantsconstants likelike π.π. DespiteDespite thisthis treatment,treatment, tthehe ffamousamous eelasticitylasticity eestimatestimate iiss iinn ffactact dderivederived ffromrom a ccombinationombination ooff eexperimentalxperimental ddataata aandnd aadditionaldditional modelingmodeling andand statisticalstatistical assumptions,assumptions, asas aanyny oout-of-sampleut-of-sample eextrapolationxtrapolation ofof experimentalexperimental treatmenttreatment effectseffects mustmust be.be. InIn usingusing iitt ooutut ooff ssample,ample, oonene nnecessarilyecessarily cconfrontsonfronts a nnumberumber ooff sstatisticaltatistical aass wwellell aass eeconomicconomic iissues.ssues.

Some Simple Attempts to Arrive at Estimates of the Price Elasticity A mmajorajor cchallengehallenge forfor anyany researcherresearcher attemptingattempting toto transformtransform thethe fi ndingsndings fromfrom eexperimentalxperimental treatmenttreatment eeffectsffects ooff hhealthealth iinsurancensurance ccontractsontracts iintonto aann eestimatestimate ooff tthehe ppricerice eelasticitylasticity ooff ddemandemand fforor mmedicaledical ccareare iiss tthathat hhealthealth iinsurancensurance ccontracts—bothontracts—both iinn thethe realreal worldworld andand inin thethe RANDRAND experiment—areexperiment—are highlyhighly nonlinear,nonlinear, withwith thethe ppricerice ffacedaced bbyy tthehe cconsumeronsumer ttypicallyypically ffallingalling aass ttotalotal mmedicaledical sspendingpending aaccumulatesccumulates dduringuring thethe year.year. TheThe RANDRAND contracts,contracts, forfor example,example, requiredrequired somesome initialinitial positivepositive ccostost ssharing,haring, butbut oout-of-pocketut-of-pocket spendingspending fallsfalls toto zzeroero aafterfter tthehe MMaximumaximum DDollarollar EExpenditurexpenditure isis reached.reached. MoreMore generally,generally, pricingpricing underunder a typicaltypical healthhealth insuranceinsurance

11 We translate the coeffi cients in column 3 into percentages by exponentiating and subtracting from one. The RAND Health Insurance Experiment, Three Decades Later 213

ccontractontract mightmight beginbegin withwith a consumerconsumer facingfacing anan out-of-pocketout-of-pocket priceprice ofof 100100 percentpercent ooff hishis medicalmedical expenditureexpenditure untiluntil a deductibledeductible isis reached,reached, atat whichwhich pointpoint thethe marginalmarginal ppricerice ffallsalls ssharplyharply toto thethe coinsurancecoinsurance raterate thatthat isis typicallytypically aroundaround 1010 –20–20 percent,percent, aandnd tthenhen ffallsalls ttoo zzeroero ooncence aann oout-of-pocketut-of-pocket limitlimit hhasas bbeeneen rreached.eached. DDueue toto thethe nonlinearnonlinear formform ofof thethe healthhealth insuranceinsurance contracts,contracts, anyany researcherresearcher wwhoho attemptsattempts toto summarizesummarize thethe experimentexperiment withwith a singlesingle priceprice elasticityelasticity mustmust makemake sseveraleveral decisions.decisions. OneOne questionquestion isis howhow toto analyzeanalyze medicalmedical expendituresexpenditures thatthat occuroccur aatt differentdifferent times,times, andand thereforetherefore underunder potentiallypotentially differentdifferent cost-sharingcost-sharing rules,rules, bbutut whichwhich stemstem fromfrom thethe samesame underlyingunderlying healthhealth event.event. AnotherAnother issueissue isis thatthat thethe rresearcheresearcher hashas toto makemake anan assumptionassumption asas toto whichwhich priceprice individualsindividuals respondrespond toto inin mmakingaking theirtheir medicalmedical spendingspending decision.decision. ItIt isis notnot obviousobvious whatwhat singlesingle priceprice toto use.use. OOnene mightmight useuse 1)1) thethe currentcurrent “spot”“spot” priceprice ofof carecare paidpaid atat thethe timetime healthcarehealthcare sserviceservices areare receivedreceived (on(on thethe assumptionassumption thatthat individualsindividuals areare fullyfully myopic),myopic), 2)2) thethe eexpectedxpected end-of-yearend-of-year priceprice (based(based onon thethe assumptionassumption thatthat individualsindividuals areare fullyfully fforwardorward lookinglooking andand withwith anan explicitexplicit modelmodel ofof expectationexpectation formation),formation), 3)3) thethe real-real- iizedzed end-of-yearend-of-year priceprice (on(on thethe assumptionassumption thatthat changeschanges inin healthcarehealthcare consumptionconsumption hhappenappen atat thatthat margin),margin), oror perhapsperhaps 4)4) somesome weighted-averageweighted-average ofof thethe pricesprices paidpaid ooverver a year.year. TheseThese typestypes ofof modelingmodeling challengeschallenges —which—which werewere thoroughlythoroughly studiedstudied aandnd thoughtthought throughthrough byby thethe originaloriginal RANDRAND investigatorsinvestigators (Keeler,(Keeler, Newhouse,Newhouse, andand PPhelpshelps 1977)—are1977)—are inherentinherent toto thethe problemproblem ofof extrapolatingextrapolating fromfrom estimatesestimates ofof thethe sspendingpending impactimpact ofof particularparticular healthhealth insuranceinsurance plansplans andand inin thisthis sensesense areare notnot uuniquenique toto thethe RANDRAND experiment.experiment. TToo ggetet ssomeome iideadea ooff tthehe cchallengeshallenges iinvolvednvolved iinn ttranslatingranslating tthehe eexperimentalxperimental ttreatmentreatment eeffectsffects iintonto aann eestimatestimate ooff tthehe ppricerice eelasticitylasticity ooff ddemand,emand, TTableable 4 rreportseports a sserieseries ooff eelasticitylasticity eestimatesstimates tthathat ccanan bbee oobtainedbtained ffromrom ddifferent,ifferent, rrelativelyelatively ssimpleimple aandnd ttransparentransparent aad-hocd-hoc mmanipulationsanipulations ooff tthehe bbasicasic eexperimentalxperimental ttreatmentreatment eeffects.ffects. IInn ppanelanel A ooff TTableable 4 wwee cconvert—separatelyonvert—separately fforor eeachach ppairair ooff pplans—thelans—the eexperimentalxperimental ttreatmentreatment eeffectsffects ffromrom ccolumnolumn 2 ooff TTableable 2 ttoo aarcrc eelasticitieslasticities wwithith rrespectespect ttoo tthehe ccoinsuranceoinsurance rrate.ate. ((TheseThese ppairwiseairwise aarcrc eelasticitieslasticities aarere ccalculatedalculated aass tthehe cchangehange iinn ttotalotal sspendingpending aass a ppercentageercentage ooff tthehe aaverageverage sspending,pending, ddividedivided bbyy tthehe cchangehange iinn ppricerice aass a ppercentageercentage ooff tthehe aaverageverage pprice;rice; iinn ppanelanel A wwee ddefiefi nene thethe ppricerice aass tthehe ccoinsuranceoinsurance rrateate ooff tthehe pplan).lan).1122 WWee oobtainbtain ppairwiseairwise eelasticitieslasticities tthathat aarere fforor tthehe mmostost ppartart nnega-ega- ttive,ive, rranginganging ffromrom aaboutbout – 00.1.1 ttoo – 00.5;.5; tthehe ffewew ppositiveositive eestimatesstimates aarere aassociatedssociated wwithith ccoinsuranceoinsurance rratesates tthathat aarere ssimilarimilar aandnd pplanslans tthathat aarere ssmall.mall. WWee uusese panelpanel B ofof TableTable 4 toto reportreport weightedweighted averagesaverages ofof pairwisepairwise estimatesestimates uundernder alternativealternative assumptionsassumptions regardingregarding 1)1) thethe defidefi nnitionition ofof thethe price,price, andand 2)2) thethe ddefiefi nitionnition ofof thethe elasticity.elasticity. InIn termsterms ofof thethe defidefi nnitionition ofof thethe price,price, inin computingcomputing tthehe elasticitieselasticities inin panelpanel A wewe usedused thethe plan’splan’s coinsurancecoinsurance raterate asas thethe priceprice andand

12 The arc elasticity of x with respect to y is defi ned as the ratio of the percent change in x to the percent change in y, where the percent change is computed relative to the average, namely (x2 – x1)/((x2 + x1)/2). As x2 and x1 gets closer to each other, the arc elasticity converges to the standard elasticity. Although not commonly used elsewhere, it was heavily used by the RAND researchers because the largest plan in RAND was the free care plan. Starting with a price of zero, a percent change is not well defi ned, so arc elasticities are easier to work with. 214 Journal of Economic Perspectives

Table 4 Sensitivity of Elasticity Estimates to Choice of Plan Comparisons and Price Measures

Panel A: Arc elasticities of total spending with regard to coinsurance rate, for different plan pairs a 25% Mixed 50% Individual 95% Coinsurance Coinsurance c Coinsurance Deductible c Coinsurance

Free Care – 0.180 – 0.091 – 0.149 – 0.119 – 0.234 (0.044) (0.051) (0.080) (0.031) (0.039) 25% Coinsurance 0.749 0.097 0.159 – 0.097 (0.533) (0.281) (0.128) (0.101) Mixed Coinsurance – 0.266 – 0.101 – 0.295 (0.422) (0.195) (0.126) 50% Coinsurance 0.429 – 0.286 (1.176) (0.280) Individual Deductible – 0.487 (0.187)

Panel B: Elasticities of total spending with regard to various price measures Coinsurance rate Average out-of-pocket price

Arc elasticity a Elasticity b Arc elasticity a Elasticity b

All plans – 0.094 NA – 0.144 NA (0.066) (0.051) All plans except Free Care – 0.039 – 0.523 – 0.133 – 0.524 (0.131) (0.082) (0.097) (0.085) All plans except Free Care and Individual – 0.039 – 0.537 – 0.038 – 0.600 Deductible (0.108) (0.084) (0.108) (0.094)

Notes: Panel A reports the pairwise arc elasticities calculated based on Table 2, column 2. Panel B reports the sample-size weighted average of various pairwise elasticities, calculated as detailed in the column-specifi c notes. Standard errors are in parentheses below the coeffi cient values. Standard errors are clustered on family. Arc elasticity standard errors are bootstrapped standard errors based on 500 replications, clustered on family. a Pairwise arc elasticities are calculated as the change in total spending as a percentage of the average, divided by the change in price as a percentage of the average price, where the price is either the coinsurance rate of the plan (in panel A) or (in panel B) either (depending on the column) the coinsurance rate or the average out-of-pocket price paid by people assigned to that plan (the average out-of-pocket price of each plan is shown in Table 1). b Elasticities are calculated based on pairwise regressions of log(total spending + 1) on log(price), where price is either the coinsurance rate of the plan or the average out-of-pocket price paid by people assigned to that plan. c For the mixed coinsurance plan and the individual deductible plan, we take the initial price to be the average of the two coinsurance rates, weighted by the shares of initial claims that fall into each category. For the mixed coinsurance rate plans, this gives an initial price of 32 percent. For the individual deductible plan, it gives an initial price of 58 percent. iignoredgnored thethe factfact thatthat onceonce thethe MaximumMaximum DollarDollar ExpenditureExpenditure isis reachedreached thethe priceprice ddropsrops toto zerozero inin allall plans.plans. InIn panelpanel B,B, wewe considerconsider bothboth thisthis elasticityelasticity withwith respectrespect ttoo thethe plan’splan’s coinsurancecoinsurance rate,rate, butbut alsoalso reportreport thethe elasticityelasticity withwith respectrespect toto thethe Aviva Aron-Dine, Liran Einav, and Amy Finkelstein 215

aaverage,verage, plan-specifiplan-specifi c ((butbut nnotot individual-specifiindividual-specifi cc)) oout-of-pocketut-of-pocket price.price. TheThe plan’splan’s aaverageverage out-of-pocketout-of-pocket priceprice (reported(reported inin TableTable 1,1, columncolumn 3)3) willwill bebe lowerlower thanthan thethe pplan’slan’s coinsurancecoinsurance raterate sincesince itit isis a weightedweighted averageaverage ofof thethe coinsurancecoinsurance raterate andand zzero,ero, whichwhich wouldwould bebe thethe “spot”“spot” priceprice afterafter thethe MaximumMaximum DollarDollar ExpenditureExpenditure isis rreached.eached. ForFor eacheach priceprice defidefi nition,nition, wewe alsoalso considerconsider twotwo defidefi nitionsnitions ofof thethe elas-elas- tticity;icity; specifispecifi ccally,ally, wewe calculatecalculate bothboth arcarc elasticitieselasticities asas inin panelpanel A andand moremore standardstandard eelasticitieslasticities thatthat areare basedbased onon regressionregression estimatesestimates ofof thethe logarithmlogarithm ofof spendingspending onon tthehe logarithmlogarithm ofof price.price.1133 WeWe alsoalso reportreport resultsresults excludingexcluding thethe individualindividual deductibledeductible pplan,lan, whichwhich hashas a differentdifferent coinsurancecoinsurance raterate forfor inpatientinpatient andand outpatientoutpatient care.care. AAcrosscross thesethese variousvarious simplesimple manipulationsmanipulations ofof thethe experimentalexperimental treatmenttreatment effectseffects iinn panelpanel B,B, wewe fi ndnd priceprice elasticitieselasticities thatthat rangerange betweenbetween – 0.040.04 andand – 0.6.0.6. (This(This exer-exer- cciseise doesdoes notnot considerconsider thethe additionaladditional adjustmentsadjustments forfor differentialdifferential participationparticipation andand rreportingeporting discusseddiscussed inin TableTable 3).3).

TThehe RRANDAND EElasticity:lasticity: A BriefBrief ReviewReview ofof WhereWhere IItt CCameame FFromrom WWee nnowow rrevieweview thethe particularparticular assumptionsassumptions mademade byby thethe originaloriginal RANDRAND inves-inves- ttigatorsigators thatthat allowedallowed themthem toto arrivearrive atat theirtheir famousfamous estimateestimate ofof a priceprice elasticityelasticity ofof ddemandemand forfor medicalmedical carecare ofof – 0.2;0.2; KeelerKeeler andand RolphRolph (1988)(1988) provideprovide considerablyconsiderably mmoreore ddetail.etail. TToo transformtransform thethe experimentalexperimental treatmenttreatment effectseffects intointo a singlesingle estimateestimate ofof thethe ssingleingle priceprice elasticityelasticity ofof demanddemand forfor healthhealth care,care, thethe RANDRAND investigatorsinvestigators groupedgrouped iindividualndividual claimsclaims iintonto ““episodes.”episodes.” EachEach eepisode—oncepisode—once occurring—isoccurring—is thoughtthought ofof asas aann uunbreakablenbreakable aandnd pperfectlyerfectly fforecastableorecastable ““bundle”bundle” ooff iindividualndividual cclaims.laims. TThehe ppreciserecise ggroupingrouping reliesrelies onon detaileddetailed clinicalclinical inputinput andand dependsdepends onon thethe specifispecifi c diagnosis.diagnosis. FForor example,example, eacheach hospitalizationhospitalization constitutesconstitutes a separateseparate singlesingle episode.episode. RoutineRoutine sspendingpending onon diabetesdiabetes carecare overover thethe entireentire yearyear isis consideredconsidered a singlesingle episodeepisode andand iiss fullyfully anticipatedanticipated atat thethe startstart ofof thethe year,year, whilewhile “fl“fl are-ups”are-ups” areare not.not. EachEach coldcold oror aaccidentccident isis a sseparateeparate episode,episode, butbut thesethese couldcould runrun concurrently.concurrently. OnceOnce claimsclaims areare ggroupedrouped intointo episodes,episodes, thethe RANDRAND investigatorsinvestigators regressregress averageaverage costscosts perper episodeepisode oonn planplan fi xedxed effectseffects (and(and variousvarious controls)controls) andand fi ndnd thatthat planplan assignmentassignment hashas virtu-virtu- aallylly nnoo eeffectffect oonn ccostsosts pperer eepisode.pisode. FFromrom tthishis ttheyhey cconcludeonclude tthathat sspendingpending oonn tthehe iintensiventensive margin—thatmargin—that iis,s, sspendingpending cconditionalonditional oonn aann eepisodepisode ooccurring—doesccurring—does nnotot rrespondespond toto price,price, andand focusfocus theirtheir analysisanalysis onon thethe priceprice responsivenessresponsiveness ofof thethe exten-exten- ssiveive mmarginargin oonly—thatnly—that iis,s, oonn tthehe ooccurrenceccurrence rrateate ooff eepisodes.pisodes. TToo iinvestigatenvestigate thethe priceprice toto whichwhich individualsindividuals respond,respond, thethe RANDRAND investigatorsinvestigators llookedooked atat whetherwhether thethe occurrenceoccurrence raterate ofof episodesepisodes differsdiffers betweenbetween individualsindividuals whowho ffaceace ssimilarimilar ccurrenturrent pricesprices forfor medicalmedical carecare butbut differentdifferent futurefuture prices.prices. SpecifiSpecifi cally,cally, ttheyhey looklook atat whetherwhether spendingspending isis higherhigher withinwithin a planplan forfor individualsindividuals whowho areare closercloser

13 The latter calculations require that we exclude the free care plan, with a price of zero; as mentioned in an earlier footnote, this is the primary reason that the RAND investigators worked with arc elasticities. Because the arc elasticity estimates are based on treatment effects estimated in levels, and because we estimated smaller treatment effects (in percentage terms) for high-spending individuals (see Table A2), the arc elasticities are generally smaller than the more standard elasticities. 216 Journal of Economic Perspectives

ttoo hhittingitting theirtheir MaximumMaximum DDollarollar Expenditures,Expenditures, andand whetherwhether itit isis higherhigher amongamong ppeopleeople inin ccost-sharingost-sharing plansplans whowho havehave exceededexceeded theirtheir MaximumMaximum DollarDollar Expendi-Expendi- tturesures ccomparedompared toto peoplepeople inin thethe freefree carecare plan.plan. OfOf course,course, a concernconcern withwith thisthis ccomparisonomparison iiss tthathat ffamiliesamilies wwithith hhigherigher uunderlyingnderlying ppropensitiesropensities ttoo sspendpend aarere mmoreore llikelyikely toto comecome closeclose toto hittinghitting theirtheir MaximumMaximum DollarDollar Expenditures;Expenditures; thethe RANDRAND iinvestigatorsnvestigators addressaddress thisthis viavia variousvarious modelingmodeling assumptions.assumptions. FindingFinding nono eevidencevidence iinn ssupportupport ooff hhigherigher eepisodepisode rratesates aamongmong iindividualsndividuals wwhoho aarere ccloserloser ttoo hhittingitting ttheirheir MMaximumaximum DDollarollar EExpenditurexpenditure llimits,imits, tthehe RRANDAND iinvestigatorsnvestigators cconcludeonclude tthathat ppartici-artici- ppants’ants’ eextensivextensive marginmargin ddecisionsecisions aaboutbout ccareare uutilizationtilization aappearppear ttoo bbee bbasedased eentirelyntirely oonn tthehe ccurrenturrent ““spot”spot” ppricerice ooff ccare.are. GGiveniven thesethese fi ndings,ndings, inin thethe fi nalnal stepstep ofof thethe analysisanalysis thethe RANDRAND investigatorsinvestigators llimitimit tthehe ssampleample ttoo iindividualsndividuals iinn pperiodseriods ofof thethe yyearear wwhenhen ttheyhey aarere ssuffiuffi cientlyciently farfar ffromrom hittinghitting thethe MaximumMaximum DollarDollar ExpenditureExpenditure (by(by atat leastleast $400$400 inin currentcurrent dollars)dollars) ssoo thatthat theythey cancan assumeassume thatthat thethe coinsurancecoinsurance raterate (or(or “spot”“spot” price)price) isis thethe onlyonly rele-rele- vvantant pprice.rice. TTheyhey tthenhen ccomputeompute tthehe eelasticitylasticity ooff mmedicaledical sspendingpending wwithith rrespectespect ttoo tthehe eexperimentallyxperimentally assignedassigned ccoinsuranceoinsurance rrate.ate. SSpecifipecifi cally,cally, forfor eacheach categorycategory ofof medicalmedical sspending—hospital,pending—hospital, acuteacute outpatient,outpatient, andand soso on—theyon—they ccomputeompute aarcrc eelasticitieslasticities ooff spendingspending inin a particularparticular categorycategory inin thethe freefree carecare versusversus 2525 percentpercent coinsur-coinsur- aancence planplan andand inin thethe freefree carecare versusversus 9595 percentpercent coinsurancecoinsurance plan.plan. ToTo computecompute tthesehese arcarc elasticities,elasticities, theythey estimateestimate spendingspending changeschanges forfor thesethese individualsindividuals acrossacross ccontractsontracts bbyy ccombiningombining ttheirheir eestimatesstimates ooff tthehe rresponsivenessesponsiveness ooff tthehe eepisodepisode rrateate ttoo tthehe ccoinsuranceoinsurance raterate withwith datadata onon averageaverage costscosts perper episodeepisode (which(which isis assumedassumed toto bbee uunresponsivenresponsive toto thethe coinsurancecoinsurance rate).rate). TheThe enduringenduring elasticityelasticity estimateestimate ofof – 0.20.2 ccomesomes ffromrom nnotingoting tthathat mmostost ooff tthesehese aarcrc eelasticities—summarizedlasticities—summarized iinn KKeelereeler aandnd RRolpholph ((1988,1988, TTableable 111)—are1)—are ccloselose ttoo – 00.2..2.

Using the RAND Elasticity: The Need to Summarize Plans with a Single Price AApplicationpplication ooff tthehe – 00.2.2 eestimatestimate iinn a mmanneranner tthathat iiss ffullyully cconsistentonsistent wwithith tthehe wwayay thethe estimateestimate wwasas ggeneratedenerated iiss a nnontrivialontrivial ttask.ask. TThehe RRANDAND eelasticitylasticity wwasas eesti-sti- mmatedated basedbased onon thethe assumptionassumption thatthat inin decidingdeciding whetherwhether toto consumeconsume medicalmedical ccare,are, individualsindividuals ffullyully aanticipatenticipate sspendingpending wwithinithin aann ““episodeepisode ooff ccare”are” bbutut mmakeake ttheirheir decisiondecision myopically—thatmyopically—that iis,s, oonlynly wwithith regardregard ttoo thethe currentcurrent “spot”“spot” ppricerice ooff medicalmedical care—withcare—with respectrespect toto thethe potentialpotential forfor spendingspending duringduring thethe yearyear onon ootherther episodes.episodes. ThereforeTherefore a researcherresearcher whowho wantedwanted toto applyapply thisthis estimateestimate toto fforecastingorecasting thethe impactimpact ofof anan out-of-sampleout-of-sample changechange inin costcost sharingsharing wouldwould needneed ttoo obtainobtain micromicro datadata onon medicalmedical claims,claims, groupgroup thesethese claimsclaims intointo “episodes”“episodes” asas ddescribedescribed eearlier,arlier, aandnd ccalculatealculate tthehe ““spot”spot” ppricerice tthathat eeachach iindividualndividual wwouldould ffaceace iinn eeachach episode.episode. AlthoughAlthough therethere existexist notablenotable exceptionsexceptions ooff studiesstudies tthathat ddoo ppreciselyrecisely tthishis (Buchanan,(Buchanan, Keeler,Keeler, Rolph,Rolph, andand HolmerHolmer 1991;1991; Keeler,Keeler, Malkin,Malkin, Goldman,Goldman, andand BBuchananuchanan 1996),1996), mmanyany ssubsequentubsequent rresearchersesearchers hhaveave aappliedpplied tthehe RRANDAND eestimatesstimates iinn a muchmuch ssimplerimpler ffashion.ashion. IInn ddoingoing sso,o, aarguablyrguably tthehe kkeyey ddecisionecision a rresearcheresearcher ffacesaces isis howhow toto summarizesummarize thethe nonlinearnonlinear coveragecoverage withwith a singlesingle price.price. ThisThis isis bbecauseecause tthehe RRANDAND eelasticitylasticity iiss a ssingleingle eelasticitylasticity eestimate,stimate, ssoo iitt hhasas ttoo bbee aappliedpplied ttoo a singlesingle price.price. The RAND Health Insurance Experiment, Three Decades Later 217

RResearchersesearchers hhaveave ttakenaken a vvarietyariety ofof differentdifferent approachesapproaches ttoo summarizingsummarizing tthehe ppricerice ooff mmedicaledical ccareare uundernder a nnonlinearonlinear iinsurancensurance ccontractontract bbyy a ssingleingle nnumber.umber. FForor eexample,xample, iinn ppredictingredicting hhowow mmedicaledical sspendingpending wwillill rrespondespond ttoo hhigh-deductibleigh-deductible hhealthealth ssavingsavings aaccounts,ccounts, CCogan,ogan, HHubbard,ubbard, aandnd KKessleressler ((2005)2005) aappliedpplied tthehe – 00.2.2 eelasticitylasticity eestistimmateate toto thethe changechange inin thethe averageaverage priceprice thatthat waswas paidpaid outout ofof pocket,pocket, wherewhere thethe aaverageverage waswas takentaken overover claimsclaims thatthat werewere mademade atat differentdifferent partsparts ofof thethe nonlinearnonlinear ccoverage.overage. InIn extrapolatingextrapolating fromfrom thethe RANDRAND experimentexperiment toto thethe impactimpact ofof thethe spreadspread ooff insuranceinsurance onon thethe growthgrowth ofof medicalmedical spending,spending, researchersresearchers havehave alsoalso usedused anan ““averageaverage priceprice approach,”approach,” summarizingsummarizing thethe changeschanges inin thethe priceprice ofof medicalmedical ccareare bbyy cchangeshanges iinn tthehe ooverallverall rratioatio bbetweenetween oout-of-pocketut-of-pocket mmedicaledical sspendingpending aandnd ttotalotal sspendingpending ((NewhouseNewhouse 11992;992; CCutlerutler 11995;995; FFinkelsteininkelstein 22007).007). OOtherther wworkork oonn tthehe ppricerice eelasticitylasticity ofof ddemandemand fforor mmedicaledical ccareare hhasas ssummarizedummarized tthehe ppricerice aassociatedssociated wwithith a nnonlinearonlinear coveragecoverage usingusing thethe actual,actual, realizedrealized priceprice paidpaid byby eacheach individualindividual forfor hishis llastast cclaimlaim iinn thethe coveragecoverage yearyear (Eichner(Eichner 1998;1998; KowalskiKowalski 2009)2009) oror thethe expectedexpected end-end- oof-yearf-year ppricerice ((EichnerEichner 11997).997). TThesehese ddifferentifferent mmethodsethods fforor ssummarizingummarizing a nnonlinearonlinear ccoverageoverage wwithith a ssingleingle ppricerice ccanan hhaveave aann iimportantmportant eeffectffect oonn tthehe eestimatedstimated sspendingpending eeffectsffects ooff aalternativelternative ccontracts.ontracts. TToo illustrateillustrate thisthis point,point, considerconsider threethree “budget“budget neutral”neutral” alternativealternative coveragecoverage designs,designs, ddepictedepicted iinn FFigureigure 22:: a ““highhigh ddeductible”eductible” pplanlan wwithith a $$3,2503,250 pper-familyer-family ddeductibleeductible aandnd ffullull iinsurancensurance aabovebove tthehe ddeductible;eductible; a ““lowlow ddeductible”eductible” pplanlan wwithith a $$1,0001,000 pper-er- ffamilyamily ddeductibleeductible aandnd a 2200 ppercentercent ccoinsuranceoinsurance rrateate aabovebove tthehe ddeductible;eductible; aandnd a ““nono ddeduct-educt- iible”ble” pplanlan wwithith a cconstantonstant ccoinsuranceoinsurance rrateate ooff 2288 ppercent.ercent. IInn ddescribingescribing tthesehese pplanslans aass ““budgetbudget nneutral,”eutral,” wwee mmeanean tthathat wwee ppickedicked tthemhem ssoo tthathat ttheyhey wwouldould aallll hhaveave tthehe ssameame ppredictedredicted ccostost ((forfor tthehe iinsurer)nsurer) wwhenhen wwee iignoregnore ppotentialotential bbehavioralehavioral rresponsesesponses ttoo tthehe ddifferentifferent ccontractsontracts aandnd aapplypply ttoo eeachach ooff tthemhem tthehe ssameame ddistributionistribution ooff aannualnnual mmedicaledical eexpendituresxpenditures ffromrom RRAND’sAND’s ffreeree ccareare pplanlan ((inin 22011011 ddollars).ollars). TThehe ““nono ddeductible”eductible” pplanlan aalwayslways hhasas tthehe ssameame ssingleingle pprice:rice: tthathat iis,s, tthehe bbuyeruyer aalwayslways ppaysays 2288 ppercentercent ooff tthehe ccostost ooff hhealthealth sservices.ervices. HHowever,owever, iinn tthehe ttwowo nnonlinearonlinear pplans,lans, tthehe ppricerice ppaidaid bbyy tthehe iindividualndividual wwillill cchangehange ffromrom 110000 ppercentercent ooff hhealthcareealthcare ccostost bbeforeefore tthehe ddeductibleeductible iiss rreached,eached, ttoo tthehe ccoinsuranceoinsurance rrateate aabovebove tthathat llevel.evel. AAss wewe described,described, iinn ssummarizingummarizing ssuchuch a pplanlan bbyy a ssingleingle nnumber,umber, oonene mmightight llookook aatt a vvarietyariety ooff ““price”price” ddefiefi nnitions,itions, iincludingncluding tthehe ““spot”spot” ppricerice ppaidaid aatt tthehe ttimeime hhealthcareealthcare sserviceservices aarere rreceived,eceived, tthehe rrealizedealized end-of-yearend-of-year pprice,rice, tthehe expectedexpected end-of-yearend-of-year pprice,rice, oorr aatt ssomeome wweighted-averageeighted-average ooff tthehe ppricesrices ppaidaid ooverver a yyear.ear. TThehe cconcernoncern iiss tthathat wwhenhen eevaluatingvaluating hhowow cchanginghanging ffromrom oonene iinsurancensurance ccontractontract ttoo aanothernother ((oror ffromrom nnoo iinsur-nsur- aancence ttoo hhavingaving iinsurance)nsurance) wwouldould aaffectffect hhealthcareealthcare uutilization,tilization, tthehe mmethodethod tthathat iiss uusedsed ttoo bboiloil ddownown tthehe insuranceinsurance ccontractontract iintonto a ssingleingle pprice—torice—to wwhichhich tthehe – 00.2.2 eelasticitylasticity eestimatestimate iiss tthenhen applied—canapplied—can yyieldield veryvery differentdifferent conclusionsconclusions aboutabout howhow thethe changechange iinn iinsurancensurance ccontractsontracts wwouldould iincreasencrease tthehe aamountmount ooff hhealthealth ccareare cconsumed.onsumed. TToo illustrateillustrate thethe potentialpotential magnitudesmagnitudes atat stake,stake, considerconsider anan exerciseexercise inin whichwhich wwee trytry toto forecastforecast thethe effecteffect ofof reducingreducing coveragecoverage fromfrom RAND’sRAND’s 2525 percentpercent coinsur-coinsur- aancence planplan toto a planplan withwith a constantconstant coinsurancecoinsurance raterate ofof 2828 percent,percent, whichwhich isis oneone ofof tthehe optionsoptions depicteddepicted inin FigureFigure 2.2. BecauseBecause thethe newnew coveragecoverage hashas a constantconstant coinsur-coinsur- aancence rrate,ate, tthehe ppricerice ooff mmedicaledical ccareare uundernder tthishis ccoverageoverage iiss cclearlear aandnd wwellell ddefiefi ned:ned: itit 218 Journal of Economic Perspectives

Figure 2 Nonlinear Health Insurance Coverage

7,000

6,000

5,000 High Deductible Plan

4,000 Low Deductible Plan

3,000

2,000 Out-of-pocket expenditures ($US)

1,000

Constant Coinsurance Plan

0 0 2,500 5,000 7,500 10,000 12,500 15,000 17,500 20,000 22,500 25,000 Total medical expenditure ($US)

Note: Consider three “budget neutral” alternative health insurance coverage designs: a “high deductible” plan with a $3,250 per-family deductible and full insurance above the deductible; a “low deductible” plan with a $1,000 per-family deductible and a 20 percent coinsurance rate above the deductible; and a “no deductible” plan with a constant coinsurance rate of 28 percent. See text for details. iiss 2288 ccentsents fforor eeveryvery ddollarollar ooff hhealthcareealthcare sspending.pending. BButut iinn oorderrder ttoo aapplypply tthehe RRANDAND eestimatestimate ofof – 0.2,0.2, wewe alsoalso needneed toto summarizesummarize RAND’sRAND’s 2525 percentpercent coinsurancecoinsurance withwith a ssingleingle price.price. RecallRecall thatthat thethe RANDRAND planplan hadhad a MaximumMaximum DollarDollar ExpenditureExpenditure limit,limit, ssoo thethe priceprice startsstarts atat 2255 ccentsents fforor eeveryvery ddollar,ollar, bbutut tthenhen bbecomesecomes zzeroero ooncence tthehe llimitimit iiss reached,reached, soso summarizingsummarizing thethe RANDRAND planplan withwith a singlesingle priceprice essentiallyessentially meansmeans a cchoicehoice ooff wweightseights iinn tthehe cconstructiononstruction ooff aann aaverageverage pprice.rice. WeWe uusese tthreehree ddifferentifferent wwaysays ttoo ssummarizeummarize tthehe RANDRAND 2525 percentpercent coinsurancecoinsurance planplan withwith a singlesingle price:price: a dollar-dollar- wweightedeighted averageaverage price,price, a person-weightedperson-weighted averageaverage price,price, andand a person-weightedperson-weighted aaverageverage end-of-yearend-of-year price.price. ApplyingApplying tthehe ddistributionistribution ooff sspendingpending uundernder tthehe ffreeree ccareare pplan,lan, thesethese rresultesult iinn tthreehree ddifferentifferent ssummaryummary pprices,rices, ooff 110,0, 117,7, aandnd 1133 ccentsents fforor eeveryvery ddollarollar ofof medicalmedical spending,spending, respectively.respectively. ApplyingApplying thethe – 0.20.2 estimateestimate toto changingchanging ffromrom eeachach ofof thesethese pricesprices toto 2828 cents,cents, whichwhich isis thethe constantconstant priceprice inin thethe alternativealternative ccoverage,overage, wewe obtainobtain a reductionreduction inin healthcarehealthcare spendingspending ofof 18,18, 9,9, andand 1414 percent,percent, rrespectively.espectively. Thus,Thus, inin thisthis example,example, thethe decisiondecision ofof howhow toto defidefi nene thethe priceprice leadsleads toto ddifferencesifferences iinn tthehe ppredictedredicted reductionreduction ofof spendingspending thatthat varyvary byby a factorfactor ofof 2.2. Aviva Aron-Dine, Liran Einav, and Amy Finkelstein 219

The Dangers of Summarizing Nonlinear Coverage by a Single Price TThehe precedingpreceding exerciseexercise illustratedillustrated howhow thethe mannermanner byby whichwhich a nonlinearnonlinear ccoverageoverage iiss ssummarizedummarized bbyy a ssingleingle ppricerice ccouldould bbee iimportant.mportant. IInn ggeneral,eneral, ttherehere iiss nnoo ““right”right” wayway toto summarizesummarize a nonlinearnonlinear budgetbudget setset withwith a singlesingle price.price. TheThe differingdiffering iimplicationsmplications ooff aalternativelternative reasonable,reasonable, yetyet adad hochoc “fi“fi xes”xes” toto thisthis problemproblem shouldshould ggiveive usus pausepause whenwhen consideringconsidering manymany ofof thethe subsequentsubsequent applicationsapplications ofof thethe RANDRAND eexperimentalxperimental results.results. ItIt alsoalso suggestssuggests that,that, goinggoing forward,forward, attemptsattempts toto estimateestimate thethe iimpactmpact ooff hhealthealth iinsurancensurance ccontractsontracts oonn hhealthcareealthcare sspendingpending wwouldould bbenefienefi t fromfrom mmoreore aattentionttention ttoo hhowow tthehe nnonlinearitiesonlinearities inin thethe healthhealth insuranceinsurance contractscontracts maymay aaffectffect tthehe sspendingpending rresponse.esponse. FFortunately,ortunately, jjustust aass ttherehere hhasas bbeeneen iintellectualntellectual pprogressrogress iinn tthehe ddesignesign aandnd aanalysisnalysis ooff eexperimentalxperimental ttreatmentreatment eeffectsffects iinn tthehe ddecadesecades ssinceince RRAND,AND, ttherehere hhasas ssimilarlyimilarly bbeeneen pprogressrogress oonn tthehe aanalysisnalysis ooff tthehe bbehavioralehavioral rresponseesponse ttoo nnonlinearonlinear bbudgetudget setssets (for(for example,example, HausmanHausman 1985).1985). MMuchuch ooff thethe initialinitial workwork inin thisthis aarearea focusedfocused onon analyzinganalyzing thethe laborlabor supplysupply responseresponse toto progressiveprogressive taxation.taxation. RRecently,ecently, however,however, researchersresearchers havehave begunbegun toto applyapply thethe techniquestechniques ofof nonlinearnonlinear bbudgetudget ssetet eestimationstimation ttoo tthehe aanalysisnalysis ooff tthehe eeffectffect ooff ((nonlinear)nonlinear) hhealthealth iinsur-nsur- aancence contractscontracts ((MarshMarsh 22012;012; KKowalskiowalski 22012),012), aandnd ffurtherurther wworkork iinn tthishis aarearea ccouldould bbee ofof greatgreat vvalue.alue. OOff course,course, eveneven equippedequipped withwith thesethese techniques,techniques, currentcurrent researchersresearchers mustmust ggrapplerapple withwith manymany ofof thethe samesame issuesissues thatthat thethe originaloriginal RANDRAND investigatorsinvestigators faced.faced. IInn particular,particular, theythey mustmust modelmodel thethe distributiondistribution ofof medicalmedical shocksshocks throughoutthroughout thethe yyearear inin thethe populationpopulation underunder analysis,analysis, asas wellwell asas thethe evolutionevolution ofof individuals’individuals’ beliefsbeliefs aaboutbout thesethese shocks.shocks. AnotherAnother keykey issueissue isis whetherwhether individualsindividuals taketake intointo accountaccount thethe eentirentire nonlinearnonlinear budgetbudget setset inducedinduced byby thethe healthhealth insuranceinsurance contractcontract inin makingmaking ttheirheir spendingspending decision,decision, oror whetherwhether theythey respondrespond onlyonly toto thethe currentcurrent “spot”“spot” price,price, oorr toto somethingsomething inin between.between. AlthoughAlthough fullyfully forward-lookingforward-looking rationalrational individualsindividuals sshouldhould onlyonly respondrespond toto thethe expectedexpected end-of-yearend-of-year price,price, ifif individualsindividuals areare myopic,myopic, lliquidityiquidity constrained,constrained, oror unsureunsure ofof thethe detailsdetails ofof theirtheir contract,contract, theythey mightmight alsoalso rrespond,espond, atat leastleast toto somesome extent,extent, toto thethe “spot”“spot” price.price. InIn recentrecent empiricalempirical work,work, wewe iinvestigatenvestigate thisthis questionquestion usingusing datadata onon medicalmedical spendingspending byby peoplepeople coveredcovered byby eemployer-providedmployer-provided healthhealth insuranceinsurance (Aron-Dine,(Aron-Dine, Einav,Einav, Finkelstein,Finkelstein, andand CullenCullen 22012).012). WeWe concludedconcluded that,that, inin ourour specifispecifi c setting,setting, individualsindividuals dodo appearappear toto taketake iintonto accountaccount thethe nonlinearnonlinear budgetbudget setset inin makingmaking medicalmedical spendingspending decisionsdecisions butbut tthathat theythey areare notnot fullyfully forwardforward lookinglooking asas theythey alsoalso taketake accountaccount ofof thethe spotspot price.price. IInn ourour calibrationcalibration results,results, thethe predictedpredicted spendingspending changechange associatedassociated withwith intro-intro- dducingucing a nonlinearnonlinear healthhealth insuranceinsurance contractcontract cancan varyvary greatlygreatly dependingdepending onon whatwhat oonene assumesassumes aboutabout thethe degreedegree ofof forward-forward- lookinglooking behavior,behavior, suggestingsuggesting thatthat moremore eevidencevidence onon thisthis questionquestion wouldwould bebe useful.useful. MMoreore generally,generally, aanyny ttransformationransformation ooff tthehe eexperimentalxperimental ttreatmentreatment eeffectsffects iintonto eestimatesstimates tthathat ccanan bbee uusedsed oout-of-sampleut-of-sample wwillill rrequireequire mmoreore aassumptionsssumptions tthanhan rrequiredequired ttoo obtainobtain thosethose treatmenttreatment effectseffects inin thethe fi rstrst place.place. MoreMore thanthan threethree decadesdecades afterafter thethe RRANDAND eexperiment,xperiment, tthehe ddevelopmentevelopment aandnd uusese ooff nnewew aapproachespproaches ttoo ddoingoing ssuchuch oout-of-ut-of- ssampleample eextrapolationxtrapolation rremainsemains aann aactivective aandnd iinterestingnteresting aarearea fforor rresearch.esearch. 220 Journal of Economic Perspectives

Concluding Remarks

AAtt tthehe ttimeime ooff tthehe RRANDAND HealthHealth InsuranceInsurance Experiment,Experiment, itit waswas vigorouslyvigorously aarguedrgued thatthat medicalmedical carecare waswas determineddetermined byby “needs,”“needs,” andand thereforetherefore waswas notnot sensi-sensi- ttiveive ttoo pprice.rice. AsAs CutlerCutler andand ZeckhauserZeckhauser (2000)(2000) wrote,wrote, thethe RANDRAND experimentexperiment waswas iinstrumentalnstrumental inin rejectingrejecting thisthis view:view: “Sound“Sound methodology,methodology, supportedsupported byby generousgenerous ffunding,unding, carriedcarried thethe day.day. TheThe demanddemand elasticitieselasticities inin thethe RandRand ExperimentExperiment havehave bbecomeecome thethe standardstandard inin thethe literature,literature, andand essentiallyessentially allall economistseconomists acceptaccept thatthat ttraditionalraditional hhealthealth iinsurancensurance leadsleads toto moderatemoderate mmoraloral hhazardazard iinn ddemand.”emand.” BButut aass tthishis ccoreore llessonesson ooff tthehe RRANDAND experimentexperiment hashas becomebecome solidifisolidifi eded inin thethe mmindsinds ofof a ggenerationeneration ofof healthhealth economistseconomists andand policymakers,policymakers, therethere hashas beenbeen a cconcomitantoncomitant fadingfading fromfrom memorymemory ooff tthehe ooriginalriginal experimentalexperimental designdesign andand analyticalanalytical fframework.ramework. WhileWhile thisthis progressionprogression maymay bebe naturalnatural inin thethe lifecyclelifecycle ofof transforma-transforma- ttiveive rresearch,esearch, itit seemsseems usefuluseful toto remindremind a youngeryounger generationgeneration ofof economistseconomists ofof thethe ddetailsetails aandnd llimitationsimitations ooff tthehe ooriginalriginal wwork.ork. IInn thisthis essay,essay, wwee re-presentedre-presented andand reexaminedreexamined thethe fi ndingsndings ofof thethe RANDRAND experi-experi- mmentent ffromrom tthehe pperspectiveerspective ooff tthreehree ssubsequentubsequent ddecadesecades ofof progressprogress inin eempiricalmpirical wworkork oonn tthehe ddesignesign aandnd aanalysisnalysis ofof randomizedrandomized experiments,experiments, asas wwellell aass oonn tthehe aanalysisnalysis ofof mmoraloral hhazardazard eeffectsffects ooff hhealthealth iinsurance—muchnsurance—much ooff iitt iinspired,nspired, nnoo ddoubt,oubt, ttoo a largelarge degreedegree byby thethe enduringenduring inflinfl uenceuence ofof thethe RANDRAND results.results. ThisThis landmarklandmark aandnd ppioneeringioneering sstudytudy wwasas uuniquelyniquely aambitious,mbitious, rremarkablyemarkably ssophisticatedophisticated fforor iitsts ttime,ime, aandnd entrepreneurialentrepreneurial inin thethe designdesign andand implementationimplementation ofof thethe then-newthen-new sciencescience ofof rrandomizedandomized eexperimentsxperiments iinn tthehe ssocialocial ssciences.ciences. OOurur reexaminationreexamination cconcludesoncludes tthathat ddespiteespite tthehe ppotentialotential fforor ssubstantialubstantial bbiasias iinn thethe originaloriginal eestimatesstimates sstemmingtemming ffromrom ssystematicallyystematically ddifferentialifferential pparticipationarticipation aandnd reportingreporting acrossacross experimentalexperimental arms,arms, oneone ofof thethe centralcentral contributionscontributions ofof tthehe RRANDAND eexperimentxperiment iiss rrobust:obust: tthehe rrejectionejection ooff tthehe nnullull hhypothesisypothesis tthathat hhealthealth sspendingpending doesdoes notnot respondrespond toto thethe out-of-pocketout-of-pocket price.price. Naturally,Naturally, however,however, thesethese ppotentialotential biasesbiases introduceintroduce uncertaintyuncertainty aaboutbout thethe magnitudemagnitude ooff thethe impactimpact ofof thethe ddifferentifferent iinsurancensurance pplanslans oonn mmedicaledical sspending.pending. MMoreover,oreover, tthehe ttranslationranslation ooff tthesehese eexperimentalxperimental estimatesestimates intointo economiceconomic objectsobjects ofof interest—suchinterest—such asas a priceprice elas-elas- tticityicity ofof demanddemand fforor mmedicaledical ccare—requiresare—requires ffurtherurther aassumptionsssumptions aandnd mmachinery,achinery, wwhichhich gogo beyondbeyond thethe “raw”“raw” experimentalexperimental results.results. WhileWhile economiceconomic analysisanalysis hashas mmadeade pprogressrogress iinn tthehe iinterveningntervening ddecadesecades iinn ddevelopingeveloping ttechniquesechniques tthathat mmayay oofferffer newnew approachesapproaches ttoo tthehe eeconomicconomic aanalysisnalysis ooff mmoraloral hhazardazard eeffectsffects ooff hhealthealth iinsurance,nsurance, itit willwill alwaysalways bebe thethe casecase that,that, likelike thethe famousfamous – 00.2.2 ppricerice eelasticitylasticity ooff ddemandemand estimateestimate producedproduced byby thethe originaloriginal RANDRAND investigators,investigators, anyany attemptattempt byby rresearchersesearchers ttoo aapplypply tthehe eexperimentalxperimental eestimatesstimates ooutut ooff ssampleample wwillill iinvolvenvolve mmoreore aassumptions—andssumptions—and hhenceence sscopecope fforor uuncertainty—thanncertainty—than tthehe ddirectirect eexperimentalxperimental eestimatesstimates themselves.themselves. TThishis ppoint,oint, wwhilehile straightforwardstraightforward aandnd uuncontroversialncontroversial ((we’dwe’d tthink),hink), maymay havehave becomebecome somewhatsomewhat lostlost inin tthehe iinterveningntervening ddecadesecades ooff uusese ooff tthehe RRANDAND estimates.estimates. OOurur hhopeope iiss tthathat tthishis eessayssay mmayay hhelpelp pputut bbothoth tthehe ffamousamous eexperi-xperi- mmentent andand iitsts rresultsesults bbackack iinn ccontext.ontext. The RAND Health Insurance Experiment, Three Decades Later 221

■ We are grateful to the JEP editors (David Autor, John List, and the indefatigable Timothy Taylor), as well as to Ran Abramitzky, Tim Bresnahan, Dan Fetter, Emmett Keeler, Will Manning, Joe Newhouse, Matt Notowidigdo, Sarah Taubman, and Heidi Williams for helpful comments, and to the National Institute of Aging (Grant No. R01 AG032449) for fi nancial support; Aron-Dine also acknowledges support from the National Science Foundation Graduate Research Fellowship program. We thank the original RAND investigators for making their data so easily available and accessible. Aron-Dine contributed to this paper while she was a graduate student in Economics at MIT. She is currently employed as a Special Assistant to the President for Economic Policy at the National Economic Council. The views in this paper do not represent those of the National Economic Council or the White House.

References

Anderson, Michael L. 2008. “Multiple Infer- Cutler, David M. 1995. “Technology, Health ence and Gender Differences in the Effects Costs, and the NIH.” Paper prepared for of Early Intervention: A Reevaluation of the the National Institutes of Health Economics Abecedarian, Perry Preschool, and Early Training Roundtable on Biomedical Research. http:// Projects.” Journal of the American Statistical Associa- www.economics.harvard.edu/files/faculty/13 tion 103(484): 1481–95. _Technology,%20Health%20Costs%20and%20 Angrist, Joshua, Eric Bettinger, and Michael the%20NIH.pdf. Kremer. 2006. “Long-Term Educational Conse- Cutler, David M., and Richard J. Zeckhauser. quences of Secondary School Vouchers: Evidence 2000. “The Anatomy of Health Insurance.” In from Administrative Records in Columbia.” Handbook of Health Economics, edited by A. J. American Economic Review 96(3): 847– 62. Culyer and J. P. Newhouse, volume 1, 563 – 643. Aron-Dine, Aviva, Liran Einav, Amy Finkelstein, Amsterdam: Elsevier. and Mark R. Cullen. 2012. “Moral Hazard in Eichner, Matthew J. 1997. “Medical Expendi- Health Insurance: How Important is Forward tures and Major Risk Health Insurance.” MIT, PhD Looking Behavior?” NBER Working Paper 17802. Dissertation, Chapter 1. Arrow, Kenneth J. 1963. “Uncertainty and the Eichner, Matthew J. 1998. “The Demand for Welfare Economics of Medical Care.” American Medical Care: What People Pay Does Matter.” Economic Review 53(5): 941–73. American Economic Review 88(2): 117–21. Ashenfelter, Orley, and Mark W. Plant. 1990. Finkelstein, Amy. 2007. “The Aggregate Effects “Non-Parametric Estimates of the Labor-Supply of Health Insurance: Evidence from the Introduc- Effects of Negative Income Tax Programs.” Journal tion of Medicare.” Quarterly Journal of Economics of Labor Economics 8(1): S397– S415. 122(3): 1–37. Bitler, Marianne, Jonah Gelbach, and Hilary Finkelstein, Amy, Sarah Taubman, Bill Wright, Hoynes. 2006. “What Mean Impacts Miss: Distri- Mira Bernstein, Jonathan Gruber, Joseph P. butional Effects of Welfare Reform Experiments.” Newhouse, Heidi Allen, Katherine Baicker, and the American Economic Review 96(4): 988 –1012. Oregon Health Study Group. 2012. “The Oregon Buchanan, Joan L., Emmett B. Keeler, John E. Health Insurance Experiment: Evidence from the Rolph, and Martin R. Holmer. 1991. “Simulating First Year.” Quarterly Journal of Economics 127(3): Health Expenditures under Alternative Insurance 1057–1106. Plans.” Management Science 37(9): 1067– 90. Greenberg, David, and Harlan Halsey. 1983. Cogan, John F., R. Glenn Hubbard, and Daniel “Systematic Misreporting and Effects of Income P. Kessler. 2005. Healthy, Wealthy, and Wise: Five Steps Maintenance Experiments on Work Effort: to a Better Healthcare System, 1st ed. Washington, DC: Evidence from the Seattle-Denver Experiment.” AEI Press. Journal of Labor Economics 1(4): 380 – 407. 222 Journal of Economic Perspectives

Greenberg, David, and Mark Shroder. 2004. The Experiments.” American Economic Journal: Applied Digest of Social Experiments, 3rd ed. Washington, Economics 3(1): 224 –39. DC: Urban Institute Press. Manning, Willard G., Joseph P. Newhouse, Hausman, Jerry A. 1985. “The Econometrics Naihua Duan, Emmett B. Keeler, Arleen Leibowitz, of Nonlinear Budget Sets.” Econometrica 53(6): and M. Susan Marquis. 1987. “Health Insurance 1255 – 82. and the Demand for Medical Care: Evidence from Heckman, James J., Seong Hyeok Moon, a Randomized Experiment.” American Economic Rodrigo Pinto, Peter A. Savelyev, and Adam Q. Review 77(3): 251–77. Yavitz. 2010. “Analyzing Social Experiments as Manski, Charles F. 1990. “Nonparametric Implemented: A Reexamination of the Evidence Bounds on Treatment Effects.” American Economic from the High Scope Perry Preschool Program.” Review 80(2): 319 –23. Quantitative Economics 1(1): 1– 46. Marsh, Christina. 2012. “Estimating Demand Heckman, James J., Rodrigo Pinto, Azeem M. Elasticities using Nonlinear Pricing.” http:// Shaikh, and Adam Q. Yavitz. 2011. “Inference with clmarsh.myweb.uga.edu/docs/Demand Imperfect Randomization: The Case of the Perry _Elasticities_Marsh.pdf. Preschool Program.” http://home.uchicago.edu Michalopoulos, Charles, David Wittenburg, Dina /~amshaikh/webfi les/perry.pdf. A. R. Israel, Jennifer Schore, Anne Warren, Aparajita Keeler, Emmett B., Joseph P. Newhouse, and Zutshi, Stephen Freedman, and Lisa Schwartz. 2011. Charles E. Phelps. 1977. “Deductibles and the The Accelerated Benefi ts Demonstration and Evaluation Demand for Medical Care Services: The Theory Project: Impacts on Health and Employment at Twelve of a Consumer Facing a Variable Price Schedule Months. New York: MDRC. http://www.mdrc.org under Uncertainty.” Econometrica 45(3): 641– 56. /sites/default/fi les/full_528.pdf. Keeler, Emmett B., and John E. Rolph. 1988. Morris, Carl. 1979. “A Finite Selection Model “The Demand for Episodes of Treatment in the for Experimental Design of the Health Insurance Health Insurance Experiment.” Journal of Health Study.” Journal of Econometrics 11(1): 43 – 61. Economics 7(4): 337– 67. Newhouse, Joseph P. 1992. “Medical Care Costs: Keeler, Emmett B., Jesse D. Malkin, Dana P. How Much Welfare Loss?” Journal of Economic Goldman, and Joan L. Buchanan. 1996. “Can Perspectives 6(3): 3 –21. Medical Savings Accounts for the Nonelderly Newhouse, Joseph P., Robert H. Brook, Naihua Reduce Health Care Costs?” JAMA 275(21): Duan, Emmett B. Keeler, Arleen Leibowitz, Willard 1666 –71. G. Manning, M. Susan Marquis, Carl N. Morris, Kowalski, Amanda E. 2009. “Censored Quantile Charles E. Phelps, and John E. Rolph. 2008. “Attri- Instrumental Variable Estimates of the Price tion in the RAND Health Insurance Experiment: Elasticity of Expenditure on Medical Care.” NBER A Response to Nyman.” Journal of Health Politics, Working Paper 15085. Policy and Law 33(2): 295 – 308. Kowalski, Amanda E. 2012. “Estimating the Newhouse, Joseph P., and the Insurance Tradeoff between Risk Protection and Moral Experiment Group. 1993. Free for All. Cambridge: Hazard with a Nonlinear Budget Set Model of Harvard University Press. Health Insurance.” NBER Working Paper 18108. Nyman, John A. 2007. “American Health Policy: Krueger, Alan B. 1999. “Experimental Estimates Cracks in the Foundation.” Journal of Health Politics, of Education Production Functions.” Quarterly Policy and Law 32(5): 759 – 83. Journal of Economics 114(2): 497– 532. Nyman, John A. 2008. “Health Plan Switching Krueger, Alan B., and Diane M. Whitmore. and Attrition Bias in the RAND Health Insurance 2001. “The Effect of Attending a Small Class in the Experiment.” Journal of Health Politics, Policy and Early Grades on College-Test Taking and Middle Law 33(2): 309 –17. School Test Results: Evidence from Project STAR.” Pauly, Mark. 1968. “The Economics of Moral Economic Journal 111(468): 1–28. Hazard: Comment.” American Economic Review Lee, David S. 2009. “Training, Wages, and 58(3): 531–37. Sample Selection: Estimating Sharp Bounds on Rogers, William H., and Joseph P. Newhouse. Treatment Effects.” Review of Economic Studies 1985. “Measuring Unfi led Claims in the Health 76(3): 1071–1102. Insurance Experiment.” In Collecting Evaluation Levitt, Steven D., and John A. List. 2011. “Was Data: Problems and Solutions, edited by Leigh There Really a Hawthorne Effect at the Hawthorne Burstein, Howard E. Freeman, and Peter H. Rossi, Plant? An Analysis of the Original Illumination 121–133. Beverly Hills: Sage.