A Dynamic Model of Health Insurance Choices and Health Care Consumption 1. Jian Ni Johns Hopkins University

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1 A Dynmic Model of Helh Insurnce Choices nd Helh Cre Consumpion Jin Ni Johns Hopins Universiy Emil: Niin Meh Universiy of Torono Emil: Knnn Srinivsn Crnegie Mellon Universiy Emil: Bohong Sun Cheung Kong Grdue School of Business Emil: Jnury 04 This pper is bsed on Chper of Jin Ni s Ph.D. disserion Crnegie Mellon Universiy. This pper ws funded by he Andrew Mellon docorl fellowship o Jin Ni nd SSHRC grn # o Niin Meh nd Jin Ni. The uhors re greful o Sunder Kere for helping us obin he d nd o George-Levi Gyle, Hnming Fng nd Avi Goldfrb for helpful commens. The uhors lso pprecie feedbc from seminr pricipns Emory, Georgi Tech., Johns Hopins, HKUST, Minneso, Nionl Universiy of Singpore, NYU, Universiy of Souhern Cliforni, Wshingon Universiy nd Yle Universiy. The usul disclimer pplies.

2 A Dynmic Model of Helh Insurnce Choices nd Helh Cre Consumpion Absrc The increse in helhcre coss over he ls few decdes is priculrly relevn for chronic diseses, which ccoun for 75% of helhcre expendiure. Individuls suffering from chronic diseses cn consume hree ypes of services: secondry-prevenive cre which includes dignosic ess, primryprevenive cre which consiss of drugs h help preven he illness from geing worse, nd curive cre which includes surgeries nd more expensive drugs h provide qunum boos o he consumer s helh. Alhough mjoriy of cses cn be mnged by prevenive cre, mos consumers op for more expensive curive cre h leds o subsnil increse in overll coss. To exmine hese inefficiencies, we build dynmic model of consumers nnul insurnce pln decisions nd periodic consumpion decisions, nd pply i o pnel dse on hese wo consumers decisions. Our resuls indice h here exiss sizble segmen of consumers who purchse more comprehensive plns hn needed becuse of high unceriny vis-à-vis heir helh sus; nd once in he pln, hey op for curive cre even when heir illness could be mnged hrough prevenive cre. We exmine how chnging cos shring chrcerisics of insurnce plns nd providing more ccure informion o consumers vi secondry-prevenive cre cn reduce hese inefficiencies. Keywords: Insurnce Choice, Helhcre Service, Nesed Dynmic Decisions, Primry nd Secondry Prevenive Cre, Curive Cre, Informive Effec, Invesmen Effec, Dynmic Progrmming

3 Secion : Inroducion Helhcre is one of he mos imporn nd personl services h consumers buy nd i hs pervsive impc on he quliy of dily life nd he economy. In he U.S., insurnce firms re he mjor helh insurnce providers. They cover 58.5% of he populion hrough employer-sponsored helh insurnce, followed by Medicre nd Medicid which cover 9.0% of he populion (Economic Policy Insiue 009). During he ps decde, helh cre coss incurred by hese providers hve more hn doubled, resuling in price g of $.6 rillion in 008 h consiues 7% of U.S. GDP (New Yor Times 009). Such n increse hs resuled in insurnce firms pssing on he coss o consumers, which hs cused 9% increse in premiums over he ps 0 yers. These syroceing premiums hve no only imposed huge burden on he consumer s wlle, bu hs lso led o drmic increse in he number of people who cnno py such hefy premiums (Price Wer House Coopers 008). Consequenly mny people re lef eiher uninsured or covered by governmen-run progrms, which hs in urn cused n enormous increse in governmen spending. Consumer choices nd consumpion hs been he cornersone of reserch in mreing for he ps severl decdes. They hve exmined number of cegories such s echup, dipers, sod, yogur, coffee o nme few (Given he enormous number of sudies, we omi ciions). Surprisingly, when one shifs wy from produc choices o services, he lierure in mreing becomes incredibly sprse. Consumers choices of morgges, life insurnce nd muul funds re imporn nd ofen dwrf he consumer pcged goods h hs been so exensively sudied. Similrly, we re unwre of ny reserch in mreing focused on purchse nd consumpion of helh insurnce nd helhcre services, mre h is so lrge h only hndful of economies in he world exceed is size. Reserch in mreing ends o exmine he inerdependency beween choice nd consumpion. For exmple, here re sudies h exmine wheher or no purchse of lrger size increses consumpion (for exmple, see Sun 005). Ye he iner-relionship is fr more criicl in he re of helhcre. Consumers expecion of helh sus in fuure will drive heir insurnce pln choices nd given hose choices, heir consumpion behvior of helhcre services. Thus, his cegory offers excellen scope for undersnding his spec h hs been he cynosure of reserch in mreing for longime. The need o undersnd helhcre consumpion hs ssumed greer urgency due o he explosive growh in cos. The increse in coss is priculrly relevn in he conex of chronic diseses such s her disese, cncer, dibees nd hyperension, which fflic more hn 33 million 3

4 people, nd ccoun for 75% of he overll helh cre coss in U.S (New Yor Times, 009). See Tble A for some ypicl exmples of chronic diseses. Chronic diseses differ from cue diseses nd oher ilmens in wo respecs: firs, unlie oher ilmens, individuls suffering from chronic diseses require helh cre over much longer ime horizon; second, unlie oher ilmens, individuls suffering from chronic diseses cn e wo ypes of helhcre services o mnge heir illnesses: prevenive cre nd curive cre (Kenel 000). Prevenive cre s defined by Cener for Disese Conrol nd Prevenion consiues wo ypes of services: primry prevenion nd secondry prevenion. Primry prevenion refers o services h include cerin ypes of drugs, which help preven he disese from geing worse so h he consumers cn led norml life. Secondry prevenion refers o services h help deec he illness nd he exen of is severiy. These include dignosic ess, screening nd rouine physicl exms. Curive cre refers o remens such s surgeries nd cerin ypes of drugs h help improve sympoms or cure he medicl problems. See Tble B for some ypicl exmples of services nd remens h fll under primry prevenive, secondry prevenive nd curive cre. Alhough primry prevenive nd curive cres serve similr purpose, hey differ in wo respecs. Firs, curive cre is more expensive nd provides greer boos o consumer s helh compred o primry prevenion. Second, primry prevenion is useful only when he illness is deeced n erly sge nd is severiy rnges from low o modere. On he oher hnd, curive cre is useful when he severiy rnges from modere o high. The disincion beween prevenive cre nd curive cre is crucil in he conex of chronic diseses since ccording o expers, vs mjoriy of cses in chronic diseses cn be effecively mnged by prevenive cre (Grossmn & Rnd 974; Thorpe 008). An nlysis from RAND (Mnning e l. 987) climed h beer mngemen of chronic diseses hrough prevenive cre could resul in weny million fewer impien dys nd nine million fewer office visis bsed on only four chronic diseses. However he reliy is h more hn 96% of overll helh cre expendiure for chronic diseses goes o curive cre (Thorpe 008). For insnce, consider prose cncer which inflics round 00,000 men every yer in he U.S. (Wll Sree Journl 00). An esimed 85% of umors grow so slowly h hey will never cuse problems s long s hey re effecively mnged hrough prevenive cre, which minly includes ing primry prevenive cre drugs such s sins h conrol he spred of prose cncer (long wih using secondry prevenive cre on Acue disese refers o disese or disorder h lss shor ime, inflics rpidly nd is ccompnied by disinc sympoms such s frcures 4

5 periodic bsis such s PSA ess nd digil recl exms). However less hn 0% of consumers op o go for prevenive cre; insed, hey undergo expensive curive remens such s surgeries nd rdiion herpy, which subsnilly increse he overll helhcre coss. I follows from he bove discussion h here could be inefficiencies in mnging chronic diseses: insed of seeing less expensive primry prevenive cre, consumers suffering from chronic diseses op for he more expensive curive cre h leds o disproporionlly higher helhcre coss. In his pper we see o invesige one of he resons for his inefficiency, which is morl hzrd. Recll from our erlier discussion h consumers suffering from chronic diseses wih modere levels of severiy cn be reed by eiher curive cre or primry prevenive cre where curive cre, lhough more expensive, provides greer boos o he consumer s helh s compred o primry prevenive cre. Thus, if he cos of remen o he consumers (i.e., he ou of poce expenses incurred by consumers when seeing he remen) ws no n issue, such consumers will lwys op for curive cre. Now since consumers obin helhcre services hrough insurnce plns, i follows h he more comprehensive he consumer s insurnce pln, he lower will be he shre of he helhcre expense incurred by he consumer, nd consequenly he greer will be he incenive for such consumer o op for curive cre. In summry, morl hzrd rises when consumers suffering from chronic diseses wih modere levels of severiy purchse comprehensive insurnce plns in which lrge pr of he cos of remen is shred by he insurnce firm; s resul, hese consumers op for he more expensive curive cre o mnge heir illness h could hve been mnged by primry prevenive cre. This premble leds us o he gol of our pper, which is o exmine in he conex of chronic diseses, wheher nd o wh exen does morl hzrd ply role in creing inefficiencies nd he ypes of policies h cn be employed o reduce hese inefficiencies. To chieve his gol, we hve hree imporn objecives.. Reserch Objecives nd Min Findings The firs objecive is o model how consumers me nnul insurnce pln decisions nd periodic helhcre consumpion decisions condiionl on heir chosen insurnce plns. The insurnce pln decision enils choosing beween differen ypes of helh insurnce plns h differ in erms of nnul premiums nd cos shring chrcerisics. And he helhcre consumpion decision enils choosing beween primry prevenive, secondry prevenive, curive cres or he no-consumpion 5

6 opion in ech period in policy yer. We model he wo decisions in nesed dynmic frmewor wih ris-verse nd forwrd looing consumers who re uncerin bou heir helh sus. We model he helhcre consumpion decision s rdeoff beween he exen o which curive, primry prevenive nd secondry prevenive cres impc he consumer s helh sus nd he ou of poce expenses incurred by he consumer while consuming ech of hese services. We model he impc of curive, primry nd secondry prevenive cres on consumer s helh sus vi wo mechnisms: invesmen nd informive effecs (Arrow 963; Grossmn 97). The invesmen effec refers o he increse in consumer s helh fer consuming he helhcre service nd informive effec refers o he informion h he helhcre service provides o he consumer bou her curren helh sus h enbles her o judiciously decide on fuure course of remen. And regrding he nnul insurnce pln decision, we model i s rdeoff beween he nnul premium chrged in he insurnce pln nd consumer s expeced fuure helh cre consumpion where he helh cre consumpion, s discussed before, depends on he consumer s helh sus, consumer s unceriny in her helh sus nd he cos shring chrcerisics of he insurnce pln. The second objecive is o esime our model on pnel d h consiss of consumers insurnce pln nd consumpion choices over ime. The pnel d hs deiled informion on insurnce plns vilble o ech consumer ech yer, chrcerisics of ech pln, pln chosen by ech consumer ech yer, helhcre consumpion decisions on weely level, nd he cos incurred by he consumer nd insurnce compny for ech consumpion decision. Our ey empiricl resuls re s follows. A. Boh prevenive nd curive cres hve significn impc on consumer s helh sus. Specificlly, he informive effec of secondry prevenive cre is significn; nd while boh primry prevenive nd curive cres hve significn invesmen effec, he invesmen effec is much higher for curive cre. B. The vriion in insurnce pln decisions cross consumers sems more from heerogeneiy in heir helh sus, heir unceriny vis-à-vis heir helh sus nd degrdion in heir helh sus hn he heerogeneiy in heir price sensiiviies. C. The usge of boh primry nd secondry prevenive cres is ffeced mos by chnges in copymen, followed by chnges in he deducible nd coinsurnce re, while he opposie is rue for curive cre. D. morl hzrd plys crucil role in creing inefficiencies. Our resuls indice h he underlying reson for inefficiencies is h here exiss sizble segmen of problem consumers (3% of consumers) who hve modere helh sus, high unceriny bou heir helh sus nd low price sensiiviies. Becuse of high unceriny, hese consumers choose he comprehensive pln s 6

7 opposed o he medium pln h would hve been beer mch for heir modere helh sus; nd once in he pln, hey op for more expensive curive cre insed of primry prevenive cre. The hird objecive is o invesige how he inefficiencies cn be reduced. We exmine wo roues. The firs is he immedie roue in which we chnge cos shring chrcerisics of insurnce plns he beginning of he policy yer, which would incenivize problem consumers o choose he medium pln in h policy yer iself. The second is he delyed roue in which we incenivize he problem consumers o consume more secondry prevenive cre in he firs yer (nd onwrds). Doing so will decrese heir unceriny nd will induce hem o choose medium plns in fuure. Our resuls indice h he immedie roue is no fesible since hese consumers hve low price elsiciies in insurnce pln decisions. We conduc wo counerfculs in he conex of he delyed roue in which we exmine he impc of he following on helh cre coss: () chnging he cos shring chrcerisics h encourge use of secondry prevenive cre, nd (b) providing more ccure informion hrough secondry prevenive cre. In boh counerfculs, we find h helh cre coss reduce subsnilly s resul of problem consumers choosing medium plns in fuure.. Reled Lierure The ls five yers hve seen growing ineres in brod re of helhcre economics wih opics rnging from sudying he impc of lbor mre fricions on helhcre expendiures (e.g. Fng nd Gvzz 0), esing for bounded rionliy in he helhcre mre (e.g. Hndel nd Kolsd 03; Fng e l. 03) o idenifying symmeric informion nd sepring selecion from morl hzrd. Given he wide rnge of opics, we resric our enion o only hose ppers h hve resonble relevnce o our wor, nd do no discuss he ppers h re only ngenilly reled. Prior empiricl ppers h hve modeled consumers helhcre consumpion decisions hve used he Grossmn s helh invesmen frmewor (Grossmn 97; Grossmn nd Rnd 974). In his frmewor, he consumer s uiliy is modeled s funcion of her helh sus nd he ou of poce expenses for consuming helhcre service. The consumer s helh sus is ssumed o degrde over ime, nd he consumpion of helh cre service serves o increse he consumer s helh sus vi he invesmen effec only. Mos empiricl ppers h hve modeled helhcre consumpion decisions hve reed he helh insurnce decisions s exogenous. A few empiricl ppers h hve endogenized he insurnce pln decisions re Cmeron e l. (988), Crdon nd Hendel (00), Crlin nd Town (008), Bjri e l. (0), Einv e l. (03) nd Hndel (03). Unlie our pper, hey did no model consumpion decisions in erms of wheher or no consumers 7

8 should see prevenive or curive cre in ech period in he policy yer; insed, hey modeled he consumpion decision s one sho decision, nmely, how much money o spend on helhcre services in policy yer. Furher, hese ppers only modeled he invesmen effecs of consumpion opions, nd no he informive effecs. Finlly, hese ppers focused on exisence of symmeric informion nd sepring selecion from morl hzrd. In oher words, heir objecive ws o demonsre he exisence of morl hzrd by showing h condiionl on consumer s helh sus, he choice of her insurnce pln hs significn impc on her nnul helhcre expendiure 3. Our pper builds on hese ppers by modeling he underlying decision ming process of consumers h connecs he insurnce pln decision o heir nnul helhcre expendiures. We do so by modeling consumers periodic consumpion decisions wihin policy yer in erms of choosing beween primry prevenive, curive nd secondry prevenive cres. Doing so is imporn since i llows us o exmine s o how chnges in policies cn influence he exen of morl hzrd. We furher build on hese ppers by modeling he informive effecs of consumpion opions which ply crucil role in mnging chronic diseses. I llows us o exmine s o how policies h help provide cheper nd esier ccess o informion on one s helh cn reduce he exen of morl hzrd. Apr from hese differences, our pper differs from he prior ppers on wo oher grounds. Firs, he d used in he prior ppers is from single employer only. In our pper, he d is from muliple employers in which he specifics of insurnce plns (premium nd cos shring chrcerisics) differ cross employers. As rgued in Crdon nd Hendel (00), his choice se heerogeneiy llows us o do beer job of sepring selecion from morl hzrd. Second, hese ppers used cross secionl d which covered he insurnce pln nd consumpion decisions for one policy yer only 4. On he oher hnd, we use pnel d h covers he decisions over muliple yers. This hs wo imporn implicions. Unlie he prior lierure, () we re ble o do much beer job in idenifying he unobserved heerogeneiy, which s we will discuss ler, plys crucil role in idenifying he exen of morl hzrd, nd (b) we cn exmine he impc of consumpion decisions in one yer on insurnce pln nd consumpion decisions in he following yer. Poin (b) is crucil, since s we discussed before, one of our ey findings is h i is he delyed roue nd no he immedie roue h helps decrese he exen of morl hzrd. Noe h he delyed roue cn only be invesiged if we model he decisions over muliple yers. 3 The excepion here is Hndel (03) who ssumed wy morl hzrd nd focused on idenifying swiching coss. 4 The excepion here is he woring pper by Khwj (00) who proposed dynmic life-cycle model o sudy consumers insurnce nd helhcre expendiure decisions over ime. 8

9 Our pper is lso reled o empiricl conrc lierure sring wih Chippori nd Slnie s (000) posiive correlion es of symmeric informion. This es esimes he correlion beween insurnce coverge nd insurnce uilizion implied by he consumer s ris ypes. However he difficuly of sepring selecion from morl hzrd leds o mixed evidence wih some empiricl sudies finding srong suppor for dverse selecion while ohers find we suppor (Fng, Kene nd Silvermn 006). Finelsein nd McGrry (006) nd Culer, Finelsein nd McGrry 008 resolved hese mixed findings by posiing wo dimensions of heerogeneiy insed of jus one: heerogeneiy in ris preferences nd heerogeneiy in ris ype. If individuls differ in more hn one dimension, i.e., in heir ris ype s well s in heir ris preferences, hen i is possible h hese wo ypes of prive informion offse ech oher o produce n equilibrium wih no correlion beween insurnce coverge nd uilizion. Therefore, i is imporn o e ino ccoun heerogeneiy in boh he ris ype nd in he ris preference, in order o sepre ou morl hzrd from selecion. This finding is crucil since he objecive of our pper is o idenify he inefficiencies h resul from morl hzrd. In our model, we incorpore heerogeneiy in he ris ype nd he ris preference by llowing for consumers o differ in erms of heir helh sus nd heir unceriny owrd heir helh sus. Secion : D We use propriery dse provided by n nonymous helh insurer. This insurer offers employer sponsored Preferred Provider Orgnizion (PPO) plns o consumers hrough heir employers ypicl of he Americn helh cre sysem. Around 87% of he insurer s group business is in PPO produc cegory. In our d, consumers come from differen employers, bu heir helh plns re offered by he sme single insurer from 005 o Across hese hree yers, he insurer offered consumers hree plns lbeled s bsic, medium nd comprehensive. All consumers in he d re enrolled in one of he hree plns. All hree plns hve he sme hospil/physicin newor, sme covered medicl services, nd he sme conrcul greemen wih helhcre providers (such s discouns for services provided). The hree plns differ in erms of cos shring chrcerisics nd nnul premiums which deermine he mpping from ol medicl expendiure from given remen o ou-of-poce expense incurred by he consumer. The chrcerisics of he hree plns 5 Alhough we do no observe employees helh insurnce opions ouside he firm, ccording o he Kiser Annul Survey of Employer Helh Benefis, 8% of eligible worers enroll in plns offered by heir own employers. This is lso verified by he insurer who provided us he d. 9

10 vry nnully nd lso cross consumers who choose sme ype of pln. This is becuse even hough he insurer offered ol of hree plns o employers ech yer, he insurer cusomized hese hree plns for differen employers. Therefore, ny wo individuls cross differen employers who choose he sme ype of pln in he d would fce differen premium nd cos shring chrcerisics. The cos shring chrcerisics of pln include copymen, deducible, coinsurnce re nd ou-of-poce-mximum. Copymen is he specified dollr moun h consumer mus py ou of her own poce for specified docor visi he ime he service is rendered. Deducible is he fl moun h n individul mus py before he insurer will me ny benefi pymens. Coinsurnce re is he percenge of ll remining eligible helh cre expenses fer he deducible moun hs been pid which is mehod of cos-shring in he helh insurnce seing. Ou-ofpoce-mximum is he dollr moun se by he insurer h limis he moun n individul hs o py ou of her own poce for priculr helhcre services during priculr ime period. See Figure for n illusrion of pricing srucure nd he empiricl cos shring from our d. We observe every consumer s nnul helh insurnce pln choice from 005 o 007 nd her deiled clim hisory over he hree yers. For ech consumer, we hve informion on demogrphics nd he nnul premiums nd cos shring chrcerisics of ech insurnce pln in ech consumer s choice se. And for ech clim, we hve informion on when he specific helhcre service ws consumed, he dignosic, procedure nd herpeuic codes for h specific service nd he pymen informion such s copymen, deducible pid, coinsurnce pid, insurer pid nd ol billed chrged. The ypicl chronic diseses in our d re her disese, cncer, hyperension, chronic respirory diseses, dibees, Alzheimer s disese nd idney disese. We clssify consumers helh cre consumpion services ino hree ypes: (i) secondry prevenive cre, which includes dignosic ess such s mmmogrms nd Prose-Specific Anigen (PSA) ess, (ii) primry prevenive cre such s sins (Lipior) used for lowering blood choleserol, nd (iii) curive cre which includes surgeries such s coronry ngioplsy nd coronry sen plcemen nd curive drugs. The clssificion of differen remens ino primry prevenive, secondry prevenive nd curive cre is bsed on he definiion of Americn Medicl Associion (Inernionl Clssificion Ninh Revision Clinicl Modificion 008 nd Curren Procedurl Terminology 008) nd he inernl mnul provided by he insurnce compny. Tble A repors he number of differen remens h fll under given consumpion opion (i.e., secondry prevenive, primry prevenive nd curive cres) for hree common chronic diseses. Observe h for ech disese, here re muliple remens wihin given consumpion 0

11 opion. For insnce, here re five differen remens h fll under secondry prevenive cre for ype- dibees. Thus o eep he model rcble, for ech disese, we ggrege ll remens h fll under given consumpion opion ino single consumpion opion wih single ggrege cos. The procedure of ggreging he coss is explined in Appendix I of he pper, nd is similr o wh prior ppers hve done o operionlize he ggrege price of cegory or brnd composie when using scnner d ses. Essenilly, he ggrege cos of consumpion opion for given disese is clculed s weighed verge cos of ll remens h fll under h consumpion opion nd disese where he weighs re bsed on frequencies of usge of he differen remens. To see wheher or no his would led o lrge ggregion bises, we compued he weighed verge cos (nd he sd. dev. of he coss) of differen remens h fll under ech consumpion opion for he sme hree diseses. Noe h if he sndrd deviions of he coss re high, i will imply h here is lrge vriion in coss of remens h fll under given consumpion opion nd disese, which will in urn imply h ggreging hose coss my led o lrge ggregion bises. The weighed verge cos (nd he corresponding sd. dev.) of given consumpion opion nd disese is clculed bsed on he coss recorded in our d for ll hose observions in which he consumers consumed eiher of he remens h fll under h given consumpion opion nd disese. The weighed verge coss nd sndrd deviions of coss re repored in Tble A. Observe in Tble A h sndrd deviions of ll coss re n order of mgniude lower hn he verge coss. This implies h using weighed verge mesure o ggrege he coss cross remens wihin given consumpion opion nd disese, lhough no perfec, is resonble. Moving on o he oher specs, round 95% of consumers in our d consume mos one ype of service in given wee; nd in our esimion smple, his number is 00%. Thus in our model, we ssume h consumers me discree choices of helhcre consumpion (wheher o choose primry prevenive cre, secondry prevenive cre, curive cre or neiher) on weely bsis. Furher, we only model he consumpion decisions h re reled o chronic diseses. We do no model consumer s visis h re no reled o chronic diseses for wo resons. Firs, he frcion of such visis (=5.3%) is s such smll nd he expendiure on hese visis is even smller. Second, s we discussed in Secion, he consumer s consumpion choice se for non-chronic diseses does no consis of primry prevenive, secondry prevenive nd curive cre. Thus, he modeling frmewor h we propose in his pper does no pply o non-chronic diseses. We focus on individul insurnce policy holders who re coninuously enrolled for he enire period. In our esimion smple, we only consider hose consumers who hve purchsed

12 individul plns nd no fmily plns. The reson for h is becuse in our modeling frmewor, we model he insurnce pln nd consumpion decisions bsed on he helh sus of single individul. This leves us wih,833 insurnce conrc holders for esimion. In our esimion smple, 9% of consumers hve en prevenive or curive cre prescribed for chronic diseses, nd 34.% of consumers hve en prevenive or curive cre for more hn one chronic disese. This complees he discussion on he consrucion of he esimion smple. The dependen vribles re he consumers nnul insurnce pln choices (i.e., wheher o choose bsic, medium or comprehensive pln) nd heir weely consumpion choices (i.e., wheher o choose curive cre, primry prevenive cre, secondry prevenive cre or neiher). And he independen vribles re he nnul premiums nd cos shring chrcerisics for ech insurnce pln in he consumer s choice se, nd he cul price pid by ech consumer for ech opion. From he ol cos for ech opion nd he cos shring chrcerisics of he chosen pln, we consruc he cul price pid by ech consumer for ech opion. The procedure for doing so is explined ler in Secion 3. In our smple,.9% of consumers did no purchse ny of he hree consumpion opions, 5.8% purchsed ll hree consumpion opions les once, nd 79.6% purchsed secondry prevenive cre (i.e., dignosic ess) les once during heir purchse hisory. And beween primry prevenive cre nd curive cre, 4.3% of consumers did no use curive cre bu used primry prevenive cre les once, 0.% did no use primry prevenive cre bu used curive cre les once, nd 58.9% used boh primry prevenive nd curive cres les once during heir enire purchse hisory. Amongs he consumers who hve used secondry prevenive cre les once, he verge number of secondry prevenive cre visis per consumer is 5.7, nd mongs he consumers who hve used primry prevenive cre (curive cre) les once, he verge number of primry prevenive cre (curive cre) visis per consumer is 40.8 (.). And mongs he 58.9% of consumers who hve used boh primry prevenive nd curive cres, he verge number of primry prevenive cre (curive cre) visis per consumer is 44.7 (.3). Tbles B nd C presen consumers insurnce pln choices nd pln swiching behvior over he hree yers. On n verge, 43% of he consumers chose comprehensive plns, % chose bsic plns nd he res chose he medium plns; nd on n verge, 7.5% consumers chnge heir insurnce plns ech yer. Tble D provides he summry sisics of helh insurnce nd clim informion cross he hree ypes of plns. The premium h consumers py for he bsic pln is only one hird of he premium for he comprehensive pln; nd he coinsurnce re, deducible nd ou-of-poce mximum decrese s we move from he bsic pln o he comprehensive pln. On

13 n verge, people wihin comprehensive pln see helh cre imes yer, which is much higher hn h for he consumers enrolled in bsic pln. As we move from he bsic pln o he comprehensive pln, he number of visis per consumer per yer (nd helhcre cos per consumer per yer) increses for ech of he hree consumpion opions; however, his increse is he seepes for curive cre nd lowes for primry prevenive cre. Secion 3: Model We propose dynmic model of consumers helhcre decisions in which heir periodic (weely) helhcre consumpion decisions re nesed wihin heir nnul insurnce pln purchse decisions. Consumers decide he ype of helh insurnce plns on n nnul bsis bsed he premium chrged nd heir expeced helhcre consumpion in he fuure. Condiionl on he helh insurnce pln, hey hen decide heir periodic consumpion decisions which include ing primry prevenive cre, secondry prevenive cre, curive cre or he no consumpion opion. In our nlysis, we ssume h he physicin is perfec gen nd cs in he bes ineres of he pien. In oher words, we ssume h he helhcre consumpion decisions re mde by he consumer bsed on her beliefs bou her helh sus, nd her ou of poce expenses she would incur while consuming he differen opions. This is sndrd ssumpion in he helhcre lierure (Felder nd Myrhofer 0) nd resonble one in our conex since he level of informionl symmery beween docor nd pien will be smll in he conex of chronic diseses (Ver-Hernndez 003). 3. Insurnce Pln nd Helh Cre Consumpion Decisions Consider i=.. I consumers who me nnul insurnce choices from se of j=..j helh insurnce plns yer =..A. In our d, he number of vilble insurnce plns for ech consumer re J=3, where j= indices he bsic pln, j= he medium pln, nd j=3 he comprehensive pln. The chrcerisics of he hree plns differ in erms of nnul premiums, deducibles, co-insurnce res nd ou of poce mximums. Since ll consumers re enrolled in one of he hree plns over he enire period of he d, we only model he insurnce pln decisions in erms of which of he hree plns o purchse (i.e., we do no llow for no-purchse opion or n ouside opion in insurnce pln decisions). We use d ij o denoe consumer s choice of insurnce pln j yer s: d ij, if consumer ichooses pln j he beginning of yer () 0, oherwise 3

14 Condiionl on he insurnce pln in yer, he consumer mes her helh cre consumpion decision in ech period (i.e., wee) =..T. The consumpion decision enils choosing eiher primry prevenive cre pp, secondry prevenive cre sp, curive cre c or no-consumpion opion, no. Le noher vrible c i represen he helh cre consumpion decision, where {pp, sp, c, no}. c i, if consumer i chooses helh cre service wee 0, oherwise () In given period, hese lernives re muully exclusive such h c. See Figure for n illusrion of he ime line of he wo decisions. In wh follows, we discuss he fcors h influence he wo decisions: consumer s helh sus, invesmen nd informive effecs of he consumpion opions nd he insurnce pln s pricing componens. For noionl ese, we will drop he subscrip of i for he consumer in he reminder of his secion. We will inroduce he subscrip for he consumer when we discuss heerogeneiy in secion Helh Sus nd Degrdion The consumer s helh sus is ey fcor h influences her helh cre consumpion nd helh insurnce decisions. Following Grossmn s (97) helh producion frmewor, helh sus is reed s (len) humn cpil soc. Le H be he consumer s rue helh sus he end of period. Unlie he quliy lerning lierure (Erdem nd Kene 996; Erdem e l. 005; Zhng 00; Lin e l. 04) in which he rue produc quliy is ime-invrin, consumers rue helh sus cn evolve over ime due o degrdion nd invesmen effecs of medicl inervenions such s curive or prevenive cre. Sring wih degrdion, he medicl lierure hs esblished h in bsence of ny medicl inervenion, he helh sus of individuls deeriores over ime becuse of ging, nd more so if hey re suffering from chronic diseses (Kenel 000). We hus model he degrdion in consumer s rue helh sus over ime in bsence of invesmen effecs s follows: H = H - - d (3) where d represens he degrdion re, which is he deeriorion in he consumer s rue helh sus over ech period. Similr o he prior lierure, d is ssumed o be nown o he consumer. i 3.3 Invesmen Effecs Consumers see helh cre o improve heir helh sus. Following Grossmn s helh producion frmewor, we ssume h helhcre service provides qunum boos o he consumer s helh 4

15 sus. We hus model he evoluion of consumer s rue helh sus in he presence of degrdion nd invesmen effecs s follows H H d c (4) where is he invesmen effec of opion {pp, sp, c, no} consumed in period. Similr o prior lierure, is ssumed o be nown o he consumer. We llow for invesmen effecs o differ cross consumpion opions, nd we se he invesmen effec of no-consumpion opion o zero. 3.4 Informive Effecs Since consumers re no well informed bou heir rue helh sus, hey would hve unceriny bou i (Arrow 963; Hsieh & Lin 997). Therefore heir insurnce pln nd consumpion decisions will be bsed on heir beliefs of heir rue helh sus. Consumers cn lern bou heir rue helh sus vi he informive effecs of he consumpion opions. To model hese informive effecs, we ssume h consumpion opions provide noisy signls o he consumers bou heir rue helh sus, nd consumers lern bou heir rue helh sus from hese signls in Byesin fshion. To undersnd he evoluion of consumers beliefs bou heir helh sus from he end of period - o he end of period, see Figure 3 which illusres he sequence of consumer s periodic degrdion, invesmen nd informive effecs. In his sequence, we sr wih he consumer s beliefs bou her rue helh sus he beginning of period (or end of period -) s ~ N h, H (5) Following h, we upde he priors in equion (5) bsed on degrdion of he helh sus in period nd he invesmen effecs from consumpion of opion in period. Since he degrdion re nd invesmen effecs re nown o he consumer, hey will only impc he men nd no he vrince of he consumer s helh sus beliefs. Thus by he end of his sep, we ge he consumer s beliefs using equions (4) nd (5) s H ~ N h d c, (6) In he nex sep, we upde he priors in equion (6) bsed on he informive effecs from he consumpion of opion in period. 6 Le be he noisy consumpion signl h he consumer receives bou her rue helh sus from he consumpion of opion in period. This is given s = H + (7) 6 I does no mer wheher we model he invesmen or he informive effecs in he firs sep. Eiher wy, we will ge he sme evoluion of he consumer s beliefs of her helh sus. 5

16 The firs erm on he RHS of equion (7), H, represens he consumers rue helh sus he end of period fer she hs experienced degrdion in her helh in period nd he invesmen effec of he opion consumed in period. The second erm on RHS of equion (7),, represens he signl noise of opion, where is sndrd norml rndom vrible nd is he sndrd deviion of he signl noise which is mesure of he informionl inccurcy of helhcre service. If =0, i implies h he helhcre opion provides perfec informion o he consumer bou her heh sus. And if =, i implies h helhcre opion does no provide ny informion o he consumer bou her heh sus. Subsiuing he expression for H given in equion (4) ino equion (7), we ge he following expression for in erms of he consumer s rue helh sus he beginning of period : H c (8) d Given he prior in equion (6) nd he signl in equion (8), he consumer s poserior beliefs he end of period will be disribued s N, H where ~ h h h d c c c (9) c Equions (9) nd (9b) represen he evoluion of he men nd vrince of helh sus from he consumer s perspecive. To complee he specificion of his evoluion, we represen he consumer s prior beliefs he beginning of period = in yer = by H ~ Nh 0 0, (9b) 0. We ssume h he beginning of {=, =}, he consumer hs rionl expecions bou her helh sus (Crwford nd Shum 005), i.e., he men nd vrince of her prior beliefs, h 0 nd 0, re lso he men nd he vrince of he disribuion of he rue helh sus cross he consumer populion he beginning of {=, =}. 3.5 Ou-of-Poce Expenses The pricing srucure of he helh plns offered by he insurer ffecs consumers helh insurnce nd consumpion decisions hrough he ou of poce expenses incurred by he consumer when purchsing he insurnce pln nd when consuming he helhcre services. If consumer chooses 6

17 pln j, her ou of poce expense will be he premium (Prem j, ) h she pys he beginning of yer. Once enrolled in pln j, her ou of poce expense when choosing helh cre consumpion opion will depend on he cul price of he chosen opion nd he cos-shring feures of he pln. In wh follows, we discuss he consrucion of consumer s ou of poce expenses for consumpion decisions. Le p j,, be he consumer s ou of poce expense if she were o consume helhcre opion in period of yer if she were enrolled in insurnce pln j. We represen s where p, j, = p, j, cop, j, p, j, p, j, is consumer i s mrginl effecive price for opion in period, nd cop,j, is he copymen moun incurred by consumer i for using opion in yer if she were enrolled in pln j. The consumer s mrginl effecive price is given by p, j, cos, j, if cos, j, r r j, cos, j, r j, ci 0 if p,τ opm j, τ j,, j, nd if τ cos p,τ, j, opm r j, j, 0 nd τ p,τ opm where opm j, denoes he nnul ou-of-poce mximum of pln j chosen by consumer i in yer nd ci,j, is he coinsurnce re fced by consumer i in yer for opion. Furher, cos, j, is he overll cos (he sum of helhcre coss incurred by he consumer nd insurer) of helhcre opion in period of yer, whose operionlizion is discussed in Appendix I. Finlly, r, is he dollr moun remining in he consumer s nnul deducible in period, which is defined s r j, ded j, mx if 0, r p c if j,, j,, In equion (), T denoes he ls period of yer nd ded j, denoes he ol deducible moun pid by consumer i for he chosen pln j in yer before he insurer mes ny benefi pymens. Alhough we do no model he hospil/docor visis reled o non-chronic diseses, we e ino ccoun he expendiures incurred by he consumer on such visis when clculing equion (). For rcbiliy, we ssume h consumers now he cul coss of remens in ech period. This ssumpion is resonble one in our conex since he cos informion for chronic diseses is more widely vilble compred o oher diseses. Noice in equions (0) nd () he dynmics in prices induced by he deducible: s long s he deducible is no me, he cos of remen in ech period influences he ou-of-poce expenses..t j, (0) () j r j, in 7

18 in h period which in urn influences he dollrs remining in he deducible in he fuure ime period, nd hereby influences he ou of poce expenses in he fuure period ill he ou of poce mximum is me (Aron-Dine e l. 0). However, once he deducible is me, he cos of remen hs no impc on fuure ou of poce expenses, since he ou of poce expenses in ny period will simply be he cos of he remen in h period scled by he coinsurnce re. 3.6 Per period (Weely) Consumpion Uiliy We define he consumer s period uiliy for choosing he helhcre opion {pp, sp, c, no} s funcion of her ou of poce expenses p j,, nd her rue helh sus H h would resul if she were o consume h opion in period. We ssume h he uiliy sisfies he bsic propery of concviy wih respec o he helh sus (i.e., u (H )<0) which is synonymous wih ris-version. This is sndrd ssumpion in helh economics lierure (Felder nd Myrhofer 0) nd is needed in order for he model o conform o consumer behvior observed in he helhcre mre (more on his ler). We consider he CARA funcionl form for consumpion uiliy for choosing opion, which sisfies his ssumpion 7 (Chn nd Hmilon 006), nd is given s rh p, j, u exp, () In equion (), r (>0) is he consumer s degree of bsolue ris version, is he consumer s price sensiiviy nd is he economericin s error h is ssumed o be IID Type exreme vlue disribued. I cpures he unobserved fcors (which re observed by he consumer in period, bu no by he economericin) h cn influence consumer s consumpion decisions, such s helh shocs h re no cpured by degrdion/invesmen/informive effecs. For ech consumpion opion, he consumer would fce differen ou of poce expenses, p j,,, nd differen evoluion of her helh sus in he fuure. The consumer s informion se when ming consumpion decision he beginning of period consiss of (i) her beliefs of her helh sus he end of period -, which re disribued s N H ) (ii) her ou of poce expenses for ll ~ h, consumpion opions in period nd onwrds, (iii) nd unobserved fcors h influence her 7 Noe h our objecive in he pper is no o es wheher or no consumers re ris verse; we priori ssume h consumers re ris verse. This cn be seen in equion () in which he prmeer r is resriced o be posiive, which necessrily implies h consumers re ris verse (he reson why r is resriced o be posiive is becuse vlue of r<0 implies h he consumer s uiliy is decresing in her helh sus, which is incorrec). 8

19 consumpion decision in period, { }. Condiionl on his informion se, her period expeced uiliy for choosing opion follows from equion () s r E u Eexp rh h,, c p, j,, (3) In equion (3), he erm r denoes consumer s he ris premium in period, in which he specificion of condiionl on {h -, -, c =} follows from equion (9b) s (4) Equion (4) shows h he informive effecs serve o decrese he ris premium in he expeced uiliy by decresing he unceriny in perceived helh sus. Nex, in equion (3), he specificion of h condiionl on {h -, -, c =} cn be derived using equion (9), which specifies h s funcion of h -, d,, -, nd he signl. Noe h he beginning of period, lhough he consumer nows he vlues of h -, d,, -,, she does no now he vlue of he signl. This is becuse he signl from consuming opion is only relized by he consumer he end of period. Thus from he consumer s perspecive he beginning of period, will be rndom vrible h will be disribued s per equion (8). Subsiuing equion (8) ino equion (9), we ge he specificion of h condiionl on {h -, -, c =} from he consumer s perspecive he beginning of period s h h c d c (4b) where he erm is sndrd norml rndom vrible. In equion (4b), he second erm on he RHS, δ c -δ d, represens he chnge in he men helh sus which sems from degrdion nd he invesmen effec of opion ; nd he hird erm, c, represens he chnge in he men helh sus h sems from he informive effec of opion. Since he hird erm is norml rndom vrible, i implies h informive effecs impc he evoluion of he men helh sus hrough he lerning drw only where he expeced vlue of he lerning drw h sems from consumpion of opion in period (i.e., ) is zero, from he consumer s 9

20 perspecive he beginning of period. The reson for h is becuse he beginning of period when he consumer is ming he decision on wheher or no o consume opion, he consumer does no now wh he informive effec of h opion will revel o her bou her helh sus he end of period i could revel no chnge, posiive or negive chnge. Subsiuing equions (4) nd (4b) ino equion (3), we ge he consumer s period expeced uiliy condiionl on {h -, -, c =} if she were o choose opion in period s E u E r exp r h d p, j,, (5) This complees he discussion on he per-period uiliy. In he nex secion, we discuss he ey implicions of wh we hve discussed so fr. 3.7 Implicions We discuss wo implicions h follow from secions These implicions hold rue regrdless of he funcionl form of uiliy; he only sipulion required is h he uiliy be incresing nd concve in he helh sus. The firs implicion perins o concviy of he uiliy nd he usge of n invesmen remen (i.e., remen h only hs invesmen effecs nd no informive effecs). The second implicion perins o consumer s forwrd looing behvior, concviy of he uiliy nd usge of n informive service (i.e., service such s dignosic es h only hs informive effecs).. Concviy of he Uiliy nd he Overll Frequency of Usge of Invesmen Tremens: Recll from secion 3.6 h he concviy of he uiliy implies h he mrginl uiliy of helh decreses wih he increse in helh sus. Since he mrginl uiliy of helh is direcly reled o he consumer s incenive for seeing n invesmen remen, i implies he following: () he sicer he consumer, he greer will be her incenive o choose n invesmen remen over he no consumpion opion (nd vice vers). This mes sense since consumers undergo remens when hey re sic nd no when hey re helhy. (b) The greer he consumer s degrdion re, he greer will be her incenive o see n invesmen remen, nd consequenly he greer will be he frequency of usge of he invesmen remen. (c) The greer he invesmen effec of n opion, he lesser will be he frequency of usge of h opion fer is firs usge. This is becuse once consumer consumes n opion wih lrge invesmen effec, her helh sus ges significn boos which hen decreses her incenive o repurchse such n opion in fuure. This 0

21 mes sense since s discussed in secion, curive cre remens re no used frequenly. (d) As resul of degrdion in helh, he consumer s propensiy o undergo n invesmen remen increses wih he ime lpsed since is ls purchse; nd he greer he degrdion re, he greer is he increse in he consumer s propensiy o repurchse he remen over ime. Thus if here is no degrdion, her propensiy o repurchse he remen in ny given period does no depend on how long i hs been since she ls purchsed he remen.. Concviy, Forwrd Looing Behvior nd Usge of Informive Services: Recll from secion 3.6 h when consumer consumes n informive service (such s dignosic ess) he beginning of period, she receives lerning drw bou her helh sus he end of period, This lerning drw provides n opion vlue o he consumer since i enbles her o me judicious consumpion decisions (in erms of wheher or no o go for invesmen remens) in periods + nd onwrds. For insnce, if he consumer receives very negive vlue of he lerning drw he end of period, she would op for remen wih lrge invesmen effecs in period + which would increse he opiml uiliy in period +; similrly, if she receives posiive lerning drw, she would op for he no consumpion opion in period +. This poin showcses he impornce of modeling he consumers forwrd looing behvior nd for he uiliy o be concve. If consumers re no forwrd looing, here will be no incenive for hem o see informion from dignosic ess h cn help hem me judicious decisions in fuure. If he uiliy is no concve nd is insed liner in he helh sus, here will be no incenive for he consumer o see informion from dignosic ess h would help her me judicious decisions in he fuure. This is becuse here will be no opion vlue of he lerning drw since he probbiliies of purchsing he invesmen remen in period + will be he sme regrdless of wheher or no he consumer receives posiive or negive lerning drw from he dignosic es Weely Consumpion nd Annul Insurnce Pln Purchse Decisions We model he weely consumpion nd nnul insurnce pln decisions in nesed dynmic frmewor wih forwrd looing consumers. We sr wih he consumer s weely consumpion decision in period given her insurnce pln coverge nd her perceived helh sus he beginning of period, h -. Following h, we specify her nnul insurnce choice decisions ssuming opiml weely consumpion decisions.

22 Consumpion decisions in period : The consumer chooses he helhcre opion which mximizes her discouned lifeime expeced uiliy in period in yer derived from boh consumpion nd subsequen insurnce purchses. Specificlly, he vlue funcion period <T (where T is he ls period of he insurnce yer) condiionl on insurnce pln j is given s V mx d, j,, (6) In equion (6), is he weely discoun fcor which is se 0.999, nd S denoes he se r S j exp rh p E V S S, j vribles he beginning of period of yer. These se vribles re S {h -, -, {p }, { } }, where he se rnsiion processes of {h s, s } for he fuure periods from he consumer s perspecive re described in equions (4) nd (4b), nd he se rnsiion of prices re described in equion (0) nd (). In he ls ime period =T of insurnce yer, when n insurnce decision will be mde in he nex ime period, he vlue funcion is given by V r T S j mx exp rh p E W S S where W S S, T T d, j, T T T T, T (6b) represens he vlue of he fuure uiliies he beginning of he nex yer when he consumer mes noher insurnce decision, which we define in momen. To compue he vlue funcions, we employ vrin of Kene nd Wolpin (994) pproximion mehod, which we hve explined in Appendix II. Insurnce pln choice he beginning of yer : A he beginning of ech yer, he consumer chooses one of he J=3 insurnce plns in her choice se bsed on premium (Prem ij, ) nd her expeced uilizion of helh cre for he coming yer. Thus he vlue of uiliy of priculr insurnce pln j in period = of yer will be 8 S Prem j, V S j j VI j, (7) 8 We model ris preference in consumpion sge becuse consumers hve unceriny bou heir helh sus, bu we did no incorpore preference for ris in he insurnce pln sge becuse of he following resons: firs, Crdon & Hendel (00) noed he CARA ris coefficien, r, is insignificn in he pln choice sge nd preference owrd ris re deermined by boh r nd concviy of consumpion sge uiliy which we model here; Second, given he nure of employer-sponsored helh insurnce we sudied here, individuls hve more unceriny bou heir helh sus, no heir plns; Third, Ver-Herndez (003) poined ou h ris preference is more bou helh cre consumpion.

23 where he coefficien for he premium,, mesures how much he consumer i vlues premium nd is sme s he prmeer h cpures he ou of poce expenses in consumpion decisions, nd j, is n ddiive idiosyncric error h is independen cross ime nd consumers nd follows Type- exreme vlue disribuion. V S j is he coninuion vlue he beginning of he yer from he consumpion. As sed in equion (6b), he expeced lifeime uiliy he beginning of yer is S E VI S W T mx j (8) Secion 4: Economeric Specificion 4. Choice Probbiliies The choice probbiliies of insurnce pln nd consumpion decisions follow from equions (6)- (8). However, noe h he period vlue funcions in equions (6)-(8) re defined from he consumer s perspecive, where he consumer s helh sus he beginning of period, h -, is nown o he consumer. On he oher hnd, h - is no nown o he economericin. This is becuse h - is funcion of he ps signls received by he consumer from periods s= o s=- (see equion 9), nd unlie he consumer, he economericin does no observe he vlues of hese ps signls. Therefore before we use equions (6)-(8) o specify he choice probbiliies in period, we need o firs specify h - from he economericin s perspecive. From he economericin s perspecive, he ps signls will be rndom vribles s specified in equion (8). Thus subsiuing he expression for he signl given in equion (8) ino equion (9), we ge he consumer s men helh sus he end of period - s h c c h d c H h (9) where d is he degrdion re, is he invesmen effec of consumpion opion {pp, sp, c, no}, is he noise he in consumpion signl of consumpion opion, nd s is sndrd norml rndom vrible. Defining h - h - - H -, we ge he evoluion of h s from equions (4) nd (9) s c c h h h Using equion (0) recursively, we ge h - h - -H - in erms of h 0 h 0 -H 0 s (0) 3