Statutor packages of ealt care alongsde voluntar nsurance: wat treatments sould be covered? eter C. Smt Centre for Healt Economcs nverst of York York YO1 5DD nted Kngdom Februar 26 E-mal: pcs1@ork.ac.uk one: 44 194 321443 Fax: 44 194 321454 Acknowledgements A prevous verson of ts paper was presented at te nverst of Aberdeen, and I sould lke to tank te semnar partcpants for comments. I am supported b Economc and Socal esearc Councl researc fellowsp 271253. 1
Statutor packages of ealt care alongsde voluntar nsurance: wat treatments sould be covered? Abstract Ts paper examnes te economc lnk between statutor and voluntar ealt nsurance from an economc perspectve. Te statutor package s avalable to all free at te pont of access, and s funded b taxaton. Ctzens dffer n wealt and ealt, and ma coose to augment te statutor package wt voluntar nsurance, carged at an actuarall far premum. Te government s problem s to determne te optmal sze and composton of te statutor package n te lgt of effcenc and equt concerns. Te paper sows tat wen ealt care s nsured solel under a statutor package, equt concerns ma be mportant n selectng te nterventons to nsure. However, wen voluntar nsurance s also avalable, nterventons for te statutor package can be selected solel accordng to ter cost-effectveness. Equt concerns are nstead addressed troug te sze of te mplct tax transfer from rc to poor. ossble extensons to te model, ncludng a publc coce perspectve, are outlned. Te results ave mportant mplcatons for polc on ealt tecnolog assessment and natonal prort settng. 2
Statutor packages of ealt care alongsde voluntar nsurance: wat treatments sould be covered? Introducton Te prncpal means of fnancng most mature ealt sstems s a statutor ealt care nsurance sceme, coverng all ctzens watever ter crcumstances. Ts s often supplemented b a non-statutor nsurance sstem, used onl b tose wllng and able to pa (Mossalos et al. 22. Te statutor sstem s usuall funded b some sort of taxaton or socal nsurance, wt contrbutons unrelated to ealt status. Te non-statutor sstem s funded eter b user fees or b voluntar nsurance, wt fnancal contrbutons terefore usuall reflectng actual or expected use of servces (Mossalos and Tomson 24. Most wealt countres seek to make te statutor package reasonabl compreensve, ensurng tat all ctzens are nsured for rembursement of most manstream ealt care (albet sometmes wt a modest user copament. However, ealt care s offerng rapdl ncreasng opportuntes to address sckness and dsablt, and ctzens are placng ncreasng demands on ter ealt care sstems. At te same tme, man commentators clam tat tere are lmts to te extent to wc te tradtonal sources of fnance for statutor nsurance can be exploted. Te prncple of compreensveness s terefore comng under stran. Te polc questons terefore arse: sould some nterventons be removed from te statutor package; and f so, wc ones? In low ncome countres, tere are often lmted fnancal resources avalable for statutor nsurance, based on a slender tax base and (sometmes donor funds. Tere s terefore usuall no attempt to offer compreensve coverage, and a muc eaver relance s placed on personal fnance of ealt care, usuall n te form of user carges (Gertler and Van der Gaag 199. A ke polc queston n tese crcumstances s te extent to wc te lmted statutor sstem s beng deploed to best effect. In man countres tere as been a persstent concern tat te statutor funds avalable are beng deploed on nterventons tat are not cost-effectve, or are not supportng tose most n need (te sck and te poor (Hauck, Smt and Goddard 22. Suc concerns ave led to an ncreasngl concerted effort n all tpes of ealt sstem to specf explctl an essental package of ealt care tat s covered b te statutor nsurance fund (Jost 25. Te ntenton s to create a set of nterventons to wc all qualfng ctzens ave a rgt wen clncal ndcatons are satsfed. 1 Te usual assumpton s tat recept wll be free or subject to a small copament. Of course, te scope of te essental package s constraned b te fnancal resources avalable to te statutor sceme. Economsts ave camponed te use of te cost-effectveness rato as te man crteron for selectng nterventons for ncluson n te essental package of care (Drummond et al. 1997. Ts polc prescrpton flows from te noton of maxmzng ealt benefts subject to a budget constrant. Cost-effectveness analss ma terefore be relevant at te margn for coosng nterventons to exclude from a 3
near-compreensve statutor package of ealt care. However, te costeffectveness crteron ma on ts own be napproprate for determnng te essental package wen prvate paments pla a sgnfcant role n fundng ealt care. Te purpose of ts paper s to dentf optmalt condtons for selectng nterventons to nclude n te essental package wen ctzens can pa for voluntar nsurance to supplement or replace te statutor coverage. Te paper s structured as follows. Te next secton brefl dscusses te role of voluntar ealt nsurance n ealt sstems, and te relevant academc lterature. A stlzed model of ealt care s ten ntroduced, n wc governments must coose a statutor package of nsured ealt care, and ctzens coose te nature of an addtonal voluntar nsurance. Te optmal government package of care s descrbed. Extensons to te model are suggested n wc te possble resstance of te rc to fnancng publc nsurance s modelled. Te paper ends wt polc conclusons. INTODCTION Countres rel to greatl varng extents on voluntar ealt nsurance (Colombo and Tapa 24. Te orld Healt eport 22 ndcates tat 9 out of te 149 countres wt populatons over 1 mllon ave recorded expendture of less tan 1% of all ealt fnanced from prepad prvate nsurance (orld Healt Organzaton 22. Te account for 67% of te world s populaton. However, Table 1 sows tat a small number of countres make ver eav relance on prvate nsurance. Altoug n certan countres, suc as te Neterlands, prvate coverage s mandator for some ctzens, prvate coverage s n most countres voluntar. Sout Afrca 44.3 rugua 36.8 SA 34.8 Namba 32.1 Zmbabwe 26.7 Neterlands 24.9 Cle 23.1 Brazl 2.8 Canada 19.8 Swtzerland 18.8 Table 1: Countres wt eavest relance on prvate nsurance as a percentage of all ealt care fnancng (source: orld Healt eport 22. Te unversal pressure on all sources of ealt fnance as led man countres to reexamne te potental for ncreasng te use of voluntar nsurance to fnance ealt care, especall were tere as been a tradtonall g relance on user carges. Te frst requrement for a vable nsurance functon s to establs approprate and relable sstems of governance, to assure te collecton and stewardsp of nsurance premums, and to ensure tat provders are rembursed accordng to te use made b 4
nsurees. Tese basc requrements mpl te need for a mnmum degree of longterm trust n te nsttutons of ealt care, a rudmentar flow of adequate nformaton, and te relable enforcement of contracts. Te are essental for an sstem of nsurance, and are regrettabl absent n man low ncome countres. However, n ts paper we must assume tat te are satsfed. rvate ealt nsurance (alongsde a publcl funded compulsor package can take tree broad forms: substtutve, supplementar or complementar (Mossalos and Tomson 24. Substtutve nsurance s purcased as an alternatve to te statutor nsurance, wt te mplcaton tat tose wo elect to take out suc coverage are at least partall exempt from te premums or taxes assocated wt te statutor package. Substtutve nsurance ma lead to te creaton of a voluntar rsk pool wt a relatvel low expendture requrement, as t wll tend to be attractve to te rc and ealt. Supplementar prvate nsurance covers servces n te statutor package, but nsurees receve no exempton from paments towards te statutor package, and terefore enjo double coverage. A market n supplementar nsurance mples tat t must offer a perceved qualt advantage over te care secured b te statutor package, peraps n te form of reduced watng tmes or access to superor facltes. In contrast, complementar nsurance offers full or partal cover for servces tat are excluded or not full covered b te statutor ealt care sstem. In partcular, as n France, t ma cover lablt for copaments leved on servces wtn te statutor package. Tere as been a small economc lterature on te role of voluntar ealt nsurance alongsde a statutor publcl-funded essental package of ealt care. Besle (1989 examnes te extent to wc te problem of moral azard can be abated b augmentng a compettve nsurance market wt publcl funded catastropc ealt nsurance. Te paper stmulated a lvel academc excange tat s not strctl relevant to te problem addressed n ts paper, but wc does glgt te complext of formulatng matematcal models n ts doman, and te need for clart about te assumptons underlng an modellng (Selden 1993; Blomqvst and Joansson 1997. etretto (1999 examnes te functonng of a publcl nsured essental package of care alongsde a market n prvate complementar nsurance. Te ctzen s free to coose te nsured copament rate for te complementar servces. Ctzens make tree contrbutons to ealt care fnancng: a tax contrbuton; a prvate nsurance premum; and te resdual copament. A form of optmal ncome taxaton model s used to analse te government s problem, wc s to select te optmal statutor copament rate, n te lgt of response n te prvate nsurance market. Tese models requre specfcaton of a socal welfare functon n order to nfer optmal polc. In contrast, Epple and omano (1996b model te mx of publc and prvate ealt nsurance from a publc coce perspectve. Te demonstrate tat a mx of publc and prvate provson wll n man crcumstances be socall preferred to sstems relng solel on government or prvate provson. 5
Tere s also a broader publc economcs lterature on te publc/prvate mx. Blackorb and Donaldson (1988 note tat te sort of n knd transfers mpled b socal nsurance ma be preferred to cas transfers wen (as n te case of ealt care te are non-tradeable. In contrast to cas transfers, n-knd transfers can ensure tat onl te ntended benefcares receve te relevant servce. Munro (1991 examnes te mplcatons for optmal taxaton polc of suc transfers. Ireland (199 models te ntegraton of n-knd transfers and cas transfers, n te form of uncondtonal paments to te poor, and condtonal subsdes of prvate consumpton, for example n te form of voucers. Epple and omano (Epple and omano 1996a examne te publc prvate mx wtn a majort votng model, and fnds tat socet s coce ma depend on te balance of electoral power between mddle ncome voters (wo prefer ger publc provson and a coalton of g and low earners (wo prefer lower publc provson. Fnall, Besle and Coate (1991 note te crucal redstrbutve functon of socal provson of prvate goods. rovdng te qualt of te socal good s not too g, some rcer ouseolds wll - wtout te need for fnancal compensaton - opt out of te socal good n order to consume ts prvate counterpart, eldng an mplct fnancal transfer to te poor. In a smlar ven, Blomqvst and Horn (1984 examne te transfer from te ealt to te sck mplct n a sstem of statutor nsurance n a ealt care settng. None of ts lterature explctl models te great eterogenet of servces tat make up ealt care, or te varatons n epdemolog across socal groups. Te focus prncpall on te coce of taxaton and copament rates, and do not address a fundamental concern of polc-makers wc tpes of servce to nclude n te essental package. Ts paper terefore examnes tat coce wen tere s a market n voluntar prvate nsurance. It does not consder varable copament rates, wc are treated elsewere (Smt fortcomng. Instead, I assume tat procedures are eter full subsdsed b publc funds (terefore n te essental package or must be nsured at market rates troug prvate nsurance. THE MODEL Assume tere s a set of n ealt care problems, and for eac problem tere s a tecnolog avalable at a known constant prce x, wt known constant ealt beneft b tat does not dffer between ndvduals. Also assume tat te tecnologes are effcent, n te sense tat for eac te benefts exceed te costs, and no tecnolog s domnated b an oter for te specfed condton (.e. tese are te best tecnologes for eac condton. Te decson-makers are a natonal government and ndvduals. Te government must decde wat package of ealt care to subsdze from publc funds. Te package comprses a subset of te ealt tecnologes tat s offered at zero prce to te patent. Ts statutor package s fnanced b a tax on all ctzens. An tecnolog not n te government package s avalable at market prce x to patents, and prvate nsurance exsts wt wc te ndvdual can purcase coverage for all procedures not n te government package. In te frst nstance I assume tat tere are no dfferences between publc and prvate sector n te costs or benefts of procedures. Ts assumpton s later relaxed. Te voluntar nsurance market s presumed to be complete and effcent. 6
Moral azard and adverse selecton are not a central concern of ts model. Ctzens are presumed to receve an nterventon f and onl f te wll secure te expected beneft b. Moral azard ma arse, but s not a central concern of te model. Treatments can onl be secured troug nsurance (eter publc or prvate, and te parameter b sould terefore reflect te average expected net benefts of treatment, ncludng an opportunt cost assocated wt unnecessar treatment. rvate premums are rsk-related, and te assumpton of no adverse selecton n te voluntar nsurance market presumes tat nsurers ave adequate nformaton wt wc to set actuarall far premums. Indvduals optmze ter voluntar coverage knowng te statutor package cosen b te government. Te government cooses te statutor package n te lgt of te known responses of ndvduals n te voluntar nsurance sector. Te model s solved usng backwards nducton. Te next secton terefore consders te ndvdual s response to a statutor package, and te government s optmzaton problem s ten consdered. Te ndvdual Te ndvdual (or ouseold s te startng pont of te analss. Indvduals dffer n wealt and ealt. In te frst nstance I consder a dcotom of just rc and poor people. Te ncdence of dsease dffers accordng to wealt (toug t ma not alwas be te poor wo ave ger ncdence for all dseases. Te mplcatons of a contnuous dstrbuton of wealt are consdered later n te paper. Indvdual utlt (, depends on ealt and wealt, wt te usual propertes (dmnsng margnal utlt n ealt and wealt. Healt state wt no ealt care for rc and poor s >. ealt wt no ealt care expendture s >. Te proporton of rc people n te populaton s. Te annual ncdence of te ealt problem requrng nterventon s dstrbuted as and n rc and poor populatons respectvel, wt te aggregate ncdence equal to Π ( 1. Altoug I make no explct assumpton about rsk averson, tere s an mplcaton tat te benefts b nclude an utlt gans from rsk reducton assocated wt te nsured nterventon. t no statutor ealt care package, te prvate nsurance problem for an ndvdual n wealt group Z s to coose te set of nterventons tat: Z Z Z Z Maxmze ( θ b, θ z x n θ 1 were te decson varables { } are bnar varables ndcatng weter or not te nterventon s nsured. Ts elds te famlar rule tat nterventon s covered f and onl f: Z Z b. x were te margnal condtons appl at wealt after te relevant premum as been pad. nder most reasonable assumptons, ts rato decreases wt wealt, eldng te obvous result tat te rc wll purcase a more extensve nsurance coverage 7
tan te poor. Note ts soluton requres te exstence of a complete nsurance market tat s able to offer bespoke polces to all ctzens. Now consder te ndvdual s nsurance decson wen tere s a statutor package, funded from taxaton. Te ndvdual must decde weter or not to purcase some form of nsurance; and f so weter to purcase complementar nsurance (coverng non-statutor ealt care or substtutve nsurance (compreensve voluntar nsurance replacng te statutor nsurance. I subsume supplementar nsurance as a specal case of substtutve nsurance n wc te nsure gans no fnancal relef from statutor coverage. Te ndvdual s coce can be modelled b comparng expected utlt under te followng tree nsurance arrangements: a publc nsurance onl; b complementar plus statutor nsurance; c substtutve nsurance. Expected benefts of te cosen statutor package wll n general var accordng to wealt and te epdemolog of dsease. Te cosen publc package reduces te wealt of all accordng to te requred tax rate. tlt wll be as follows: a under publc nsurance onl, utlt wll be a functon of te expected benefts of te publc package and ts personal tax cost; b under complementar plus publc nsurance, utlt wll be a functon of te expected benefts of te combned voluntar and statutor packages, and te personal tax cost plus te voluntar nsurance premum; c under substtute nsurance, utlt wll be a functon of te expected benefts of te replacement prvate package, and te tax cost of te unused publc package plus te prvate nsurance premum. Te status of nterventon n te statutor package s ndcated b a bnar coce varable λ, were λ 1 f nterventon s n te statutor package, λ oterwse. Tax paments for te rc and poor are ndcated b t and t. Frst assume tat te mode of coverage (statutor or voluntar makes no dfference to te qualt or prce of an nterventon. Ctzens terefore ave no ncentve to purcase substtute or supplementar nsurance. However, ndvduals ma purcase complementar nsurance, coverng nterventons not ncluded n te statutor package λ. Te extent of te complementar package s ndcated b te bnar coce varables θ, were θ 1 f nterventon s n te complementar package, θ oterwse. Te voluntar nsurance premum s actuarall far, equal to te expected cost of utlzaton. An ndvdual n wealt group z wll ten coose a complementar coverage package { θ } n so as to: 1 z z z z z Maxmze ( ( θ λ b, t θ x subject to θ λ 1 If complementar nsurance s selected (some θ 1 ten te margnal condtons for te selected nterventons (after te relevant tax and voluntar premum ave been pad are: 8
Z Z b x wt equalt for te margnal nterventon. In general, a bgger statutor package wll reduce te wealt of all ctzens (troug te necessar tax contrbutons, terefore ncreasng te tresold for ncluson n te voluntar package. tn te framework used so far tere s no cause for ndvduals to take out substtutve nsurance (wc duplcates and ma augment te statutor package. In order for suc nsurance to be attractve, tere must be eter a fnancal or a qualt advantage to replacng te benefts alread nsured troug te statutor package. An fnancal ncentve to take out substtute nsurance s smpl a transfer pament, and s not analtcall nterestng, as t merel nvolves adjustments to te tax paments t and t. However, substtute nsurance ma become attractve f te prvate package enjos a qualt advantage over te statutor package. Qualt dfferences of ts sort are readl observed n ealt sstems wt sgnfcant prvate nsurance markets, for example n te form of reduced watng tmes (n te K or superor coce and otel arrangements (n German. For a full treatment of te welfare mplcatons of qualt dfferences see Besle and Coate (1991 and Ireland (199. Here I merel note te crteron for te rc replcatng coverage of a lower qualt publc nterventon n ter voluntar package. Suppose enanced qualt under prvate cover for nterventon enter te utlt functon troug te ealt argument. Denote te assocated benefts b b > b and te costs x x. Ten an nterventon alread n te statutor package wll also be ncluded n te prvate supplementar package f and onl f te addtonal benefts b b are suffcentl valued n relaton to te addtonal costs tat s: b x b Z Z. A sstem of publcl funded ealt care voucers ma be used, under wc patents are offered a cas pament equvalent to some proporton φ of te cost of te nterventon n te publc sector f te secure treatment troug a prvate nsurer. In tese crcumstances, t wll be necessar to secure supplementar nsurance coverage onl for te ncremental prvate cost not covered b te value of te voucer. rocedures ncluded n te supplementar package wll ten satsf: Z Z b b. x φ x Note terefore tat te qualt of te publc sector (relatve to ts prvate counterpart { } n b / b and te set of voucer paments { φ } n 1 potentall offer te government 1 furter polc nstruments, n addton to te tax paments and te statutor package n λ specfcaton { } tat are te focus of ts paper. 1 x 9
Te government Te government must decde wc nterventons to nclude n a statutor package of ealt care, avalable to all at no drect carge. Tere s a socal welfare functon tat te government wses to maxmze, subject to te constrant tat te costs of te cosen statutor package must be funded b tax paments b all ctzens.,(1 ( 2 Frst assume tat tere s no voluntar nsurance. Ten te government s problem s to coose nterventons { } n 1 λ and taxes t and for te rc and poor so as to: t {,1} (1 } (1 { Subject to, (,(1, ( Maxmze t t x t b t b λ λ λ λ Frst order condtons eld te resul tat nterventon s selected f and onl f: t [ ] [ ] x b β β µ µ (1 (1 (1 Π were µ s te opportunt cost of tax funds and Z Z Z β s te margnal socal value of an mprovement n ealt for group Z. Ts equaton effectvel adjusts µ for varatons n te socal mportance of te two populaton groups, reducng te urdle rate for nterventons wt a g ncdence n te poorer group f tere s a pro-poor equt concern. It s consstent wt te polc recommendaton of adjustng te cost-effectveness ratos of clncal nterventons accordng to ter equt mplcatons (llams, Tsuca and Dolan 25. Te tax contrbutons satsf te margnal condtons: µ A crucal role of te tax paments s terefore to equalze socal margnal utlt of wealt across socal groups. Te specal case of a lnear wealt tax constrans te government s optons for effectng transfers 3, and te margnalt condton becomes: ( (1 1 ( µ. Suppose now tat prvate complementar nsurance s avalable. If neter group cooses to nsure, te stuaton remans as just examned (no voluntar nsurance. If bot groups coose to nsure, te margnal condtons are tose dscussed earler (wt no statutor nsurance, altoug note tere wll ave been an effectve cas transfer between groups brougt about b te tax contrbutons. However, te analtcall nterestng case s wen te rc group cooses to nsure wle te poor group does not. 1
Assumng te rc coose a complementar package { } n 1 θ, te government s optmzaton problem becomes: {,1} (1 } (1 { Subject to, ( (1,, ( ( Maxmze t t x t b x t b λ λ λ θ λ θ Ts elds te soluton tat for an nterventon to be n te statutor package: x b Π µ µ (1 ( and for an nterventon to be ncluded n te complementar package purcased b te rc: x b Te polc maker s decson rule s stragtforward. Te essental package s cosen b a smple rankng of nterventons n lne wt ter cost-effectveness ratos, wt te cut-off rate beng te post-tax preferences of te poor. It dffers from te no statutor nsurance case onl n te sense tat te poor receve a tax transfer from te rc, n lne wt socal preferences (and terefore te mplct tresold for acceptng tecnologes nto te nsured package for te poor as been relaxed compared to te purel prvate case wt no transfers. Te rc use te statutor package and secure addtonal complementar nsurance, up to te pont were for te margnal nterventon: x b Tus te man role of te statutor package under tese crcumstances s to effect a fnancal transfer from rc to poor, allowng te poor access to a broader package of care tan would oterwse ave been te case. Te magntude of ts transfer wll depend on te nature of te socal welfare functon, wc wll be determned b consderatons suc as equt or te government s re-electon concerns. Te rc ma stll ws to purcase complementar nsurance. However, te extent of te package for te rc s less tan under no statutor nsurance because te transfer to te poor reduces ter wealt, and terefore ter wllngness to pa for coverage. Te beneft/cost rato remans te crteron for selectng bot statutor and voluntar package. Tus te sstem of combned statutor and voluntar nsurance replcates a frst best soluton to ealt nsurance after a socall optmal cas transfer between wealt groups as been effected. It mgt at frst glance be surprsng to see no reference to te epdemolog of dseases n te coce of statutor package, as t s commonl argued tat a government concerned wt redstrbuton sould concentrate on nsurng dseases wt g prevalence amongst te poor. However, wt complementar prvate 11
nsurance ts s not necessar. If treatments wt relatvel g use amongst te rc are ncluded n te statutor package (because te are gl cost-effectve, ten te assocated nsurance costs can be recouped n te taxes leved on te rc. Healt care paments of te rc comprse (a an element of tax requred to fund ter own part of te statutor package, (b an element of tax requred to subsdze te poor s part of te statutor package, and (c te voluntar nsurance premum. Elements (a and (c merel reflect n aggregate te costs of ter preferred nsurance package. Te real polc coce s te sze of (b, te transfer to te poor. It s wort notng ere te mplcatons of excludng procedure from te statutor package: a for a poor person, te procedure s no longer avalable, so tere s an expected ealt loss b ; b for te rc, te procedure must now be covered troug voluntar nsurance, at a cost of x ; c for bot groups, tere s a reducton n te tax pament, n sum equal to Π x. For te margnal procedure, te welfare losses assocated wt (a and (b wll be balanced aganst te gans (c. An equvalent wa of formulatng te condtons for te margnal nterventon k s terefore as follows. ( 1. k bk. k xk µ Π k xk On left and sde, te frst expresson gves te ealt benefts to te poor of ncludng nterventon k n te statutor package. Te second expresson gves te fnancal benefts to te rc of removng nterventon k from te voluntar package. Te rgt and sde gves te ncremental tax cost to bot rc and poor of ncludng nterventon k n te statutor package. Te soluton can be llustrated dagrammatcall. Fgure 1 sows te ealt producton functon for a poor person. Ts s constructed b computng te cumulatve mpact on ealt of all potental nterventons, ranked n decreasng order of cost-effectveness. t no subsd, expendture X s cosen. Te mplct subsd from te rc ntroduced b a statutor nsurance package effectvel sfts te producton functon to te left b te amount of te subsd. Ts leads to a revsed coce of expendture b te poor (wc s effectvel ter tax contrbuton t. Total expendture on statutor nsurance for te poor s ten X 1, wt te tax subsd from te rc beng X 1 -t. Bot utlt and ealt outcome are ger tan under no statutor nsurance. <Fgure 1 about ere> Fgure 2 sows te ealt producton functon for a rc person. t no subsd, expendture X s cosen. Te mplct subsd to te poor ntroduced b a statutor nsurance package sfts te producton functon to te rgt b te amount of te subsd. Ts leads to a revsed coce of expendture b te rc T, comprsng te tax contrbuton t and an voluntar nsurance expendture. Total expendture on nsurance for te rc s ten X 1, wt te tax subsd to te poor beng T -X 1. In general, te nsurance cover of te rc wll comprse a mx of te statutor package 12
and some complementar voluntar coverage. tlt and ealt outcome are lower tan under no statutor nsurance. <Fgure 2 about ere> For a gven statutor package (wt voluntar supplement a rc person can be nduced to wtdraw entrel from te publc coverage f pad a sutable transfer ŷ. Te mnmum value of te transfer s suc tat utlt wt statutor plus supplementar nsurance s equal to utlt wt purel prvate nsurance plus te transfer, after all taxes and nsurance premums ave been pad. In te context of Fgure 2, te mnmum transfer a form of compensatng varaton s calculated b constructng te ndfference curve troug te outcome (X1, H 1. Te personal producton functon s ten sfted to te rgt untl tangenc s secured, te magntude of te sft ndcatng te requred transfer. Note tat te pament of suc transfers dlutes te redstrbutve role of statutor ealt nsurance. If te rc opt out of te statutor package, te tax base avalable for te statutor package s reduced. In general, t wll usuall be te case tat te net tax revenue lost b te ext of te rcest ctzen n te statutor sceme wll exceed te reducton n costs assocated wt ter statutor ealt care expendture lablt. nder tese crcumstances, tere wll usuall be no equlbrum socal provson, and te statutor package s unvable (Ireland 199. If te costs and benefts of ealt care secured under prvate nsurance dffer from tose under statutor care, ten te rc face a dfferent ealt producton functon dependng on wc nsurance arrangement te coose. Te government can affect te relatve sape of tese functons b adjustng te benefts of selected statutor treatments (suc as allowng watng tmes to ncrease under publc provson or alterng te costs of prvate treatment (troug specfc taxes or subsdes n te form of voucers. For example, under a gven statutor package, te rc can be nduced to nsure nterventon prvatel troug recept of a voucer φˆ suc tat te addtonal benefts of prvate coverage balance te addtonal costs x φˆ x. Clearl, voucers ave polc relevance onl f prvate coverage offers a qualt advantage over statutor coverage, and te requred sze of s nversel related to te magntude of tat advantage b b. Hterto, we ave assumed tat a government can effect a redstrbuton from rc to poor b levng te requred tax rate n accordance wt ts cosen socal welfare functon. In practce, partcularl n low ncome countres, tere mgt be a lmt to te extent to wc a tax base can be exploted, as tose pang taxes greatl n excess of te benefts te receve ma resst te mpled redstrbuton. Suc resstance mgt take a number of forms, most obvousl te ncreased dffcult and costs of collectng te tax amongst te wealt, n te extreme leadng to tax evason or emgraton. Loss of te tax base can readl be modelled wtn te framework set up above. Assume tat tax collecton costs f(. amongst te rc ncrease wt te dfference φˆ 13
between tax pament and an actuarall fare premum, f f t λ x, were f (.. Tat s, te effectve sze of te tax base depends to some extent on te mx of nterventons ncluded n te statutor nsurance package. nder tese crcumstances, te prort settng rules sould be amended n order to mtgate te loss of tax revenue assocated wt a more redstrbutve statutor package. For example, te budget constrant wt statutor nsurance onl ten becomes: λ { (1 } x t (1 t f t λ x and te assocated decson rule s: b µ [ { 1 f } (1 ]. x β (1 β [ ] Te addtonal term { 1 on te top lne serves to reduce te urdle rate for procedures wt relatvel g prevalence amongst te rc, and ma to some extent counteract an pro-poor mplcatons of te bottom lne. f } CONTINOS EALTH DISTIBTION So far, we ave consdered a dcotomous dstrbuton of rc and poor. Ts representaton glgts some of te ke ssues underlng te polc problem, and ma be a reasonable reflecton of realt n man low ncome countres. However, t s less realstc n ger ncome countres wt large mddle ncome groups. It also conceals mportant subtletes underlng polc coces. In partcular, te analss to date as assumed tat a government can secure an preferred redstrbuton of wealt. In practce, te range of tax nstruments s often severel restrcted. In ts secton I terefore consder a stuaton wt a contnuous dstrbuton of wealt, dstrbuted as γ ( and a lnear wealt tax. Te ncdence of dsease s dstrbuted as (. Ten a gven statutor package { λ } wll generate total costs λ x ( γ ( d Assumng a lnear wealt tax rate t, ts wll be fnanced b tax revenue t γ ( d tt. were T s te tax base. Te results of te prevous sectons can be readl generalzed to ts stuaton. For example, te socal welfare functon could be wrtten as an addtve functon: w( γ ( ( (, d were w( s te socal wegt attaced to someone wt wealt. Ten wt no voluntar nsurance procedures are ncluded n te package f and onl f: 14
b x µ γ ( ( d γ ( β ( ( d were β ( s te margnal socal value of an mprovement n ealt for a person of wealt level. Assumng a pro-poor socal welfare functon, oter tngs equal ts crteron favours procedures wt gest prevalence amongst te poorest. Note tat te opportunt cost of publc funds s: µ α( γ ( d γ ( d were α ( s te margnal socal value placed on wealt. 4 Suppose now tat complementar voluntar ealt nsurance s avalable, and tere s a complete market n prvate nsurance. Defne te set S [, to be te subset of wealt values at wc voluntar nsurance s declned. Te statutor package comprses procedures for wc: µ d b γ ( ( S x γ ( β ( ( d S Tat s, te statutor package s determned b te caracterstcs of te populaton tat declnes voluntar nsurance, and favours condtons concentrated amongst te poorest wo declne VHI. Tose wo accept voluntar nsurance wll seek a complementar package tat comprses all procedures tat do not fall wtn te statutor package, and for b wc <. x Tere wll n general be at least one crtcal wealt level * at wc VHI becomes accepted. Because te ncdence of dseases s not alwas gest n low wealt groups (tat s, ( does not alwas decrease monotoncall wt, tere s no guarantee tat tere exsts a unque * at all levels of. It s owever probabl reasonable to sa tat te probablt of VHI beng accepted ncreases wt wealt (see below. A SOCIAL CHOICE ESECTIVE ater tan seek to optmze socal welfare, one mgt examne te coce of statutor package from a publc coce perspectve. Dfferent socal groups wll ave dfferent preferences as to te sze and consttuton of te statutor ealt nsurance package, and dfferent atttudes towards te assocated tax paments. en tere s a lmted tax nstrument (suc as a lnear wealt tax, governments wll not n general be able to secure a frst-best soluton from a socal welfare perspectve, and wll ave to take 15
cognsance of dfferent atttudes towards tax expendture and ealt gans amongst dfferent wealt groups. e can llustrate n ver broad terms an ndvdual s preferences b constructng a utlt map, as sown n Fgure 3 (Epple and omano 1996b. Ts ndcates utlt ndfference between tax rates and expendture on te statutor package for an ndvdual wt wealt. It assumes tat at eac level of expendture te government cooses statutor provson n lne wt te polc rule of rankng procedures accordng to cost-effectveness. Also, n te frst nstance, I make te strong assumpton tat tat te ncdence of dsease relatve to te populaton average, ( / Π for wealt group s te same for eac dseases. Ts assumpton ensures tat all groups agree on te rankng of treatments for ncluson n te statutor package. < Fgure 3 about ere > Te ndfference curve for wealt group s constructed as follows. At eac tax rate tere s a unque crtcal level of expendture * on te statutor package above wc te ndvdual prefers to forego voluntar nsurance. Below tat level of expendture, te cas benefts to te ndvdual of te margnal removal of a procedure from te statutor package are proportonal to te ndvdual s wealt (te bass for er contrbuton to te tax cost. So te local slope of te ndfference curve s proportonal to 1/. Above te crtcal level of expendture, te ndfference curve reflects te trade off between addtonal tax paments and ealt gans ( b. Te assumpton of constant ( / Π ensures ts segment s concave. Te curve M( ndcates te locus of crtcal values * to te left of te curve, voluntar nsurance s purcased, above te curve te ctzen reles solel on te statutor sceme. It as everwere a negatve slope. Te feasble expanson of te government package s ndcated b te budget lne OB. nder our assumptons, for an level of tax rate t te crtcal value of expendture on te statutor package at wc voluntar nsurance s abandoned ncrease wt wealt. Tat s, te curve M( 1 wll le strctl to te rgt of te curve M( 2 for all 1 > 2. Te mplcatons for te preferred statutor package are llustrated n Fgure 4, wc sows te utlt-maxmzng ndfference curves for tree ndvduals, wt crtcal expendture levels for eac ndcated b te blob. Te poor person (a swtces to relance on te statutor package at low levels of provson, but also as low levels of tolerance for tax paments. Te g wealt ndvdual (c suffers a loss of utlt at all levels of socal provson (as tax paments exceed te cost of voluntar nsurance and would terefore prefer zero statutor expendture. Te mddle wealt person (b s better able to tolerate tax expendture tan te poor person, and enjos benefts n excess of tax paments for lower levels of te statutor package. Se terefore prefers a larger statutor package tan eter te rc or te poor person. Ten, f te sze of te statutor package s cosen troug majort votng, te crucal determnant of te outcome wll be te dstrbuton of wealt specfcall, te extent to wc mddle ncome voters (preferrng ger expendture levels domnate an allance of rc and poor (preferrng lower levels (Epple and omano 1996b. < Fgure 4 about ere > 16
For an ndvdual wt wealt, te tax cost of ncludng nterventon n te package s x Π Y, were Y ndcates total natonal wealt, wlst ealt benefts are ( / b. Te ndvdual terefore ranks nterventons for ncluson n te statutor package accordng to te rato b ( / x Π. I ave assumed tat te procedures enter te statutor package n strctl decreasng beneft/cost order b / x as expendture ncreases. However, te benefts to partcular wealt groups also depend on te relatve epdemolog of te dsease for tose groups, ( / Π, wc s not n general constant between nterventons. So an one wealt group wll not necessarl rank nterventons for ncluson n a fxed budget package n te same wa as oter groups. Tus altoug an ndvdual s ndfference curve wll ave a non-negatve slope, and s lkel on average to exbt decreasng margnal benefts of treatments (as b /x decreases, local varatons n te relatve prevalence of dseases ( / Π ma render te curve non-concave. Ts rudmentar exploraton ndcates tat tere ma not n general be a unque level of expendture on te statutor package at wc te ndvdual abandons voluntar nsurance. Even wen voluntar nsurance s purcased, te ndvdual ma ws to see n te statutor package certan addtonal treatments for wc se suffers relatvel g ncdence ( / Π, because te personal tax cost of ncludng tem s less tan te cost of purcasng rsk-rated voluntar nsurance. Te ntroducton of non-concavt complcates te tecncal analss consderabl, and mples te exstence of multple socal equlbra. However, t s unlkel n practce to alter te general pattern of results sown ere. Conclusons A conventonal welfare economcs perspectve mgt suggest tat - settng asde concerns of moral azard or adverse selecton - a frst-best soluton n ealt nsurance can be secured b mplementng a compettve nsurance market, wt no requrement for a government package. Equt concerns could be addressed b sutable fnancal transfers from rc to poor, or from ealt to sck. In practce ts vew appears to be untenable. Most developed countres offer some basc guarantee of ealt care to all ctzens, regardless of ter personal preferences. Te arguments for suc a polc are dverse, ncludng market falures (often due to nformaton weaknesses, transacton costs, altrusm, soldart and mert goods, but do not strctl concern us ere. ater we assume tat suc a polc s requred, and examne te consequent optmal coce of statutor package. Te analss ndcates tat under some lmtng assumptons a socal planner can replcate te preferred frst best outcome b mplementng a statutor package alongsde complementar nsurance for te rc. However, deploment of substtute prvate nsurance alongsde a statutor package s more problematc. It requres eter a transfer to te rc (dlutng te redstrbutve functon of te statutor package or reduced qualt n te publc sector, neter of wc s lkel to be an attractve polc. Te paper as also noted tat moblt of te tax base and electoral consderatons ma constran te planner s ablt to secure a preferred outcome. 17
Te results ave mportant mplcatons for tose evaluatng ealt care tecnologes. Te mpl tat a concern wt equt ma not be a major concern wen coosng wc tecnologes to nclude n a statutor package f te rc are able to purcase complementar nsurance. Te relevant nstrument for addressng equt concerns n ts case s troug te tax sstem rater tan troug te ealt care package. However, equt concerns ma become mportant f tere s no voluntar nsurance. Te models presented ere are gl stlzed, and ma need to be amended accordng to polc nterests. For example, tere ma be a polc mperatve allow onl communt-rated voluntar nsurance premums, or nadequate nformaton for nsurers to set far voluntar premums. nder suc crcumstances, adverse selecton ma become mportant n te voluntar market, and te models sould be amended to accommodate ts. Oter possble extensons nclude te use of copaments n eter statutor or voluntar sector, and varatons n ealt wtn a sngle wealt group. I beleve te results presented ere offer a useful framework for tnkng about voluntar ealt nsurance alongsde a statutor package of ealt care. However, t s mportant to note tat pscologcal and socologcal as muc as economc consderatons ma affect polc n ts doman. Te sustanablt of socal ealt nsurance reles on te wllngness of ctzens to tolerate large transfers from rc to poor and from ealt to sck. An apparent falure explctl to reflect ctzens equt concerns n te ealt sstem ma compromse support for te mx of statutor and voluntar nsurance tat emprcall appears to be assocated wt g-performng ealt sstems (orld Healt Organzaton 2. olc makers sould terefore exercse extreme cauton n ts doman. 18
Healt H 1 H O X t p X 1 Expendture Fgure 1: Extent of te statutor package for te poor Healt H H 1 O X X 1 T Expendture Fgure 2: Expendture coces of te rc 19
Tax rate B M Z O M Z Statutor package Fgure 3: Indfference curves wt voluntar nsurance Tax rate B (b (a (c O Statutor package Fgure 4: references of (a low wealt (b mddle wealt (c g wealt ctzens 2
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Mossalos, E., A. Dxon, J. Fgueras and J. Kutzn, Eds. (22. Fundng ealt care: optons for Europe. Buckngam: Open nverst ress. Mossalos, E. and S. Tomson, Eds. (24. Voluntar ealt nsurance n te European non. Brussels: orld Healt Organzaton. Munro, A. (1991. "Te optmal publc provson of prvate goods." Journal of ublc Economcs 44(2, 239-261. etretto, A. (1999. "Optmal socal ealt nsurance wt supplementar prvate nsurance." Journal of Healt Economcs 18(6, 727-745. Selden, T. M. (1993. "Sould te Government rovde Catastropc Insurance." Journal of ublc Economcs 51(2, 241-247. Smt,. (fortcomng. "ser carges and prort settng n ealt care: balancng equt and effcenc." Journal of Healt Economcs. llams, A., A. Tsuca and. Dolan (25. "Elctng equt-effcenc trade-offs n ealt". n. Smt, L. Gnnell and M. Sculper (ed Healt polc and economcs: opportuntes and callenges. Madenead, Open nverst ress. orld Healt Organzaton (2. orld Healt eport 2. Geneva: HO. orld Healt Organzaton (22. orld Healt eport 22: reducng rsks, promotng ealt lfe. Geneva: orld Healt Organzaton. 22
Footnotes 1 Some efforts ave been made to confne te recept of statutor ealt benefts to te poor. However, suc means testng as often been found to be mpractcal, and s not commonl used. See: Btrán,. and. Gedon (22. avers and exemptons for ealt servces n developng countres. asngton DC: orld Bank.. 2 Te nature of te socal welfare functon approprate for modellng ealt care as been a matter of debate, and as not et been entrel resolved Fleurbae, M. (fortcomng. "Healt, wealt and farness." Journal of ublc Economc Teor.. Muc of te lterature n ealt economcs merel seeks to maxmze (equt wegted ealt, wlst oters argue tat ealt s merel one argument n an ndvdual s utlt functon tat sould not be afforded prvleged status. Ts paper adopts an ntermedate poston tat remans reasonabl general. 3 Ts formulaton gnores te potental dstortonar costs to te econom assocated wt an ncome tax, but f necessar ts s readl ncorporated nto te analss. 4 In prncple, under a dstortonar ncome tax, one sould also ncrease te cost of publc funds n order to capture te dead wegt loss of tax fundng. Ts refnement s not germane to ts paper. 23