Reimbursement and Investment: Why the Market Share of For-profit Hospitals Increased after Prospective Payment?

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1 Dra o or quoaio or aribuio Reimburseme ad Ivesme: Why he Marke Share o For-proi Hospials Icreased aer Prospecive Payme? Seugchul Lee 1 ad Rober Rosema 2 School o Ecoomic Sciece Washigo Sae Uiversiy Absrac This paper sudies how he chage rom rerospecive cos-based reimburseme o prospecive payme sysem shied hospial ivesme sraegies rom qualiy-ehacig echologies o cos-savig echologies. A cosequece o his chage was he opporuiy or or-proi hospials o capure a larger share o he marke. Whe all o a paie s reame coss are paid uder a rerospecive average cosbased program, o-or-proi hospials ives oly i he qualiy-ehacig echology. For-proi hospials have o iceive o ives i eiher echology. As a resul, mos paies selec o-or-proi hospials ad or-proi hospials arac oly hose ew paies who have exreme ime coss. A key eleme i his resul is he abiliy o o-or-proi hospials o use chariable doaios o pay or qualiy ehacig ivesmes. Whe hospials are reimbursed prospecively, however, o-or-proi hospials ives i boh qualiy-improvig ad he cos-savig echologies, as do or-proi hospials, alhough a lesser amous. Oe resul is ha marke shares are more equal uder prospecive payme, helpig o explai he icreasig marke share o or-proi hospials as prospecive payme has become he orm. Keywords: Hospial reimburseme; Hospial compeiio; Techology ivesme JEL Classiicaio: I11; O33; L33 This work would o have bee possible wihou he paie guidace o Rober Rosema. The commes o Seug Mo Choi ad Bidisha Madal are graeully ackowledged. 1 Graduae Sude, School o Ecoomic Scieces, PO Box , Hulber 313, Washigo Sae Uiversiy, Pullma WA , U.S.A. lsc1026@gmail.com. 2 Associae Direcor ad Proessor, School o Ecoomic Scieces, PO Box , Hulber 101B, Washigo Sae Uiversiy, Pullma WA , U.S.A. yamaka@wsu.edu 1

2 1. Iroducio This work is moivaed by wo observaios. Oe is ha over he pas decade hospials have become icreasigly cocered abou cos corol, someimes, i appears, a he expese o ivesme ha would ehace he qualiy o paie care. The secod observaio is he sigiica growh i marke share o or-proi hospials. From 1980 o 2007, he growh o orproi hospials amog U.S. commuiy hospials was 5.3%, aser ha he 2.7% growh o oor-proi hospials, Goverme hospials marke share declied by 7.8% durig his same period, (Table 1). Oe quesio o arise rom hese observaios is wheher hey are jus coicideal or has he operaio o he healh care marke udergoe a udameal shi due o a srucural chage? The mos obvious srucural chage i rece decades is he shi rom rerospecive o a prospecive payme or a large share o paies, sarig wih hose covered by Medicare. This paper provides a heoreical argume ha he move o prospecive payme is a leas parially resposible or shiig he ocus o hospial ivesme rom qualiy-ehacig echologies o cos-savig echologies, ad his chage has allowed or-proi hospials o become more compeiive i he hospial marke. The source hrough which reimburseme aecs hospial behavior comes rom he ac ha hospials, wheher or-proi or o-or-proi, ca improve heir boom lies eiher by aracig more paies or by corollig coss. Paies are araced by high qualiy ad low cos, while ivesmes ca serve o icrease qualiy or lower coss or boh. How a hospial is reimbursed chages is payo rom each ype o ivesme. I, as we cojecure, he payme sysem aecs ivesme sraegies, i becomes a impora ool or qualiy as well as or cos. This las poi is o paricularly ovel. Weisbrod (1991) discussed a legh abou how he payme sysem aecs ivesme sraegies by hospials, oig ha rerospecive payme iduces he developme o qualiy ehacig echologies, while prospecive payme iduces he developme o cos savig echologies.. Wha is ovel, however, i his paper, is how he chages i he payme sysem caused a srucural shi leadig o a growig marke share or or-proi hospials. 2

3 2. Lieraure Review Mos o he previous work likig he payme sysem o ivesme sraegy ocused o or-proi hospials. Ma (1994) compared wo reimburseme programs o he adopio o cos reducig ad qualiy ehace echology. Modelig a sigle or-proi hospial, he cocluded ha here is o iceive o reduce cos uder cos reimburseme. Uder prospecive payme, however, he hospial ivesed i boh cos savig ad qualiy ehacig echologies. Selder (2005) aalyzed provider iceives ad welare implicaios or adopig ew echologies uder various reimburseme schemes. Usig a ramework o a social plaer ad a or-proi hospial, he ocused o how echology choice aeced paie demad or healh care, ad o he ieracio o reimburseme wih echology adopio. Miraldo (2007) also sudied he iluece o various reimbursemes o he developme ad adopio o echology. Alhough she ocuses o he opimal goverme policy, several o her coclusios are releva o our aalysis. I hospials are reimbursed less ha heir ull coss, he payme sysem does o maer boh rerospecive ad prospecive sysems lead o cos savig ivesme. However, i he reimburseme rae ully covers coss hospials ives wholly i qualiy ehacig echologies. 3 Her mai resul wih respec o he payme ssem (her Proposiio 10) is ha cos based reimburseme leads o he developme ad adopio o boh qualiy ad cos decreasig echologies, while a pure prospecive payme sysem will be cos decreasig. Despie he sparse heoreical lieraure relaig echology adopio o orms o reimburseme, he empirical lieraure is relaively large. Bokhari (2008) ivesigaes maaged care compeiio ad he adopio o hospial echology i he case o cardiac caheerizaio. He shows ha a hospial is less likely o adop a echology as maaged care compeiio (which oe meas icreased prospecive payme) icreases. Hirh e al (2000) shows or-proi hospials deliverig lower qualiy care bu more ameiies, while o-or-proi hospials avor qualiy o care over ameiies. 3 Miraldo ocuses o margial cos reimburseme i her aalysis, so a casual reader migh ierpre ha he reimburseme rae mus exceed average coss o achieve he resuls we cie. However, her ull reimburseme igores ixed coss, ad oly whe she discusses a reimburseme rae exceedig 1 are hospial coss ully covered. 3

4 Lackig i all hese papers is he likage bewee payme srucure,, or-proi ad oor-proi compeiio, ad echology adopio..i coras, his paper aalyzes hospial behavior o he adopio o diere ypes o echologies or various hospial owerships i he coex o dier reimbursemes sysems, ad he ies hese chages o compeiio bewee he wo ypes o hospials, hus explaiig chages i marke share. 3. A Model o Hospial Compeiio The marke cosiss o N paies. Each paie demads oe ui o medical service. Paies gai uiliy rom higher qualiy medical service ad lose uiliy rom higher priced reame ad rom more ime spe waiig or reame. They are assumed o be heerogeeous wih diere relaive preereces or qualiy, low price ad shor waiig ime. Each paie chooses bewee a or-proi hospial (h=) ad a o-or-proi hospial (h=), hece h (, ). Demad or each hospial h is give by: (1) (,, (, )) 1 (,, (, )) Q = Ng q p T q p Q = N g q p T q p where, Q ad Q are demad or he or-proi hospial ad he o-or-proi hospial respecively. The aggregae demad or he o-or-proi hospial is derived by our assumpio ha he oal umber o paies is ixed, N. The variables p h ad q h represe hospial price ad qualiy. We assume ha q h has a sae licesig requireme a q >0, so q [ q, ) ad q h is h hough o as a improveme over a miimally accepable qualiy, hus a hospial wih qh = q sill mees some hreshold ad aracs hose paies wih a srog bias agais waiig or higher prices, as explaied below. The variables p ad q are he price ad qualiy o he or-proi hospial relaive o he (uweighed) average marke price ad qualiy. We will reer o hese, respecively, as he relaive price ad relaive quaiy. Hece p p /[( p + p ) / 2] ad q q /[( q + q )/ 2]. 4

5 Thus p [0,2] ad q (0,2) so whe p=1 (or q=1) i meas he price (or qualiy) o boh hospials are equal. 4 The variable T is waiig ime a he or-proi hospial relaive o he waiig ime a he o-or-proi hospial, ad depeds o relaive demad, hece o p ad q., Paie preereces abou waiig ime are heerogeous ad some people will choose a relaively lower qualiy or higher price i exchage or a shorer waiig ime. The waiig ime ucio T( ) is sricly icreasig i q, sricly decreasig i p, ad we resric i so 0<T< or ay se o q h ad p h. This preerece or shorer waiig ime meas ha some paies may choose a hospial wih a relaively higher price (lower qualiy) eve i qualiy (price) is he same, ad explais why a hospial may keep paies eve i i has boh a higher price ad lower qualiy ha is compeiio. The ucio g ( ) is a coiuous, wice diereiable ucio ha maps price, qualiy ad waiig ime o he proporio o paies choosig he or-proi hospial, i.e., 4 g : + + [0,1] R R. The properies o he ucio ( ) icreasig ad cocave i g are; sricly decreasig i T, sricly q, sricly decreasig ad covex i p, ad here are always a umber o ime sesiive paies such ha 0< g ( ) <1 or ay se q h ad p h as log as boh hospials are i he marke. We assume, however, ha or mos paies, qualiy is more impora ha waiig ime. Thereore, he demad or each hospial, Q = Ng ad Q = N(1 g), is icreasig ad cocave i is ow relaive qualiy, ad decreasig ad covex i is ow relaive price. Due o he srucure o paies demad, compeiio bewee he or-proi ad he o-or-proi hospial diers rom Berrad syle compeiio. 4. Hospial ivesme behavior uder diere payme schemes Paies choose bewee he or-proi hospial ad he o-or-proi hospial based o relaive qualiy, relaive price, ad waiig ime. Faced wih heir respecive demad ucios, he hospials make ivesme decisios o eiher maximize proi (he or-proi hospial) or uiliy 4 Price ca be 0 or eiher ype o hospial, hece he se o possible p is o he closed se [0,2]. However, he miimum qualiy requireme meas ha q is o he ope se (0,2). 5

6 wih a o-egaive proi cosrai (he o-or-proi hospial).par o each hospial s decisio process is a decisio abou ivesme i a qualiy ehacig echology, a cos savig echology, or a mix o he wo. We examie hese decisios ad heir cosequeces uder diere payme schemes Goverme provides ull payme or medical service Cosider he simples case where he goverme pays he eire cos o medical services or every paie. I his case, qualiy ad waiig ime are he oly crieria paies use i choosig bewee he hospials hece he demad ucios simpliy o Q Ng ( q, T( q) ) ( ( )) Q = N Q = N 1 g q, T q = ad. Boh hospials choose amous o a qualiy ehacig echology, 1h, ad a cos savig echology, 2h. The qualiy ehacig echology improves he qualiy o medical care hrough produc iovaio, while icreasig he cos 5 o reame. I coras, he cos savig echology reduces he cos o providig healh care wihou chagig he level o qualiy (Ma, 1994 ad Miraldo, 2007). Because he qualiy (improveme) o he or-proi hospial is deermied by 1h, wih a miimum hreshold o q, he hospial qualiy ucio ca be wrie as: (2) q h q i 1 h = 0 = q( 1 h) i 1 h > 0 The level o qualiy improveme is o-decreasig ad cocave i 1h. Jegers e al (2002) geerally represe a mixed payme scheme as s (payme) = θ + ϕ (cos) where θ is he prospecive amou ad ϕ (cos) is he rerospecive amou. A ully prospecive sysem ses θ >0 ad ϕ =0 while a ully rerospecive sysem ses θ =0 ad ϕ >0. Miraldo (2007) deies a mixed reimburseme sysem as boh θ >0 ad ϕ >0. I is geerally hough ha a prospecive 5 There are wo diere kids o cos chages ha ca come rom produc iovaio ivesme. The irs icreases ixed cos bu may lower margial cos, ad he secod icreases boh ixed cos ad margial cos. A his ime we assume he iovaio does o chage ixed coss ad icreases margial cos. 6

7 payme sysem gives providers a iacial iceive o corol coss, while a rerospecive sysem removes all (or mos) iacial risk rom he provider. The or-proi hospial s problem is give by: (3) 1, 2 ( ) MaxQ ( ) p c, r r s.. 0, Whe he goverme pays he eire cos o care paies care oly abou qualiy so he choice o qualiy ehacig echology deermies he quaiy demaded or he hospial s services, ad quaiy demaded plus he process iovaio echology deermies he variable cos. Here ph is he amou o he cos ha he goverme reimburses; 1 h ad 2 h are he amous o qualiy improvig ad cos savig echology adoped; ad r 1 ad r 2 are he respecive prices o each ype o echology which are sricly posiive. We assume he or-proi hospial opimizes is echology adopio levels as hough he qualiy o he o-or-proi is a give. 6 The hospial s ui reame cos c( 1h, 2h ) has he ollowig properies; icreasig ad covex i 1h, decreasig ad covex i 2h, he echologies are urelaed o each oher wih 2 respec o cos, i.e., c =, or ay 1 h 0, c( 1 h, 2h) > 0 (a larger 1h always iduces a 1h 2h 0 larger ui reame cos regardless o 2h,i.e., 1 h 1 > h, 2 h 2 h c( 1 h, 2 h ) c( 1 h, 2 7 > > h ) ), ad zero ivesme i boh echologies iduce a posiive ui reame cos, i.e., c(0,0)=c*>0 8. The o-or-proi hospial gais uiliy rom boh qualiy ad quaiy ad aces a objecive ucio o 9 : < (4) MaxU Q 1, 2 [ ( ), q ( )] 1 1 s.. 0, [ ] [ ] Q ( ) p c(, ) r r + D Q ( ), q ( ) This is esseially Couro syle compleio. 7 The las propery o he ui cos reame cos ucio says ha he cos savig echology cao ully ose he cos icreasig rom he qualiy ehacig echology. 8 Ivesig i 2h pushes c* lower, bu ever o egaive amous. 9 The Newhouse-ype model is ormalized by Sloa(2000). I his model, U=U(X,Y,π) where X =oupu, Y=qualiy, ad π=proi. I our model, we exrac proi rom he uiliy o he o-or-proi hospial, ad se i as a oegaive cosrai. Hoerger (1991) ids empirical suppor ha he o-or-proi hospial maximizes uiliy subjec o zero proi cosrai. 7

8 We assume he uiliy o he o-or-proi hospial is o-decreasig ad cocave i boh quaiy ad qualiy, i.e., U / Q 0, U / q 0, 2 2 / 0, ad 2 2 U Q U / q 0, bu a leas oe saisies a iequaliy codiio or he sric moooiciy o he o-or-proi hospial s preerece, i.e., U / Q > 0 or U / q > 0. The o-or-proi hospial also opimizes is echologies adopio levels as he qualiy o he or-proi is give. The characers o he qualiy ucio ad he ui reame cos o he o-or-proi hospial are ideical wih hose o he or-proi hospial. I addiio o beig paid or services by he goverme, he o-or-proi hospial ca raise moey hrough doaios, [ ( ), ( )] D Q q, which deped o hospial qualiy ad he 1 1 quaiy o paies i serves 10. All he argumes o he doaio ucio are same as hose o he uiliy ucio o he o-or-proi hospial. I addiio o hose, we assume ha i here is o ivesme i qualiy improvig echology here are o doaios, i.e., D Q ( 1 = 0), q = q ( 1 = 0) = Boh hospials ca ry o icrease heir level o qualiy i order o arac paies by icreasig 1h, however c( 1h, 2h ) is icreased as well. The cos savig echology, 2h oly he ui reame cos. decreases Rerospecive reimburseme o average cos wihou ivesme expediures Suppose boh hospials are reimbursed rerospecively based o average operaig cos hece ivesme coss are excluded rom he goverme payme. The prices are hus se as = ( 1, 2 ) ad p c( 1, 2 ) p c he or-proi hospial is ow =. Because average reveue equals average cos he problem o 10 Oe o he diereial characerisics o o-or-proi eerprises is is abiliy o arac chariable doaios. Eve i here were ax advaages or doaig o or-proi eerprise, ew doors would do so because hey would simply be erichig he or-proi irm s shareholders (Hasma, 1980, 1998 ad Sloa, 2000). Alhough he poeial or doaios would seem o be a big advaage or o-or-proi hospials, i rece years, doaios have become a uimpora source o reveue or o-or-proi hospials. I 1983, oly 0.4% o reveue is derived rom he doaios. Oe o he reasos or he declie is hough as he growh o he healh care isurace (Sloa, 2000). 11 The moey cosrai o he o-or-proi hospial ca be decomposed as he proi par ( [ ] ) ad he doaio par ( [ ( ), ( )] Q ( ) p c(, ) r r D Q q ). Because he o-or-proi hospial 1 1 ca raise moey by udraisig, i ca acually make a egaive operaig proi as log as he oal e reveue is o-egaive.

9 Max r 1 1 r2 2 1, 2 (5) s.. 0, while he problem or he o-or-proi hospial reduces o (6) MaxU Q 1, 2 [ ( ), q ( )] 1 1 s.. 0, [ ] r r + D Q ( ), q ( ) The soluios o equaios (5) ad (6) lead o Proposiio 1. Proposiio 1 Uder ull goverme payme o he paies reame coss, i which hospials are reimbursed heir average cos wihou ivesme expediures, he o-or-proi hospial ivess oly i qualiy ehacig echology while he or-proi hospial does o ives i eiher echology. Proo. Proo i Appedix P.1. Proposiio 1 explais he behaviors o boh hospials uder rerospecive average reame cos based reimburseme (wihou ivesme expediures). Chalkley ad Malcomso (2000) poi ou ha cos reimburseme provides o iceive o reduce coss (eve he or-proi hospial barely has a moivaio o decrease coss). Whe cos reimburseme allows a mark up over cos, hospials have a srog iceive o icrease cos. Because hospials are o allowed a mark up over reveues, however, he or-proi hospial always has a egaive proi i i ivess i ay echology. Thereore, he acual maximum proi o he or-proi hospial is zero wih o ivesme i 1 ad 2. I coras, because he o-or-proi hospial ca raise moey hrough doaios i ca make egaive operaig reveue ad sill have a posiive ivesme i I here is o doaio i he o-or-proi hospial, he he proi codiio o equaio (6) becomes 1 r r. The o egaive proi codiio implies 1 = 0 ad 2 = 0.which meas Q = Q = N wih q = q = q. Thereore, i he absece o doaios he o-or-proi hospial loses is domiace i he marke i here is average cos based reimburseme. 2 9

10 Rerospecive reimburseme o average cos wih ivesme expediures Whe boh hospials are reimbursed rerospecively based o he average cos icludig ivesme expediures, he prices a each hospial are r1 1 + r2 2 ( 1, 2 ) Q ( 1 ) p = c + ad p = c(, ) +. By deiiio he or-proi hospial ears, a bes, zero proi, ad has o r1 1 + r Q ( 1 ) iceive o ives i he marke, hece is opimizaio problem is degeerae. The o-or-proi hospial has he ollowig problem: (7) MaxU Q 1, 2 [ ( ), q ( )] 1 1 s.. 0, [ q ] D Q ( ), ( ) The soluio o (7) combied wih he degeerae soluio o he or-proi hospial leads o Proposiio 2: Proposiio 2 Where he goverme pays he ull cos o reame ad hospials are reimbursed heir average cos plus ivesme expediures, he o-or-proi hospial ivess oly i qualiy ehacig echology ad ca obai he globally maximal level o qualiy. Meawhile he or-proi hospial agai makes o ivesme o eiher ype. Proo. Proo i Appedix P.2. From Proposiios 1 ad 2, Corollary 1 compares he amous o qualiy improvig echology adoped by he o-or-proi hospial uder margial cos ad average cos based rerospecive reimburseme. Corollary 1 The amou o qualiy ehacig echology adoped by he o-or-proi hospial uder he average cos-based rerospecive reimburseme sysem is greaer whe he payme 10

11 icludes ivesme expediures ha whe he payme does o iclude ivesme expediures, i.e., * < Proo. Proo i Appedix P.3. Oe impora oucome uder rerospecive payme o average cos is ha o-or-proi hospials have higher qualiy ha or-proi hospials, ad hus arac a larger share o paies. Oly hose paies wih a large preerece or shor waiig imes will use he or-proi hospial. A ieresig side oe is ha i he reimburseme excludes ivesme coss he o-or-proi hospial has icreased moivaio o raise ivesme capial rom chariable sources Prospecive reimburseme Ideical reimburseme amous o boh hospials Whe boh hospials are reimbursed prospecively, he prices o boh hospials are se ex ae ad are ideical ( p = p = p ). The problems o boh hospials, he, are oherwise he same as equaios (3) ad (4). We assume ha he goverme ses p so ha i he or-proi hospial ives i cos savig echology oly i will make egaive prois, i.e., ( ) Ng p c 0, 2 r2 2 < 0. Thereore, o obai a o-egaive proi, he hospial mus adop o oly cos savig echology bu also qualiy ehacig echology, movig is qualiy level above he miimum. Maximizig equaio (3) wih respec o 1 ad 2 wih iequaliy cosrais, he opimum o he or-proi hospial is characerized by Kuh-Tucker irs order codiios: L Q : p - c Q c 0 r + µ = (8) ( ) (9) L 2 : Q c r + µ = A superscrip * ad idicaes he opimal value uder he average cos wihou ivesme expediure based rerospecive reimburseme sysem ad ha wih ivesme expediure respecively. 11

12 The complemeary slackess codiios are: (10) µ 1 1 = 0, µ 1 0 (11) µ 2 2 = 0, µ 2 0 Ad he Kuh-Tucker irs order codiios o maximize equaio (4) wih he iequaliy cosrai codiios are: L Q Q Q : U + ( - ) (12) Q + U q q λ p c Qc + D Q + D q q r + µ = (13) L 2 : λ [ Q c r ] + µ = The complemeary slackess codiios are: (14) µ 11 = 0, µ 1 0 (15) µ 22 = 0, µ 2 0 (16) λ Q p c r r D( Q q ) ( ) +, = 0, λ where µ 1h ad λ are a se o Kuh-Tucker mulipliers.14 Because he same echologies are available o boh hospials, he ollowig codiios holdor boh hospials.: q = q * * 0, = c = c =, c 1 = c =, ad c c = 2 = 0 Tucker irs order codiios, we obai Proposiio = <. From he above Kuh- = ch c( 1 h, 2h ) = U = U / q, D = D Q, ad D = D q 14 We have simpliied hese expressios by usig he ollowig oaios: qh qh / 1h, c = c /, c = c / 2 2h, UQ U / Q, 1 h 1h h q 12 Q q =,

13 Proposiio 3 Uder ull goverme reimburseme o paies reame coss, where hospials are reimbursed prospecively he same amous, hospials adop posiive amous o boh ypes o echology. The o-or-proi hospial ivess more i boh echologies ha does he or-proi hospial, i.e., 1 < 1 ad 2 < 2. However he o-or-proi hospial cao reach a globally maximal level o qualiy or he miimal ui reame cos. 15 Proo. Proo i Appedix P.4. Noice ha 1 < 1 implies Q < Q. Propery 3 implies ha he o-or-proi hospial will domiae he or-proi hospial uder prospecive reimburseme whe qualiy is he oly crierio o cocer o paies. Accordig o Sloa (2000), he domiace o he o-or-proi hospial is suppored by several argumes such as he rasacio coss o owership; iduciary relaioships ad complex oupu; implici subsidies; explici subsidies; ieria; he carel heory; ad proiabiliy ad or-proi ery. I our model, by allowig chariable doaios o he oor-proi hospial, he hospial ca icrease qualiy eve whe reveues do o cover coss. Oe ieresig aspec o Proposiio 3 is ha he o-or-proi hospial ivess more i cos savig echolodgy ha he or-proi hospial; his ca be explaied by he abiliy o he o-or-proi hospial o brig i doaios. Because o-or-proi hospial ca ives i boh qualiy ehacig ad cos savig echology wih egaive reveue, i has more room o ives ha he or-proi hospial. We provide more isigh io he marke domiace o he o-orproi hospial i Corollary 2. Corollary 2 The marke domiace o he o-or-proi hospial is aribued o boh he isiuios objecives ad is abiliy o solici doaios. Excludig doaios, he o-or-proi hospial remais domia i he marke, however hey lose marke share compared o whe hey have doaios. Proo. Proo i Appedix P A superscrip idicaes he opimal value uder he prospecive reimburseme sysem. 13

14 Corollary 2 shows ha he more doaios he o-or-proi hospial receives, he larger he marke share i obais. As oed earlier, o-or-proi hospials have become less depede o chariable givig i rece years. A he same ime, or-proi hospials have gaied marke share. While his correlaio ascribes o causaliy oe way or he oher, he oucome is cosise wih Corollary 2. Aoher criical cocer is he comparaive amous o qualiy ehacig echology, 1, adoped by o-or-proi hospials uder diere reimburseme sysems. Corollary 1 shows ha he o-or-proi hospial ca icrease is qualiy o he globally maximal level i is average coss are reimbursed rerospecively, hereore, <, where he opimal qualiy ehacig * 1 1 echology level uder he margial, cos-based, rerospecive reimburseme ad ha o he average, cos-based, rerospecive reimburseme are * 1 ad 1 respecively. Nex we compare * 1 ad 1, where, 1 is he o-or-proi hospial s qualiy ehacig level uder he prospecive reimburseme sysem. Corollary 3 explais he compariso bewee * 1 ad 1. Corollary 3 The amou o qualiy ehacig ivesme made by he o-or-proi hospial uder a prospecive reimburseme sysem would be o smaller ha whe i is reimbursed rerospecively or average cos wihou ivesme, i.e., * 1 1, i he magiude o oal margial beei o he qualiy improvig echology hrough he quaiy is o smaller ha oal margial cos o he qualiy ehacig echology, ad vice versa. Proo. Proo i Appedix P.6 Noice ha he vagueess o Corollary 3 comes rom he eecs ha qualiy improvig echology has o margial beei hrough wo pahways, quaiy ad qualiy. I he o-orproi hospial gais uiliy ad doaios oly by icreasig quaiy, he he amou o qualiy ehacig echology ha he o-or-proi hospial adops uder he prospecive reimburseme sysem is larger ha ha uder he margial cos based rerospecive reimburseme sysem. Assumig oe or-proi hospial i a healh care marke, Miraldo (2007) has show ha i a pure cos based reimburseme sysem, he adoped echology is cos savig echology, ad o avoid egaive proi, o qualiy improvig echology is adoped. Bu i a pure 14

15 prospecive payme sysem wih suiciely high reimburseme ees, boh qualiy improvig ad cos savig echologies are adoped. I he case o he or-proi hospial, Miraldo s idigs are cosise wih our resul i case o he prospecive reimburseme sysem. I he cos based reimburseme sysem, we have he same resul i ha o qualiy improvig echology is adoped, bu i her model, corary o our resul, cos savig echology is adoped i all reimburseme payme sysems. This is because she allows parial cos based rerospecive reimburseme, while we oly have ull cos rerospecive reimburseme. I rerospecive reimburseme ully covers cos, her resuls would mach ours. Table 2 compares our model wih Miraldo s model i he sese o qualiy ehacig ad cos savig echologies. From Table2, we ca explai a relaive growh o he or-proi hospial. Swichig o a prospecive payme sysem makes he or-proi hospial more compeiive sice i ca icrease is qualiy level by adopig posiive amou o qualiy ehacig echology. Table 3 represes he relaive marke share o each hospial uder rerospecive ad prospecive reimburseme sysem respecively. As we ca see i Table 3, he o-or-proi hospial domiaes he or-proi hospial, bu less so wih prospecive reimburseme. 5. Coclusio This work has ocused o he ivesme decisios bewee qualiy improvig ad cos savig echology o or-proi ad o-or-proi hospials uder diere payme sysems ad he resulig marke shares o each hospial ype. Our mos impora resul is ha he swich o a prospecive payme sysem made or-proi hospials more compeiive. I addiio o his srucural chage, decliig doaios o o-or-proi hospials weake heir abiliy o domiae he markes, ad he marke share o or-proi hospials icreased. Also impora, however, is ha o-or-proi hospials always ives more i qualiy ehacig echology whe compared o or-proi hospials. Our idigs provide some isighs useul o policymakers. Firs is ha prospecive reimburseme makes i possible or or-proi hospials o compee wih o-or-proi hospials. 15

16 To he exe ha he proi moive is viewed avorably or uavorably by policymakers, his resul should help guide how reimburseme is se. Perhaps more imporaly, we show ha corollig coss, which is perhaps he primary moivaio or goig o a prospecive payme mechaism, comes a he expese o qualiy ivesme. Thus reimburseme mechaism becomes a impora policy ool o balace bewee qualiy-ehacig ad cos-savig echologies. This paper uses a simple seup which allows us o obai clear-cu resuls ad o highligh he eecs drivig he ivesme choices uder each reimburseme program. Neverheless, he model could be exeded i a umber o direcios. Oe could cosider he case whe paies, raher ha he goverme, pay or heir reame cos. I ca be show i such a case ha he price charged by he or-proi hospial is always higher ha ha o he o-or-proi hospial ad he o-or-proi hospial adops more qualiy ehacig ad cos savig echologies. 16 I cosideraio o space ad relevace, his case is o discussed i he paper. However, he implicaios rom ha resul are ha i he absece o isurace or-proi hospials could o eecively compee. I addiio, addig a ormal isurace marke could poeially ehace our udersadig o how he swich rom rerospecive o prospecive payme aeced boh ivesme decisios ad he abiliy o or-proi hospials o compee as he ype o reimburseme could aec premiums people pay. I 2008 approximaely 85% o Americas had healh isurace, wih abou wo-hirds o he populace covered by privae healh isurace ad 29% covered by goverme plas. 17 Over 87% o hose wih privae healh isurace were covered by policies obaied hrough employme. (Bureau o he Cesus, 2009). Thus he majoriy o he isured have some level o separaio rom heir premiums eiher hrough goverme provisio or by heir employer. A he same ime, isurers may be more resposive o price ha cosumers, hus addig isurace markes migh ehace wha we could lear orm his model. I is ieresig o oe ha by 1992 approximaely oe-hird o privae isurers used some orm o DRG-based reimburseme (Ellis & McGuire, 1993), idicaig ha he privae isurace marke rapidly joied he march owards prospecive reimburseme. 16 The proo o his resul ca be obaied rom he auhors. 17 Coverage is o muually exclusive. These perceages idicae ha approximaely 10% o he populaio has boh privae healh isurace ad coverage rom a goverme program. 16

17 Appedix P.1. Proo o Proposiio 1 Proo Because boh hospials are reimbursed rerospecively based o he average cos wihou ivesme expediures, eiher hospial has a iceive o ives i cos savig echology because doig so will simply lower heir payme dollar-or-dollar. Thereore * 2 = 0 ad * 2 = The we immediaely see * 1 = 0 because he maximal proi or he or-proi hospial is zero, which is achieved oly uder his codiio. Applyig q ( = 0) = q, he or-proi * 1 hospial has he miimal (ad ixed) paies who srogly dislike waiig, Ng. Because he oor-proi hospial maximizes is uiliy, which is aeced by quaiy ad qualiy, i will always have iceive o ives i 1 >0. Thereore, q Q = N(1 g). > q, which implies ha whe 1 =0, Q = Ng ad By sric moooiciy o he uiliy o he o-or-proi hospial, he moey cosrai is bidig (zero e reveue). Ad by applyig * 1 equaio (p1-1), = 0, * 1 > 0, * 2 = 0, ad * 2 = 0, we obai (p1-1) D N (1 g), q ( ) = r * * Also * 1 saisies he ollowig irs order codiio (p1-2) U q q λ Dq q r = where Uq = U / q, q = q / 1, Dq = D / q, ad λ 0 is a Lagrage muliplier. 18 A superscrip * idicaes he opimal value uder he average cos wihou ivesme expediure based rerospecive reimburseme sysem. 17

18 Combiig (p1-1) ad (p1-2), we ca obai (p1-3) * D N (1 g), q( 1 ) U q q 0 + λ Dq q = * 1 Thereore, he opimal ivesmes o boh hospials uder he margial cos reimburseme are * 1 = 0, * 2 = 0, * 1 > 0 where i saisies equaio (p1-3), ad * 2 = 0. This implies ha he o-or-proi hospial ges mos o he paies (o all o hem) ad he orproi hospial is i he marke wihou ivesig ay kids o echologies (wih keepig he miimal qualiy level). Q.E.D. P.2. Proo o Proposiio 2 Proo The problem o he or-proi hospial is reduda because i ears zero proi regardless o is echology ivesme choices uder a average, cos-based, rerospecive payme sysem. I his case, he or-proi hospial has o iceive o ives i eiher echology. Thereore, = 0, = Furher, he o-or-proi hospial has o iceive o ives i 2 because he variable average cos is ully reimbursed 20, hece 2 = 0. Because 1 = 0, he same logic as Proposiio 1, he o-or-proi hospial always has a iceive o ives i 1 o maximize is uiliy by icreasig qualiy ad i his way he hospial obais maximal quaiy, N(1 g). I ac, eve hough he o-or-proi hospial ges zero proi rom operaios, i will always have posiive e reveue because ivesig i 1 iduces he maximal umber o paies ad hus brigs i posiive doaio. Thereore, uder he average-cos, rerospecive, reimburseme sysem he 19 A superscrip idicaes he opimal value uder he average cos wih ivesme expediure based rerospecive reimburseme sysem. 20 We see immediaely ha he proi o he o-or-proi hospial is zero ad ay ivesme i 2 cao give a iceive o maximize is uiliy. 18

19 o-or-proi hospial problem wih a o-egaive moey cosrai becomes he ucosraied maximizaio problem due o he udraisig by doaio 21. Cosiderig he qualiy level o he or-proi hospial equaio (p2-1). q = q whe 1 =0, he irs order codiio o equaio (7) became ollowig (p2-1) U q = 0 q Noice ha U Q Q = N(1 g). = 0 whe 1 = 0, because he quaiy level o each hospial is ixed, By he sric moooiciy o he uiliy o he o-or-proi hospial, equaio (p2-1) is saisied i ad oly i q = q 1 = 0. Thereore, 1 = 0, 2 = 0, 1 = 1 > 0, ad q ( ) = 0 =. Q.E.D P.3. Proo o Corollary 2 Proo Le he opimal level o qualiy ehacig echology uder he average, cos-based, rerospecive reimburseme wihou ivesme expediures ad ha wih ivesme expediures equal * 1 ad 1 respecively. The opimal * 1 saisies a equaio (p1-3). Because he moey cosrai o he o-or-proi hospial is bidig due o he sric moooiciy o he * * uiliy o he o-or-proi hospial, we assume λ > 0. I λ > 0, he cosrai mus be bidig ad he Kuh-Tucker problem becomes a sadard Lagragia problem. 22 The equaio (p1-3) 21 Due o our assumpio o dimiishig margial reur o qualiy o doaio, he o-or-proi hospial icreases qualiy as log as doaios are available o pay or i. 22 * Now i λ = 0, his meas ha he cosrai is slack r r + D [ Q ( ), q ( ) 1 1 ] > 0. The, udraisig D wo make he cosrai bidig ad so he cosrai will sill be slack, ad hereore he maximized uiliy level o he o-or-proi hospial wo chage a all. 19

20 ca be rewrie as D N (1 g), q ( ) q U D, which implies * q = q > * 1 = λ * q + λ q because U q > 0, D q > 0 23, λ > 0 * *, ad D N(1 g), q ( 1 ) 1 > 0. From Proposiio 2, we iduced q =. 1 0 Because he level o qualiy is icreasig ad cocave i 1h, we immediaely see ha * <. Q.E.D. 1 1 P.4. Proo o Proposiio 3 Proo The diereces bewee hospial price ad coss vary wih ivesmes i boh echologies uder prospecive reimburseme because he prices o boh hospials are arbirarily se ex ae. We will, hereore, cosider all cases o hospial ivesmes. As i Proposiio 1, by he sric moooiciy o he uiliy o he o-or-proi hospial, is moey cosrai is bidig, i.e., zero e reveue. To cosider he geeral case, we assume λ > 0. Firs, we show ha boh hospials ives i boh caegories o echology, i.e., 1 >0, 2 >0, 1 >0, ad 2 >0. Iuiively we ca see ha where 1 = 0, 2 = 0, ad 1 = 0are reduda. The or-proi hospial has a iceive o adop 2 o icrease proi by reducig ui reame cos because he price is ixed ex ae. The or-proi hospial will adop posiive amous o 1 oherwise, due o goverme price resricio, i obais a egaive proi. The o-or-proi hospial will surely ives i 1 arac paies by lowerig is price. because i is he oly way o icrease is uiliy ad i cao Now suppose 2 = 0. By equaios (9), by µ 2 = 0, ad by he complemeary slackess codiio o equaio (11), r = Q c. Usig his i equaio (13), ad because µ 2 0 ad 2 2 λ > 0, we ca obai equaio (p3-1), 23 We assume U 0, D 0. However, sice U = 0, D = 0 due o Q = N(1 g) (he o-or-proi hospial akes q q Q Q mos o he paies ad i is ixed because 1 =0. so here are o margial uiliy ad doaio o he quaiy), U > 0, D > 0 by he sric moooiciy assumpio. q q 20

21 (p3-1) Q c Q c 2 2 Because c = > c 2 2 > 0 by he covexiy o he cos savig echology, we id Q Q q q > o saisy iequaliy (p3-1). Thereore he o-or-proi hospial 1 2 will deviae rom 2 = 0 because 2 > 0 makes he moey cosrai slack ad allows a larger which icreases uiliy uil i bids. Thus, 2 > 0. As a resul, we id ha boh hospials 1 ives i boh echologies. Now, we show 1 < 1 ad 2 < By he complemeary slackess codiios, all he Kuh-Tucker mulipliers are zero excep λ > 0. Usig equaios (9) ad (13), we ca obai equaio (p3-2). (p3-2) Q Q = c c 2 2 From equaio (12), we obai he iequaliy Q Q Q 1 q Q 1 q ( p - c ) < r + Q c, because Q U + U q + λ[ D + D q ] > 0. Usig equaio (8), we replace r 1 as Q ( - ) 1 p c Q c 1, ad obai equaio (p3-3). Q Q (p3-3) ( p - c ) < ( p - c ) + ( Q c 1 Q c 1 ) 1 1 Suppose 1 > 1, he q > q ad Q > Q. By he cocaviy assumpios o he quaiy ucios o boh hospials i q h ad qualiy ucio i 1h, > q > q Q > Q. Also, usig he covexiy assumpio o he ui reame cos ucio i, 1h Qc Q 0 1 c <. Equaio (p3-3) is hereore saisied i ad 1 24 A superscrip idicaes he opimal value uder he prospecive reimburseme sysem. 21

22 oly i p - c < p - c. However, his is a coradicio because c > c by he propery (ⅶ) o he ui reame cos ucio. Suppose 1 = 1, he q = q ad Q = Q. From our assumpio ha he same kids o echologies are available o boh hospials, Q = 1 Q ad Q 1 c Q 0 1 c =, 1 equaio (p3-3) is saisied i ad oly i p - c < p - c. However his oo, is a coradicio give c = c (based o equaio (p3-2), 2 = 2, ad because 1 = 1 i his case, c = c ). Suppose 1 < 1, he q < q, Q < Q ad c < c. Based o he cocaviy assumpio, Q 1 < Q 1. Also, by he covexiy assumpio 1h, Q c Q c > 0. ' ' 1 1 Sice p c < p c (c > c ), equaio (p3-2) is always saisied. Ad by equaio (p3-2), <. Thereore, i all hree cases, 1 < 1 ad 2 < Now, we will show ha he o-or-proi hospial cao reach he globally maximal level o qualiy or he miimal cos a his qualiy level. Suppose he o-or-proi hospial reaches globally maximal qualiy. The q ( ) = 0 ad equaio (12) ca be rewrie as λ Qc r = ' 1. However his cao be saisied because Thereore, he o-or-proi hospial cao reach maximal qualiy. Q c > 0, r 1 > 0, ad µ 1 = 0. Suppose he o or-proi hospial is able o reduce he ui reame cos o he miimum or his opimal qualiy level, he c ( 2 1, 2 ) = 0. However, equaio (13) cao be saisied because r 2 > 0 ad µ 2 = 0. Thereore, uder he prospecive reimburseme sysem, 1 < 1, 2 < 2, he o-orproi hospial cao reach globally maximal qualiy or he miimal cos o his qualiy level. Q.E.D. 1 P.5. Proo o Corollary 2 Proo By rewriig equaio (12), we have 22

23 1 λ D Q Q Q UQ ( - ) + U 1 q q + DQ + D 1 q q + p c 1 = r1 + Qc. Le 1 Q Q 1 q U 1 Q λ Q 1 q + U q beω ad + D q beτ. The ω is he margial uiliy ad τ is he margial doaio o he o-orproi hospial. Replace 1 Q p -c Q c r as ( ) 1 1 ( ) ( 1 1 ) Q Q 1 1 rom equaio (8), ad we have ω + τ + ( p - c ) = p - c + Q c Q c. Because ω, τ > 0, we have iequaliy (c2-1). Q Q Q (c2-1) p c < ( p c ) + ( Q c ) ( ) 1 Q c < 1 p c + ( Q c 1 Q c 1 ) ( - ) - - D= 0 D> where 1 ad 1 are 1 wihou ad wih doaios respecively. From Proposiio 3, we kow 1 < 1. The, based o he cocaviy assumpio, we see < <, which implies Q < Q < Q. Q.E.D P.6. Proo o Corollary 3 Proo * 1 ad 1 are iduced rom equaios (p1-2) ad (12). Equaio (p1-2) ca be rewrie as r 1 U = + D q. Pluggig his io equaio (12), ad µ 1 = 0 by he complemeary slackess * * q q * λ q o equaio (14), he we obai: * * Uq q * ( * * λ ) U Q U q Q ( p c ) Q c D Q D q D q + + λ = 0. Q 1 q 1 1 q 1 q q By rearragig his, we obai equaio (c3-1): Q 1 U p c D Q c U U D D q q (c3-1) ' *' ' + λ ( ) + λ = λ ( * + ) + * + ( ) Q Q 1 * q q q q 1 λ Noice ha U + λ ( p c ) + D Q 1 Q Q is he o-or-proi hospial s oal margial beei (uiliy + e proi o operaio + doaio) o qualiy ehacig echology hrough he quaiy o he o-or-proi hospial. Ad λ Q c is he o-or-proi hospial s oal margial 1 23

24 cos o he qualiy improvig echology uder he prospecive reimburseme sysem. I ecoomic sese, he oal margial beei o he qualiy improvig echology should be o less ha he oal margial cos o he qualiy ehacig echology, bu because 1 aecs oal margial beei hrough boh quaiy ad qualiy, we cao compare he oal margial beei o 1 hrough quaiy ad he oal margial cos o 1. I he le had side o equaio (c2-1) is o egaive, he he righ had side o equaio (c2-1) * also should be o-egaive, which implies Because he erm * ( U * + U ) + D * + D is λ q q q q posiive, ad due o he cocaviy o he qualiy ucio, he righ had side o equaio (c2-1) is o egaive i ad oly i * 1 1. O he oher had, i he le had side o equaio (c2-1) is egaive, he * 1 < 1 usig he same logic. Thereore, he amou o qualiy ehacig echology ha he o-or-proi hospial adops uder he prospecive reimburseme sysem would be larger or smaller ha ha uder he margial cos based rerospecive reimburseme sysem (i.e., < ) uder hese speciic codiios. Q.E.D. > *

25 Reereces Bureau o he Cesus, Icome, Povery, ad Healh Isurace Coverage i he Uied Saes: hp:// Ceers or Medicare ad Medicaid Services. No dae. Prospecive Payme Sysems - Geeral Iormaio. hp:// Chalkley M ad Malcomso JM Goverme purchasig o healh services, Hadbook o Healh Ecoomics, Vol. 1:

26 Ellis, R. ad McGuire, T Supply-Side ad Demad-Side Cos Sharig i Healh Care. Joural o Ecoomic Perspecives, Vol. 7, No. 4, pp Gayor, M ad Vog WB Compeiio amog hospials, The RAND Joural o Ecoomics, Vol. 34, No. 4, Wier: Goddeeris, Joh H Isurace ad iceives or iovaio i medical care, Souher ecoomic joural, Vol.51, No.2, Oc: Hoerger,Thomas J 'Proi' variabiliy i or-proi ad o-or-proi hospials, Joural o healh ecoomics 10 (3): Hasma, Hery B The role o oproi eerprise, The Yale law joural, Vol. 89, No 5: Hasma, Hery B Owership o he irm, The joural o law, ecoomics, ad orgaizaio, Vol.4, No.2: Hederso, James W Healh Ecoomics ad Policy 4 h Ediio, Souh-Weser Cegage Learig: 270. Hirh RA, Cherew ME, ad Orzol SM Owership, compeiio, ad he adopio o ew echologies ad cos-savig pracices i a ixed-price evirome, A Joural o medical care orgaizaio, provisio ad iacig 37(3), Fall: Ma, Chig-To Alber Joural o ecoomics ad maageme sraegy, Vol.3, No.1, Sprig: Miraldo, Marisa Hospial iacig ad he developme ad adopio o ew echologies, CHE Research Paper 26, Ceer or healh ecoomics, The Uiversiy o York: Selder, Asrid Physicia reimburseme ad echology adopio, Joural o healh ecoomics 24: Sloa, Frak A No-or-proi hospial owership ad hospial behavior, Hadbook o healh ecoomics Vol.1: Weisbrod, Buro A The healh care quadrilemma: A essay o echological chage, isurace, qualiy o care, ad cos coaime, Joural o ecoomic lieraure, Vol.29, No.2. Jue:

27 TABLE 1. Number ad Perceage o U.S. Commuiy hospials by Owership Type, seleced year Year Toal For-proi No-or-proi Goverme Numbers Numbers Perceage Numbers Perceage Numbers Perceage , , ,

28 1980 5, , , , , , , , , , , , , , , , , , , , , , , , , , , Source: 1975 o 2005 daa; James W. Hederso, Healh Ecoomics ad Policy 4 h Ediio, p daa; America Healh Associaio Resource Ceer TABLE 2. Compariso o Our Model ad Miraldo Model Ivesme i qualiy ehacig Miraldo Our model Model For-proi No-or-proi For-proi 28

29 Rerospecive reimburseme wih ivesme expediures 1 =0 < 1 >0 = > 1 = 0 wihou ivesme expediures * 1 =0 < * 1 > 0 Prospecive reimburseme 1 >0 < 1 > 0 1 > 0 Ivesme i cos savig Rerospecive reimburseme wih ivesme expediures < < = > 2 = 0 2 = 0 wihou ivesme expediures * 2 = 0 * 2 = 0 Prospecive reimburseme 2 > 0 < 2 > 0 2 >0 = < = < < 2 >0 TABLE 3. Relaive marke share o hospials For-proi No-or-proi Rerospecive payme Q = Ng( 1 = 0) < Q ( 1 > 0) = N (1 g( 1 = 0)) 29

30 > < Prospecive payme Q ( 1 > 0) < Q ( 1 > 0) 30

31 31