Provided in Cooperation with: Ifo Institute Leibniz Institute for Economic Research at the University of Munich

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1 econsor Der Open-Access-Publikaionsserver der ZBW Leibniz-Informaionszenrum Wirschaf The Open Access Publicaion Server of he ZBW Leibniz Informaion Cenre for Economics Brekke, Kur R.; Siciliani, Luigi; Sraume, Odd Rune Working Paper Hospial compeiion and qualiy wih regulaed prices CESifo Working Paper, No Provided in Cooperaion wih: Ifo Insiue Leibniz Insiue for Economic Research a he Universiy of Munich Suggesed Ciaion: Brekke, Kur R.; Siciliani, Luigi; Sraume, Odd Rune (2009) : Hospial compeiion and qualiy wih regulaed prices, CESifo Working Paper, No This Version is available a: hp://hdl.handle.ne/10419/30561 Sandard-Nuzungsbedingungen: Die Dokumene auf EconSor dürfen zu eigenen wissenschaflichen Zwecken und zum Privagebrauch gespeicher und kopier werden. Sie dürfen die Dokumene nich für öffenliche oder kommerzielle Zwecke vervielfäligen, öffenlich aussellen, öffenlich zugänglich machen, verreiben oder anderweiig nuzen. Sofern die Verfasser die Dokumene uner Open-Conen-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gesell haben sollen, gelen abweichend von diesen Nuzungsbedingungen die in der dor genannen Lizenz gewähren Nuzungsreche. Terms of use: Documens in EconSor may be saved and copied for your personal and scholarly purposes. You are no o copy documens for public or commercial purposes, o exhibi he documens publicly, o make hem publicly available on he inerne, or o disribue or oherwise use he documens in public. If he documens have been made available under an Open Conen Licence (especially Creaive Commons Licences), you may exercise furher usage righs as specified in he indicaed licence. zbw Leibniz-Informaionszenrum Wirschaf Leibniz Informaion Cenre for Economics

2 Hospial Compeiion and Qualiy wih Regulaed Prices KURT R. BREKKE LUIGI SICILIANI ODD RUNE STRAUME CESIFO WORKING PAPER NO CATEGORY 11: INDUSTRIAL ORGANISATION APRIL 2009 An elecronic version of he paper may be downloaded from he SSRN websie: from he RePEc websie: from he CESifo websie: Twww.CESifo-group.org/wpT

3 CESifo Working Paper No Hospial Compeiion and Qualiy wih Regulaed Prices Absrac We analyse he effec of compeiion on qualiy in hospial markes wih regulaed prices, considering boh he effec of (i) inroducing compeiion (monopoly versus compeiion) and (ii) increasing compeiion hrough lower ransporaion coss (increased subsiuabiliy) or a higher number of hospials. Wih semi-alruisic providers and a fairly general cos srucure, we show ha he relaionship beween compeiion and qualiy is generally ambiguous. In conras o he received heoreical lieraure, his is consisen wih, and poenially explains, he mixed empirical evidence. JEL Code: H42, I11, I18, L13. Keywords: hospials, compeiion, qualiy. Kur R. Brekke Deparmen of Economics and Healh Economics Bergen Norwegian School of Economics and Business Adminisraion Helleveien Bergen Norway kur.brekke@nhh.no Luigi Siciliani Deparmen of Economics and Relaed Sudies & Cenre for Healh Economics Universiy of York Heslingon, York YO10 5DD Unied Kingdom ls24@york.ac.uk Odd Rune Sraume Deparmen of Economics Universiy of Minho Campus de Gualar Braga Porugal o.r.sraume@eeg.uminho.p

4 1 Inroducion Qualiy is a major concern in healh care. Recen and ongoing reforms in several counries o simulae compeiion and paien choice among publicly funded hospials have highlighed he imporance of esablishing more knowledge abou he relaionship beween compeiion and qualiy. 1 While he presen paper is a new aemp o address his general opic, we resric our aenion o he case of qualiy compeiion beween healh care providers facing regulaed prices, which is relevan for mos European healh care sysems as well as he U.S. Medicare and Medicaid programmes. The inroducion of marke mechanisms in he healh care secor hrough a combinaion of prospecive paymen sysems and free paien choice aims a giving healh care providers incenives o arac more paiens (and hus paymens) by offering a higher qualiy of care. Indeed, he exising heoreical lieraure on qualiy compeiion wih regulaed prices is pracically unanimous in reporing a posiive relaionship beween compeiion measured eiher as a swich from monopoly o (imperfec) compeiion or as a marginal increase in he inensiy of compeiion and qualiy. In a general seing, his conclusion is reached in, e.g., Ma and Burgess (1993), Wolinsky (1997), Brekke, Nuscheler and Sraume (2006) and Masumura and Masushima (2007), while, in a more specific healh care seing, he same conclusion is reached in, e.g., Calem and Rizzo (1995), Gravelle (1999), Lyon (1999), Gravelle and Masiero (2000), Beiia (2003), Nuscheler (2003), Brekke, Nuscheler and Sraume (2007) and Karlsson (2007). However, he empirical evidence, hough relaively scarce, seems o be considerably more ambiguous. For example, while Kessler and McClellan (2000) and Tay (2003) find aposiiveeffec of compeiion on qualiy in he healh care secor (wih fixed prices), Gowrinsankaran and Town (2003) find a negaive effec, Shen (2003) finds mixed effecs, and Shorell and Hughes (1988) and Mukamel, Zwanziger and Tomaszewski (2001) find 1 Examples include he UK, where hospials are paid a ariff for every paiens reaed (Paymen by Resuls) and paiens have been given a free choice of hospial. Similar reforms have been inroduced in Norway, Denmark, Ialy and several oher European counries. 2

5 no effecs. 2,3 In his paper we exend and generalise he received heoreical lieraure in several direcions by simulaneously including (i) heerogeneous paiens and elasic oal demand for healh care, (ii) semi-alruisic healh care providers, and (iii) general cos funcions ha are non-separable in aciviy and qualiy. We analyse, firs, he effec of a policy regime swich from monopoly o compeiion (i.e., inroducing free paien choice). Second, we sudy he effec of increasing compeiion eiher hrough lower ransporaion coss (i.e., increasing he degree of subsiuabiliy among hospials) or by increasing he number of hospials. In our choice of heoreical framework a Salop model wih symmerically disribued healh care providers we follow he exising heoreical lieraure, where qualiy compeiion is ypically analysed wihin a spaial compeiion framework. Our key conribuion is o model healh care providers as being semi-alruisic. While his is a quie common assumpion in he general lieraure on healh care supply, i has seldom been applied in a conex of compeiion beween healh care providers. 4 Indeed, he presen paper is o he bes of our knowledge he firs aemp o incorporae alruisic behaviour when sudying he relaionship beween compeiion and qualiy. 5 Our analysis shows ha his assumpion poenially makes a huge difference. Wheher we consider he inroducion of compeiion or an increase in he degree of compeiion, we show ha he relaionship beween compeiion and qualiy is generally ambiguous and depends crucially on hospial cos srucure and he degree of alruism. More specifically, 2 See Gaynor (2006) for a survey of heoreical and empirical lieraure on he relaionship beween hospial compeiion and qualiy. 3 There are also several empirical sudies analysing he relaionship beween compeiion and qualiy finding mixed resuls when prices are se by he hospials. See, e.g., Dranove and Saerhwaie (1992), Dranove, Shanley and Simon (1992), Ho and Hamilon (2000), Sari (2002) and Propper, Burgess and Green (2004). The case of qualiy compeiion wih endogenous prices is no addressed in he presen paper. Besides, i is well known ha he relaionship beween compeiion and qualiy is heoreically more ambiguous in his paricular case. 4 Hirh (1999) and Harrison and Lybecker (2005) inroduce non-profi objecivesinaseingofcompeiion beween healh care providers. However, since compeiion is analysed in a seing of flexible prices and he relaionship beween compeiion and qualiy is no an issue in eiher paper, hese sudies are quie differen from ours. A more general analysis of compeiion in non-profi versus for-profi indusries is found in Lakdawalla and Philipson (2006). 5 Ellis (1998) also models compeiion beween semi-alruisic healh care providers. However, he does no address he relaionship beween compeiion and qualiy bu focuses insead on he effec of differen reimbursemen schemes on providers incenives for over- versus under-provision of services o differen ypes of paiens. 3

6 a sufficien degree of alruism may, for cerain hospial cos srucures, lead o a negaive relaionship beween compeiion and equilibrium qualiy. Comparing monopoly and compeiion, a negaive relaionship beween compeiion and qualiy is more likely o occur (for a given degree of alruism) if he number of paiens who make choices beween differen hospials wha we dub he "compeiive demand segmen" is sufficienly large relaive o he number of paiens who do no make such choices. The key mechanism ha conribues o his reversal resul is ha semi-alruisic behaviour may lead o negaive marginal profis in equilibrium. 6 Due o mechanisms ha will be described in deail in subsequen secions, his implies ha compeiion has an a priori ambiguous effec on hospial qualiy incenives. We also show ha inensified compeiion measured by reduced ransporaion coss may lead o lower equilibrium qualiy even if healh care providers are pure profi maximisers, implying posiive marginal profis in equilibrium. Though apparenly counerinuiive and in conras wih previous lieraure he resul is due o sric convexiy and nonseparabiliy in he cos funcion we can show ha his paricular resul depends on he presence of a non-compeiive demand segmen and is essenially a demand effec, raher han a pure compeiion effec. Finally, we show ha qualiy incenives are generally ambiguous also wih respec o he perhaps mos usual compeiion measure, namely he number of hospials in he marke. This resul crucially hinges on he degree of alruism. In he absence of alruism, a higher hospial densiy will always lead o higher qualiy. However, if he degree of alruism is sufficienly high relaive o he degree of cos convexiy (and/or cos subsiuabiliy beween quaniy and qualiy), he effec of more hospials is in fac reversed. The inuiion is relaed o he fac ha, when he number of hospials increases, each hospial faces a lower demand, which resuls in fewer reaed paiens and lower marginal paien benefi of qualiy invesmens a hospial level. The main srucure of our model which is presened in he nex secion is based 6 We ensure of course ha he (semi-alruisic) hospials earn non-negaive profis in equilibrium, alhough heir marginal profis migh be negaive. Wih sricly convex producion coss, negaive marginal profis do no imply ha overall profis are negaive in equilibrium. 4

7 on Brekke, Siciliani and Sraume (2008). In ha paper, we analyse he effec of hospial compeiion on waiing imes, raher han qualiy. While here are clear parallels beween waiing imes and more general qualiy of care as he former can be inerpreed as a negaive form of hospial qualiy here are also imporan differences. While increasing qualiy is cosly for he provider, reducing waiing imes is no. More precisely, while increasing qualiy has a direc and an indirec cos for he provider, reducing waiing imes only has an indirec cos, hrough a higher demand. Thus, he resuls in Brekke, Siciliani and Sraume (2008) do no auomaically carry over o he case of qualiy compeiion. For example, while a higher hospial densiy unambiguously reduces waiing imes, he effec on hospial qualiy is ambiguous. More generally, while he degree of alruism does no generally affec he relaionship beween compeiion and waiing imes, i plays a crucial role in explaining he relaionship beween compeiion and qualiy, as we will show below. The res of he paper is organised as follows. In Secion 2, we presen he model. In Secion 3, we derive equilibrium qualiy under, respecively, local monopoly and compeiion, and analyse which regime ha provides more incenives for qualiy provision. In Secion 4, we consider a regime of free paien choice (compeiion) and invesigae he impac of inensified compeiion, boh in erms of lower ransporaion coss and a higher number of hospials. Secion 5 concludes he paper. 2 Model Consider a marke for elecive hospial reamen where n hospials are equidisanly locaed on a circle wih circumference equal o 1. There are wo paien ypes L(ow) and H(igh) differing wih respec o he gross valuaion of reamen. Boh ypes are uniformly disribued on he circle wih densiy normalised o 1. A paien demands eiher one reamen from he mos preferred hospial, or no reamen a all. The uiliy of a paien of ype s {L, H}, who is locaed a x and being reaed a hospial i, locaed a 5

8 z i,isgivenby U s V x z i + kq i if s = H (x, z i )= v x z i + kq i if s = L, (1) where q i q is he qualiy a hospial i, k is a parameer measuring he (marginal) uiliy of qualiy, is a ransporaion cos parameer, and V v>0 measures he difference in he gross valuaion of reamen beween he wo ypes. 7,8 The lower bound q on hospial qualiy represens he minimum reamen qualiy hospials are allowed o offer, implying ha q < qcan be inerpreed as malpracice. For simpliciy, we se q =0. Moreover, we normalise he marginal uiliy of qualiy o one, i.e., k =1, wihou loss of generaliy. This implies ha can be inerpreed as he marginal disuiliy of ravelling relaive o qualiy. Thus, a low (high) means ha qualiy is of relaively more (less) imporance o he paien han ravelling disance. 9 The H-segmen consiues a share λ of he oal number of paiens, which is normalised o 1. We focus on equilibria where he H-segmen is fully covered, while he L-segmen is only parly covered, i.e., some L-paiens will no seek reamen in equilibrium. 10 The former assumpion means ha here is compeiion (or scope for compeiion) in he marke, while he laer assumpion implies ha oal demand for hospial reamen is elasic wih respec o qualiy. 11 We will inermienly refer o he L- andh-segmens 7 Differences in gross valuaions across paiens can be due o differences in age, gender, illness severiy, or simply opporuniy coss. For example, old paiens wih a non-severe condiion migh have a low valuaion of medical reamen. 8 Transporaion coss can be given a broad inerpreaion o include all coss (disuiliy) associaed wih being far from "home" o receive reamen. There is also srong empirical evidence showing ha disance is a major predicor of paiens choice of hospial, see, e.g., Kessler and McClellan (2000) and Tay (2003). 9 An alernaive non-physical inerpreaion of he horizonal dimension is a disease space, where he locaion of a paien is associaed wih he disease she suffers from, and he hospials are differeniaed wih respec o he disease hey are bes able o cure, reflecing hospial specialisaion or "service mix" (see, e.g., Calem and Rizzo, 1995, and Brekke, Nuscheler and Sraume, 2007). 10 This essenially requires ha he difference in gross valuaion of reamen is sufficienly large beween he wo paien ypes. 11 Noice ha, by focusing on he equilibrium wih a fully covered H-segmen and a parly covered L-segmen, we are able o cover he oher possibiliy full marke coverage in boh demand segmens as a special case. By seing λ =1, he model is reduced o a sandard model wih only one demand segmen (where oal demand is inelasic), bu his is qualiaively equivalen o he case of wo demand segmens where boh are fully covered in equilibrium. 6

9 as he monopoly and compeiive demand segmens, respecively. Hospials are prospecively financed by a hird-pary payer offering a per-reamen price p and poenially a lump-sum ransfer T. The objecive funcion of hospial i is assumed o be given by π i (q i, q i )=T + px i (q i, q i )+αb i (q i, q i ) C (X i (q i, q i ),q i ), (2) where X i (q i, q i ) is demand for reamen a hospial i (derived from individual uiliy maximisaion) and q i represens he vecor of qualiies a neighbouring hospials. The cos of supplying hospial reamens is given by he cos funcion C (X i,q i ),wihc X > 0, C q > 0, C XX 0 and C qq > We also assume C Xq 0, i.e., qualiy and quaniy are (weakly) subsiues: an increase in qualiy is more cosly when more paiens are reaed. The funcion B i ( ) represens he oal benefi of he paiens receiving reamen a hospial i, while he parameer α [0, 1] capures he degree of alruism of he provider. 13 We assume ha hospials canno urn down paiens seeking reamen, implying ha we do no allow for explici raioning. The hospials simulaneously and independenly choose qualiies, in order o maximise heir objecive funcions. Maximising (2) wih respec o q i and applying symmery, he equilibrium qualiy, q,isgivenby 14,15 X i (q ) q i [p C X (X i (q ),q )] + α B i (q ) q i = C q (X i (q ),q ), i =1, 2, (3) where X i / q i > 0 and B i / q i > A convex variable cos funcion is suppored by evidence suggesing ha economies of scale are quie rapidly exhaused in he hospial secor (see, e.g., Ferguson e al., 1999, and Folland e al., 2004, for lieraure surveys). 13 This formulaion is consisen wih, e.g., Ellis and McGuire (1986), Chalkley and Malcolmson (1998) and Jack (2005). Noice also ha i is general, since he special case of a profi-maximising hospial can be recovered by seing α =0. 14 This equilibrium is characerised by a fully covered H-segmen and a parially covered L-segmen if (v + 2n q,v + q ). 15 Noice ha he inerior equilibrium implicily relies on he assumpion ha a limied liabiliy consrain is no binding, i.e., T + px (q ) C (X (q ),q ) 0. 7

10 The marginal benefi from qualiy is given by he higher revenues and he non-moneary benefi arising from alruism. The marginal cos of qualiy includes he direc marginal cos of qualiy invesmens and he increased marginal cos of reamen ha arises from he demand increase. The combinaion of alruisic preferences and increasing marginal reamen coss makes he sign of marginal profis, p C X, ambiguous in equilibrium. 16 More specifically, marginal profis are negaive in equilibrium if he marginal alruisic gain of a qualiy increase is larger han he direc marginal cos: α ( B i / q i ) >C q Compeiion or monopoly? Consider wo disincly differen policy regimes: 1) a benchmark case of no compeiion, where paiens are assigned o hospials purely according o geographical disance and hospials are in effec local monopolies; 2) compeiion, where paiens are free o choose among hospials when demanding reamen. 18 Thechoiceofpolicyregimeaffecs he demand responsiveness o qualiy, X i / q i, which, in urn, affecs he marginal alruisic uiliy gain, B i / q i. From (3) we see ha hese are he wo channels hrough which compeiion migh affec qualiy. 3.1 Monopoly Wihou free paien choice, hospial i s demand from he H-segmen is exogenously given by X H i =1/n. In he L-segmen, he paien who is indifferen beween reamen a hospial i and no reamen is locaed a x L i,givenbyv xl i + q i =0, or, more explicily, x L i =(v + q i ) /. Toal demand for hospial i from he L-segmen is given by X L i =2x L i. 16 Noice ha, by marginal profis we refer here (and hroughou he paper) o he change in profis due o a marginal increase in producion, no qualiy. 17 Noice ha, wih sricly convex producion coss, negaive marginal profis do no imply ha profis are negaive in equilibrium. 18 General Pracioners (GPs) are ofen involved in he choice of hospial, especially in gaekeeping sysems. A GP is an exper and migh recommend a hospial o he paien based on qualiy (and disance); see Brekke, Nuscheler and Sraume (2007). I is no crucial for he analysis wheher i is he GP or he paien ha makes he choice of hospial. 8

11 Toal demand for hospial i (from boh paien segmens) is hus given by X i (q i )= λ n +(1 λ) 2(v + q i), (4) while oal uiliy for he paiens reaed a hospial i is given by Z 1 2n B i (q i )=λ2 (V + q i x) dx +(1 λ)2 0 Z v+q i 0 (v + q i x) dx, (5) yielding and X i (q i ) 2(1 λ) = > 0 (6) q i B i (q i ) q i = X i (q i ) > 0. (7) Noice ha lower ransporaion coss makes i less cosly for paiens o demand reamen; his increases demand responsiveness from L-ype paiens o hospial qualiy changes. Regarding (7), noice ha a qualiy increase a hospial i has, in general, wo effecs on oal uiliy for paiens reaed a he hospial: firs, i increases uiliy for all paiens ha are already reaed a he hospial; second, i increases demand for hospial i reamen. Since, in he absence of compeiion, he demand increase only comes from he L-segmen, he uiliy conribuion is zero a he margin. Thus, here is a posiive uiliy conribuion only from inframarginal paiens. Equilibrium qualiy under monopoly, q = q m, is hen found by subsiuing (4)-(7) ino (3) Compeiion Wih free paien choice, he hospials qualiy choices affec demand also in he H- segmen. Since he disance beween hospials is equal o 1/n, he H-paien who is indifferen beween seeking reamen a hospial i and hospial j is locaed a x H i,given 19 The second-order condiion is given by 2 π i / qi 2 2(1 λ) = C XX +2C Xq α 2(1 λ) C qq < 0, which holds if he cos funcion is sufficienlyconvexinqualiy. 9

12 by V x H i + q i = V 1/n x H i + qj, or, more explicily, x H i = q i q j + n /2. Assuming ha qualiy is he same a boh neighbouring hospials 20,andgivenbyq j, oal demand for hospial i from he H-segmen is given by X H i =2x H i. Demand from he L-segmen is he same as before. Toal demand facing hospial i from boh segmens is hus given by X i (q i,q j )=λx H i +(1 λ) X L i = 2(1 λ) v + q i (2 λ) λq j + λ n, (8) while he surplus o paiens reaed a hospial i is given by Z 1 B i (q i,q j )=2λ 0 2(q i q j + n) Z v+q i (V + q i x) dx +2(1 λ) (v + q i x) dx, (9) 0 yielding X i (q i,q j ) q i = 2 λ (10) and B i (q i,q j ) q i = X i (q i,q j )+ λ µ V + q i + q j 2. (11) 2n Comparing (6) and (10), we see ha he demand responsiveness o qualiy changes is higher under compeiion han under monopoly. The reason is simply ha, under compeiion, here is a demand response also in he H-segmen: anincreaseinhequaliy offered by hospial i will no only induce more L -ypes o seek reamen, i will also arac H-ypes who would oherwise have sough reamen a a neighbouring hospial. Comparing (7) and (11), we also see ha he increase in oal paien uiliy from a marginal increase in qualiy a hospial i is higher under compeiion han under monopoly. The reason is ha, wih compeiion, a qualiy increase leads o an inflow of paiens (from he compeiive segmen) wih a sricly posiive ne uiliy of hospial reamen. In oher words, here is a uiliy conribuion from boh marginal and inframarginal paiens. Inu- 20 Since he model is symmeric, noice ha, when solving for he Nash equilibrium, we can define X i and B i for q i 1 = q i+1 = q j,maximiseπ i wih respec o q i andhenseq i = q j o derive he qualiy level in he symmeric equilibrium. 10

13 iively, he difference beween (7) and (11) depends on he relaive size of he compeiive segmen, given by λ. Equilibrium qualiy under compeiion, q = q c, is found by subsiuing (8)-(11) ino (3) and seing q i = q j = q c Compeiion versus monopoly A comparison of he wo policy regimes wih respec o equilibrium qualiy yields he following resul: Proposiion 1 Compeiion beween hospials lead o higher (lower) qualiy in equilibrium if he compeiive segmen (λ) isbelow(above)ahresholdlevel b λ,givenby bλ := 1 + µ Cq (X i (q m ),q m ) 1. (12) 2(V v) α n Proof. Combining he wo equilibrium condiions (under monopoly and compeiion, respecively) yields, afer some manipulaions, 2 α [C X (X i (q m ),q m ) C X (X i (q c ),q c )] + 2 (q c q m ) 2 + α (2 λ) [C q (X i (q m ),q m ) C q (X i (q c ),q c )] λ 2(V v) n (1 λ) = (1 λ)(2 λ) n + C q (X i (q m ),q m ) α. We need firs o confirm monooniciy of he lef-hand side (LHS) of he above equaion in q m and q c.takinghefirs-order derivaive yields (LHS) q c = 2 α µ 2 λ C XX + C Xq +2 µ 2 α (2 λ) C qq + C Xq 2 λ 21 The second-order condiion is 2 π i / qi 2 = 2 λ C XX +2C Xq α 2 λ α λ + C 2 qq < 0, whichis always saisfied if he cos funcion is sufficienly convex in qualiy. 11

14 and (LHS) q m = 2 α µ µ 2(1 λ) 2 2(1 λ) C XX + C Xq 2+ C qq + C Xq. α (2 λ) By applying he second-order condiions we confirm ha (LHS)/ q c < 0 and (LHS)/ q m > 0. Since LHS =0if q c = q m, i follows ha q c > (<)q m if he righ-hand side of he equaion is negaive (posiive), which is he case if λ<(>)1+ µ Cq (X i (q m ),q m ) 1. 2(V v) α n Consider firs he benchmark case of pure profi-maximising behaviour. From (12) we see ha α 0 implies b λ. Thus, wihou alruism, compeiion leads o higher equilibrium qualiy for all λ (0, 1), as expeced. In he presence of alruism, however, he effec of compeiion on qualiy is a resul of wo couneracing forces. On he one hand, compeiion increases he marginal alruisic gain of qualiy (cf. (7) and (11)), since hospials can arac high-benefi paiens by increasing qualiy. Ceeris paribus, his leads o higher hospial qualiy in equilibrium. On he oher hand, compeiion increases he demand responsiveness o qualiy (cf. (6) and (10)). Wheher or no he laer effec increases qualiy incenives depends on he sign of he marginal profis, p C X, in he monopoly equilibrium. If marginal profis are posiive, hospials will compee more fiercely o arac paiens also for purely profioriened reasons, and compeiion will unambiguously increase qualiy. However, if he marginal profis are negaive which requires a cerain degree of alruism a more qualiy-responsive demand implies, ceeris paribus, ha hospials have less incenives o inves in qualiy, since he marginal paien is financially unprofiable o rea. If his is he case, hen he inroducion of compeiion has an ambiguous effec on equilibrium qualiy, and compeiion will lead o lower qualiy if he (financial) incenive o avoid unprofiable paiens is sronger han he (alruisic) incenive o arac 12

15 high-benefi paiens. In general, he former incenive ends o dominae esablishing a negaive relaionship beween compeiion and qualiy if marginal profis are sufficienly negaive in he monopoly equilibrium. This ends o be he case if he degree alruism is high and hospial densiy is low, relaive o he direc marginal cos of qualiy. 22 As he above analysis shows, α>0 is a necessary bu no sufficien condiion for a negaive relaionship beween compeiion and qualiy. However, i should be sressed ha our way of modeling of alruism is a somewha exreme case among he plausible alernaives. We have assumed ha decision makers have semi-alruisic preferences only owards paiens reaed a heir own hospial. The oher exreme case would be o assume ha decision makers a each hospial care equally much abou all paiens in he marke, regardless of where hey are reaed. In his case, he marginal alruisic gain of qualiy would be he same under monopoly and compeiion. 23 This would eliminae he incenive o arac high-benefi paiens for alruisic reasons, implying ha, if marginal profis are negaive in he monopoly equilibrium, compeiion would always reduce equilibrium qualiy. Thus, he condiion given in Proposiion 1 should be seen as a lower bound on he likelihood ha semi-alruisic behaviour leads o a negaive relaionship beween compeiion and qualiy. 4 Inensiy of compeiion In his secion we consider a compeiion regime wih free paien choice and analyse wheher or no inensified compeiion will lead o higher qualiy. We measure inensified compeiion in wo ways: firs, we sudy he impac of lower ransporaion coss (i.e., increased subsiuabiliy); second, we analyse he impac of more hospials in he marke. 22 Noice ha λ>(<)1 if C q > (<) α n, i.e., if he direc marginal cos of qualiy is larger (smaller) han he marginal alruisic gain in he monopoly equilibrium, implying posiive (negaive) marginal profis. 23 In boh cases, B/ q i = X i. 13

16 4.1 Transporaion coss (subsiuabiliy) Consider he effec of increasing he degree of compeiion in he marke hrough lower ransporaion coss, i.e., increasing he subsiuabiliy among he hospials in he marke, which is a sandard compeiion measure in he previously cied lieraure. 24 In our framework, lower ransporaion coss have wo differen effecs: i makes demand more responsive o qualiy changes and i increases oal demand from he L- segmen. Toally differeniaing he firs-order condiions in he compeiion regime, and applying Cramer s rule, we obain a generally indeerminae oal effec: q c X = 2 λ i (V + q c ) α X h C XX + C Xq (2 λ) (p C 2 X )+ αλ 2 2 λ C XX + C Xq α 2(1 λ) α λ + C 2 λ qq + C Xq 0, (13) where X/ = 2(1 λ)(q c + v) / 2. The second-order condiion ensures ha he denominaor is posiive, so he sign of he expression is deermined by he sign of he numeraor. Consider firs, as a benchmark, he sandard case of pure profi-maximising behaviour (α =0) and inelasic oal demand (λ =1). Since λ =1eliminaes he demand effec ( X/ =0), he numeraor reduces o (2 λ)(p C X ) / 2. Since α =0ensures ha p>c X in equilibrium, his expression in unambiguously negaive. Thus, we recover he sandard resul from he lieraure ha lower ransporaion coss increase qualiy. In he more general case of α (0, 1) and λ (0, 1), resuls are more ambiguous. The firs erm in he numeraor is always posiive (since X/ < 0). Using he firs-order condiion, we can show ha he second erm is also posiive if αλ/2n >C q ( ), i.e., if alruism is sufficienly high relaive o he direc marginal cos of qualiy invesmens. 25 In his case, q c / > 0, implying ha increased compeiion unambiguously reduces 24 Noice ha can, o some exen, be hough of as a policy variable. For example, in Norway paiens ravelling coss are parially reimbursed by he public payer. In many counries, here is also an increased (policy-induced) availabiliy of performance indicaors on qualiy which faciliaes comparison across healh care providers. Alhough his is mainly relaed o informaional issues, which are no explicily modelled in he presen paper, Brekke, Nuscheler and Sraume (2006) have shown, in a similar model, ha increased paien informaion is qualiaively equivalen o reduced ransporaion coss. 25 Noice ha his condiion implies negaive marginal profis, since 2 λ λ (V + qc )+ 2(1 λ) (v + q c ) in equilibrium. 14 (p C X )= C q α λ 2n

17 qualiy. Noice ha his resul ha lower ransporaion coss reduce qualiy if he degree of alruism is sufficienly high holds qualiaively also for he special case of λ =1, and he inuiion for he resul closely mirrors he inuiion given for Proposiion 1. On he oher hand, if marginal profis are posiive and sufficienly large, we obain he sandard resul from he lieraure, ha more compeiion increases qualiy. Noice, however, ha posiive marginal profis is no asufficien condiion for increased compeiion o increase qualiy. Furhermore, even wihou alruism, i is no necessarily he case ha lower ransporaion coss increase qualiy. By seing α =0in (13) we sill obain q / 0, in conras o he received lieraure. This is due o our assumpions of increasing marginal aciviy coss and non-separabiliy in he cos funcion. I is imporan o sress, hough, ha his is a demand effec raher han a compeiion effec. If we eliminae he demand effec by seing λ =1, he ambiguiy of he relaionship beween and q only survives for α>0. We summarise he above analysis and discussion as follows: Proposiion 2 (i) Lower ransporaion coss have in general an indeerminae effec on qualiy, even if marginal profis are posiive in equilibrium, and even if he degree of alruism is zero; (ii) Lower ransporaion coss always reduce qualiy if he degree of alruism is large relaive o he direc marginal cos of qualiy; (iii) If marginal profis are posiive in equilibrium, he marginal cos of reamen is consan and he cos funcion is separable in qualiy and aciviy, hen lower ransporaion cossalwaysincreasequaliy. 4.2 The number of hospials (densiy) The perhaps mos direc and obvious compeiion variable is he number of hospials. In our framework here is local compeiion. This means ha a higher number of hospials will increase he densiy of hospials in he marke. The effec of more hospials migh seem 15

18 obvious in he sense ha we would expec hospials o compee more fiercely for paiens. Thus, we would expec ha qualiy increases as more hospials ener he marke. As we will see, he relaionship beween hospial densiy and qualiy is no so obvious. The impac of a higher number of hospials on equilibrium qualiy is obained by oally differeniaing he firs-order condiions in he compeiion regime, and applying he Cramer s rule, yielding q c i n = 2 λ Xi n 2 λ CXX + C qx α 2 C XX + C Xq α 2(1 λ) α λ + C, (14) 2 λ qq + C Xq where X i / n = λ/n 2. The second-order condiion ensures ha he denominaor is posiive, so he sign of he expression is deermined by he sign of he numeraor. Proposiion 3 A higher number of hospials leads o lower (higher) qualiy in equilibrium if he degree of alruism is above (below) a hreshold level bα, givenby µ 2 λ bα := 2 C XX + C qx. (15) In order o explain he inuiion behind his resul, le us once more sar by considering he benchmark case of pure profi-maximising behaviour. If α =0, he numeraor in (14) is unambiguously posiive, implying ha more hospials always lead o higher qualiy, as long as C XX and/or C Xq are sricly posiive. Higher hospial densiy means ha each hospial faces lower demand and hus performs fewer reamens. If hospial coss are sriclyconvexinoupu,lowerdemand increases marginal profis (p C X ), making i more profiable for each hospial o arac exra paiens by increasing qualiy. Cos subsiuabiliy beween quaniy and qualiy (C Xq > 0) amplifies his effec. However, wih semi-alruisic providers, a couneracing effec is inroduced. When fewer paiens are reaed a each hospial, he marginal paien benefi of higher qualiy is correspondingly reduced (see (11)). All else equal, his gives each hospial weaker incenives o increase qualiy for alruisic reasons. If he degree of alruism is sufficienly high relaive o he degree of producion cos convexiy and/or cos subsiuabiliy beween 16

19 quaniy and qualiy, he couneracing effec dominaes and a higher number of hospials resuls in lower qualiy. For example, in he case of consan marginal cos of producion and cos independence beween quaniy and qualiy, which are sandard assumpions in he cied lieraure, we see from (15) ha he hreshold level of alruism reduces o bα =0, implying ha here is always a negaive relaionship beween he number of hospials and equilibrium qualiy wih semi-alruisic providers. Finally, observe ha, alhough he effecs of higher hospial densiy are relaed o changes in individual hospial demand, he presence of a compeiive segmen is crucial for he resuls. If here is no compeiive segmen (λ =0), hen a higher number of hospials has no effec on qualiy incenives. 5 Concluding remarks Wih semi-alruisic healh care providers and a general convex cos srucure, a posiive relaionship beween hospial compeiion and qualiy is no longer guaraneed. Therefore, our model which exends and generalises he exising heoreical lieraure is useful o clarify under which condiions we migh expec compeiion o increase (resp., decrease) qualiy. Our key conribuion is o carry he assumpion of semi-alruisic healh care providers over o a conex of qualiy compeiion. There are several feaures ha are hough o disinguish he marke for healh care from markes for oher consumpion goods. One imporan disinguishing feaure is semi-alruisic provider preferences, an assumpion ha is reasonably common in he lieraure on healh care supply bu rarely used in oher conexs. Wha we have shown in his paper is ha his paricular assumpion can lead o counerinuiive and perhaps unexpeced effecs of compeiion. Besides offeringapossible explanaion for he mixed empirical evidence on he effec of compeiion on qualiy, here is also a poenial lesson o be learned for policy makers as well as analyss of healh care markes: if we believe ha here are some imporan feaures ha disinguish healh care markes from oher markes, such as alruisic provider preferences, we should also be 17

20 careful abou carrying sandard inuiion abou produc marke compeiion ha more compeiion leads o higher qualiy over o markes for healh care. By way of conclusion, we would also like o emphasise ha even if policy measures o increase compeiion among healh care providers do no lead o he expeced resul higher qualiy of healh care i does no auomaically follow ha such policy measures should no be underaken. However, an analysis of he desirabiliy of such policies would require a full-fledged welfare analysis, which is beyond he scope of his paper. 18

21 References [1] Beiia, A., Hospial qualiy choice and marke srucure in a regulaed duopoly. Journal of Healh Economics, 22, [2] Brekke, K.R., Nuscheler, R., Sraume, O.R., Qualiy and locaion choices under price regulaion. Journal of Economics & Managemen Sraegy, 15, [3] Brekke, K.R., Nuscheler, R., Sraume, O.R., Gaekeeping in healh care. Journal of Healh Economics, 26, [4] Brekke, K.R., Siciliani, L., Sraume, O.R., Compeiion and waiing imes in hospial markes. Journal of Public Economics, 92, [5] Calem, P.S., Rizzo, J.A., Compeiion and specializaion in he hospial indusry: an applicaion of Hoelling s locaion model. Souhern Economic Journal, 61, [6] Chalkley, M., Malcomson, J.M., Conracing for Healh Services when paien demand does no reflec qualiy. Journal of Healh Economics, 17, [7] Dranove, D. D., Saerhwaie, M. A., Monopolisic compeiion when price and qualiy are imperfecly observable. Rand Journal of Economics, 23, [8] Dranove, D. D., Shanley, M., Simon, C., Is hospial compeiion waseful? Rand Journal of Economics, 23, [9] Ellis, R.P., Creaming, skimping and dumping: provider compeiion on he inensive and exensive margins. Journal of Healh Economics, 17, [10] Ellis, R.P., McGuire, T., Provider behavior under prospecive reimbursemen: Cos sharing and supply. Journal of Healh Economics, 5, [11] Ferguson, B., Sheldon, T., Posne, J. (eds.), Concenraion and choice in healh care. London: Royal Sociey of Medicine. 19

22 [12] Folland, S., Goodman, A.C., Sano, M., The economics of healh and healh care. Upper Saddle River, NJ: Prenice Hall. [13] Gaynor, M., Wha do we know abou compeiion and qualiy in healh care markes? Foundaions and Trends in Microeconomics, Vol. 2, Issue 6. [14] Gowrisankaran, G., Town, R., Compeiion, payers, and hospial qualiy. Healh Services Research, 38, [15] Gravelle, H., Capiaion conracs: access and qualiy. Journal of Healh Economics, 18, 3, [16] Gravelle, H., Masiero, G., Qualiy incenives in a regulaed marke wih imperfec compeiion and swiching coss: capiaion in general pracice. Journal of Healh Economics, 19, [17] Harrison, T.D., Lybecker, K.M., The effec of he nonprofi moive on hospial compeiive behavior. Conribuions o Economic Analysis & Policy: Vol. 4: Iss. 1, Aricle 3. [18] Hirh, R.A., Consumer informaion and compeiion beween nonprofi and for-profi nursing homes. Journal of Healh Economics, 18, [19] Ho, V., Hamilon, B. H., Hospial mergers and acquisiions: does marke consolidaion harm paiens? Journal of Healh Economics, 19, [20] Jack, W., Purchasing healh care services from providers wih unknown alruism. Journal of Healh Economics, 24, [21] Karlsson, M., Qualiy incenives for GPs in a regulaed marke. Journal of Healh Economics, 26, [22] Kessler, D., McClellan, M., Is hospial compeiion socially waseful? Quarerly Journal of Economics, 115,

23 [23] Lakdawalla, D., Philipson, T., The nonprofi secor and indusry performance. Journal of Public Economics, 90, [24] Lyon, T. P., Qualiy compeiion, insurance, and consumer choice in healh care markes. Journal of Economics & Managemen Sraegy, 8, [25] Ma, C.A., Burgess, J.F., Qualiy compeiion, welfare, and regulaion. Journal of Economics, 58, [26] Masumura, T., Masushima, N., Congesion-reducing invesmens and economic welfare in a Hoelling model. Economics Leers, 96, [27] Mukamel, D., Zwanziger, J., Tomaszewski, K.J., HMO peneraion, compeiion and risk-adjused hospial moraliy. Healh Services Research, 36, [28] Nuscheler, R., Physician reimbursemen, ime-consisency and he qualiy of care. Journal of Insiuional and Theoreical Economics, 159, [29] Propper, C., Burgess, S., Green, K., Does compeiion beween hospials improve he qualiy of care? Hospial deah raes and he NHS inernal marke. Journal of Public Economics, 88, [30] Sari, N., Do compeiion and managed care improve qualiy? Healh Economics, 11, [31] Shen, Y.-S., The effec of financial pressure on he qualiy of care in hospials. Journal of Healh Economics, 22, [32] Shorell, S. M., Hughes, E. F., The effecs of regulaion, compeiion, and ownership on moraliy raes among hospial inpaiens. New England Journal of Medicine, 318, [33] Tay, A., Assessing compeiion in hospial care markes: he imporance of accouning for qualiy differeniaion. RAND Journal of Economics, 34,

24 [34] Wolinsky, A., Regulaion of duopoly: Managed compeiion vs regulaed monopolies. Journal of Economics & Managemen Sraegy, 6,

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