Hospital s activity-based financing system and manager - physician interaction

Transcription

1 Hospital s activity-based financing system and manager - pysician interaction David Crainic CRESGE/LEM/FLSEG, Université Catolique de Lille. dcrainic@cresge.fr Hervé Leleu CNRS and CORE, Université Catolique de Louvain and LEM (UMR 8179), Université Catolique de Lille leleu@core.ucl.ac.be Ana Mauleon FNRS and CEREC, Facultés Universitaires Saint-Louis, and CORE. mauleon@fusl.ac.be Marc 27, 2006 Abstract Hospital financing systems determine major decisions made by pysicians and managers witin ospitals. Tis paper examines te impact of te transition toward an activity-based reimbursement system tat as emerged in most OCDE countries. We consider two initial situations, one for a private for-profit sectorwerebotospitals and pysicians are paid on a fee-for-service basis and te oter for a public sector under prospective budget and salaried pysicians. For te private sector, our model focuses on te type of interaction (simultaneous, sequential or joint decision-making games) tat sould emerge between agents after te indroduction of te activity-based financing system. In te public sector, te elasticity of te demand to te level of inputs seems to play a more crucial rôle in te transition. JEL Classification: I11, D4, D2 Key words: Hospital s financing system, Strategic interaction, Activity-based payment system. Ana Mauleon is Researc Associate of te National Fund for Scientific Researc (FNRS), Belgium.

2 1 Introduction Te provision of ealt care services now constitutes one of te largest industries in OECD countries, representing on average 8.5% of te per capita GDP of all OECD countries in 2002 (10.2% of te GDP for te seven most industrialized countries and 14.6% for United States only). During te last decade , te annual growt rate of ealt care expenditures was still significantly iger tan te GDP growt rate (3.4% in average versus 2.1% in OECD countries) and te sare of ospitals expenditures in total ealt spending was about 40% during tis period 1. As a consequence, ospitals ave attracted te attention of policymakers attempting to curb growt in ealt care costs by canging te financial landscape. Tree main issues associated to ospital financing system are mostly considered in te economic literature. Namely, te ability to control te total cost, to induce efficiency (minimal unit cost or maximal level of activity by unit of input) and to ensure a ig level of te quality of care delivered. Among industrialized countries and until te 1980s cost reimbursement was te main form of payment for public or private not-for-profit ospitals. Wile it allows for ig quality of care, tis system neiter offers incentives to reduce costs nor to increase efficiency. In te early 1980s, policy makers began to consider te switc from te cost-based reimbursement to prospective budgets to cope wit continuously increasing growt of ospital spending; tis capped ospital expenditure at an exogenous growt rate. Wile tis system allows for cost containment, it is completely disconnected from te real activity of ospitals and creates no incentives for efficiency or a ig level of quality of care. On te oter and, te private for-profit ospitals were traditionally financed on a fee-for-service basis. Finally, in te last decade, most of te OECD countries joined te US wo ad initiated an activity-based payment for bot public and private ospitals as early as in 1983 for te Medicare program. Tis activity-based system works on a flat amount per admission given te patient s diagnosis and tus encourages te ospital to lower its unit cost in order to turn a profit. Clearly, tis activity-based payment creates uge incentives for efficiency. Actually, most countries opt for a mix of financing systems were strong incentives are placed on efficiency by te activity-based system wile external controls ensure an expected level on te quality of ealt care services and a global expenditure cap policy aims to contain te total spending. In Western Europe combinations of prospective budgeting wit activity-based payment are found in Austria, Belgium, France, Finland, Germany, Italy, Ireland, Norway, Portugal, Spain and Sweden. Wen comparing different ospital payment systems, two main topics ave been con- 1 Source: OECD Healt Data

3 sidered in te economic literature. First, te comparison of te systems from a social welfare standpoint as been a major concern in te ealt economics literature. Ma (1994) and Calkley and Malcomsom (1998) ave sown tat an activity-based payment system will imply bot productive efficiency (te minimization of per-patient costs) and allocative efficiency (te treatment of te socially optimal number of patients) provided tat te demand depends on te quality of ealt care services. Mougeot and Naegelen (2004) ave analyzed te strategies of te providers facing a global expenditure cap policy and evaluate its effects on provider and patient surplus. More generally, Pope (1990) or Newouse (1996) ave pointed out te value of a payment system based on a mix between a prospective and a retrospective system. An alternative to tis social optimum approac is to analyze te impact of an exogenous cange in te financing policy on te beavior of te economic agents (ospital s managers, pysicians, patients). Muc less literature as been devoted to tis issue. To our knowledge, only Custer et al. (1990) and Dor and Watson (1995) ave analyzed ow different payment systems affect ospital-pysicians interactions. Custer et al. (1990) ave treated ospital-pysician interactions from a productive efficiency angle witout directly taking into account te impact on patients demand. Dor and Watson (1995) ave compared two kind of prospective payment systems: a single fee to be sared between ospital and pysicians and distinct fees for eac of tem. A major issue in te introduction of an activity-based financing system is ow it will affect te decisions of managers and pysicians wen tey bot ave teir own and separated economic objectives and wen tey interact witin te ospital to satisfy te demand. Tis issue as first been considered in Coudeville, Mauleon and Dervaux (2004) for te private for-profit sector. In tis paper, we depart from teir model for te privatefor-profit sector by focusing on te type of interaction tat sould be promoted by an activity-based financing system. We also extend te analysis to te public sector since bot beaviors and objectives differ among pysicians and managers in te two sectors. Moreover, current financing system are quite different (prospective budget and salaried pysicians in te public sector and fee-for-service for bot te ospital and pysicians in te private sector). Our main focus is ow te transition to a common activity-based financing sceme may affect differently public and private ospitals and ow it may modify te type of interactions between ospital s managers and pysicians depending tey ave conflicting interests or incentives to cooperate under te new payment system. Since we are mainly interested in te modification of te beavior, we consider a neutral financing reform wic does not affect te amount of te global budget but only te reimbursement scemes. 2

4 Te paper is organized as follows. In Section 2, te model is presented. Section 3 analyzes te impact on te manager-pysician interaction of te introduction of an activitybased financing system for te private for-profit sector wile Section 4 is devoted to te public sector. Section 5 concludes and discusses some possible extensions. 2 Te model We suppose tat major decisions taken witin ospitals are made by pysicians and managers. Te former make decisions about a level of effort tat corresponds to a number of acts (denoted by e and tat can be medical or surgical acts, pre or post surgery consultations...) tey undertake per day wile te latter define te input provided by te ospital (denoted by q and wic includes expenses related to te operating rooms, beds, tecnical equipment, nursing care, administrative and tecnical staff...). We also suppose tat a given number a of acts is required to treat te representative disease for omogeneous patients. Te patient s average lengt of stay (denoted by ) is terefore directly related to te level of effort suppliedbypysiciansperday(wit(e) =a/e by definition). Te issue of te quality of treatment is not dealt wit troug te pysician s daily effort (e) - tat must be considered as a variable tat implicitly determines patients lengt of stay at te ospital - but rater troug te ospital input (q). Since we assume tat no minimal duration is required for te administration of te treatment and tat at least one act is made per day, te bounds for e and are suc tat: e [1,a] and [1,a]. Patients are sensitive to te input q and to te daily effort e provided by ospitals and pysicians respectively. Patients utility function is assumed to be additive and increasing, continuous and strictly concave in bot arguments. U(e, q) =E(e)+Q(q) wit E e > 0, E ee < 0, Q q > 0 and Q qq < 0. Te first assumption simply states tat patients prefer to be treated as quickly as possible. Tere are no quality differences between treatments since eac treatment - weter administered in a sort or a long period of time - as te same impact on te patient s ealt state. Oter tings being equal, patients tus prefer not to spend time in ospitals 2. Te assumptions about te second argument of te utility function (ospitals input) are obvious. 2 Instead of assuming tat te patient s utility depends on te pysician s effort level e, wecouldave considered tat it depends on te lengt of stay. We ave toug preferred to consider e as te argument of te utility function since it is a control variable determined by te pysician. However tis modification in te model setting does not affect our final results. 3

5 We consider te situation of a single ospital tat does not face competition. In tat case patients decide to go to te ospital only if te utility associated to te treatment is iger tan a certain tresold tat is patient specific and tat depends on elements suc as patient s preferences for private vs. public ospital, pysical or psycological distance... If tis tresold is uniformly distributed between U and U and if te population size is normalized to 1, te demand faced by te ospital (tat is, te number of patients treated) can be defined as follows: 0 if U U U(e,q) D(e, q) = if U <U<U U U 1 if U U Interior solutions will only be considered (0 <D(e, q) < 1). Let D e, D ee, D q and D qq denote te first and second derivatives of te demand wit respect to te effort level and to te ospital input respectively wit D e > 0, D ee < 0, D q > 0 and D qq < 0 given te assumptions made about te patients utility function. Since we focus on te impact of te financing reform on te interaction between pysicians and managers witin private (for-profit) and public (not-for-profit) ospitals, we ave to consider four agents (a representative pysician and a representative manager for eac type of ospital) wo determine te four decision variables (effort and input witin eac type of ospital) of te model. To do so, let us first define te agents objectives. Pysicians and managers working in private ospitals aim at maximizing teir profits. Te representative pysician tries to maximize is/er daily net income Π p (e) wen defining is/er daily level of effort e. Pysicians net income is written in te following way: Π p (e) =D(e, q)[rp (e) CP(e)] (1) were RP (e) represents is/er total fee per patient and CP(e) represents te financial cost per patient associated to te medical activity (borne by pysicians temselves in private ospitals) plus te monetary equivalent of te effort disutility. RP (e) >CP(e) since we assume tat te agents present on te market make a positive profit. Bot variables depend obviously on te effort level. Tere is a linear relationsip between fees and te medical activity suc tat RP (e) =r e e (we tus implicitly assume tat a given fee is granted per medical intervention; te fee is constant across te various interventions). Te cost CP(e) is assumed to be continuous, increasing and convex in e (CP e > 0,CP ee > 0) andcp(0) = 0. Te convexity of te cost function is justified by te increasing disutility of te effort expressed in monetary terms. 4

6 Hospital managers maximize te daily ospital profit Π (q) defined as follows 3 : RH CH() Π (q) =D(e, q) CQ(q) (2) Te fee RH is received by ospitals for te wole patients lengt of stay. Te structure of te ospital s revenue depends on te financing system (fee-for-service vs. activitybased payment) examined in te next section 4. Tere are two types of costs borne by te ospital: tose related to te patient lengt of stay denoted CH() (supposed to be continuous, increasing and strictly concave in (CH > 0,CH < 0 and CH(0) = 0) and tat include expenses related to drugs, bedding, food...; and tose related to te ospital input expressed per day (supposed to be linear in te input q suc tat CQ(q) =c q q). Te concentration of care during te firstpartoftelengtofstayjustifies te strict concavity of CH() wile te linearity of CQ(q) is explained by te relative stability of equipment and staff expenses. Te ospitals present in te market make a positive profit wic implies tat RH > CH(). Let us notice tat pysicians and managers decisions are related. Managers decisions about te ospital input affect te demand and tus te profit made by pysicians. In te same way, pysicians efforts ave an impact on te demand and on te patients lengt of staywicbotenterintoteospitalprofit. Te type of interaction between pysicians and managers witin te ospital is tus crucial in te coice of te two decision variables e and q. Turning now to te public sector, pysicians working in public ospitals earn a fixed wage tat is independent of teir activity. Tey tus maximize teir utility instead of teir profits. Tis utility depends on te number of patients treated (because of te conscientiousness or because of te pleasure and te prestige of working in a igly demanded ospital for example) and on te disutility related to te effort (because te time spent next to teir patients prevent tem from oter activities suc as leisure or paid consultations outside te ospital). Teir utility function is written as follows: U p (e) =D(e, q) ED(e, q) (3) were ED(e, q) stands for te effort disutility wic is supposed to be continuous, increasing and convex in te effort (ED e > 0 and ED ee > 0 meaning tat te disutility 3 We suppose tat ospitals maximize teir daily profits - instead of teir profits evaluated along te wole lengt of stay for example - in order to be consistent wit te pysician objective. Tis will be useful wen examining situations of cooperation between pysicians and ospitals managers tat imply te maximization of teir joint profits. 4 A mix of tese two payments systems, called two-parts tariffs, is most often used in practice. Our model remains owever valid to deal wit te impact of te introduction of any intermediate financing between te fee-for-service payment and te activity-based system. 5

7 related to eac additional effort is increasing). Te effort disutility also depends on te ospital input q since we suppose tat pysicians enjoy more teir work and tat medical treatments take less time if pysicians can take advantage of a developed medical input (ED q < 0 and ED qq > 0). Te convexity of te effort disutility is justified by te increasing strenuousness of work and by te increasing opportunity cost of forgone leisure. In public ospitals, managers are responsible of te wole cost related to te ospital activity: tose related to te medical acts (e), to te lengt of stay () andtoteospital input (q). Te assumptions made previously about te costs related to te lengt of stay and to te inputs old for bot private and public ospitals. Te public ospital only bears te financial carge of te effort tat is supposed to be linear (CP(e) =c e e)since te disutility of te effort is a burden for te pysician and tus enters in is/er objective function 5. Public ospital managers ave at teir disposal a budget tat depends on te financing system and are supposed to be responsible of te ospital financial equilibrium. In oter words, managers coose te public ospital input level in order to respect te following daily budgetary constraint: BC D(e, q) c e e + CH() + c q q B (4) were B stands for te ospital budget granted to cover expenses related to all patients entire lengt of stay. Public ospitals managers are also concerned wit patient s utility so tat tey spend te budget left by improving te ospital input so tat te expression (4) is always satisfied as an equality. 3 Financing systems and private ospitals Tis section defines te impact of te ospital financing system on effort and input equilibrium values and seeks to determine wic type of interaction between pysicians and managers is promoted by te financing system in private ospitals. We consider ere a transition from a fee-for-service payment to an activity-based financing system but te latter only affects payments related to carges supported directly by te ospital (nursing care, use of operating rooms, drug consumption, etc.). Fees-for-service paid to pysicians working in tese ospitals are not affected. Unlike te fee-for-service system, te activitybased payment allows ospitals a fixed fee per patient independent of te patients lengt 5 We must make te distinction between te cost of te effort tat pysicians totally bear in private ospital and tat is split up between pysicians (for te disutility) and managers (for its financial part) in public ospitals. Te convexity of te cost of te effortistusnotjustified for public ospital (te convex part of te cost being borne by pysicians). 6

8 of stay. Te introduction of te latter payment system tus gives direct incentives to reduce te patient s lengt of stay. In order to igligt te impact of te new financing system on pysicians and managers beavior, we suppose tat te amount allocated to te representative ospital in te activity-based payment system remains te same tan in te previous reimbursement system. Doing so, we focus on te way te various financing systems affect pysicians and ospital activity and isolate our model from canging beaviors explained by per patient endowment variations. We consider tree possible types of interactions between pysicians and ospital managers (simultaneous decision-making, sequential decision-making or joint decision-making) and sow ow an activity-based financing system for te ospital improves pysicians and managers incentives to coordinate teir activities by promoting a sequential decisionmaking interaction or a joint decision-making interaction. For eac type of decision-making game, we first define te equilibrium values of e and q under bot financing systems and ten sow ow te introduction of te activity-based payment system modifies agents beavior. 3.1 Te simultaneous decision-making game We first consider te transition from a fee-for-service payment to an activity-based payment system under a simultaneous decision-making game. Under te fee-for-service reimbursement system, te pysician s objective function is given by equation (1) and te first-order condition (5) associated to tis optimization program defines te effort level equilibrium value be s : D e [r e e CP(e)] + D(e, q)[r e CP e ]=0 (5) were te first term of te equation represents te marginal gain associated to an additional effort (te product of te average gain per patient and te increase in demand due to te extra effort) wile te second term represents te marginal cost due to tat effort (te reduction of te average gain per patient due to te extra effort). Let us indeed notice tat r e CP e < 0 at te equilibrium. Te second-order condition is satisfied since: D ee [r e e CP(e)] + 2D e [r e CP e ]+D(e, q)[ CP ee ] < 0 Under te fee-for-service system, ospitals revenues depend on te lengt of stay wit a constant fee r granted per patient and per day (for te entire ospitalization period) so tat RH = r in te objective function (2). Te ospital optimization program (2) is tus written: MaxΠ (q) =D(e, q) r CH() c q q q 7

9 Te first-order condition tat defines bq s is: D q r CH() c q =0 (6) wic states tat te marginal gain of an additional input (te product of te average gain per day and te increase in demand due to te extra input) is equal to its marginal cost (c q ) at te equilibrium. Te second-order condition for a maximum is satisfied since: D qq r CH() < 0 We now consider te activity-based payment system. First, it is obvious tat te pysician optimization program remains te one tat prevailed under te fee-for-service system (see first-order condition (5)) since we assume tat te new payment system only modifies te ospital financing system. Terefore, te effort level equilibrium value does not cange, be s = be s. However, under te new system, ospitals revenues are independent of te lengt of stay, and ten RH = RH in te objective function (2). Te ospital still maximizes its daily profit defined now by te following expression: RH CH() MaxΠ (q) =D(e, q) c q q q Te first-order condition (defining bq s ) associated to tis maximization program is: RH CH() D q c q =0 (7) Te second-order condition required to obtain a maximum is satisfied: RH CH() D qq < 0 Since te transition between te two systems is done assuming te condition of budget neutrality (RH = r b s ), te reform does not modify te Nas equilibrium wen pysicians and managers interact simultaneously. Terefore be s = be s and bq s = bq s. Tis result is summarized in te following proposition. Proposition 1 Te transition from a fee-for-service payment system to an activity-based payment system in private ospitals does not modify te pysician s effort level and te ospital s input level under a simultaneous decision-making game. Te financing reform as no impact on te agents beavior witin te private for-profit ospitals if tey are engaged in a simultaneous decision-making game. Te intuition beind tis result is straigtforward. Te new payment system does not affect te pysician 8

10 directly wile te latter controls te lengt of stay, te key variable for maximizing te ospital s profit. Since bot agents play simultaneously, te pysician does not take into account te ospital incentives to reduce te lengt of stay. Tis status quo allows us to use te simultaneous Nas equilibrium as a bencmark to analyze te incentives for te pysician and te manager to better coordinate teir decisions under te oter decisionmaking interactions. 3.2 Te sequential decision-making game Hospital manager leader We first consider te ospital manager as te leader in te sequential decision-making game. Under te fee-for-service reimbursement system, te ospital manager optimization program (see equation (2)) is: MaxΠ (q) =D(e, q) r CH() c q q q Wen te ospital manager is acting as te leader, te first-order condition tat defines bq sml is written: de D q + D e dq r CH() + D(e, q) de d dq de CH CH() 2 c q =0 (8) Compared to te first-order condition under te simultaneous decision-making game (equation (6)), we notice tat te manager takes into account te fact tat is/er input level decision implies a pysician reaction de dq tat affects te demand but also a variation de d in te lengt of stay, dq de,tataffects te cost. Te first order condition defining be s (equation (5)) and te implicit function teorem allows us to state tat: de dq = D q [r e CP e ] D ee [r e e CP(e)] + 2D e [r e CP e ]+D(e, q)[ CP ee ] < 0 (9) We also ave by definition of (e) =a/e: de d dq de d > 0 and D(e, q)de dq de CH CH() > 0 since te total cost related to te patients lengt of stay CH() is concave wit CH(0) = 0. By comparing equation (8) to te simultaneous Nas equilibrium (equation (6)), we are unable to determine if te ospital input level will be lower or iger compared to te simultaneous case (bq sml bq s ) because te two new terms tat appear in equation (8) ave opposite signs. Because of its first-mover advantage, te ospital profit is necessarily iger tan in te simultaneous case but te effect on te pysician profit is ambiguous 9 2

11 (te impact on te demand is indeterminate since e and q move in opposite directions). Terefore, te fee-for-service payment system does not bring clear incentives for bot agents to act in a sequential game (wit ospital leader) instead of te simultaneous decision-making game. We now consider te activity-based payment system. Te modification of te payment system does not cange te pysician s reaction function (equation (9)) defined under te fee-for-service payment system since te reform does not directly affect pysician s first order condition (equation (5)). Tus de dq is still negative. But te activity-based payment modifies te ospital first order condition: de RH CH() D q + D e c q + D(e, q) de d RH CH()+CH dq dq de 2 =0 (10) were D(e, q) de d RH CH()+CH dq de 2 < 0 In te activity-based payment system, a decrease in te lengt of stay increases te ospital per patient profit because te cost falls wile te payment RH remains fixed. Tis leads te ospital manager to reduce te level of input (bq sml < bq s )comparedto te simultaneous Nas equilibrium. However, as de dq is still negative, te pysician effort increases (be sml > be s )andteeffect on te demand and on te pysician profit arestill ambiguous. Proposition 2 Compared to te simultaneous Nas equilibrium, bot payment systems do not give clear incentives to te ospital manager andtotepysiciantoactinasequential game wit te ospital moving first. Wile te ospital profit necessarily increases, te effect on te pysician profit is ambiguous in bot systems and te activity-based payment system does not give incentives to te agents to better coordinate teir decisions by using tis type of sequential game. Te intuition beind te result is tat since te optimal level of effort and input move in opposite direction compared to te simultaneous interaction situation (bencmark case), an increase in demand and tus iger profits for bot agents are not guaranteed. Te effort and te input are terefore strategic substitutes in tis case. Tings are different if te pysician acts as te leader in te sequential game Pysician leader We now consider te pysician leader in te sequential decision-making game. Under te fee-for-service reimbursement system, te pysician optimization program (see equation 10

12 (1)) is: MaxΠ p (e) =D(e, q)[r e e CP(e)] e Te first-order condition tat defines be spl is tus written: dq D e + D q [r e e CP(e)] + D(e, q)[r e CP e ]=0 (11) de Compared to te first-order condition under te simultaneous decision-making game (equation 5), we notice tat te pysician takes into account te fact tat is/er effort decision implies an indirect effect on te demand (and terefore on is/er profit) troug te managers reaction to tis effort variation. If dq de is positive (resp. negative), tis indirect effect of e raises (resp. lowers) te demand and tus generates a iger (resp. lower) marginal benefit and equilibrium level of effort. Te first order condition defining bq s (equation 6) and te implicit function teorem allows us to state tat: CH CH() 2 i d de dq D q de = D qq [r CH()] < 0 (12) Te sign of te expression (12) expresses te fact tat a lower lengt of stay (resulting from a iger effort e made by te pysician) reduces te ospital daily margin per patient since te total cost related to te patients lengt of stay CH() is concave. Te indirect impact of te effort on te ospital input is tus negative under a fee-for-service payment. Tis prompts pysicians to reduce teir efforts (be s > be spl ) in order to increase patients lengt of stay ( b s < b spl ) and give incentives to managers to increase te ospital input (bq s < bq spl ) compared to te simultaneous game equilibrium (equations (11) and (5)). Profits made by pysicians necessarily increase (because of teir leading position) but te effect on te ospital profit is ambiguous (tey increase teir profit per patient because of te increase in but teir input costs rises wit q and te impact on te demand is indeterminate since e and q move in opposite directions). We now consider te activity-based payment system. Te pysician optimization program defining is/er optimal effort (be spl ) remains te one defined under te fee-for-service payment system (equation (11)) since te reform does not directly affect pysician s payment. But te modification of te payment system canges te ospital s reaction function (wic defines b bq spl ) suc tat dq de is now positive: dq de = D q i RH CH()+C d de 2 D qq RH CH() i > 0 (13) Te positive sign of te reaction function is explained by te fact tat incentives to attract new patients by raising te ospital input are enanced wen pysicians increase teir 11

13 efforts because te activity-based payment system rewards ospitals wit sort lengts of stay. From wic it follows tat be spl > be spl and bq spl > bq spl tat lead to a iger demand and to a iger profit for bot te pysician and te ospital. Patients satisfaction also benefits from iger levels of pysician s effort and ospital s input. We note te fact tat, te ospital also benefits from tat sequential decision-making game because its profit is iger tan in te fee-for-service payment system since it enjoys bot a iger demand and a reduced lengt of stay. It actually illustrates ow te activity-based payment system introduces a strategic complementarity between decisions made by agents witin te ospital. Tis strategic complementarity between e and q also gives better incentives for te pysician and te manager to act in a sequential decision-making game. Since te indirect impact of te effort on te ospital input is positive under te activity-based payment system, tis prompts pysicians to increase teir efforts (be spl > be s ) in order to decrease patients lengt of stay ( b spl < b s ) and give incentives to managers to increase te ospital input (bq spl > bq s ) compared to te simultaneous game equilibrium (equations (5) and (7)). An additional effort made by te pysician indeed reduces te lengt of stay, improves te per-patient profit made by te ospital and tus its input expenditure. Terefore, an increase in e and q simultaneously increases te per-patient profit and te demand and results in a greater profit for te ospital compared to te simultaneous Nas equilibrium. 6 Tis contrasts wit te fee-for-service case and leads to te following proposition. Proposition 3 Te transition from a fee-for-service payment system to an activity-based payment system gives better incentives to te pysician and te ospital manager to act in a sequential game if te pysician benefits from te first-mover advantage. Wile, under te fee-for-service payment system, te ospital manager may ave lower profits in te sequential game tan in te simultaneous game, bot agents can be better off in tesequentialgameaftertefinancing reform. Te activity-based payment system gives incentives to te pysician and to te ospital manager to better coordinate teir decisions by using tis type of sequential game. 6 Te strategic complementarity between decisions in case of pysician leadersip contrasts wit te strategic substitutability between decisions in case of manager leadersip. Following Hamilton and Slutsky (1990) and Amir (1995), we can assert tat only one player prefers is Stackelberg follower payoff to is simultaneous Nas payoff: te player wose best response function slopes up. See also Vives (1999), capter 7. 12

14 3.3 Te joint decision-making game Under te fee-for-service reimbursement system, te pysician and te ospital manager acting togeter maximize now teir joint profit given by te following expression: MaxΠ j (e, q) =D(e, q) r e e CP(e)+r CH() c q q e,q Te first-order conditions (defining be j and bq j )aretefollowing: i D e r e e CP(e)+r CH() + i D(e, q) r e CP e d de =0 ³ CH CH() 2 (14) D q r e e CP(e)+r CH() c q =0 (15) Compared to te first-order condition defining te simultaneous decision-making game equilibrium (equation (5)), te benefit of an additional effort made by te pysician increases since te extra patients attracted also benefit to te ospitals (r CH() > 0). But tis additional effort also increases te marginal cost of te effort by reducing te lengt of stay (and tus te margin per day since te total cost related to te patient lengt of stay CH() is concave). Te variation in te effort level tus cannot be determined and leads to an indetermination in te cange of te optimal input level (equation (15)) compared to te one in te simultaneous decision-making game (equation (6)). Because of tecooperation,tejointprofit made by pysicians and managers rises compared to te sum of te agents individual profits under te simultaneous decision-making equilibrium. We owever cannot say weter tis profit improvement is acieved troug an increase or adecreaseofe and q and noting can terefore be said about individual profit variations (effort and input are strategic substitutes). Under te activity-based payment system, te pysician and te ospital manager optimize te following program: MaxΠ j RH CH() (e, q) =D(e, q) r e e CP(e)+ c q q e,q First-order conditions defining be j and bq j respectively are given by: i D e r e e CP(e)+ RH CH() + i D(e, q) r e CP e ( RH CH()+CH ) d 2 de =0 (16) D q r e e CP(e)+ RH CH() c q =0 (17) 13

15 Here again te introduction of te activity-based payment system creates a strategic complementarity between decisions made by te agents wo ave terefore more incentives to cooperate tan under te fee-for-service payment system. Te reason is te same (even if te interaction is different) tat under te sequential decision-making game wit pysicians acting as leaders. An additional effort made by te pysician indeed reduces te lengt of stay, improves te per-patient profit made by te ospital and tus increases its input expenditure. Te consideration of te joint profit increases - compared to te simultaneous decision-making game equilibrium - te marginal benefit ofteeffort and of te input (comparisons of equations (5) and (16) and of equations (7) and (17)). Terefore, an increase in e and q simultaneously increases te per-patient profit and te demand. We can tus conclude tat be s < be j and bq s < bq j but also tat be j < be j and bq j < bq j wen comparing equations (14) wit (16) and (15) wit (17). Finally, because e and q are strategic complements, te joint profit under te activity-based payment system is iger tan te joint profit in te fee-for-service-system. Proposition 4 Te transition from a fee-for-service payment system to an activity-based payment system gives better incentives to te pysician and te ospital manager to act in a joint decision-making game. Te strategic complementarity between te decisions made by te agents in an activity-based payment leads to a iger joint profit comparedtote fee-for-service system. 4 Financing systems and public ospitals Tis section analyses te impact of te introduction of an activity-based payment system on te number of acts undertaken daily by pysicians, on te lengt of stay and on te input invested witin public ospitals. Te initial revenue granted to public ospitals was - unlike te revenue granted to private ospitals - a prospective budget independent of bot te number of patients and te lengt of stay (see te budget constraint (4)). Te political will to armonize financing systems across all type of ospitals (for-profit, not-for-profit) terefore implies tat te transition to te activity-based payment system is not similar between private and public ospitals. Te activity-based payment system gives owever an indirect incentive to reduce te patients lengt of stay since te financing depends on te demand D(e, q). We sow tat te impact of an activity-based payment system on te public ospital s equilibrium values of e and q depends on te elasticity of demand wit respect to te input (input elasticity of demand). 14

16 4.1 Te simultaneous decision-making game We first examine ow te transition from a prospective budget system to an activity-based payment system affects te decision variables wen pysicians and managers interact in a simultaneous way witin te public ospital. Here again we suppose tat te financing reform only affects ospitals payment. Te pysician objective is given by te equation (3) tat implies te following first-order condition: D e ED e (e, q) =0 (18) Equation (4) defines te daily budget constraint faced by a public ospital under a prospective budget. Wen te payment is based on te activity, tis constraint becomes: BC D(e, q) CP(e)+ CH() + CQ(q) D(e, q) RH (19) Since we are interested in te agent s beavior modification resulting from payment system canges, te switc from a financing system to te oter is assumed to be financially neutral. Te daily per-patient fee under te new system (RH) istendefinedinte following way: RH = B (20) D(be, bq) were D(be, bq) denotes te equilibrium demand under te prospective financing system. Public ospitals are concerned wit te demand (patients utility) so tat tey spend teir wole budgets. Te expression (19) is tus always satisfied as an equality: D(e, q) RH CH() CP(e) c q q =0 (21) Proposition 5 Te transition from a prospective budget system to an activity-based payment system witin public ospitals increases te input invested, te effort made by pysicians and te demand if te input elasticity of demand is iger tan unity. It does not affect te optimal values of tese variables if te input elasticity of demand is lower tan or equal to unity. We establis te above proposition by evaluating te variation of te budget constraint (21) wit q. δbc RH CH() = D q CP(e) c q (22) δq We know from equation (21) tat RH CH() CP(e) = cqq D(e,q) suc tat (22) can after rearrangements be written: δbc δq = c q D q q D(e, q) 1 = c q εd,q 1 (23) 15

17 Te intuition of Proposition 5 is straigtforward. By raising te input, managers increase bot te revenue and te expense of te ospital. But since te ospital s revenue is related to te demand, its increase is iger tan tat of te cost (wose growt is constant) if te input elasticity of demand is iger tan unity. Managers tus raise q as long as ε D,q > 1. Tis increase in te level of input caused by te implementation of an activity-based payment system reduces te pysician disutility of effort (see (18)) and tus increases is/er equilibrium effort level (and reduces te lengt of stay at te same time). Bot modifications (e and q) lead to an increase in demand. We may tus conclude tat te transition from a prospective budget system to an activity-based payment system benefits to te managers of te ospital, to te pysicians and to te patients if te input elasticity is initially (i.e. before te implementation of te reform) iger tan unity. In te opposite case, te financing system reform does not modify te equilibrium in public ospitals. 4.2 Oter forms of interactions between agents We briefly consider in tis section te sequential interaction and te cooperation between pysicians and managers witin public ospitals and sow wy te impact of te implementation of an activity-based payment system is indeterminate in tese situations. Tese indeterminations are explained by te fact tat we cannot - given te very general assumptions made about te cost functions - determine weter te simultaneous variation of e and leads to a budgetary surplus tat allows te improvement of te ospital input or if it brings a budget deficit tat forces te managers to reduce q. Additional assumptions about te marginal costs of e and sould ten be made to answer tis question. Expression (24) evaluates te variation of te ospital financial constraint wit e under te activity-based payment system (equation (21)). i ³ i dq D RH e CP(e) CH() de = + D(e, q) RH CH +CH() a c 2 e 2 e i (24) D RH q CP(e) CH() c q A pysician trying to influence te manager s input decision cannot determine weter is/er cange in effort (combined wit a cange in te lengt of patient s stay) improves or deteriorates te ospital financial constraint and tus weter managers would ave money left to increase te input or would be forced to cut back on expenses. In te same way, a manager leader in te sequential interaction wit te pysician cannot - for te same reason - determine wic combination of e, and q is preferable to increase te demand wile keeping te budget balanced. Terefore our model does not tell ow a manager could take advantage of is/er first-mover advantage. Furter assumptions 16

18 would be required to solve tis problem but we prefer to remain witin te limits of te model at tis stage. Te same reasoning olds wen we deal wit te joint decision-making game. A manager and a pysician - wen acting togeter - cannot define te best policy (in terms of e, and q) to maximize teir joint profits witout furter assumptions on costs functions. 5 Conclusion Te comparison of retrospective versus prospective payment systems in te ospital sector as been a major concern of ealt economics literature during te last decade. But now, since most OECD countries ave opted for an activity-based financing system, te question is no longer to discuss te economic superiority of one system over anoter but instead to investigate ow will te economic agents witin te ospital sector respond to te financial reform in place. Our paper gives some insigts on te expected impact involved by te introduction of an activity-based system in te private and public ospital sectors. For te former, te benefit of a transition from a fee-for-service system to an activity-based system relies on te type of interaction between managers and pysicians. Under a simultaneous interaction, te status quo prevails wile more coordination under a sequential or a cooperative interaction could be beneficial for bot agents in te private sector. In tat case, te patients satisfaction is also enanced by an increase in te pysician s effort and a iger level of ospital s input. In te public sector, te initial financing system is different and te transition goes from a prospective budget system to te activity-based system. Here, te key parameter is te input elasticity of demand and bot te pysician and te manager will be better off after te reform if te patient s demand reacts sufficiently to an increase in te ospital s services. Te latter case also induces an increased patients satisfaction. We are aware tat our model as some limitations and we now discuss some possible extensions. First, our conclusions are drawn wen ospitals are considered in isolation. Te demand for private and public ospitals is terefore not constrained and iger levels of efforts or inputs necessarily increase te demand for bot ospitals. It could be interesting to analyze weter tese results are still robust once competition is introduced and wen te demand faced by ospitals is exogenously given. Some of our conclusions migt indeed be altered once competition is introduced in te model. As suc an example, assume tat, previous to te financing reform, te input elasticity of te demand is greater tan unity for te public ospital wile in te private sector te pysician and te manager interact in a simultaneous way and ave terefore no incentives to react to te introduction of te prospective payment system. Te expected results from our model are 17

19 a iger level of te public ospital s input and a iger level of te public pysician s effort tat lead to a iger demand and patients utility in te public sector wile a status quo prevails in te private sector. But if an exogenous given demand is now considered in a competition framework, te increase in te public ospital demand will result in a decrease in te private ospital demand. Our model sows tat te private agents react to tis variation. A simple examination of te private pysician s first order condition (5) indeed sows tat te marginal cost of te effort made by te pysician depends on te overall demand and ence tat te pysician sould increase er/is level of effort if te demand falls sort. Tis in turn triggers an increase in te private ospital input since te effort increase reduces te patients lengt of stay and gives - under an activitybased payment system - incentives to managers to raise te input level. Terefore, wen competition is considered, te private agents necessarily react to any variation in teir demand and at te new equilibrium, we cannot exclude tat te private sector could gain market sares even if te public ospital was initially te only beneficiary of te financing reform. Wile we ave examined some of tese competition s issues, our very general model - were no functional form are specified for te demand, te disutility and te cost functions - precludes to compute definite equilibria in an oligopoly setting. Competition s effects could be introduced in a simplified framework. Second, we initially consider a representative disease for omogenous patients. Tis latter assumption could be relaxed in order to analyze ospital s and pysician s reactions wen tey face different types of patients wo differ in severity of illness. Tis extension could allow for analyzing strategic beavior suc as creaming over-provision of services to low severity patients; skimping under-provision of services to ig severity patients; and dumping te explicit avoidance of ig severity patients as described in Ellis (1998). Tird, different types of patologies wit specific level of costs and reimbursement rates could be considered to analyze te impact of an activity-based financing system on te mix of ospital s activities. Again, tese two extensions must clearly take place in an oligopoly framework as discussed above in order to take into account te competition among ospitals for low severity patients or low cost patients. Anoter possible extension is to consider a prospective payment system for te pysician in te private sector. Wile we keep a fee-for-service basis in our model, it seems likely tat pysicians could be prospectively paid in te near future if countries cannot curb te growt in ealt care costs. Te increase in total ealt care costs can be induced from our results since we sow tat te activity-based payment system tends to increase te level of pysicians efforts and ospitals services wile te demand reacts positively to all of tese arguments. Tis finally leads to te possibility of introducing te regulator 18

20 into our model via a global budget cap on ealt expenditures. However, as sown in Mougeot and Naegelen (2004) or van de Ven (1995), incentives given by a prospective payment system may be partly destroy by a global budget constraint. Tis lets room for future researc. Acknowledgments Tis researc started wen Ana Mauleon was at LABORES (URA 362 CNRS). We would like to tank Paul Belleflamme for epful comments and discussions. David Crainic as benefited from te financial support of Merck Santé France. Financial support from l Union Régionale des Médecins Libéraux du Languedoc Rousillon, support from Spanis Ministerio de Ciencia y Tecnologia under te project BEC , and support of a SSTC grant from te Belgian Federal government under te IAP contract 5/26 (FUSL) are gratefully acknowledged. Tis paper presents researc results of te Belgian Program on Interuniversity Poles of Attraction initiated by te Belgian State, Prime Minister s Office, Science Policy Programming. References [1] Amir, R., 1995, Endogenous timing in two-player games: a counterexample, Games and Economic Beavior 9, [2] Calkley M. and Malcomson J.M., 1998, Contracting for ealt services wit unmonitored quality, Economic Journal, 108, [3] Coudeville L., Mauleon A. and Dervaux B., 2004, Prospective payment system : consequences for ospital-pysician interactions in te private sector, Discussion Paper , Institut de Recerces Economiques et Sociales, Université Catolique de Louvain, Louvain-la-Neuve. [4] Custer W.S., Moser J.W., Musaccio R.A and Willke R.J., 1990, Te production of ealt care services and canging ospital reimbursement - Te role of ospitalmedical staff relationsips, Journal of Healt Economics, 9, [5] Dor A. and Watson H., 1995, Te ospital-pysician interaction in U.S. ospitals : evolving payment scemes and teir incentives, European Economic Review, 39-3/4,

21 [6] Ellis, R.P., 1998, Creaming, skimping, and dumping: provider competition on te intensive and extensive margins, Journal of Healt Economics 17, [7] Hamilton, J. and Slutsky, S., 1990, Endogenous timing in duopoly games: Stackelberg or Cournot equilibria, Games and Economic Beavior 2, [8] Ma C.A., 1994, Healt care payment systems: cost and quality incentives, Journal of Economics and Management Strategy, 3-1, [9] Mougeot M. and Naegelen F., 2004, Hospital price regulation and expenditure cap policy, Journal of Healt Economics, 24, [10] Newouse J.P., 1996, Reimbursing ealt plans and ealt providers : selection versus efficiency in production, Journal of Economic Literature, 34, [11] Pope G.C., 1990, Using ospital-specific costs to improve te fairness of prospective reimbursement. Journal of Healt Economics, 9, [12] van de Ven, W.P.M.M., 1995, Regulated competition in ealt care: wit or witout a global budget? European Economic Review 39, [13] Vives, X., 1999, Oligopoly pricing: old ideas and new tools, Te MIT Press, Cambridge, Massacusetts. 20