Incentives for cooperation in quality improvement among hospitals—the impact of the reimbursement system

Journal of Health Economics 17 Ž1998. 701–728

Incentives for cooperation in quality improvement among hospitals—the impact of the reimbursement system K. Kesteloot a

a,)

, N. Voet

b

Center for Health SerÕices and Nursing Research and Department of Applied Economics, K.U. LeuÕen, Belgium b Department of Economics, K.U. LeuÕen, campus Kortrijk, Belgium Received 30 November 1995; revised 10 June 1997; accepted 18 December 1997

Abstract Up to now, few analytical models have studied the incentives for cooperation in quality improvements among hospitals. Only those dealing with reimbursement systems have shown that, from the point of view of individual or competing hospitals, retrospective reimbursement is more likely to encourage quality improvements than prospective financing, while the reverse holds for efficiency improvements. This paper studies the incentives to improve the quality of hospital care, in an analytical model, taking into account the possibility of cooperative agreements, price besides non-price Žquality. competition and quality improvements that may simultaneously increase demand, increase or reduce costs and spill over to rival hospitals. In this setting quality improvement efforts rise with the rate of prospective reimbursement, while the impact of the rate of retrospective reimbursement is ambiguous, but likely to be negative for quality improvements that are highly cost-reducing and create large spillovers. Cooperation may lead to more or less quality improvement than non-cooperative conduct, depending on the magnitude of spillovers and the degree of product market competition, relative to the net effect of quality on profits and the share of costs that is reimbursed retrospectively. Finally, the stability of cooperative agreements,

)

Corresponding author. Kapucijnenvoer 35, 3000 Leuven, Belgium. Tel.: q32-16-336975; fax: q32-16-336970; e-mail: [email protected]. 0167-6296r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 6 2 9 6 Ž 9 8 . 0 0 0 2 6 - 5

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supported by grim trigger strategies, is shown to depend upon exactly the opposite interaction between these factors. q 1998 Elsevier Science B.V. All rights reserved. JEL classification: 950; 610 Keywords: Retrospective; Prospective reimbursement; Quality of care

1. Introduction Hospitals are under growing pressure to monitor and improve the quality of their services and one mechanism that is used and encouraged by policymakers to realise such quality improvements, is cooperation with rival hospitals. In US, as well as in many European countries, hospitals engage in strategic partnering activities, e.g., through mergers, take-overs, joint ventures, strategic alliances, for many reasons, including quality enhancement. The availability of sophisticated medical equipment, information systems etc. have provided ample opportunity to improve the quality of care. It is further well known that hospitals may use the quality of their services Žmuch more than price. as a competitive weapon to attract customers Žpatients., in a sector where most customers are highly insured. This article investigates the incentives for quality improvement in hospitals, both when hospitals apply quality improvement as a weapon in their competitive struggle with rivals, as well as when they cooperate with rivals in this field. Both scenarios are compared and how quality improvement initiatives are influenced by several factors, such as the reimbursement system, the impact of quality improvement on hospital demand and costs and the degree of product differentiation, is analysed. Also the stability of such cooperative ventures is investigated. Most analytical models that have studied incentives to engage in quality improvement focused on the impact of the reimbursement system. The main findings were that retrospective reimbursement will typically encourage high quality but will not stimulate hospitals to manage their resources efficiently, while the reverse holds for prospective reimbursement Že.g., Lee et al., 1983; Nyman, 1985; Nyman, 1988a,b; Holahan and Cohen, 1987; Gertler, 1989 and Cohen and Dubay, 1990.. Schleifer Ž1985. shows that hospitals will invest an efficient amount of effort under prospective reimbursement because they keep the full reward from doing so. Newhouse Ž1996. argues that under more general assumptions Žheterogeneous patients, imperfect agency, uncertainty about the hospital cost function. prospective reimbursement will not be optimal. Under many circumstances a superior outcome can thus be achieved by introducing mixed reimbursement systems. 1 Some of these models have analysed this problem from the point of view of a single hospital Že.g., Ellis and McGuire, 1

One exception is Ma Ž1994., where it is shown that a Žconstrained. optimal quality level can also be reached by setting an appropriate prospective reimbursement level.

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1986; Barnett et al., 1993; Hodgkin and McGuire, 1994; Ma, 1994; Chalkley and Malcomson, 1995., thereby eliminating the potential impact of intra-industry rivalry on the quality of care, as well as on the incentives to reduce costs, in order to gain market share from rivals. 2 Others have included non-price competition, e.g., in quality, in location or an increase in the number of hospitals. Joskow Ž1983. and Wilson and Jadlow Ž1982. dealt with retrospective reimbursement and Pope Ž1989. and Massart Ž1994. compared retro- with prospective reimbursement. In the empirical literature, however, prospective reimbursement is often shown not to have the expected negative effect on quality Že.g., DesHarnais et al., 1987, 1988; Lave et al., 1988; Frank and Lave, 1989; Kahn et al., 1990a,b; Rogers et al., 1990; Rubenstein et al., 1990; Cutler, 1995; Cohen and Spector, 1996.. Despite the fact that hospitals are nowadays engaging more frequently in cooperative ventures, none of the previous papers has considered the possibility of cooperative conduct among hospitals; they all assumed non-cooperative conduct, with zero conjectural variations. Therefore, our model will compare both non-cooperative and cooperative outcomes. Since explicit cooperation may be prohibited by antitrust legislation, implicit cooperation is also envisaged. Furthermore, our model incorporates not only quality competition, but also price competition, although it must be recognised that the price sensitivity of patients is limited due to high insurance coverage; but still price competition is not absent in practice, although sometimes restricted to the amenity services, providing only added patient comfort. While most of the other papers assume that hospitals’ services are Žim.perfect substitutes—due to, e.g., locational factors Žcf. Pope, 1989; Massart, 1994., our model also allows for hospital services that are complements Že.g., a local vs. a tertiary care hospital.. Moreover, in many of these papers, it is assumed that hospitals have to trade-off quality against efficiency improvements: hospitals either engage in quality improvement Žwhich is often cost-increasing., or in cost reductions Žwhich are often assumed to deteriorate quality.. ‘Quality of care’ is thus often defined as ‘intensity of care’. As a consequence, additional tests, longer hospital stays, etc. are always seen as quality improvements, which are automatically cost augmenting. We argue that delivering ‘more’ services may not always be ‘better’ for patients and therefore hospitals can think of quality improvements which are in fact cost reducing. Our model is richer in the sense that quality enhancement efforts are modelled as having several potential effects Žalthough some of them may be zero.. Quality improvements may first of all increase the demand for the hospital’s services. Simultaneously, these quality improvements may increase patient treatment costs Žlike in many of the previous papers., but they may also decrease costs; e.g., an improved scheduling of

2

This omission should not be regarded as a ‘shortcoming’ in these models. Since their focus was on the trade-off between quality and efficiency improvements, they had to simplify in other respects.

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diagnostic testing and OT-procedures may increase demand since patients are more satisfied Žless waiting times, shorter length of stay. and may also reduce treatment costs Že.g., less wasted staff time.. Wyszewianski et al. Ž1987. also argue that quality improvements may be obtained if efficiency gains are made by eliminating unnecessary services. Moreover, the possibility that results of quality improvements spill over to rival hospitals is incorporated, an aspect that has not yet received attention; e.g., rival hospitals may adopt knowledge about, e.g., the organisation of laboratories, the hospital lay out, by simple site visits; the results from market studies to identify the best outsourcing partners in, e.g., catering, laundry, maintenance, etc., may quickly spill over to other hospitals. Finally, a distinction is made between the implementation of the quality improvements, thereby resulting in the above demand increase and cost changes, and the development of the quality improvement programs Že.g., developing software for OT-planning, retraining staff., which only implies costs for the hospital. The paper is organised as follows. Section 2 describes the analytical framework. Consequently, the incentives for quality improvement are described and compared, both under non-cooperative and cooperative conduct. Section 5 discusses the stability of cooperative agreements and Section 6 concludes.

2. The analytical framework Obviously, no single analytical model is able to capture the full complexity of hospital operations, determined by, e.g., the wide presence of health insurance, the large degree of uncertainty with respect to optimal diagnostics and treatments, the dual hierarchy, with medical doctors bearing—only—medical responsibility and hospital managers’ financial responsibility, while both are strongly intertwined and the dominance of not-for-profit institutions. Hence, depending on the specific research questions, simplifying assumptions will be required. In order to address the question of incentives for quality improvement, an oligopolistic market with both price and quality competition, and whereby hospitals can be reimbursed in different ways, is envisaged. Quality improvements are modelled as having several potential effects, on the own hospital’s performance Ži.e., demand as well as costs. as well as on the rival’s Ži.e., spillovers.. In order to keep the model tractable, simplifying assumptions are used in other respects: a duopolistic market with symmetric, single product hospitals is considered and also problems due to asymmetric information are ignored. 2.1. Demand The market consists of two symmetric hospitals producing differentiated services with constant marginal production costs c i .

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Demand for each hospital i’s services is described as follows: pi s a y bqi y dq j q a x i with i / j s 1,2; b ) 0,b G < d < ,0 - a - 1 with pi s the hospital price, charged directly to the patient Žout-of-pocket payments.; qi s the quantity of hospital output, measured as the number of cases; x i s the quality efforts undertaken by the hospital. The parameters b and d reflect the inverse of price sensitivity of the patients. This price sensitivity will typically be quite low in health care, because of the substantial degree of health insurance. The parameter d may be positive Žor negative. depending on whether both hospitals market substitute Žor complementary. products. It is assumed that both hospitals supply only one type of service, but their services are perceived as Žim.perfect substitutes Ž d ) 0, d F b . or complements Ž d - 0. by patients. Hence, it is implicitly assumed that each hospital produces a homogeneous product. This is obviously a major simplification, typical of a large part of the analytical literature ŽNewhouse, 1970.. 3 The output is thus defined as the number of cases, regardless of all pathological aspects and all differences in case-mix. Since problems of asymmetric information are ignored, this demand can equally be considered as coming from the patients themselves as well as from the providers, acting as their agents. In a sector where price competition is not very strong, hospitals may have a strong incentive to engage in non-price, e.g., quality, competition. Hospitals can for instance increase demand for their products Ž a ) 0. through quality improvements of different kinds. In this paper ‘quality’ is given a broad meaning, covering care items that are crucial for patient outcomes Že.g., technical skills of surgeons., often referred to as the ‘technical’ quality, as well as care items that only improve on ‘patient comfort’ Že.g., size of the rooms, quality of the meals, availability of TV-sets, fax machines.. All factors that may affect a hospital’s reputation are in fact included in the definition of quality. Although these different items may have a different potential impact on patient outcomes, they are all included, because they are all expected to affect demand for hospital services. The introduction of high-tech equipment and hiring high-qualified medical staff are examples of inputs that may be crucial for delivering appropriate Žtechnical. care to certain patient groups, but they may also simply be perceived as signals of high quality by patients or their representatives and hence increase demand. Other examples of the ‘technical’ quality of care include, e.g., the degree of professionalism and skills of all health care workers, the sterility of materials, the timely and correct delivery of drugs, timely and accurate diagnosing in laboratories, etc. Patient comfort and satisfaction can be related to factors as waiting times before a nurse arrives after being called to the patient room, comfort of the room, information availability, etc. 3

Also for commercial firms, the analytical models often focus on single product firms, whereas most firms in practice are multiproduct firms.

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Obviously, in all this, hospitals have a strong incentive to improve the quality of those care items that can easily be monitored by patients or their representatives. But it should be recognised that those items need not have a crucial impact on the final patient outcome. They need not have such a strong incentive to improve other quality items such as, e.g., the technical skills of the physicians, the prevalence of nosocomial infections, the degree of sterility of OT environment, since these are much more difficult to observe and verify for patients and hence cannot be used so easily as competitive weapons ŽWeisbrod, 1988.. In order not to complicate the analysis too much, this distinction between easy- and difficult-tomonitor quality aspects is ignored. It is simply assumed that all quality improvements can be observed and verified by patients. Hospitals may further employ similar quality items to attract physician staff, and hence, indirectly, more patients. Hence, the size of a reflects to what extent patients, or their representatives, e.g., referring physicians, are sensitive to quality improvements, as perceived by the patients or their representatives. 4 2.2. Cost conditions Complementary to the fixed costs, F, 5 each hospital’s variable production cost structure can be characterised as follows: ci s A q V x i

with A - a; < V < - 1

If no innovative investments are undertaken, unit production cost are c i s A. Hospitals thus produce with a constant returns to scale technology Že.g., Pope, 1989; Hodgkin and McGuire, 1994; Ma, 1994.. Investments in quality improvement may increase or lower production costs, which is captured by the term V , which can be positive or negative. For instance, a better planning of admissions for elective surgery may not only improve quality Žpatient comfort., but may further reduce production costs, e.g., through better use of available capacity, a reduction in length of stay. Sometimes, quality improvement may generate higher production costs. The use of CT-scanner and MRI in imaging complementary to RX instead of replacing RX, may be quality enhancing Žbetter imaging resulting in improved diagnostics and therapeutic outcomes., but also cost increasing. The parameter V models this net production cost implication, a net effect which may be due to cost reductions in one area but cost increase in others. For instance, an additional staff member may be hired Žcost increase. in order to manage the 4

A low a could also prevail when quality improvements are not perfectly observable or verifiable. In the hospital sector fixed costs are not very important. The major share of costs consists of labour and material costs, which can all be considered as variable costs. Therefore, fixed costs can more or less be ignored in an analytical set up Žcf. Pope Ž1989... It should be kept in mind, however, that for some specialised medical hospital services, the fixed costs may be quite large, relative to the variable costs. For these specific services, our results need not apply. 5

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supply of medical materials more efficiently Žcost reduction.. Obviously, cost increasing quality improvements would only be implemented by rational hospital managers if their net effect on the hospital objective function is positive. Therefore, it is assumed that a y V ) 0 for the implemented quality improvements. Quality efforts may further entail positive or negative spillovers on rival costs or demand: 6 pi y c i s a y bqi y dq j q a x i y A y V x i q b x j

with i / j s 1,2; < b < - 1

This effect is captured through the spillover parameter b , which is assumed exogenous, it cannot be influenced by hospitals. Positive spillovers occur when rival quality efforts reduce a hospital’s cost or increase demand. This could for instance be the case when the rival makes a costrbenefit analysis of all local catering companies and picks out the most efficient one. This kind of information can easily spill over to other hospitals and thereby lower their costs too or increase demand for their services—quality is then said to have a market expansion effect ŽShaked and Sutton, 1990.. A negative spillover could be explained by rival quality efforts that reduce a hospital’s demand, e.g., hospital A purchasing a CT-scanner, may induce some of hospital B’s patients to opt for hospital A—in this case a market competition effect prevails ŽShaked and Sutton, 1990.. Finally, each hospital will have to invest resources in order to develop and implement these quality improvements Ži.e., development costs.. The quality improving efforts are modelled as involving diminishing returns, specified as increasing marginal costs of providing higher quality. The higher the quality level a hospital has already reached, the more difficult it becomes to still improve on quality. Total costs of quality improvement are tx i2r2, whereby t is positive and inversely related to the efficiency of the innovation process. 7 2.3. Reimbursement systems An important part of hospital returns does not come from patient out-of-pocket payments, but from health insurance companies, which may reimburse hospitals either retrospectively or prospectively or through a mixture of both financing mechanisms. In case of retrospective reimbursement Žg i . hospitals are reimbursed their actual costs. The reimbursed amount per case Žg i c i . may be identical to the 6

Given the linearity of the demand and production costs specifications, this formulation shows that quality improvements can both be considered as demand increasing or cost reducing. These two effects could be captured in one parameter, but here two different parameters, a and V , are used, in order to separate both effects and to allow also for cost-augmenting innovations. It should be recognised however that this formalisation implies a specific form of demand augmenting quality efforts Ži.e., parallel shifts.. Hence, this scenario cannot capture all aspects of demand augmenting quality effects. 7 Hence, for simplicity, the variable x reflects the input as well as the output of the quality development process.

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variable hospital production cost Ž c i . hence g i s 1, or these costs minus out-ofpocket payment Ž c i y pi .. Under prospective financing the reimbursement is not based on the actual costs. For instance in a DRG-financing system, hospitals are reimbursed a fixed amount of money per case Ž s .. All of these possible financing systems are included in the analytical model Že.g., a pure cost-based system is specified as g i s 1, s s 0, a DRG case payment system is captured by s ) 0, g i s 0, a mixed financing system implies s,g i ) 0., so that the impact of the financing system on the opportunities for quality cooperation and competition can be investigated. 8 2.4. Hospital objectiÕe functions Finally, the hospitals’ objective function still needs to be specified. As long as retrospective reimbursement systems are dominating the scene, it is not very common, nor very interesting to model hospitals as profit maximising institutions Žsince all costs are reimbursed, profits are zero anyway. Že.g., Feldstein, 1968, 1971; Newhouse, 1970; Davis, 1971; Pauly and Redisch, 1973; Harris, 1977, 1979; James and Rose-Ackerman, 1986.. With the introduction of prospective reimbursement, it has become more common to assume that hospitals aim at maximising profits Že.g., Danzon, 1982; Pauly, 1987; Pope, 1989; Custer et al., 1990; Gal Or, 1994; Ma, 1994., but it is still recognised that other goals may be pursued, since hospitals may have a not-for-profit status and because of the autonomy of the medical doctors Že.g., therapeutic freedom., who may pursue their own goals. This can be done by modelling the hospital objective as a utility function with profits and quality of services or patient benefits, often quantified as the intensity of services, as arguments; sometimes also size is included as a separate argument Že.g., Ellis and McGuire, 1986, 1990, 1993; Glazer and McGuire, 1994; Hodgkin and McGuire, 1994; Massart, 1994; Rogerson, 1994; Chalkley and Malcomson, 1995.. Some authors model the medical and managerial power structure separately Že.g., Custer et al., 1990; McClellan, 1994.. In order to incorporate these considerations as much as possible, in the basic scenario it is assumed that hospitals aim at maximising profits. Under the assumptions outlined above, each hospital’s total profits can be described as: 9 Vi s a y Ž 1 y g i . A q s y bqi y dq j q a x i q Ž 1 y g i . b x j y Ž 1 y g i . V x i qi y tx i2r2 y F Subsequently, the additional goals are taken into account by assuming that hospitals maximise a utility function, which is a weighted average of profits, size 8

Note that the previously imposed condition a y V ) 0 becomes less severe when part of the costs are reimbursed retrospectively, i.e., a yŽ1yg . V ) 0. 9 In specifying this objective function, it was assumed that quality spillovers affect rivals’ costs rather than demand. Hence, the objective function includes Ž1yg . b x rather than b x.

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Žquantity of services. and quality. This approach integrates the goals of the hospital managers Žprofits and probably size. and the medical doctors Žquality and probably size.. While the medical and managerial decision making structures are not modelled separately, the utility function can be interpreted as the outcome of a bargaining process between the different agents whereby the weights of the different objectives can be seen as a reflection of the power structure within the hospital Žcf. Glazer and McGuire, 1994.. This approach allows to show how a strong medical line of authority vs. managerial authority will affect hospital performance, by varying the weights of the different objectives. The hospital’s utility function can hence be described as: Ui s z 1 x i q z 2 qi q Ž 1 y z 1 y z 2 . Vi where z 1 s relative weight given to quality; x i s level of quality efforts; z 2 s relative weight given to size; qi s quantity of hospital output Žnumber of cases, hospital size.; z 3 s 1 y z 1 y z 2 s relative weight given to profits; Vi s profits.

3. Equilibria Two scenarios will be analysed. First, it is assumed that hospitals compete in quality and output. In this scenario, the equilibrium quality, output and profits level are determined and it is investigated how the quality efforts are affected by several exogenous shocks, such as the reimbursement mechanism, the quality sensitivity of patients, the cost impact of quality enhancement, etc. Also, the impact of the objective function is highlighted by comparing quality efforts in case of pure profit maximisation with quality efforts under utility maximisation. Secondly, the equilibrium under cooperative conduct is investigated. By comparing both scenarios, it can be investigated how cooperation, relative to independent conduct, affects hospitals’ incentives for quality improvement, under different reimbursement conditions and for several hospital objective functions. Since both hospitals are assumed to be symmetric, firm-specific subscripts can be omitted. 3.1. Non-cooperatiÕe equilibrium In a Nash equilibrium, firms independently and simultaneously choose their optimal quality effort and output level in order to maximise utility. The first order conditions for this equilibrium are: z1 q Ž 1 y z1 y z 2 .

Ž a y Ž 1 y g i . V . qi y tx i

s0

i s 1,2

z 2 q Ž 1 y z 1 y z z . a y Ž 1 y g i . A q s y 2 bqi y dq j q x i Ž a y Ž 1 y g i . V . qx j Ž 1 y g i . b s 0

i/j

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Fig. 1.

which yield the following equilibrium quality effort and output levels:

10

x n s ag z 2 q z 3 Ž Ag q s . q z 1 Ž 2 b q d . rag rz 3 t Ž 2 b q d . y ag bg

Ž 1a . qn s t z 2 q z 3 Ž Ag q s . q z 1 bgrt rz 3 t Ž 2 b q d . y ag bg

Ž 1b .

with ag s a y Ž1 y g i . V ; bg s a q Ž1 y g i .Ž b y V .; Ag s a y Ž1 y g i . A. The characteristics of this equilibrium can be further explored by rearranging the first order conditions for a profit maximising hospital, as

Ž a y Ž 1 y g i . V . qi s tx i

Ž 2a .

a q s y 2 bqi y dq j q a x i s Ž 1 y g i . Ž A q V x j y b x j .

Ž 2b .

Eq. Ž2a. expresses the optimal quality improvement efforts in terms of the optimal quantity Ž qi s qi )., which is illustrated in Fig. 1. Eq. Ž2b. expresses the optimal output level in terms of the optimal quality improvement efforts Ž x i s x i )., which is illustrated in Fig. 2. Higher Žpositive. spillovers Ž b . tend to decrease the marginal cost of producing one unit of output and therefore increase the optimal output level Ž q ). in Fig. 2. In Fig. 1, this higher optimal output will increase the return on a unit of quality, defined as w a y Ž1 y g i . V x qi ). Therefore, a profit maximising hospital will increase its quality efforts until the Žhigher. marginal return on quality equals the marginal cost of these quality efforts Ž tx i .. This effect is moreover reinforced by the fact that quality is a positive function of quantity Žfollowing from Fig. 2.. 10

Second order conditions are t Ž2 bq d .yŽ a yŽ1yg i . V .w a yŽ1yg i . V q b Ž1yg i .x ) 0, 2 t Ž bq d .yw a yŽ1yg i . V q b Ž1yg i .x 2 ) 0 and 2 bt yw a yŽ1yg i . V x 2 ) 0.

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Fig. 2.

3.2. CooperatiÕe equilibrium By coordinating quality improvement efforts, output market cooperation may be facilitated. Therefore, it is assumed that in the cooperative arrangement, hospitals cooperate both in quality and output simultaneously. In this situation, firms choose their quality and output levels simultaneously, in order to maximise their joint utility. The corresponding first order conditions are: z1 q Ž 1 y z1 y z 2 .

Ž a y Ž 1 y g i . V . qi

qq j Ž 1 y g i . b y tx i s 0

i s 1,2

z 2 q Ž 1 y z 1 y z z . a y Ž 1 y g i . A q s y 2 bqi y 2 dq j qx i Ž a y Ž 1 y g i . V . q x i Ž 1 y g i . b s 0

i/j

which yield the following optimal quality and output levels ŽSee footnote

10 .

:

x c s bg z 2 q z 3 Ž Ag q s . q 2 z 1 Ž b q d . rbg rz 3 2 t Ž b q d . y bg2

Ž 3a .

qc s t z 2 q z 3 Ž Ag q s . q z 1 bgrt rz 3 2 t Ž b q d . y bg2

Ž 3b .

Table 1 summarises the equilibrium quality and output levels for both scenarios. However, hospitals, like other organisations, may not always be allowed to engage in cooperative conduct, e.g., because of antitrust legislation. Moreover, they may have an incentive to deviate from the cooperative outcome in order to improve their own position, to the detriment of the rival. Partners can try to avoid such deviations by specifying punishment strategies, to be executed should cheating occur. All of these ideas can be captured by implicit cooperation strategies, such as grim trigger strategies ŽFriedman, 1971.. In this setting, where

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Table 1 Quality-improving initiatives Ž x . and number of cases treated Ž q . Nash Žn.

Cooperation Žc.

ag z 2 q z 3 Ž Ag q s . q z1 Ž 2 bq d . r ag

x

z 3 w t Ž 2 bq d . y ag bg x t z 2 q z 3 Ž Ag q s . q z1 bg r t

q

z 3 w t Ž 2 bq d . y ag bg x

bg z 2 q z 3 Ž Ag q s . q2 z1 Ž bq d . r bg z 3 2 t Ž bq d . y bg2 t z 2 q z 3 Ž Ag q s . q z1 bg r t z 3 2 t Ž bq d . y bg2

hospitals are assumed to play this quality and output game for an infinite number of periods, 11 strategies are specified as follows. The game consists of two phases: a cooperative phase and a punishment phase. Both hospitals start in the cooperative phase Žcf. supra.. If one hospital deviates from the cooperative outcome, both hospitals revert to the punishment phase, being the non-cooperative Nash equilibrium, from the next period on and eternally. If this punishment is severe enough, it will prevent hospitals from defecting in the first place, resulting in a stable cooperative outcome. If they stick to the cooperative equilibrium, hospitals reach the cooperative utility level ŽUc . eternally. The net present value of this flow is UcrŽ1 y m . where m is the discount factor Ž m s 1rŽ1 q r . where r is the interest rate.. Given that its rival is loyal, a firm may improve on its own position by deviating from this cooperative outcome, thereby realising utility level Ud Žwith Ud G Uc .. After defection has been detected, both parties revert to the Nash equilibrium eternally and realise utility level Un Žwith Un F Uc .. Given that detection and consequent punishment take one period to unfold, the net present value of the flow of utility with cheating and punishment following is Ud q mUnrŽ1 y m .. Cooperation will be stable if the present value of cooperative utility is higher than the utility from deviation and consequent punishment: Ucr Ž 1 y m . G Ud q mUnr Ž 1 y m . or put differently Žwith m s 1rŽ1 q r ..: r F r ) s Ž Uc y Un . r Ž Ud y Uc . In this last notation, it becomes clear that, the larger the gains from deviation ŽUd y Uc . are, the smaller will be r ) and hence the more difficult it will be to maintain cooperation. Inversely, the higher the gains from cooperation as expressed by ŽUc y Un ., the more stable cooperation will be. In order to characterise these strategies and the corresponding maximal interest rate in this scenario, the cheating outcome must still be determined. If its rival is 11

The same equilibrium concept and interpretation applies if the game is played for a finite number of periods with unknown end date.

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loyal a hospital may improve its position by deviating from the cooperative agreement: maxUi s z 1 x i q z 2 qi q Ž 1 y z 1 y z 2 . Vi qi , x i

s.t. q j s qc ; x j s x c

for which the first order conditions are: z1 q Ž 1 y z1 y z 2 .

Ž a y Ž 1 y g i . V . qi y tx i

s0

i s 1, 2

z 2 q Ž 1 y z 1 y z z . a y Ž 1 y g i . A q s y 2 bqi y dqc q x i Ž a y Ž 1 y g i . V . qx c Ž 1 y g i . b s 0

i/j

Hospitals will stick to the cooperative agreement if the interest rate is lower than: r ) s Ž 2 bt y ag2 .Ž 2 t Ž b q d . y bg2 . r t Ž 2 b q d . y ag bg

2

Ž 4.

being the maximal interest rate for which cooperation is stable Ži.e., no incentive to deviate..

4. Quality improvement efforts First of all, it will be analysed how hospitals’ quality enhancement efforts are affected by the different parameters in the model. This will be done for both the non-cooperative and cooperative equilibrium simultaneously, since the sign of the comparative static effects is often similar in both scenarios. This will first be done, assuming hospitals are profit maximisers Ž z 1 s z 2 s 0. and subsequently, the impact of the additional objectives, size and quality, will be described. Finally, the cooperative and non-cooperative scenarios are compared. 4.1. Profit-maximising hospitals First, the case of profit maximising hospitals is analysed. The superscript Õ will be used to denote equilibrium levels that hold in the case of profit maximisation. Obviously, E x nÕrE a G 0 and E x nÕrE V F 0. Quality enhancement efforts of competing hospitals will be larger, as quality improvement leads to larger demand increases and to larger cost reductions. Moreover, non-cooperative quality improvement initiatives will only be undertaken Ž x nÕ ) 0. if a y Ž1 y g . V ) 0. Since, g F 1, a sufficient Žbut not necessary, as long as g ) 0. condition is

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a y V ) 0. Contrary to the non-cooperative case, even if quality has no net direct effect on profits Ž a y V s 0., cooperating profit maximising hospitals would invest in quality improvement, as long as spillovers are positive. In the cooperative setting, no quality efforts will be undertaken if quality has no net internalised effect on profits Ž a q Ž b y V .Ž1 y g . s 0.. The non-cooperative quality level increases with spillovers ŽE x nÕrEb G 0.. This is the result of a direct effect and an indirect effect. The direct effect of higher spillovers is to stimulate hospital quality efforts because of higher returns on quality, and this effect is partially offset by an indirect effect of hospitals anticipating leakage of their quality improvements on the rival, thereby benefiting the rival Žlower costs. and hence indirectly hurting its own position. Cooperative innovations ŽE x crEb G 0. likewise increase with b simply because higher spillovers, which are fully internalised in a cooperative setting, imply higher returns on quality. This result is analogous to the well-established effect of spillovers on Žnon-. cooperative R & D-efforts in commercial firms Žsee Kesteloot and Veugelers, 1995 and the references cited therein.. Finally, the impact of the reimbursement system can be analysed. If health care financing authorities augment the prospective capitation reimbursement levels Ž s ., hospital quality will be enhanced: E x nÕrE s s agr t Ž 2 b q d . y ag bg ) 0

Ž 5a .

E x cÕrE s s bgr 2 t Ž b q d . y bg2 ) 0

Ž 5b .

In Fig. 2, a higher prospective reimbursement level Ž s . raises the profit maximising output and hence increases quality efforts. This is contrary to the suggestion that patients are discharged ‘quicker and sicker’ under a prospective system of DRG-case payments. In our model, the net marginal return on quality is assumed to be strictly positive Ž a y Ž1 y g . V ) 0.. If this marginal return should become negative Že.g., because a is zero and quality is only cost increasing., no quality efforts would be made in our model. Apparently, the reputational aspect of quality ensures higher quality improvements in this setting. Obviously, these results could be different if higher quality fails to attract additional patients Že.g., because the quality aspects are difficult to observe.. The positive effect of prospective reimbursement on quality is higher, in the cooperative as well as in the non-cooperative scenario, the larger the demand-augmenting and cost-reducing effect of quality Ž a y V larger. and the larger the rate of spillovers Ž b .. In response to augmenting financial support for medical care, hospitals will thus be encouraged to improve the quality of care more if patients or their representatives are very sensitive to quality improvements Ž a high. andror if quality enhancement reduces production costs substantially Žhigh < V <, with V - 0. and if quality improvements easily spill over from one hospital to another Žhigh b ..

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The impact of a higher rate of cost-based reimbursement can likewise be analysed: sign E x nÕrEg s sign  ag A q Ž Ag q s . V

t Ž 2 b q d . y ag bg

qag Ž Ag q s . ag Ž V y b . q Vbg sign E x cÕrEg s sign

½

A bg q Ž Ag q s . Ž V y b .

q2 Ž V y b . Ž Ag q s . bg2 c 0

5

4 c0

Ž 6a .

2 t Ž b q d . y bg2

Ž 6b .

These expressions show that both cooperative and non-cooperative quality improvements can rise or decline with higher retrospective reimbursement. This result ŽEqs. Ž6a. and Ž6b.., as well as the above ŽEqs. Ž5a. and Ž5b.., run counter to the intuition that augmenting the share of retrospective Žprospective. reimbursement will typically generate higher Žlower. quality enhancement efforts. For instance, where quality improvements are cost-reducing Ž V - 0., it is very likely that both cooperative and non-cooperative quality efforts decrease with g , and even more so when spillovers Ž b . are positive and large. Increasing the share of retrospective reimbursement may thus have perverse effects on quality efforts: quality investments may diminish, especially the quality improvements that are socially most beneficial, i.e., those that yield major cost reductions and that generate useful, cost-reducing, know how for other hospitals Žlarge b ., are most likely to suffer. Intuitively this occurs, because as g increases, hospitals become less sensitive to these beneficial impacts of quality improvements since they decide on the basis of Ž1 y g .Ž V y b . rather than Ž V y b . and hence ‘under’ invest in these quality areas. And this lack of cost sensitivity grows with the rate of retrospective reimbursement. Under cost based reimbursement, there is no particular return to investing in cost-reducing quality efforts. Quality improvements which raise demand are more attractive than those which reduce the marginal cost of treatment. In terms of Fig. 2, the attractive investments are those which shift the marginal revenue curve of quantity up, regardless of their effect on marginal costs. This result may provide some intuition as to why hospitals are not very eager, neither individually nor in cooperation with other hospitals, to invest in research to improve the quality of care, especially in those areas where the benefits are substantial, both for the hospital itself Žlarge a y V . as well as for the rivals Žlarge b .. For instance, hospitals are not very eager to invest in research on appropriate use of procedures, on cost-effective health care interventions, although the results from such research may increase hospital profits substantially, by reducing the hospital costs and augmenting demand for the hospital’s services Žsince patients know they will get the appropriate care.. And this holds even if health care financing institutions are prepared to cover the—potentially—higher

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treatment costs associated with quality improvements, by raising the rate of retrospective reimbursement. Contrary to the available intuition, our model illustrates that introducing prospective reimbursement may indeed be a better strategy to improve the quality of care, because prospective reimbursement at least avoids this lack of cost-sensitivity. Chalkley and Malcomson Ž1995. already showed that an efficient level of quality efforts can be achieved by a prospective reimbursement system if it is possible to reward providers for the number of patients wanting treatment, as well as for the number actually treated. Norton Ž1992. and Hanchak et al. Ž1996. also show that financial incentives may induce higher quality levels, even in a prospective reimbursement system. 4.2. Utility maximising hospitals Secondly, the impact of a size andror quality objective, besides a profit motive, on quality enhancement is analysed. The superscript u will be added, to refer to the additional objectives:

E x nurE z 1 ) 0, E x curE z 1 ) 0

Ž 7a .

E x nurE z 2 ) 0, E x curE z 2 ) 0

Ž 7b .

E x nurE z 3 - 0, E x curE z 3 - 0

Ž 7c .

Intuitively, it is easy to see that, the more weight is given to quality in the utility function, the more quality improving initiatives will be undertaken, independent of whether firms compete or cooperate. As size becomes more important in the utility function, more quality efforts are undertaken, intuitively in order to attract additional patients. But all of this implies that, as more weight is attached to the pure profit motive, less quality enhancement efforts will be undertaken. Hence, if many hospitals can be considered as pure profit maximisers, the prospects for improved quality in health care delivery are not very good, even in this simple scenario where quality improvement is perfectly observable for patients and thereby allows to increase demand. Quality improvements will be encouraged more strongly if hospitals pursue, besides profits, other objectives, which may directly or indirectly be achieved through quality improvement, e.g., if hospitals value quality per se. 12

12

It should be noted however that in the present model, it cannot be evaluated whether these quality levels are ‘too high or low’, since the socially optimal quality levels are not considered.

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4.3. CooperatiÕe Õs. competitiÕe quality improÕement Now it will be investigated whether cooperation between hospitals is likely to improve the quality of care. 4.3.1. Profit-maximising hospitals First of all, for profit maximising hospitals, it can easily be established that cooperation may result in more or less quality efforts than non-cooperative conduct: sign Ž x cÕ y x nÕ . s sign  Ž 1 y g i . br a y Ž 1 y g i . V y dr Ž 2 b q d . 4 c 0 Ž 8. Whether a hospital will invest more or less in quality improvements in a cooperative equilibrium than in a Nash equilibrium, depends on the magnitude of the quality spillovers Ž b ., the net effect of quality on demand and costs Ž a y V ., the share of costs that is reimbursed retrospectively Žg . and the nature and degree of product differentiation Ž d vs. b .. Quite unexpectedly, neither the size of the prospective capitation payment Ž s ., nor the costs of quality improvement itself Ž t . affect the relative size of the quality improvement efforts. If hospitals can keep their quality proprietary, that is if no spillovers occur Ž b s 0., cooperation will result in less Žmore. quality enhancement than in the non-cooperative equilibrium if hospitals deliver services that are substitutes Žcomplements.. If there is no competition in the market for hospital services Ž d s 0, i.e., both hospitals deliver independent services, or a hospital cooperates with another health care institution., positive Žnegative. spillovers imply that cooperating hospitals will engage more Žless. in quality improvement than in the non-cooperative equilibrium. With spillovers and market competition, both effects will be combined. If hospitals deliver substitutes Žcomplements., cooperating hospitals will invest less Žmore. in quality than non-cooperating hospitals in the presence of negative Žpositive. spillovers. Under other combinations, e.g., when hospitals deliver substitutes with positive spillovers, the outcome depends upon the relative size of the spillover vs. the degree of market competition. Notably, in this scenario, the magnitude of the prospective reimbursement does not affect the quality improving efforts differently in a cooperative and a non-cooperative scenario, but the rate of cost-based reimbursement Žg i . does have an impact. In the case of full cost-based reimbursement Žg i s 1., cooperative conduct always implies less Žmore. quality enhancement than non-cooperative conduct if hospitals deliver substitute Žcomplementary. services. Intuitively, in the case where hospitals deliver substitutes Ž d ) 0., since all patient-related variable costs are reimbursed anyway, competing hospitals are encouraged to overinvest in

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quality improvement in order to gain market share to the detriment of the rival. In a cooperative framework, where the hospitals simply divide the market, there is no need for such high quality effort levels. Hence encouraging cooperation among hospitals that are reimbursed on the basis of their actual costs would lead to lower quality of care levels than if hospitals compete for patients. In case of complementary services Ž d - 0., with cooperation all benefits of improved quality Žhigher own and rival service level. are internalised, implying that cooperating hospitals invest more in quality improvement than competing institutions. It should furthermore be noted that with full cost-based reimbursement neither the size of the cost reduction Ž V . nor the magnitude of spillovers Ž b . is taken into consideration when deciding about optimal quality levels. Such a reimbursement system will surely not encourage hospitals to invest in quality improvements that may be very beneficial from a societal perspective Žlarge negative V andror large positive b ., cf. Eqs. Ž6a. and Ž6b.. Hence, the finding in the literature that partial retrospective reimbursement besides a prospective component may be a good mechanism to encourage a sufficient level of quality besides efficiency should be qualified Že.g., Ellis and McGuire, 1986; Pope, 1989; Siegel, 1991; Chalkley and Malcomson, 1995.. Our analysis shows that, besides the nature of the reimbursement system, hospital conduct and the nature of the services of the rival hospitals also play a crucial role. Retrospective reimbursement will stimulate quality improvement more if hospitals compete for patients than if they coordinate their efforts, at least when they supply substitute services; the reverse holds in the case of complementary services. The finding that competition between hospitals may encourage quality, and hence can be used as a mechanism to substitute for the quality-enhancing nature of retrospective financing Žor, in other words, counteract the quality-reducing nature of prospective reimbursement elements. was also noted by Pope Ž1989.. 13 However, our results show that this mechanism need not always work: many circumstances can be identified whereby quality competition will yield less quality improvements than cooperative conduct. Under pure prospective reimbursement Žg s 0., this result need not hold. In this scenario: sign Ž x cÕ y x nÕ . s sign  br Ž a y V . y dr Ž 2 b q d . 4 c 0 Ž 9. Hence, it is more likely that cooperation yields higher quality of care levels than non-cooperative conduct as: Ø products are complements or bad substitutes Žlow d . Ø quality improvement has a limited demand-augmenting effect Ø quality improvement has a large cost increasing or limited cost-reducing effect Ø spillovers are positive and large. 13

But Pope Ž1989. did not make a comparison with cooperative conduct and neither product differentiation nor spillovers were included.

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Cooperation is thus more likely to be quality enhancing for hospitals that deliver complementary services Že.g., a local hospital cooperating with a tertiary care hospital. than for hospitals that deliver services that are considered as substitutes Žand engage in a fierce ‘medical arms’ race.. Rival hospitals are not very eager to invest in quality if their quality efforts have a limited effect on profits, that is if Ž a y V . is small. In that case, cooperation may entail higher quality efforts. Positive spillovers that are internalised in a cooperative setting will entail higher quality because the positive effect quality efforts has on profits is not counteracted by the potential effect on rival cost or demand. For instance, cooperative and competitive conduct will yield identical levels of quality improvement if b s dŽ a y V .rŽ2 b q d .; that is for negative Žpositive. spillovers, if firms produce complements Žsubstitutes.. Moreover, this critical b is higher as products become better substitutes, andror as patients value quality improvements more highly and these quality initiatives yield larger cost reductions. Although the prospective capitation reimbursement s does not determine whether cooperation will result in more or less quality improvement than non-cooperative conduct, its impact on the magnitude of the quality improvement is different in both scenarios: sign Ž E x cÕrE s y E x nÕrE s . s sign  Ž 1 y g i . br a y Ž 1 y g i . V ydr Ž 2 b q d . 4 c 0

Ž 10 .

Although quality effort levels always respond positively to increases in prospective reimbursement levels Žcf. Eqs. Ž5a. and Ž5b.., the impact of an increase in s is different under cooperative vs. non-cooperative conduct. Cooperative quality improvement levels are likely to increase more with an increase in s as products are complements or bad substitutes, the net direct profit effect of quality improvement is limited and spillovers are large-positive Žcf. supra.. 4.3.2. Utility maximising hospitals If these results for profit maximising hospitals are compared with these for hospitals maximising a weighted average of quality, size and profits, the following can be reported: x cÕ - x cu x nÕ - x nu

Ž 11 .

Intuitively, it can easily be seen that if quality and size are incorporated in the utility function in addition to profits, ceteris paribus, more quality improving initiatives will be undertaken than if quality and size were not explicitly incorporated in the objective function.

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Moreover, the cooperative and non-cooperative quality effort levels can also be compared in the case firms pursue these additional objectives, besides profits: sign Ž x cu y x nu . s sign  Ž 1 y g i . br a y Ž 1 y g i . V y dr Ž 2 b q d . 4 c 0 Ž 12 . Again, the difference between quality improvement effort levels under cooperative and non-cooperative conduct is determined by the same interaction of factors Žcf. Eq. Ž8.., even if hospitals pursue goals other than pure profits, and with our specification of objective functions, this result is even independent of the relative weights attached to the different goals.

5. Stability of cooperation In Section 4.3, it was shown that under certain circumstances, it may be a good idea to encourage hospital cooperation in order to enhance the quality of care. However, it must still be investigated whether these cooperative equilibria will be stable, i.e., whether firms do not have an incentive to deviate from the cooperative outcome. It was already indicated that a cooperative agreement will be stable only if the interest rate of the hospitals is lower than r ) Žcf. Eq. Ž4... This maximal interest rate depends on the rate of spillovers, the nature and degree of product differentiation, the net effect of higher quality on demand and costs and the retrospective reimbursement conditions. In this section, the link between this critical interest rate Ži.e., the stability of cooperation. and the different model parameters is further analysed. Quite unexpectedly, the relative weights of quality and size in the objective function do not affect the stability of cooperation. Therefore, the stability problem will only be discussed for the case where hospitals are assumed to maximise profits. It is first investigated how quality spillovers affect the stability of cooperation. sign E r )rEb s y  Ž 1 y g i . br a y Ž 1 y g i . V y dr Ž 2 b q d . 4 c 0

Ž 13 . Whether cooperation becomes more or less stable with increasing spillovers is dependent upon exactly the opposite interaction between product differentiation, the direct profit impact of quality improvement, spillovers and the degree of cost-based reimbursement, as indicated above in Eq. Ž8.. Hence, if parameter values are such that cooperative conduct yields higher quality improvement efforts than non-cooperative conduct, this beneficial outcome need not materialise, because such parameter values typically imply a lower degree of stability; i.e., the incentive to deviate from the cooperative effort level may be too large.

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One way to further describe this relationship between stability and the degree of spillovers, is by identifying the spillover level for which the cooperative agreement is easiest to sustain:

b ) s d a y Ž 1 y gi . V rŽ 1 y gi . Ž 2 b q d . c 0

Ž 14 .

If hospitals deliver substitute services Ž d ) 0., the RHS of this expression is positive and hence cooperation is easiest to sustain in areas with positive spillovers, such as in informatisation of patient administration. If hospitals deliver complementary services, cooperation will be easiest to sustain with negative spillovers. Whether the spillovers that yield maximal cooperation are large or small depends on how close substitutes or complements the hospitals’ services are, how strongly patients value quality improvement, how quality improvements affect costs and how large the share of retrospective reimbursement is. Secondly, the impact of b on the level of r ) can be described. If for instance, hospitals are reimbursed entirely retrospectively Žg s 1., the stability of cooperation is not affected by the above parameters. If hospitals are reimbursed entirely prospectively Žg s 0., the picture becomes more complicated, since the stability of cooperation depends on the interaction between the degree of product differentiation, the net direct profit effect of quality improvement and the degree of spillovers Žcf. supra.. For instance, suppose hospitals supply homogeneous products Ž d s b ., in that case cooperation becomes less stable as b increases from the moment that b ) Ž a y V .r3. These results are further illustrated for a numerical example in Figs. 3 and 4 Žwith a y A q s s 110, t s 2, b s 2, d s 1, F s 100, B s g s 0, a s 0.25 and V s 0.2 and z 1 s z 2 s 0.. Fig. 4 reveals that under prospective reimbursement, if hospitals supply substitute services and for the given parameter values, the cooperative outcome is most likely to be stable when spillovers are positive and small, since a y V is small Žcf. Eq. Ž14... In that case quality improvement efforts are however low Ževen lower than under non-cooperative conduct.. With large spillovers, cooperative quality improvement efforts are larger than under non-cooperative conduct, but this outcome is much less likely to materialise, because of stronger incentives to deviate from the cooperative outcome. Secondly, the impact of the demand augmenting quality effect Ž a . on the stability of cooperation is analysed: 2

½

sign E r )rEa s sign 3 b Ž 1 y g . d Ž a y Ž 1 y g . V . q Ž a y Ž 1 y g . V . 2

2

= b 2 Ž 1 y g . d y 2 d 2 t y 4 b Ž 1 y g . b 2 y 2 bb 2

= Ž 1 y g . Ž b 2 Ž 1 y g . y dt . c 0

5

Ž 15 .

In case of full retrospective reimbursement Žg s 1., the results are fairly obvious: it becomes more difficult to sustain cooperation as a grows larger. Since general results for less than full retrospective reimbursement are difficult to obtain, the

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Fig. 3.

tendencies are reported by means of a numerical example with a y A q s s 110, t s 2, b s 2, d s 1, F s 100, B s g s 0, b s 0.25 and V s 0.20 and z 1 s z 2 s 0 Žin Figs. 5 and 6.. From Fig. 6, it is clear that for most parameter values of a ,

Fig. 4.

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723

Fig. 5.

cooperation is likely to be sustainable Žsince r ) is large and even close to 1.. Moreover, r ) does not vary substantially with a , which can be explained by means of Fig. 5, which shows how profits vary with variations in a : both the cheating incentive Ž Vd y Vc . and the strength of the punishment Ž Vc y Vn . do not

Fig. 6.

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change substantially with the size of the demand-augmenting quality effect. Therefore, the size of a does not have a substantial impact on the stability of cooperation. 14 Finally, also the impact of the reimbursement conditions on the stability of cooperation can be analysed. First of all, the magnitude of prospective capitation reimbursement Žsize of s . does not influence the stability. The rate of retrospective reimbursement again plays a role. The comparative statics reveal that:

E r )rEg c 0

Ž 16 .

Cooperation can as well become more as less stable when the degree of cost-based reimbursement is increased. However, numerous numerical simulations reveal that this maximal interest rate does not vary substantially with the degree of cost-sharing. In many instances r ) remains quite high, and thus stable cooperation is likely to be achievable for many degrees of retrospective reimbursement.

6. Conclusions and extensions The main message of this paper can be summarised as follows. Encouraging cooperation among hospitals in order to improve the quality of care need not be the most appropriate way to achieve the desired result; on the contrary: circumstances can be identified where cooperation will yield less quality improvement efforts than independent conduct. Hospitals that deliver services that are considered as substitutes use quality as a strategic weapon in attracting patients. If their quality efforts have an important effect on profits, they may undertake more quality improvements than under cooperation. If spillovers are small or non-existing, rival hospitals will deliver higher quality than in the case of cooperation. Furthermore, the impact of the reimbursement system on the incentives to improve the quality of care is more complex than has up to now been shown in the literature. Our results run counter to the intuition that augmenting the share of retrospective Žprospective. reimbursement will typically generate higher Žlower. quality enhancement efforts. In response to a higher level of prospective reimbursement, hospitals will be encouraged to improve the quality of care. This effect is stronger if patients or their representatives are very sensitive to quality improvements andror if quality enhancement reduces production costs substantially and if quality improvements easily spill over from one hospital to another. Increasing the share of retrospective reimbursement may have perverse effects on quality improvement efforts because the lack of cost sensitivity grows with the rate of retrospective reimbursement: quality investments may diminish, especially 14

In all the other numerical simulations that were performed, the same tendencies were observed, but they are not reported here.

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the quality improvements that are socially most beneficial, i.e., those that yield major cost reductions and that generate useful, cost-reducing, know how for other hospitals. It was furthermore shown how quality improving initiatives and the stability of cooperation depend upon the interaction between spillovers, the net effect of quality on profits, product market competition and the rate of retrospective reimbursement. These results were derived within a very simple framework. The specific assumptions with respect to the demand and cost functions allow to focus on the effect certain parameters have on the equilibrium values. It would be interesting to analyse how they are affected when the model is made increasingly realistic in several respects. The model did not take into account the various uncertainties faced by hospitals. Demand for health care is derived from the demand for health by potential patients. Price and quality aspects start being relevant only after the patient Žor his medical doctor. has decided health care is necessary. Moreover, there often exists a substantial degree of asymmetric information between patients and providers, regarding, e.g., the required level of care, the quality of care. The hospital may furthermore have incomplete information about the type of its cooperating partner, about the efficiency and final outcome of its quality efforts and the impact of these quality improvements on demand and costs. Finally, in practice quality improvements will not be perfectly verifiable by patients nor by providers. It would be interesting to analyse the quality improving incentives in a setting where hospitals can engage in both easily verifiable and difficult or unverifiable quality enhancement strategies, whereby these quality improvements may differ in their impact on patient outcomes Žcf. Weisbrod, 1988, 1991.. Certainly in terms of achieving social optimality, quality promotion is especially important in terms of those aspects that may crucially affect patient outcomes. Another area of uncertainty is in the level of costs: typically health care financing organisations cannot perfectly observe, nor verify Ževen ex post. the cost levels reported by the hospitals, although this is crucial under retrospective financing conditions ŽGlazer and McGuire, 1994.. This may complicate the picture regarding hospitals’ incentives to engage in quality improvement, and should further be investigated. The aggregation of all possible medical services into a single output is certainly an important simplification. A more realistic model would take into account the case-mix of patients more realistically. Our objective function incorporated the separate arguments in a simple linear combination; further research should include more general specifications of the utility function, allowing for decreasing marginal utility in each of the arguments and for non-zero cross effects. Furthermore, it may also be worthwhile to analyse the impact of cooperation on quality improvement when hospitals keep on competing in the product market

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andror with sequential decision making, whereby hospitals decide on output contingent on the own and observed rival quality efforts. But in another paper ŽKesteloot and Veugelers, 1995., it was shown that, at least in a framework of pure profit maximising commercial firms, these variations in model hypotheses do not affect the results qualitatively. Finally, empirical testing of some of the analytical results derived in this paper would constitute a very useful complement of this work.

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