Is there scope for mixed markets in the provision of hospital care?

Social Science & Medicine 247 (2020) 112810

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Is there scope for mixed markets in the provision of hospital care? a

b,∗

Laura Levaggi , Rosella Levaggi a b

T

Faculty of Science and Technology, Free University of Bolzano, Piazza Università 5, Bolzano, Italy Department of Economics and Management, University of Brescia, Italy

ARTICLE INFO

ABSTRACT

Keywords: Hospital care provision Public hospitals Mixed markets

Market oriented reforms in hospital care have produced a variety of quasi markets that differ for the type of providers that are allowed to compete. Mixed markets, where public hospitals compete alongside private ones, are increasingly common, but the literature does not agree on their performances and their desirability. We review the contributions in this field by proposing a common framework which allows to account for the different approaches proposed to model public hospitals. In this paper we show under which conditions mixed markets perform better in terms of average quality, and we review the empirical literature to determine whether these conditions are met. In general, pure forms (private or public competition) are superior to mixed markets, unless patients interpret public hospitals as reference suppliers, and quality of care is important. The empirical evidence on these key questions shows that public hospitals behave differently from private organisations, but they are not necessarily less efficient. Research into patients choices seems to suggest that ownership is a value, but the empirical literature is still rather scant. From a policy point of view, our review suggests that there does not seem to be a clear answer to whether this market form should be used. Local conditions are going to play an important role.

1. Introduction Hospital care accounts for about 50% of total health care expenditure; the pressure to increase value for money in the public sector has induced policy-makers to introduce competition for its provision, in spite of mixed evidence on its effects on quality improvements and equity (Gaynor et al., 2016, 2015). One of the most interesting emerging patterns is the increasing presence of mixed markets where public hospitals compete with private providers for treating publicly-funded patients (Rechel et al., 2018; Siciliani et al., 2017). According to Eurostat (2017), in 2015 most hospitals were still public in Slovenia, Lithuania, Croatia, Romania, Malta, Finland, Denmark, Estonia Latvia, the UK, Norway. A second group of countries is close to a fair share (Cyprus 53%, France 62%, Greece 65%, Germany 40%), while in the Netherlands all the hospitals are privately owned. The trend points towards a reduction in the share of the public sector, especially in countries where public ownership is still relevant. The idea behind mixed markets for hospital care is rather simple: private providers should promote efficiency in service delivery because they can retain the difference between revenues and costs; the presence of public hospitals (which may share with patients quality objectives) allows to improve equity (Siciliani and Straume, 2019) and

∗

to reduce the risk that more severe and/or less remunerative patients are not treated due to strategic behaviour by private providers (Ellis, 1998). However, the presence of asymmetric competitors as concerns objectives and constraints may prevent this market form from obtaining the intended outcomes. The evidence on the performance of mixed markets is not cleacut: the theoretical literature shows a limited scope, while the empirical literature is fairly inconclusive. In fact, it agrees neither on the estimation of the productivity differential between organisations pursuing different objectives (Chang et al., 2004; Tiemann et al., 2012), nor on hospital responses to changes in quality by other competitors, the two distinctive characteristics of public and private providers. In this article we review the theory and the empirical evidence on mixed markets for hospital care in order to determine whether this market form is a valid alternative. We define a general theoretical framework that allows to understand how the different assumptions on the behaviour of public hospitals proposed by the literature (market size maximisation, altruism and intrinsic motivation) affect the equilibrium conditions, average quality and the level of competition. This analysis shows that the success of mixed markets does not only depend on the assumptions made about the objectives of the competitors and on patients responses to the quality of care, but also on the

Corresponding author. Dipartimento di Economia e Management, Università di Brescia, Via San Faustino 74b, 25122, Brescia, Italy. E-mail addresses: [email protected] (L. Levaggi), [email protected] (R. Levaggi).

https://doi.org/10.1016/j.socscimed.2020.112810 Received 8 July 2019; Received in revised form 9 January 2020; Accepted 17 January 2020 Available online 21 January 2020 0277-9536/ © 2020 Elsevier Ltd. All rights reserved.

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Table 1 The taxonomy of public hospitals competing on the market. Independent body (IB)

Public Control (PC)

Direct Management (DM)

Altruism/intrinsic motivation No Imperfect observation Some slack

Payment system

Profit/Altruism Partial Not observed Depends on profit retainment PPS

PPS + budget

Shared with provider No Observed Maximum Slack PPS + budget

Soft budget

No

Yes

Yes

Objectives Surplus retainment Costs Slack

intrinsic value of public provision. If being a public hospital is not considered a value by patients, and information on costs is asymmetric, mixed markets have a limited scope (Brekke et al., 2018, 2012; Dulleck and Kerschbamer, 2006; Levaggi and Levaggi, 2017a). Pure forms (either private providers or public providers) allow to get a better quality level for the same price; the choice among the two depends on the level of altruism or intrinsic motivation of public hospitals. On the other hand, if hospitals pursue different objectives (Herr, 2011; Sanjo, 2009), or their non-profit status is a value to patients (Besley and Ghatak, 2001; Laine and Ma, 2017; Levaggi and Levaggi, 2017a), or providers share with patients quality concerns (Besley and Malcomson, 2018) mixed markets may be superior to pure forms. The empirical investigation on patients' choices, on the efficiency differential, and on the objectives of public hospitals is then essential to inform policy decisions. In this respect, the answer of the empirical studies is rather inconclusive: while some evidence seems to suggest that patients attach a value to hospital ownership, the evaluation of the productivity differential is more controversial, as well as the assessment of the differences in the objectives pursued by public hospitals. The paper is organised as follows. In the next section we present the economic rationale behind internal markets and the taxonomy of public hospitals. Section 3 presents the methods we will be using in our assessment; Section 4 reviews and compares the results of the theoretical literature, while in Section 5 we compare the evidence from the empirical literature with the predictions of the theory. Section 6 concludes the paper.

characteristics of the service produced may introduce some constraints (for example the presence of sunk costs may reduce the number of firms willing to enter the market), from a theoretical point of view, their objectives and cost functions are similar to what one would assume for a firm competing in a private market. On the other hand, the objectives of public providers may be more difficult to define because they also depend on their governance and on the process that led to the creation of an internal market for health care. 2.1. Public hospitals: taxonomy and objectives Public hospitals are fairly heterogeneous as concerns their objectives and constraints. They may be independent bodies like the NHS Foundation Trust in the UK, they may still be run by the regulator as Centre Hospitaliers in France or Presidi Ospedalieri in Italy (Paris et al., 2010). In some health care systems they have contractual obligations towards the regulator (for example as regards the range of treatments they should supply and the destination of the financial surplus) which reduce their level of efficiency (Barbetta et al., 2007; Brekke et al., 2012; Chang et al., 2004; Dormont and Milcent, 2012; Verzulli et al., 2018). Table 1 summarises the most important taxonomies of public hospitals competing in the market for hospital care. In their pure form, independent bodies (IB) are separated entities from the purchasers, have the right to withhold information as concerns their running costs and may be considered profit maximisers. Their services are paid through a contract that sets their obligations, and they can refuse any clause that limits their independence. Efficiency is an objective since these hospitals are basically run as private firms. Prospective, output based payment systems (PPS) are usually used to reimburse these providers and the most common system is a DRG (Diagnosis Related Group) payment (Busse et al., 2013). As a general rule, these organisations are not bailed out if they run into a deficit, i.e. they face a hard budget constraint. Hospitals that are publicly controlled (PC) have a high degree of independence as far as their organisation is concerned. The main difference with IB is related to governance issues: these organisations are not for profit, i.e. they are not able to retain any profit. For this reason, they pursue other interests, ranging from altruism and market share, to reputation and case mix (Brekke et al., 2012; Herr, 2011; Sanjo, 2009). The payment method used depends on the architecture of the system: in a third-payer competition setting, where these hospitals compete with private organisations, they are usually reimbursed using Prospective Payment Systems; in other contexts where they compete with similar organisations, mixed payment systems may emerge. The governance of these providers should be carefully studied: cost containment is no longer an objective because they cannot retain any surplus and the purchaser may bail them out if they run into a deficit (see Brekke et al., 2015 and Levaggi, 2018 for the implications of soft budget constraint policies). At the same time, since true costs are not observed by the purchaser, these organisations may be inefficient (Eggleston and Shen, 2011; Rainey and Chun, 2005; Tiemann et al., 2012; Tjerbo and Hagen, 2009) or they may use strategic revelation of information on costs to induce the purchaser to allocate resources according to their

2. The internal market for hospital care Internal markets for publicly provided health care were created to shift power from producers to consumers (Jones and Cullis, 1996). However, these markets do not follow the rules of perfect competition. Hospital care is produced on demand, cannot be stocked or transported, and quality is difficult to be verified (Bos and De Fraja, 2002; Chalkley and Malcomson, 2000; Montefiori, 2008, 2005). The technology of production needs fixed, sunk investments, which restricts the number of firms that can acquire it and reduces the level of competition. From the demand side, hospital care is often associated with the notion that health care is an essential service. This implies that access should be granted irrespective of ability to pay, hence health care is usually free at the point of use and the user charge covers only a fraction of the cost (if any). On the other hand, given the personal nature of the service produced, freedom of choice may imply that patients incur significant transportation costs to receive care. In this uncertain world, health care systems have adopted different solutions to organise the market for hospital care (Levaggi, 2008, 2007; Rechel et al., 2018; Siciliani et al., 2017; Wolinsky, 1997). The main differences are represented by the nature of bodies allowed to compete, their independence in decision-making, and the contractual rules for service provision. In this article we focus on the characteristics of mixed market for hospital care, where private providers compete with public organisations. The objectives of private providers are quite straightforward to define: they are profit maximisers. Although the 2

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preferences (Levaggi and Levaggi, 2010). Finally, hospitals that are directly managed (DM) have a limited degree of autonomy; they cannot withhold information from the purchaser that can make them pursue their own objectives. These constraints mean more slacks in the productive process and cost inflation by an X-inefficiency parameter. The theory on public hospitals also suggests that the differences in the objectives pursued by these organisations may not simply derive from governance choices: also workers may be different and may influence them. Brekke et al. (2012) assume that public hospitals behave as nonprofit organisations whose objective function depends on profit maximisation and altruism. The first element is a common feature with private hospitals and is given by the difference between revenue and costs. The second element is represented by the utility function of patients receiving care from these providers, which in turn depends on the level of quality provided. Altruism makes providers increase quality of care for two reasons: a) to increase the utility of patients that are already using their services; b) to increase market share so that more patients can get higher quality services. More recent literature assumes that the staff in public hospitals may be intrinsically motivated and share with patients some objectives, usually measured through quality (Besley and Ghatak, 2005, 2001; Delfgaauw, 2007; Delfgaauw and Dur, 2010; Galizzi et al., 2015; Ghatak and Mueller, 2011). This implies that the staff is willing to work for a lower salary (Barigozzi and Burani, 2016; Lakdawalla and Philipson, 2006). Contrary to altruism, in this case the quality level may be set independently from any consideration relating to patients and competition: in other words intrinsically motivated providers increase quality for their own benefit and for the amount that maximises their utility function. Intrinsic motivation may improve quality and may also speed up technology adoption (Levaggi et al., 2009), something that may explain why public hospitals are quite reactive to new technology, even when it may not produce the same advantages in terms of profit maximisation. However, when the evaluation of quality of intrinsically motivated providers and patients diverges too much, intrinsic motivation may reduce welfare (Besley and Malcomson, 2018). The heterogeneous objectives and constraints that characterise public hospitals may explain why the literature has followed several avenues in modelling mixed market for hospital care, both as concerns the competition framework and the objectives pursued by competitors.

most common) to Bertrand/Cournot oligopoly. As per the objectives of providers, while private hospitals are profit maximisers, public providers are assumed to have a range of objectives which reflects the different governance systems adopted at national level, as shown above. Most literature shares the following assumptions:

• health care is financed by a third payer, hence competition is made • • •

on quality levels. Hospital care is free at the point of use, but patients incur travel costs to reach their preferred provider; quality cannot be verified, but it can be privately observed by patients, sometimes with an error bias (Brekke et al., 2014; Montefiori, 2005); the number of services to be provided is fixed and patients always choose to be treated; hospitals cannot choose their location. This assumption grants the existence of an equilibrium solution. Sanjo (2009) shows that when hospitals can choose their location, the presence of asymmetric objectives may prevent reaching a stable solution.

In what follows we will first review models that assume spatial competition, and then move to the emerging literature that uses a Bertrand/Cournot competition. 4.1. Spatial competition Spatial competition is an interesting framework for studying hospital decisions, because empirical evidence on patients choices (Dardanoni et al., 2018; Krabbe-Alkemade et al., 2017; Moscelli et al., 2016; Propper, 2018; Riganti et al., 2017; Siciliani, 2018; Varkevisser and Van der Geest, 2007) shows that hospitals have a degree of monopoly power deriving from the distance patients have to travel in order to be admitted. The general framework can be described as follows. A community consisting of a mass of individuals (normalized to 1 for simplicity) is uniformly distributed on a line segment of unit length. Hospital care is provided using two facilities located at 0 and 1. Provision is fully subsidised by the public sector that pays for each admission a fixed DRG-type reimbursement T. A minimum level of quality (set to zero for simplicity) can be verified; any improvement above this level, although privately observable, cannot be made legally binding. Users are indexed by their position on the line, meaning that x represents those located at distance x from the origin. The quality levels q0 and q1 offered in the two facilities may be different: patients choose the preferred provider by evaluating both service quality and travel costs in order maximise their net utility. We write the utility of an individual located at x as:

3. Mixed markets for hospital care: theory and empirical evidence We propose to study the role of mixed markets in hospital care by comparing the results of the most important models in the theoretical literature in order to determine the conditions under which these forms should be preferred. We define a general framework where the regulator sets a fixed reimbursement for each treatment, the market is fully covered, patients can observe quality of care and providers have a fixed location. The different models can then be assessed in terms of the average quality level of hospital care they provide to patients. The variety of objectives and constraints in Table 1 is reflected in the models proposed by the literature; the general framework we propose allows to understand how each assumption about the behaviour of public hospitals affects the equilibrium conditions. From this literature we derive a set of predictions that are then compared with the evidence derived from the empirical studies.

U (x ) = v + max { q0

mx , q1

m (1

x )}

(1)

where m are unit travel costs and v represents intrinsic individual utility. The latter set high enough to make all individuals choose to receive care from some provider. Finally, > 0 is the evaluation of the quality. The choice of individual located in x, is represented in Fig. 1. The hospital located in 0 supplies a quality level q0 , but to reach this hospital the patient has to bear mx as transport costs. The quality of the other hospital (located in 1) is q1 and the private cost is m (1 x ) . Based on its quality evaluation , the patient chooses the hospital that maximises the difference between the utility from quality and transport costs. Hospitals maximise a composite function that depends on profit and possibly other objectives, according to the models. In general, we can write:

4. The theory behind mixed markets for hospital care

Vj = (1

The models in the theoretical literature define frameworks that allow to compare the performances of several market settings: competition among private providers, competition among public providers and mixed markets. Given the restrictions to perfect competition, different market forms are assumed, ranging from spatial competition (the

)(TDj

Cj )

Fj + Uj

(3)

where T is the payment for each treatment and Dj = x (q0 , q1, m) is the hospital demand, which depends on the quality differential among providers and on the travel costs. Cj is the monetary cost incurred by the hospital in producing health care, while Fj is a non-monetary disutility. 3

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Fig. 1. Patients choice in a spatial competition model.

4.1.1. Altruistic motivation Brekke et al. (2012) argue that, non-profit providers are altruistic, i.e. they take also into account the utility of patients they treat. The objective function for a generic provider in this case is:

Table 2 Quality in the different markets according to the type of competitors. Quality

q1

q0 Public altruistic

m

m

Dj m

2(

)

2(

)

Public motivate

2 m

m

2 m

m

Private

S+ 2 k

Mixed altruistic 5

Mixed motivated

2 6

1 S+ 2 3 k

S+ 2 k

m S+ 2 k

m

+

3m

4 m 3

3 5

Vj = (1

m

2 S+ 2 3 k

j

2 ej ) Dj + (1

Fj = e 2j Dj +

) g (qj , Dj )

( qj

j

ms ) ds

(4)

where:

Cj = (

S+ 2 k

m

+

2m

2 ej ) Dj + (1

) kqj Dj Fj = (ej2 +

qj ) Dj

(5)

and λ is the level of altruism. For j = 0 the provider is a private organisation; when j = 1 the hospital is public. The former maximises profit and bears a unit monetary cost k to increase quality. Public hospitals cannot retain any surplus and maximise the utility of their patients, net of non-monetary costs, which are assumed to be a linear function equal to qj Dj . In order to avoid losses, we set S = T > 0. From a policy point of view, the main result of this analysis is that the average quality in a mixed market is lower than in a public or a private market (see the Appendix and Table 2). Depending on the level of altruism, patients evaluation of quality and the efficiency of the cost reducing effort, the quality supplied by a private provider may be higher or lower than the quality of a public provider; if altruism is “sufficiently high” public competition should be preferred to a private market, even when public suppliers are less efficient than private ones.

2 m 3

Both measures are hospital-dependent as shown below. Finally 0 1 denotes profit retention. For = 0 the hospital is a private organisation (100% profit retention) while = 1 denotes a public hospital. Herr (2011) assumes that public hospitals wish to maximise the sum of profit and market share, an objective similar to the traditional literature on hospital behaviour (Newhouse, 1970). Brekke et al. (2012) and Levaggi and Levaggi (2017b) assume that they are altruistic providers, while Levaggi and Levaggi (2017a) assume intrinsic motivation. The provision of health care produces costs that depend on the type of provider. These differences may arise by assumption (Herr, 2011; Levaggi and Levaggi, 2017b; Levaggi, 2005), as a consequence of profit retention (Brekke et al., 2015, 2012) or because of competing objectives (Delfgaauw and Dur, 2008). Providers incur both running costs (Cj ) and non-monetary disutility (Fj ) :

Cj = (

Cj ) + Fj +

0

m 4 6

j )(TDj

4.1.2. Intrinsic motivation Intrinsic motivation in hospital care means that quality increases providers' utility directly, but its enhancement may not be a goal shared with patients. Contrary to altruism, patients utility does not enter the objective function: hospitals are interested in quality per se, not on the number of patients that will enjoy it. In this case the objective function is:

(2)

(qj , Dj )

In Equation (2) βj represents the unit cost to produce care with a minimum verifiable quality level, while 2γ is the marginal cost-reducing effort. In other words, βj can be reduced by 2 ej through a managerial effort that has a non-monetary cost equal to ej2 . The second term in both equations accounts for the effects on costs of the different hospital's structure. The degree of profit retention changes the nature of the cost to improve quality. For altruistic/intrinsically motivated providers, it is a non-monetary (disutility) cost represented by the function (qj , Dj ) increasing and convex in both arguments. Altruism and intrinsic motivation are however crowded out (Galizzi et al., 2015) by ) . For private hospitals (that can retain 100% of profit retention (1 their profit), quality can be improved only through an increase in running costs, modelled through the function g (qj , Dj ) . In what follows, we will review the most significant models proposed by the literature presented above. A simplified approach which allows comparing their solutions is presented in the Appendix.

Vj = (1

j )(TDj

Cj ) + Fj +

j

qj

(6)

with Cj and Fj as defined in equation (5). Again, if the provider is a private organisation j = 0 , while j = 1 if the hospital is public. Incentives to cost minimisation and the cost function are the same as what proposed for altruistic providers. In a linear model where two hospitals compete, a mixed market is always dominated by public or private competition as shown in Table 2 (the analytical details are available in the Appendix). Note also that in pure public markets altruistic hospitals provide a higher level of quality than intrinsically motivated ones if 4 > + 4 . In other words, if the disutility in increasing the effort is “sufficiently high”, altruism allows to get a better quality level. In general motivated public hospitals are poor competitors: an increase in competition does not make them react with any action aimed at preventing a reduction in their market share, a fact that also stems from recent empirical studies (Berta et al., 2018a; Moscelli et al., 2018). 4

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This may not be the case if patients have a bias towards some providers. Levaggi and Levaggi (2017b) model a mixed market for hospital care where intrinsic motivation is combined with monopolistic competition. Private hospitals compete with a reference supplier represented by the public hospital, an assumption that seems to be supported by recent empirical evidence (Levaggi et al., 2018). In this case, quality and welfare in the mixed market can be improved with respect to pure forms, provided that the efficiency in cost reducing activities is sufficiently high. In the other cases, a trade-off emerges and the choice might also depend on the importance that the regulator assigns to each component of the welfare function. In general, when quality improvements have relative importance, mixed markets may increase the profit of private providers, but not consumer surplus. Hehenkamp and Kaarboe (2017) propose a model that is halfway between altruism and intrinsic motivation by considering the case where public hospitals maximise a function that depends on profit as well as on quality. As in Brekke et al. (2006), the authors allow hospitals to choose their location on the line and, contrary to Sanjo (2009), they always find an equilibrium. Their model shows that introducing competition may increase quality, but the private provider strategically locates towards the corner of the market to avoid costly quality competition. The effect on social welfare depends on two different elements: the level of intrinsic motivation of public providers and the size of the budget. If the latter is sufficiently high, welfare is highest when two hospitals compete along the line; in all the other cases it is better to have a public hospital serving the market.

quality evaluation, but a fixed proportion will always choose the incumbent, irrespective of the quality provided by new entrants. The rest of the market is up for competition and care may be supplied by two different providers: a private, profit maximising hospital and a public one. Quality has two components: an observable, non verifiable characteristic q and an unobservable one Q. Private providers maximise profits, while public hospitals maximise a function which depends on their quality preferences. Private hospitals set Q to zero: this quality has no economic value in their objective function and, being unobservable, it will not be used by patients in their decision. For public hospitals, both levels of quality are positive, but their level may not be optimal. From a benchmark setting where a public hospital supplies care as a monopolist, the authors show that allowing competition through the entry of a private hospital may be welfare improving. This is especially relevant when the preferences for quality of the hospital and of the patients are similar. The authors also show that a prospective/DRG payment system where both hospitals are paid the same amount may not be optimal: a differentiated price may in fact improve welfare. Laine and Ma (2017) study a multistage, quality-then-price game between a public firm and a private one which may be applied to hospital care in the presence of copayments. The public organisation maximises social surplus, whereas the private firm maximises profit. In the first stage firms choose quality, while in the second stage the price is chosen. The authors show that several equilibria are possible in this setting and it may well be that the quality/price mix offered by either firm (public or private) is superior.

4.1.3. Market share Herr (2011) assumes that the difference between public and private hospitals depends on their objective function: while private providers maximise profit, public providers also consider their market share. The objective function for a generic provider j can be written as:

4.3. Discussion

Vj = (1

j )(TDj

Cj ) +

j

Dj

The models presented in the previous sections show that there does not seem to be a unique answer to the question of whether mixed markets may increase quality in health care. The objectives of public providers and the efficiency differential with private providers (which may in turn be determined by profit retention) are the key factors in determining the performance of this market form. In general, altruistic providers are more responsive to competition than intrinsically motivated providers, to the point that they may outperform private providers. Intrinsic motivation may be a value for patients, but only if the preferences for quality of patients and providers are quite similar. It is also interesting to note that efficiency is simply one dimension on which the performances of public hospitals should be evaluated: the second and perhaps even more important is the willingness to use cost savings to improve quality. Quality is of course only a part of the story. Regulators may be interested in a more general evaluation of the market that includes consumer surplus, the profit of private providers and the shadow cost of public funds. Levaggi and Levaggi (2017b) show for a more general case the conditions under which public competition is superior to a private market from a welfare point of view, while Brekke et al. (2012) find the conditions under which profit constraints and regulated prices may be combined together to improve welfare. In our analysis we have preferred to take into account average quality for a fixed price to avoid the problem of defining weights for the other components of the welfare.

(7)

Both kinds of providers care about profit, but only public hospitals are interested in their market share. Providers differ in their level of efficiency by assumption are located at the extremes of a unit line. The cost function becomes:

Cj =

j Dj

+

1 2 q 2 j

(8)

The cost to enhance quality can be interpreted as an optional fixed cost since it does not depend on the level of demand, but the hospital may not incur it if it decides to supply a quality equal to the benchmark level. As shown in the Appendix, for a fixed DRG price T, symmetric markets (either two private hospitals or two public hospitals) outperform a mixed market. The optimal choice depends on the relative efficiency of the hospitals and on the importance public hospitals attach to market shares. However, when welfare considerations are taken into account and T is set to maximise consumer surplus, it may be possible that a mixed market allows to reach a higher level of welfare. These results are quite interesting from a policy point of view, but they may depend on the specific functional form used to describe hospital behaviour which lead both hospitals to set their quality level independently of what the other competitor does. The original model also assumes non-linear travel costs which implies that hospitals have a substantial degree of market power.

5. Empirical evidence The theoretical literature reviewed above shows that mixed markets for health care might be used to improve average quality only if some specific conditions are met, namely:

4.2. Other approaches Besley and Malcomson (2018) consider a general model for the role of public organisations that can also be applied to health care. The setting is quite different from spatial competition, although some features of the models reviewed so far are retained. The authors consider whether it is desirable to open competition in a monopoly setting. They assume the presence of a continuum of patients that differ in their

a) patients attach a value to the institutional setting of hospitals; b) public hospitals have different objectives from private ones; c) the differential in productivity is neither “too high” nor “too low”. This means that their desirability could simply be a matter of 5

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empirical investigation. In what follows we will present the most significant findings from the literature.

adjusted. Dormont and Milcent (2012) study French hospitals and show that the lower productivity of public hospitals is related to external factors, such as patient characteristics and the case mix. Once patients and production characteristics are taken into account, large and medium-sized public hospitals appear to be more efficient than private hospitals. For Italy, evidence is rather mixed, but in general, private hospitals are more prone to opportunistic behaviour (Berta et al., 2013). Kruse et al. (2018) analyse and compare performances of hospitals and access to care in Italy, Germany, U.K., France, Greece, Austria, Spain, and Portugal. Public hospitals are as efficient as the private counterpart, but the latter seem to be more reactive to financial incentives. Finally, it is interesting to note that the level of productivity and the objectives of public hospitals may vary according to the market where they compete. Horwitz and Nichols (2009) use US data to show that the behaviour of public hospitals changes significantly according to the share of market that is served by private hospitals. This evidence may show that mixed markets may have a value per se: they make public hospitals become more competitive and this may be a possible added value of using this market form.

5.1. Patients choice Most contributions in the empirical literature assume rather than test that patients do not attach a value to the ownership status of hospitals, but this may not be the case. Gu and Johar (2017) show that patients choices are influenced by past experiences (which may create a bias towards public hospitals, given the recent introduction of private providers), and that they are concerned by the cost reducing drive of private hospitals, while (Jones et al., 2017) argue that for profit hospitals in the US may change their status to non profit because patients expect the latter to supply higher levels of quality (Drevs et al., 2014). Furthermore, the information on quality disclosed by regulators is quite different across countries (Siciliani et al., 2017) and this may lead patients to think that some hospitals are intrinsically better than others (Varkevisser et al., 2012; Varkevisser and Van der Geest, 2007). 5.2. Hospital objectives

6. Conclusions

Tynkkynen and Vrangbæk (2018) compare empirical estimations for Europe and find that public hospitals treat patients who are slightly older, have lower socio-economic status, riskier lifestyles, higher levels of co-morbidities and complications than patients treated in private hospitals; this result is also confirmed by the analysis by Bjorvatn (2018) using data for Norway. This may be the reason why quality in terms of outcomes for public hospitals is sometimes lower; a conclusion in line with Moscelli et al. (2018), who study quality differences among hospitals in the UK. The second interesting difference is that socio-economic status matters: patients with a higher economic status are more likely to be admitted to private hospitals, especially where a parallel system exists (Dardanoni et al., 2018). Herrera et al. (2014) argue that only few empirical estimations have strong methodological quality. In most cases it is difficult to compare the performances of for profit institutions with public hospitals, especially in developing countries. When the results are comparable, the difference in quality indicators is not statistically significant. In general, what seems more important is the governance of hospital care rather than the status of the providers (Rumbold et al., 2015). An interesting question is to understand whether there is a difference in behaviour between public hospitals and non-profit organisations. The more recent literature (see Siciliani, 2018 and Sloan, 2000 for a review) confirms that not for profit organisations behave differently from private ones; how similar they are to public hospitals is still not clear. For example, an analysis of the evidences produced for Lombardy (Berta et al., 2018b, 2013; Riganti et al., 2017) shows that the behaviour of non-profit organisations is different from public and private hospitals alike; on the other hand for Norway there does not seem to be any significant change in hospital behaviour after adjusting for patients severity (Holom and Hagen, 2017).

Hospital care organisation has been thoroughly reformed through the introduction of competition among providers. However, given the nature of the good produced, a fully competitive market is not a viable choice, at least in countries dominated by public health care finance. Relevant fixed, sunk costs, a very specialised labour force, the characteristics of health care have induced national regulators to choose pseudo markets and hybrid forms of privatisation. Against this backdrop, we have reviewed the literature on mixed markets. The theoretical literature shows that mixed markets may be welfare improving only if some conditions on the relative degree of efficiency of providers and on the objectives they pursue are met. In health care, the presence of motivated workers may increase quality, and this is certainly very important from a policy point of view. Profit maximising hospitals, although more efficient, use their competitive advantage to increase profits; on the contrary, altruistic providers may be less efficient, but more “productive” in terms of quality. It is however important to remember that intrinsic motivation is different from altruism. The more an intrinsically motivated provider is also altruistic, the larger the scope for its presence in the market (Besley and Malcomson, 2018). Mixed markets may also improve on this element because profit and non-profit organisations may react differently to quality competition (Hansmann, 1980). These results could also explain the rationale behind public competition, an instrument still widely used for the provision of hospital care. It should however be noted that the choice of opening the market to private competitors may have added value when patients preferences for quality are too different from those of the intrinsically motivated hospital staff (Besley and Malcomson, 2018). The empirical evidence is not conclusive, but in general there does not seem to be a significant difference in efficiency across hospital type, especially in developed countries. However, this may not necessarily mean that opening to private hospitals cannot produce any effect: it may be the presence of private competitors that makes public hospitals increase their efficiency (Horwitz and Nichols, 2009). Another important consideration in the study of performances of mixed markets is that fiscal rules play an important role: in some countries the difference in the fiscal treatment of for profit and non-profit organisations creates a strong incentive to choose the second form. This means that on the same market several actors compete: private hospitals, public hospitals and non-profit organisations, some of which are however acting as for profit providers (Jones et al., 2017). This consideration is often overlooked by empirical studies and it is certainly an interesting avenue for further research, especially in the light of the recent studies on patients preferences (Drevs et al., 2014). The general message that comes out of this literature is that

5.3. Productivity differential The estimation of the productivity differential between for profit and non-profit organisations (Boitani et al., 2013; Chang et al., 2004; Tiemann et al., 2012) has produced mixed results. For Germany, DRGbased reimbursement schemes have enhanced hospital performances and this seems to be the most important factor determining the improvement in Total Factor Productivity (TFP) (Karmann and Roesel, 2017). This allows to conclude that in general private hospitals are not necessarily associated with higher efficiency (Tiemann et al., 2012). A similar conclusion is reached by Tynkkynen and Vrangbæk (2018) in their comparison of empirical estimations for Europe. Futhermore, these differences are not significant once the case mix is properly 6

Social Science & Medicine 247 (2020) 112810

L. Levaggi and R. Levaggi

governance is important. Rumbold et al. (2015) highlights five key elements for a good governance: concentrating on efficiency across all hospitals; tackling variation; thinking carefully about how purchasers can use incentives to improve efficiency and service delivery; ensuring good measurement, and using international comparisons thoughtfully. Some recent studies point towards an interesting evidence: non-profit and public hospitals may change their behaviour when are made compete with private hospitals. This is an important finding from a policy point of view which may mean that comparing performances is not sufficient to make decisions: in other words, even if we observe that public hospitals in a mixed market are sufficiently efficient to perform better than their private counterpart, this does not necessarily mean that they would be so efficient if they were made compete with other organisations. Finally, an area which would be worth investigating is worker

motivation, which is emerging as an important characteristic of public/ non-profit health care providers. More research should be devoted to studying how relevant this characteristic is in public organisations and what happens to motivation when public hospitals are privatised or made more independent. Intrinsic motivation allows to reduce the cost and/or to enhance the quality of public providers. However, when the hospital becomes privatised intrinsic motivation may be crowded out by profit retention. CRediT authorship contribution statement Laura Levaggi: Methodology, Formal analysis, Writing - original draft, Writing - review & editing. Rosella Levaggi: Conceptualization, Methodology, Writing - original draft, Writing - review & editing.

Appendix. Quality choice in a mixed market for hospital care The utility of a generic individual located at x can be written as:

U (x ) = v + max { q0

mx , q1

m (1

(A1)

x )}

From equation (A1) we can define the demand as (q0

D0 = x 0 = D1 = 1

q1 )

1 2 q0 )

+

2m (q1

x0 =

2m

1 2

+

(A2)

Altruistic providers Competition between public providers Let us consider a public provider located in 0. The cost function and the non-monetary disutility are:

2 e0) x 0 , F0 = (e02 + q0) x 0 ,

C0 = (

therefore the provider's objective can be written as: x0

Max q0, e0

( q0

ms ) ds

( q0 + e02 ) x 0

(A3)

0

The FOCs are:

e0

2 (3q 0

q1) +

(q0

q1) + m

m

2 [ (2q0 4m

q1) + m]

e02

=0

=0

2m

and the reaction function is:

e0 = 0 q0 =

2 4

3

q1 +

m

e02

2 m (4

3

(A4)

)

When the two providers are symmetric it holds q0 = q1 and the optimal solution is:

q0 = q1 =

m

m

2(

(A5)

)

< 2 for the quality to be positive. which requires < Competition between private providers Let us now consider a private provider located in 1. The cost function and the non-monetary disutility are:

C1 = (

2 e1 + kq1)(1

x 0) F1 = e12 (1

x 0)

and the objective function to be maximized is:

T (1

x 0)

(

2 e1 + kq1)(1

Defining S = T

Max q1, e1 (S + 2 e1

x 0)

e12 (1

x 0)

the objective of the private hospital is:

kq1

e12 )(1

(A6)

x 0)

and from the FOCs:

7

Social Science & Medicine 247 (2020) 112810

L. Levaggi and R. Levaggi S

2 k (q1

(e1

2q0) + e1 (2 2m q1) m

(q0

)

e1)

km

k 2

=0

=0

m

the reaction function is:

e1 = q1 =

q0 2

S+ 2 2k

+

m 2

(A7)

Given that hospitals are symmetric, we can write q0 = q1 and the solution can be written as: 2

S+ k

q0 = q1 =

m (A8)

Mixed market Let us now consider the case where a public provider located in 0 competes with a private one located in 1. For the private hospital, the reaction function is represented by equation (A7), while for the public hospital we can use equation (A4). The solution can be obtained by solving the following system:

e0 = 0 q0 = e1 = q1 =

2 0 4 0 3 q0 2

(4 0

S+ 2 2k

+

2 0m 3

m

q1 +

e02 )

m 2

The solution is:

q0 =

5

2 6

q1 =

3 5

4 6

( (

) )

S+ 2 k

3m

S+ 2 k

2m

(A9)

It is easy to show that the solution for the mixed market is a combination of the optimal qualities obtained by pure market forms. In particular, indicating the qualities of the mixed market with a superscript M, it is:

q0M = q1M

=

2 1+ 1 1+

with

=

1

q0 +

1+

q1

q0 +

1+

q1

3 2(

)

4

. The average quality in the mixed market is thus:

Aq M = q0M x 0 + q1M (1

x 0) = q1

x0 1+

+ q0

1 + x0 1+

If q1 > q0 the quality offered in a pure private market is higher than the quality in the mixed market; if q1 < q0 the quality offered in a pure public market is the optimal one. Intrinsic motivation Public competition The cost function and the non-monetary disutility are the same as in the case of altruistic providers:

2 e0) x 0 , F0 = (e02 + q0) x 0

C0 = (

while the objective of the hospital is

Max q0, e0 ( q0

q0 x 0

e02 x 0 )

(A10)

The FOCs are: 2

q0

2m q1) + m

(q0

e0

q1 + m + e02

2 m

2m

=0

=0

The reaction function is 1

q0 = 2 q1 +

2 m 2

m

(A11)

e0 = 0 For a public market q0 = q1 and the optimal values are:

q0 =

2 m

m

(A12)

e0 = 0 8

Social Science & Medicine 247 (2020) 112810

L. Levaggi and R. Levaggi

Mixed market In this case it is sufficient to combine the reaction functions of the private hospital in equation (A7) with the reaction of the public hospital in equation (A11) to obtain the following solution:

q0 =

1 S+ 2 3 k

m

+

4 m 3

m

+

2 m 3

e0 = 0 q1 =

2 S+ 2 3 k

(A13)

e1 =

As in the previous case, the solution for the mixed market is a combination of the optimal qualities obtained for the pure market forms. By denoting the qualities of the mixed market with a superscript M, we can write: 2

1

2

1

q0M = 3 q0 + 3 q1 q1M = 3 q1 + 3 q0 therefore, the average quality in the mixed market is:

Aq M = q0M x 0 + q1M (1

x 0) = q1

x 0 + 2(1 3

x 0)

+ q0

2x 0 + (1 3

x 0)

As before, the average quality is less than the maximum obtained by the pure market forms. Market share For this model, the generic cost function is:

Cj =

j Dj

1 2 q 2 j

+

The objective function is provider-specific and equal to:

V j = (T

1 2 q + 2 j

j ) Dj

j Dj

and demand is as in (A2). The objective of a generic provider i is:

Max qj (T

j

+

j)

(qj 2m

qi )

+

1 1 + qj2 + 2 2

j xj

(A14)

thus the FOC is:

(T

j

+

j)

2m

qj = 0

There is no strategic interaction in the choice of the quality level which is:

qj = (T

j

+

j)

(A15)

2m

For private hospitals j = 0 and j = p ; for public hospitals j = and j = s with p < s . If p < s a private market should be preferred. The mixed market is always dominated by a pure form.

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