The profitability of vertical mergers between hospitals and physician practices

Journal of Health Economics 18 Ž1999. 623–654 www.elsevier.nlrlocatereconbase

The profitability of vertical mergers between hospitals and physician practices Esther Gal-Or

)

210 MerÕis Hall, Katz Graduate School of Business, UniÕersity of Pittsburgh, Pittsburgh, PA 15260, USA

Abstract We demonstrate that the existence of incentives for vertical mergers between hospitals and physician practices depends upon the relative degree of competitiveness of the two providers’ markets. When the degree of competitiveness is comparable, a vertical merger enhances the bargaining position of both merging parties vis-a-vis insurers. In contrast, ` when one provider’s market is much more competitive than the other a vertical merger may reduce the joint profits of the merged entity. Prohibiting the parties from offering their services in conjunction with outside independent entities may restore the profitability of the vertical merger even in this case. q 1999 Elsevier Science B.V. All rights reserved. JEL classification: I11; L13; L22 Keywords: Vertical mergers; Hospitals; Physicians

1. Introduction Health care markets have experienced significant changes during the last decade. The degree of industry concentration both in health insurance and in the provision of health care services has risen in some markets due to the increased role of managed care in health insurance, on one hand, and due to efficiency improving mergers among health care providers, on the other hand. With greater concentration on each side of the market, it is common to observe long-term )

Tel.: q1-412-648-1722; Fax: q1-412-648-1693; E-mail: [email protected]

0167-6296r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 6 2 9 6 Ž 9 9 . 0 0 0 1 3 - 2

624

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

relationships arising between providers of health insurance Žpayers. and providers of health care services Žhospitals and physicians. with the terms of the relationship negotiated between the parties via contracts. In addition to horizontal mergers, many health care markets have witnessed a wave of vertical mergers between hospitals and physicians practices. For example, the number of physician practices owned or managed by hospital-based systems increased by 60% between 1994 and 1995, from 7015 to 11,234 ŽJaklevic, 1996.. Allina Health System which covers approximately one-fourth of Minnesota’s residents through its HMO and PPO, is the result of a 1994 merger between a hospital chain and a health plan, and Allina is continuing to acquire hospitals and physician practices. Similarly, both the University of Pittsburgh Medical Center and Blue Cross of Western Pennsylvania have been purchasing physician practices. In addition to mergers, the vertical relationship between hospitals and physician practices has been frequently characterized by exclusive contracts. American Hospital Association surveys indicate, for instance, that 73% of hospitals had exclusive contracts with various physician Specialties in 1989 ŽFrech and Danger, 1998.. In the present paper, we investigate the implication of different types of vertical mergers between hospitals and physician practices upon the bargaining position of the merged entity vis-a-vis insurers. We examine, in particular, whether the ` imposition of restrictions on the merging parties, in the form of exclusivity arrangements improves the terms of contracting that can be secured by the merged entity; thus, translating to higher reimbursement rates of providers and higher premia charged from consumers. The Agency and Transaction Costs literature provides various efficiently grounds for vertical integration ŽArrow, 1975; Williamson, 1979; Grossman and Hart, 1986.. For example, tasks of monitoring and controlling health care utilization and quality may be done more efficiently in organizations where physicians and hospitals are vertically integrated. The integrated unit can also lower the transaction costs of negotiating, coordinating and enforcing agreements with different components of the delivery system. As well, the larger size facilitates better spreading of the risk of capitation and allows for the utilization of economies of scale Žfor a detailed discussion for an efficiency rationale for mergers in health care, see Robinson and Casalino, 1996 or Gaynor and Haas-Wilson, 1998.. Similar efficiency considerations may also underlie the existence of exclusive arrangements between hospitals and physicians. In the present paper we abstract from such efficiency issues and focus primarily on the market power that vertical integration or exclusivity clauses can confer on the parties in their negotiations with insurers. While the Industrial Organization literature does address some issues related to the anti-competitive implications of vertical mergers, especially in the context of market foreclosure ŽBork, 1978; Salinger, 1988; Hart and Tirole, 1990; Ordover et al., 1990., the prevailing view has been that of the ‘Chicago school’ that a tying

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

625

relationship between two vertically related firms cannot be profitable. In the present paper, we demonstrate that such a conclusion may be wrong in the context of health care markets where negotiations with insurers play an important role in determining the terms of reimbursement of health care providers. We find that the profitability of vertical mergers to the merging partners crucially depends upon the relative degree of competitiveness of the hospital vis-a-vis the physician markets. When the two provider’s markets are character` ized by comparable degrees of competitiveness as measured by number of competitors and degree of differentiation among them both the merging hospital and the merging physician can negotiate higher rates with insurers. Moreover, even the independent providers can secure more favorable rates in this case. Consumers are obviously worse off, as a result, since the higher rates translate to higher premia charged by insurers. When the extent of competitiveness of the two provider’s markets sharply differ, vertical mergers that do not impose restrictions on the merging partners may be unprofitable. Prohibiting the partners from offering their services in conjunction with outside independent entities may restore the profitability of the vertical merger, even in this case. While in the Industrial Organization literature, the imposition of such restrictions on the merging parties has been interpreted as attempts to foreclose the markets from competitors, in the present analysis the imposition of such restrictions can actually benefit even the independent hospitals or physicians. Since each provider can command higher rates from insurers if its competitors have an improved negotiating position vis-a-vis insurers, the imposition of restrictions may benefit both the merging and ` the independent providers. Even though most of the antitrust activity related to mergers focused on horizontal mergers among physicians or among hospitals, there have been several recent cases related to vertical mergers and exclusive dealings in health care markets. In a Wisconsin 1996 court case, Blue CrossrBlue Shield of Wisconsin charged that Marshfield Clinic, a physician owned clinic that was vertically integrated with its HMO had excluded the Blue CrossrBlue Shield HMO by foreclosing the market for physician services. The court found in favor of Marshfield Clinic since it concluded that the clinic did not have the market power to foreclose the plaintiff from the HMO market. In 1996, the DOJ charged Woman’s Hospital Ža monopoly provider of inpatient obstetrical services in Baton Rouge. and Woman’s Physician Health Organization Ža PHO formed by Woman’s Hospital with nearly every member of the hospital’s medical staff. with using the PHO agreement to reduce competition among OBrGYNs. In this case as well, the court found in favor of the defendant due to low entry barriers to the physician market. In New Hampshire legislation, banning exclusive contracts between HMO’s and health care providers took effect in June 1997 and, lastly, the Department of Justice ŽDOJ. brought civil enforcement actions against physician hospital organizations in Danbury, CT and St. Joseph, MO arguing against vertical restraints between monopoly hospitals and a large share of physicians in the

626

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

market. The current Industrial Organization literature related to the anti-competitive implications of vertical restraints has been of limited use in guiding the courts in all of the above cases since this literature fails to capture several important characteristics of health care markets. We try to correct the shortcomings of this literature by the way we model the structure of the insurance and health care provision industries and the manner in which different participants in those industries interact. In particular, since reimbursement rates that are approved by payers are usually negotiated with providers via contracts, we model the negotiation process among the parties and investigate how the terms of contracting depend upon vertical mergers between hospitals and physicians. The distinction between the ‘restrictive’ and ‘unrestrictive’ vertical mergers that we consider in the present paper resembles, to some extent, the distinction between ‘pure bundling’ and ‘mixed bundling’ strategies that have been discussed in the Industrial Organization literature Žsee McAfee et al., 1989; Salinger, 1995; Chen, 1997.. While with restrictions consumers have to obtain care from the merged hospital–physician pair only as a ‘pure bundle’, in the absence of restrictions consumers can ‘mix and match’ between one of the merging partners and outside, independent entities. While in ŽMcAfee et al., 1989., ‘mixed bundling’ is always considered to be a weakly dominating strategy from the perspective of a single firm, Chen Ž1997. demonstrates that competition among firms can reverse this result. Similarly, in our paper where competition among hospitals and physicians is explicitly modeled, ‘pure bundling’ type of mergers may be more profitable than ‘mixed bundling’ type of mergers. The remaining part of the paper is organized as follows. In Section 2, we describe the main assumptions of the model. In Section 3, we evaluate the implications of unrestrictive vertical mergers upon the outcome in the market. In Section 4, we conduct a similar evaluation of the implication of imposed restrictions on the negotiating position of the merged entity. In Section 5, we relax an earlier assumption concerning the distribution of preferences among hospitals and among physicians and, in Section 6, we conclude.

2. The model Assume a market that consists of two health insurance companies, n physicians and m hospitals. Insured individuals who become sick require care from a hospital as well as a physician. Individuals perceive the different health care providers as offering differentiated type of services when treating them. To capture this differentiation we assume that in evaluating hospitals the preferences of patients can be described as uniformly distributed on a circle of one unit length with the m different hospitals located on this circle at equal distance from each other. When a patient obtains care from a hospital located away from his ‘address’ on the circle he incurs transportation costs amounting to t per unit of distance. Similarly, in

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

627

evaluating the different physicians, patients are uniformly distributed on the same circle with the n physicians positioned at equal distance from each other. The variable s measures the transportation costs per unit of distance when obtaining care from a physician located away from the patient’s ‘address’ on the circle. The parameters t and s capture the degree of differentiation among hospitals and physicians, respectively, with higher values indicating increased differentiation. The different position of the health care providers on the circle can be interpreted either as geographic location or as specialization in treating different types of diseases or both. Initially, we assume that in choosing among hospitals the preferences of the patients are determined independently of his preferences among physicians. 1 For instance, if the physician is the internist or the family doctor who refers the patient to the hospital, the attribute of the physician that matters to the patient the most is the proximity of his office to the place of residence or place of work of the patient. In contrast, in choosing among hospitals, the patient is more concerned about the suitability of the hospital for treating the specific disease that the patient suffers from. In essence, while hospitals can treat a spectrum of different ailments each may decide to specialize in a certain subset in order to acquire a reputation for excellence in treating diseases in the selected set. We assume that in the absence of any restriction imposed by either the health insurance companies or the hospitals, insured individuals are free to choose any hospital or physician from those available in the market. Individuals obtain insurance through their place of employment. Employers choose insurers with the welfare of employees in mind. They consider the two insurance companies to be differentiated. Such differentiation may be the result of different networks of providers Žother than the m hospitals and n physicians modeled above. that are approved by the insurers, additional services Žother than health insurance. that the companies provide, or the existence of switching costs which yield a preference for the insurer with whom the employer contracted in the past. To capture this differentiation we assume, once again, a uniform distribution of preferences on a circle of one unit length with the location of the insurance companies splitting the market into two equal segments. The transportation parameter M captures the degree of differentiation among insurance companies. Since we assume that employers are benevolent representatives of their employees the distribution of preferences between insurers reflects the employers’ preferences as well as that of an ‘average’, representative individual they employ. In describing the preferences of the population, we have distinguished between the ex-ante distribution of preferences that applies when employers choose insurers on behalf of their employees and the ex-post distributions of preferences

1 The independence assumption simplifies the analysis significantly. It can be relaxed, however, without affecting the qualitative results of the paper. Later in the paper, we allow for correlation between the two distributions.

628

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

among hospitals and physicians that apply when subscribers become sick. We assume that the ex-ante distribution, that determines the choice of insurance company is independent of the ex-post distributions. This assumption is reasonable if insurers do not impose any restriction on choice on their subscribers and if at the time insurance is purchased employers are unaware of the exact future ailments of their employees. They assume, therefore, that the distribution of ailments or preferred locations of physicians is as specified by the ex-post distribution. The distinction between the ex-ante and ex-post distributions allows us to capture the notion of ‘option demand’ Žsee Dranove and White, 1996. that refers to the patient’s demand for the option to use a specific provider when becoming sick. Designating by u the probability that the individual becomes sick, by y his distance Žas well as that of his employer. from insurer i in the ex-ante distribution of preferences and by Fi the premium charged by this insurer, Ui Ž y . expresses the expected utility of a representative individual who obtains insurance from i. We specify this utility as follows: Ui Ž y . s Ž 1 y u . H q u S y w Fi q My x q u Õ y 2 tm

1r2 m

H0

xd x y 2 sn

1r2 n

H0

zd z

Ž 1.

The first bracketed expression in Ui Ž y . is the expected payoff of the individual in the absence of insurance where H and S designate his level of utility when he is healthy and sick, respectively. The second bracketed term measures the cost of insurance which amounts to the premium payment Fi plus the transportation cost My resulting from having to obtain insurance from a company located away from the ‘address’ of the individual’s employer in the ex-ante distribution of preferences. The last bracketed term measures the net benefit from obtaining insurance. This net benefit is computed by subtracting from the gross benefit of obtaining care Õ, the expected ex-post transportation costs that are incurred by a patient who becomes sick. Note that in computing those ex-post transportation costs we capture the assumption that a representative individual is equally likely to obtain care from any one of the m participating hospitals and n participating physicians. Since the population was assumed to be uniformly distributed in the ex-post distributions of preferences, at the time insurance is purchased employers expect their employees to be equally likely to suffer from the different diseases or to reside in any of the geographic locations captured by the ex-post distributions. In addition, as the number of hospitals or physicians increases the expected ex-post transportation costs decline since individuals have a greater choice among providers when they become sick. Note that the utility specification in Eq. Ž1. implies that when an individual becomes sick he uses the services of the hospital and physician at a fixed proportion of 1:1. This assumption can be easily relaxed to allow for any fixed proportion of k physician visits for every hospital stay. With k ) 1, such a specification captures the more realistic assumption that sick individuals are more

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

629

likely to use physician rather than hospital services. By normalizing units of physician services so that a single unit accounts for k visits the fixed proportion k:1 is captured by our model as well. 2 If the insurance companies do not impose any restrictions on the choice of subscribers the demand facing company i can be derived from Eq. Ž1. as follows: Di Ž Fi , Fj . s

1 q 2

Fj y Fi M

i , j s i ,2; i / j.

Ž 2.

To simplify the analysis, we assume that the participants in the market incur no variable costs associated with the level of service they provide. 3 We designate by K I , K H and K D the level of fixed cost that an insurance company, a hospital and a physician incurs, respectively. Before considering the possibility of vertical mergers between hospitals and physician practices, we derive the equilibria when hospitals and physicians negotiate independently with insurance companies. To model this negotiation process, we employ the Nash Bargaining Solution and we assume that each insurance company negotiates with a single provider at each round of negotiations. A given provider cannot observe the negotiations between the insurance companies and other providers nor can one insurer observe the negotiations of its competitor. Let y ki designate the reimbursement rate per patient that is agreed between insurance company i and hospital k and, similarly, let z Õi designate the negotiated rate between insurance company i and physician Õ. In case of disagreement with hospital k, the individuals who subscribe to insurance company i experience an increase in their expected ex-post transportation costs amounting to Ž tr2 m2 . and in case of disagreement with physician Õ subscribers experience an increase in transportation cost amounting to Ž sr2 n 2 .. When the insurance company fails to reach an agreement with one of the providers Žhospitals or physicians. its subscribers have to choose among a smaller set of providers which, in turn, increases their ex-post transportation costs. The additional costs are more significant the greater the degree of differentiation between the providers Ž t for hospitals and s for physicians. and the smaller is the initial number of providers Ž m for hospitals and n for physicians.. Given our assumption that the ex-post distribution of preferences among hospitals and among physicians are independent of each other the additional transportation cost incurred in case of disagreement with a given hospital is independent of the characteristics of the physicians’ market and vice versa. With correlation between the two distribution functions the cost 2

Our model is limited, however, only to a fixed proportion, hospital–physician technology. It cannot capture, in particular, a variable proportion technology. 3 An alternative, equivalent assumption is that each party incurs a constant variable cost per unit of service provided.

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

630

increase induced by a disagreement with any provider would depend upon the characteristics of both the physician and the hospital markets. 4 When a given insurer and provider pair negotiate over the reimbursement rate both parties consider the agreements with outside parties to the negotiation Žbetween the given insurer and other providers or the given provider and the other insurer. as fixed. The negotiated reimbursement rate depends upon the benefit that each party derives from reaching an agreement net of the outside option that this party can secure in case an agreement cannot be reached. The expressions for JiH and Hk , defined below, correspond to the payoffs that accrue to insurance company i and hospital k, respectively, in case these two parties are successful in reaching an agreement between Uthem. In case of disagreement their payoffs Žor outside options. are given by JiH and HkU Žthe superscript H designates negotiation with a hospital.. JiH s Hk s

1

ž ž

q

Fj y Fi

2

M

1 q

Fj y Fi

2

M

/ž /

1

Fi y u

u

m

y ki q

m

Ý yli q

m ls1

ž

1 q 2

1

n

Ý z ri

n rs1

Fi y Fj M

/

u m

/

yKI

y kj y K H

i , j s 1,2; i / j; k s 1,m. U

JiH s

ž

1 q 2

Fj y Fi

Ž 3. ut

y

M

2

/ž

ut

u

2m M

Fi y u

1

m

1

n

Ý yiq Ý zi Ž m y 1 . ls1;l/k l n rs1 r

/

yKI HkU s

ž

1 q 2

Fi y Fj m

q

2

/

2m M m

y kj y K H

i , j s 1,2; i / j; k s i ,m.

Ž 4. In the derivation of the disagreement payoffs, we have used the assumption that other than itself, each party to the negotiation considers the composition of the networks serving different insurers as fixed. 5 In case of disagreement between 4

Later, when we allow for such correlation we evaluate the incentives of a given hospital to vertically integrate with a certain physician practice as implied by the degree to which consumers view the specific hospital–physician pair an ‘‘ideal’’ bundle given their correlated preference structure. With our assumption about the independence between the two distribution functions, a given hospital is actually indifferent as to which physician practice it acquires in case of vertical integration. 5 If the insurer and the provider do not know the overall composition of the networks serving the two insurers the Shapley value is probably a better solution concept to characterize the results of the negotiations. Also note that if a given party had the full bargaining power to set the reimbursement rate it would choose it to maximize its own profits. Hence, insurer i would choose yki s 0 and hospital k would choose yki to extract the entire remaining surplus of the insurer Ži.e., Ž u r m. yki s Fi y u wŽ1r m.Ý l / k yli qŽ1r n.Ý mrs1 z ri x.. The Nash bargaining solution guarantees that the negotiating parties split evenly the added surplus generated in their negotiations.

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

631

insurer i and hospital k, the subscribers of insurer i have a more limited choice among hospitals, thus, raising their ex-post transportation costs by tr2 m2 and reducing the demand facing this insurer correspondingly. The demand facing the competing insurer rises as a result. This explains in Eq. Ž4. the decline in sales volume confronting insurer i when hospital k drops out of its approved set to subscribers. It explains also the larger stream of customers insured by j that seek treatment from hospital k in that case. The reimbursement rate y ki maximizes the following product of the added benefits to the parties involved: Max Ž JiH y JiH

U

yki

. Ž Hk y HkU .

Ž 5.

In a similar manner, when an insurer negotiates with a physician, the following expression correspond to the agreement and disagreement payoffs of the parties U involved Ž JiD , JiD for insurer i and DÕ , DÕU for physician Õ .. JiD s

DÕ s

ž ž

U

JiD s DÕU s

1 q

Fj y Fi

2

M

1 q

Fj y Fi

2

ž ž

M

1 q

/ž / ž u

n

Fj y Fi

2

Fi y u

z Õi q

us y

2 n2 M

M

1 q

Fi y Fj

2

M

us q

2

m

1

1

n

Ý yli q n Ý z ri m ls1

1 q

rs1

Fi y Fj

2

M

/ž /

u

2n M n

Fi y u

/

1

u n

/

yKI

z Õj y K D

m

Ž 6. 1

n

Ý yli q n y 1 Ý m ls1

z Õj y K D

z ri

rs1; r/Õ

/

yKI

i , j s 1,2; i / j; Õ s 1,n.

Ž 7. The reimbursement rate of the physician, z Õi solves the following product of net benefits to the parties involved: Max Ž JiD y JiD z Õi

U

. Ž DÕ y DÕU . .

Ž 8.

Simultaneously with the negotiations over reimbursement rates insurers set the level of premia in order to maximize their equilibrium payoffs. Choosing Fi to maximize the agreement payoff JiH Ž JiD . yields the following system of first order conditions: 1 q 2

Fj y 2 Fi M

u q M

1

m

1

n

Ý yli q n Ý z ri m ls1

rs1

s0

i , j s 1,2; i / j.

Ž 9.

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

632

We focus attention on the characterization of symmetric equilibria where Fi s Fj ' F U , y ki s y kj ' yU for all k and z Õi s z Õj ' zU for all Õ. Substituting such symmetry into Eqs. Ž5., Ž8. and Ž9. yields the following solution: mtM yU s 2 2Ž m M y u t . nsM zU s 2 2Ž n M y u s . M FU s q u Ž y q z . . Ž 10 . 2 The joint profits that accrue to a hospital–physician pair in the absence of a vertical merger is given, therefore, as: zU yU P VS s u q yKH yKD , m n where VS designates vertical separation. The expressions in Eq. Ž10. imply that to guarantee an interior solution insurers have to be sufficiently differentiated in comparison to the degree of competitiveness of the providers’ market Ži.e., M ) Max u trm2 , u srn2 4.. 6 Note that a given provider receives lower reimbursement rates when the extent of competition among the providers is more intense; as reflected by high values of m and low values of t for the hospital market and high values of n and low values of s for the physician market. In addition, if the degree of differentiation between insurers is more significant, as reflected by higher values of M, health care providers are forced to accept lower reimbursement rates. In essence, the rate that a given provider can negotiate is higher the less competitive is this provider’s market in comparison to the insurance market.

ž

/

3. Unrestrictive vertical mergers If a certain hospital–physician pair decides to vertically integrate the integrated entity negotiates on behalf of both the hospital and the physician. 7 If an insurer 6

For instance, when t s s and ms n, the restriction implies that Mr t ) u r m2 . With probability 0.1 of becoming sick and with two providers in each market this condition states that the ratio Mr t is bigger than 0.025 Ži.e., the degree of differentiation among providers cannot be more than 40 times the degree of differentiation among insurers.. Hence, while insurers are normally not significantly differentiated, some minimal degree of differentiation is necessary to support an interior equilibrium. This minimal required level tends to be small, especially with more than two providers in each market Žfor ns ms 3 the ratio Mr t has to exceed 0.011 and with ns ms10 it should exceed 0.001.. 7 While in reality a vertical merger between a hospital and a physician practice does not always yield the unified pricing decision we assume in the model, it definitely supports greater coordination between parties in their negotiations with insurers.

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

633

fails to reach an agreement with this integrated unit its subscribers incur additional ex-post transportation costs amounting to w tr2 m2 q sr2 n 2 x. Such an increase in cost results in a more dramatic decline of the demand facing the insurer than in the case that it fails to reach an agreement with a single independent provider Žhospital or physician.. The improved bargaining position of the integrated unit may yield, therefore, higher joint profits to the parties involved in theU vertical merger. To evaluate this possibility we designate by JiH D and JiH D the agreement and disagreement payoffs of insurer i when negotiating with a vertically integrated entity comprising of hospital k and physician Õ. We designate by Hk DÕ and Hk DÕU the agreement and disagreement payoffs of this entity. The payoffs to the parties are given as follows: JiH D s

1

ž

q 2

ž ž

U

M 1

Hk DÕ s

JiH D s

Fj y Fi

Fj y Fi

q 2

M

1 q

/ž /ž

Fi y u

Fj y Fi

2

ž

q 2

n

/ ž

ž

1

q

t

s

M 2 m2

Ý

z ri

Fi y Fj

q

n y 1 rs1, r/Õ 1

z Õi

rs1

q

2 n2

q

/

Fi y Fj

2

M

//ž

Fi y u

y kj

/ž u

m

1

q

z Õj n

/

Ž 11 .

m

Ý

m y 1 ls1,l/k

y li

n

1

Hk DÕU s

q

m

u

M

q

y ki

n

1

Ý yli q n Ý z ri m ls1

u

y

m

1

M

/ u

ž

t

M 2 m2

i , j s 1,2; i / j; k s 1,m; Õ s 1,n.

s q

2 n2

// ž u

y kj m

q

z Õj n

/ Ž 12 .

Note that the underlying assumption in the above specification is that the parties involved in the merger are allowed to offer their services in combination with outside independent providers. Hence, any physician can provide service to a patient that chooses to obtain care from hospital k and any hospital can similarly be utilized in combination with physician Õ. The merger does not prohibit either the physician or the hospital from offering their services independent of each other. In a later section, we will analyze the consequences of vertical mergers that impose such restrictions on the parties involved. In negotiating with independent hospitals or physicians that are not part of the merger the agreement and disagreement payoffs are still specified by the expressions given in Eqs. Ž3., Ž4., Ž6. and Ž7.. Similarly, the first order conditions that determine the premia payments are still given by system Ž9.. Solving for the

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

634

symmetric equilibrium where Fi s Fj ' F; y ki s y kj ' y k ; z Õi s z Õj ' z Õ ; y lj s y lj ' yyk , l s 1,m, l / k; and z ri s z rj ' zyÕ , r s 1,n, r / Õ yields: yk s z Õ

s

Ž n2 t q m2 s . M Ž m y 1 . tM Ž n y 1 . sM q q 2 m Ž m2 M y u t . 2 n Ž n2 M y u s . 2 Mm2 n2 y u Ž n 2 t q m2 s . 2my1 m

2

2ny1 q

n2

Ž 13 . yyk s

zyÕ s

yk

q

Ž m y 1 . tM 2 Ž m2 M y u t .

Ž 14 .

q

Ž n y 1 . sM , 2 Ž n2 M y u s .

Ž 15 .

m yk n

where y k and z Õ designate the rates approved to the hospital–physician pair that comprise the merged entity and yyk and zyÕ designate the negotiated rates of each independent hospital and each independent physician, respectively, that are not part of the merger. To ensure that the negotiated rates are always positive, we impose the following restriction on the parameters of the model: M)

u Ž n2 t q m2 s . m2 n2

.

Ž 16 .

Note that this restriction is rather weak for reasonable values of the parameters. For instance, with probability 0.1 of becoming sick and with an equal number of providers in each market Ž m s n. condition Ž16. reduces to MrŽ t q s . ) 0.1rm 2 . Thus, the combined extent of differentiation between providers Ž t q s . cannot be more than 40 times the degree of differentiation between insurers when m s 2 and it cannot be more than 1000 times the degree of differentiation among insurers when m s 10. The minimal degree of differentiation among insurers that is required by Eq. Ž16. is likely to hold, for instance, if in addition to the n hospitals and m physicians mentioned above each insurer has to contract with other types of health care providers who remain unspecified in the model. For instance, if the m physicians of the model are internists, the additional providers may consist of specialists Žsuch as pathologists or radiologists. that each insurer has to contract with. If the composition of this set of additional providers is not identical across different insurers, the services offered by the insurers are considered to be differentiated.

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

635

Since hospital k and physician Õ negotiate with each insurer as a team, when an insurer fails to reach an agreement with either one of them, both parties drop out of the set of providers that the subscribers of this insurer can utilize. A disagreement with either one of the parties imposes the same additional ex-post transportation costs on subscribers and translates, therefore, in Eq. Ž13. to identical rates that both the merging hospital and the physician can command. This common negotiated rate post-merger need not exceed, though, the rate that each party could receive independently if it remained vertically separated. In Proposition 1, we characterize conditions under which approved rates are indeed higher as a result of the vertical merger. Those conditions relate to the relative degree of competitiveness of the hospital and physician markets. We measure such competitiveness by ratio mrt for the hospital market and nrs for the physician market, with higher values of either one of the measures indicating increased competitiveness. ŽProofs of all the propositions are included in the Appendix.. Proposition 1 Ži. If the extent of competitiveness of the hospital and the physician markets is comparable, in the sense that the difference ŽŽ nrs . y Ž mrt .. is sufficiently small, both the hospital and the physician who are part of the merged entity benefit from higher negotiated rates as a result of a merger. Žii. Otherwise, if the extent of competitiveness of the two markets sharply differ it is only the party who participates in the more competitive provider’s market who benefits from improved rates as a result of the merger. To understand the intuition for this result consider the case, for instance, that the hospital market is far less competitive than the physician market. By tying its fortunes to a hospital that operates in a highly concentrated market where differentiated types of services are offered to patients, a given physician can vastly improve its negotiating power vis-a-vis the insurer since a disagreement with it ` translates to a significant decline of this insurer’s potential market among subscribers. On the other hand, the hospital that has been party to the merger has diminished its leverage in the negotiations with insurers given that it is tied to a partner who is viewed as being just one of many similar providers all offering closely substitutable care. If the deteriorated bargaining position of the hospital more than offsets the improved bargaining position of the physician the vertical merger may yield the mixed results reported in part Žii. of the proposition. An inspection of the expressions obtained in Eqs. Ž13. – Ž15. allows us to compare the rates negotiated by the independent providers with those obtained by the merged entity. We conduct this comparison in Proposition 2. In stating the proposition, we utilize our earlier notation yU and zU to designate the common negotiated rate of each hospital and physician, respectively, in the absence of a vertical merger.

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

636

Proposition 2 If the merging hospital Žor physician. can negotiate a higher reimbursement rate as a result of a vertical merger then: y k ) yyk ) yU Ž or z Õ ) zyÕ ) zU . . If, however, the merging hospital Žor physician. are forced to negotiate lower rates as a result of the merger then yU ) yyk ) y k Ž or zU ) zyÕ ) z Õ . . According to Proposition 2, if the merger benefits a certain provider who has been a party to a vertical merger it also benefits all other providers who participate in the same market as the merging partner. Since the merging provider is able to negotiate higher rates, in this case, its competitors follow suit by insisting on higher rates in the negotiations with insurers. The merging provider can command, however, higher rates than those secured by its competitors who have not been party to the vertical merger. If, on the other hand, the vertical merger yields a deteriorated negotiating position to one of the merging partners, all the providers who compete against this partner in the respective provider’s market are forced to lower their rates as well. The independent providers can secure, in this case, higher rates than those secured by the adversely affected merging partner. The profits that accrue to the merged entity are given from Eq. Ž13. as follows:

P VI s u y k

ž

1

1 q

m

n

/

yKH yKD ,

where y k is expressed in Eq. Ž13. and VI designates vertical integration. In Proposition 3, we evaluate the profitability of the vertical merger. Proposition 3 The following is a sufficient condition for a vertical merger to increase the combined profits of the merging partners. L ' Ž n y m . Ž ms y nt . G 0. The condition stated in Proposition 3 is weaker than the requirement stated in Proposition 1 to guarantee that the merging parties can both command higher reimbursement rates as a result of a merger. In particular, the degree of competitiveness of the hospital market Žas expressed by mrt . can be significantly higher Žor lower. than that of the physician market Žexpressed by nrs . and a vertical merger may still offer higher joint profits than vertical separation. The condition of Proposition 3 states that if one market is much more competitive than the other, the number of participants in the opposing market should be bigger. Even though, one merging party may be positioned at a deteriorated bargaining position in this

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

637

Table 1 Numerical example Parameters of model

Vertical separation

Unrestrictive vertical merger

Restrictive vertical merger

M s1 and u s 0.1 all cases

yU

zU

P VS

yk s z Õ

yyk

zyÕ

P VI

y1 s z1

y2 s z2

R P VI

Case 1 ms ns 2, t s ss10

3.33

3.33

0.33

4.44

3.889

3.889

0.444

3.125

3.75

0.3125

Case 2 ms ns 2, t s1, ss10

0.256

3.33

0.179

1.863

1.059

2.598

0.186

2.093

2.511

0.209

Case 3 ms10, ns 2, t s1, ss10

0.05

3.33

0.167

2.674

0.312

3.004

0.160

case, the improved position of its partner more than compensates for this weakened position, thus, yielding an increase of joint profits to the merged entity. It is important to note that the condition in Proposition 3 is a sufficient rather than a necessary condition. It is possible, therefore, that a vertical merger is beneficial to the parties even when the expression defined in the proposition is negative. If the absolute value of L is sufficiently small in this case, the joint profits of the merging parties is still higher. In addition, note that when the number of participants in each provider’s market is equal, so that n s m, the vertical merger definitely benefits the merging partners. 8 We state this result in the following corollary. Corollary 1 When n s m the vertical merger is always beneficial. To illustrate our results consider the case that m s n s 2, t s s s 10, M s 1 and u s 0.1 ŽCase 1 of Table 1.. In the absence of a merger the combined payoff of a given hospital–physician pair is equal to 0.33. An unrestrictive vertical merger of the parties raises this combined payoff to 0.44 which amounts to an increase of 33%. Keeping the number of providers in each market at two and introducing some discrepancy in the extent of competitiveness of the two markets, by assuming that t s 1 and s s 10 ŽCase 2 of Table 1. maintains the profitability 8

Recall that our model allows for normalization of the units so that a fixed proportion other than 1:1 can be supported. Hence a unit of physician services can be defined as k )1.

638

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

of the unrestrictive merger but reduces the extent of benefit to the merging parties Ži.e., their combined payoff increases only by 4% in this case.. Increasing the extent of discrepancy even further by assuming a different number of participants in each market so that m s 10 and n s 2 ŽCase 3 of Table 1. eliminates the profitability of the vertical merger completely. The above calculations contradict the ‘Chicago school’ view that a vertical merger or any other tying arrangement are unprofitable. We have shown that a vertical merger can significantly raise the profits of the merged entity Žas in Case 1 above. when negotiations with insurers are factored into the analysis. Support for the ‘Chicago school’ view exists in our model only when the degree competitiveness of the two providers’ markets sharply differ ŽCase 3 above.. In assessing the welfare consequences of the vertical merger, note that social welfare, as measured by the sum of insurers’ profits, providers’ profits and consumer’s net payoff remains unaffected irrespective of the premia charged or the reimbursement rates negotiated between insurers and providers. As long as premia are sufficiently low so that the expected payoff of the consumer in Eq. Ž1. remains positive, the size of the insured population does not change as a result of the vertical merger. Even though total welfare is unaffected, consumers are obviously worse off if providers can negotiate higher rates with insurers as a result of the merger. In this case, the increase in profits of the merged entity exactly equals the loss of consumer surplus. Note that the results of Proposition 3 may yield some perverse welfare argument in favor of ‘questionable’ hospital Žhorizontal. mergers so that the physician market remains relatively competitive in comparison to the hospital market; thus, eliminating incentives for vertical integration between a given hospital–physician pair.

4. Restrictive vertical mergers In the present section, we explore the consequences of vertical mergers that impose restrictions upon the merging partners. We consider, in particular, mergers that prohibit the partners from offering their services in conjunction with any other provider who is not a party to the merger. Hence, the merging hospital is only serviced by his partner to the merger and vice versa. Even though most exclusive contracts between hospitals and physicians are single sided Žthe physicians are free to practice anywhere. there have been recently examples of double-sided exclusive contracts as well. In Texas, for instance, ColumbiarHCA Healthcare required its radiologists not to offer their services in any other hospital except the Plaza Medical Center Žsee Langley, 1997, Wall Street Journal May 2, 1997.. Using terminology borrowed from the Industrial Organization literature such double-sided exclusive contract can be interpreted as ‘pure bundling’ of a given hospital–physician pair. The mergers without restrictions that we have considered earlier can be

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

639

regarded as ‘mixed bundling’ since a given provider that is a party to the merger can be utilized by patients as part of a bundle as well as independent of it. In order to simplify the derivations we restrict attention to the case that there are two participants in each provider’s market; thus, n s m s 2. From Section 3, we know that an unrestrictive vertical merger will definitely benefit the merging parties in this case. In the present section, we will assess whether the imposition of restrictions can further benefit the parties involved. To describe the negotiations between insurers and providers, we first derive the increase in ex-post transportation costs incurred by subscribers when their insurer fails to reach an agreement with the ‘purely bundled’ merged entity. We include such derivations in Lemma 1. Lemma 1 Ži. When an insurer fails to reach an agreement with the ‘purely bundled’ merged entity its subscribers experience the following rise in their ex-post transportation costs.

°3s q t 2

~

Ds

2

24 s 3t 2 q s 2

¢

24 t

if s G t if s - t

Žii. In case of disagreement with either one of the independent providers Žeither the physician or the hospital. that are not parties to the merger transportation costs still increase by the same amount, D. Note that because of the ‘pure bundling’ aspect of the hospital– physician merger the increase in transportation costs depends upon the characteristics of both providers’ markets irrespective of whether the disagreement is with a physician or with a hospital. Using Lemma 1 in the derivation of the Nash Bargaining Solution yields the results reported in Proposition 4. Proposition 4 If Hospital 1 and Physician 1 integrate and prohibit each other from offering services in conjunction with outside, independent providers ŽHospital 2 and Physician 2., the parties can negotiate the following reimbursement rates:If s G t y1 s z1 s

y2 s z2 s

5 Ž 3s 2 q t 2 . M 8 12 sM y Ž 3s 2 q t 2 . u 3 Ž 3s 2 q t 2 . M 4 12 sM y Ž 3s 2 q t 2 . u

Ž 17 .

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

640

If s - t y1 s z1 s y2 s z2 s

5 Ž 3t 2 q s 2 . M 8 12 tM y Ž 3t 2 q s 2 . u 3 Ž 3t 2 q s 2 . M 4 12 tM y Ž 3t 2 q s 2 . u

Ž 18 .

Note that the independent providers can command higher rates in the negotiation with insurers than each of the merging partners. Even though each provider, whether independent or not imposes on subscribers the same additional costs in case of disagreement with an insurer, independent providers have a stronger bargaining position in such negotiations. When a party to the vertical merger negotiates with an insurer it is concerned about losing the stream of profits to itself as well as to its merging partner if an agreement with the insurer cannot be reached. It is willing, therefore, to make greater concessions than an independent provider who is only concerned about the loss of its own profits in case of disagreement. Even though each merging partner is worse off in comparison to an independent provider it may still be better off than under vertical separation. As in the case of the unrestrictive mergers, the restrictive vertical merger does not guarantee that each merging partner can negotiate higher rates than prior to the merger. We report this result in the next proposition. We consider only the case that s G t since the remaining case when s - t can be easily attained, according to Proposition 4, by replacing the role of t and s in the derivations. Proposition 5 If s ) t, Ži. both the merging and the independent physicians are more likely to negotiate higher rates post-merger the closer the value of t is to that of s; Žii. the merging hospital is more likely to negotiate higher rates the smaller is the value of t relative to that of s. The independent hospital can definitely negotiate higher rates post-merger; Žiii. the likelihood that the merging hospital can negotiate higher rates post-merger is higher than the likelihood that the merging physician can do so. Recall that in the unrestrictive merger, as well, it is the merging party operating in the more competitive market who benefits the most from the vertical merger. In fact, if one market is much more competitive than the other it is only the party that operates in this more competitive market than can negotiate higher rates as a result of the merger. Given that in Proposition 5, m s n s 2 and s ) t, it is the hospital and not the physician who is more likely to benefit from the merger. Since the physician, who operates in the more differentiated market, bundles his services with a party operating in a less differentiated market, his bargaining position may be weakened. In fact, the larger the discrepancy between s and t the less likely it is that the physician can benefit from the merger. Note that the positive externality

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

641

conferred on the independent providers as a result of the merger implies that they are more likely to command higher rates post-merger than the merging parties. Next, we characterize circumstances under which the imposition of restrictions on the merging partners yields higher joint profits to the parties than mergers that do not impose such restrictions. We specify those circumstances only for the case that s G t. The improved profitability of the ‘pure bundling’ merger depends critically upon the relative degree of differentiation of the hospital vis-a-vis the physician ` markets, as measured by the ratio trs. When this ratio, which we designated by w, is close to one the extent of competitiveness of the two providers’ markets is comparable, and when it is close to zero the hospital market is much more competitive than the physician market.

Proposition 6 There exists a threshold value w 1 so that: Ži. if 0 F w - w 1 , ‘pure bundling’ type of mergers always dominate ‘mixed bundling’ mergers. Žii. If w ) w1 , ‘pure bundling’ mergers continue to dominate only for certain values of the parameter M. The region of M values that supports such an outcome shrinks as w increases.

According to Proposition 6, the imposition of restrictions on the merging parties is more likely to be beneficial when the hospital market is far more competitive than the physician market Žreflected in the Proposition by small values of w .. For very small values of w close to zero restrictive mergers are always more profitable. As the value of w increases, restrictive mergers may still be profitable over a certain range of values of the parameter M, which measures the degree of differentiation between insurers. This range of values shrinks, however, as w increases. Hence, when the extent of competition in the two provider’s markets becomes more comparable it is less likely that the partners to a vertical merger will find it advantageous to impose restrictions on the merging parties. Recall from our earlier discussion that when the two provider’s markets sharply differ in their extent of competitiveness it is less likely that a vertical merger, either restrictive or not, will enhance the bargaining position of both parties. It is only the provider operating in the more competitive market who can negotiate higher rates in this case. According to Proposition 6, the imposition of restrictions serves to enhance the negotiating power even of that party. To understand the results reported in Proposition 6, note that there are both costs and benefits to the imposition of restrictions on the merging parties. On the cost side, the imposition of restrictions raises the ex-post transportation costs of subscribers since they are confronted with a more limited choice among providers. If in the absence of restrictions those expected costs, in case of agreement amount to u Ž t q s .r8, with restrictions those costs rise to u Ž3s 2 q 6 ts y t 2 .r24 s. Note

642

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

that the rise in cost is less dramatic the bigger the discrepancy between t and s, namely, the smaller 9 is the value of the ratio w s trs. On the benefit side, the imposition of restrictions improves the bargaining position of the independent providers to a greater extent than when the merging partners do not impose restrictions. In fact, the positive externality that a restrictive vertical merger confers on an independent provider implies that it can negotiate even higher rates than those secured by the parties to the merger. The partners to the merger benefit from the improved bargaining position of the independent parties since their reimbursement is positively correlated with that negotiated with ‘outsiders’. Negotiated reimbursement rates are ‘strategic complements’, following terminology introduced in the Industrial Organization literature. 10 Given that the above-mentioned cost of restrictions is relatively small when trs is small, ‘pure bundling’ vertical mergers are more likely to arise the more competitive the hospital vis-a-vis the physician market is. ` The two first cases of Table 1 demonstrate our results. 11 In Case 1, the extent of competitiveness of the two providers markets is comparable Žsince m s n s 2 and s s t s 10., implying that the imposition of restrictions is unprofitable R Ž P VI - P VI .. However, in Case 2, when the hospital market is significantly less differentiated than the physician market Ž t s 1 and s s 10. the imposition of restrictions raises the profits of the merged entity by 11%. The results reported in Proposition 6 can explain to some extent the various forms of tying arrangements that have been emerging between physician practices and hospitals. Some of those arrangements take the form of double-sided exclusivity clauses as in the above mentioned example of ColumbiarHCA. Given that intensified managed care penetration has resulted in significant excess capacity in hospital markets, those markets have become increasingly more competitive. In the context of Proposition 6, such changes can be interpreted as a decline in the value of the parameter t, which for a fixed value of s implies that restrictions are more likely to accompany vertical associations between physicians and hospitals. The ColumbiarHCA experience demonstrates, however, that exclusivity clauses may be difficult to enforce, since 1 month after the imposition of the restrictions on its radiologists Texas passed legislation prohibiting hospitals from refusing staff privileges to physicians because they practice at another hospital ŽWall Street Journal, September 16, 1997.. According to our model, in the absence of exclusivity clauses, the profitability of vertical mergers may disappear completely if the characteristics of the hospital and physician markets sharply differ. 9

The increase in cost amounts to Ž3tsy t 2 .r24 s. This expression increases in both t and s. However, the rate of increase in t is bigger than that in s; thus, implying that the change in cost is smaller if w is smaller. 10 A similar phenomenon exists in this literature at the Bertrand equilibria, where firms seek commitments to become ‘softer’ competitors in order to encourage their rivals to raise prices. 11 The parameter values satisfy Eq. Ž16. in all three cases.

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

643

Fig. 1.

Even though our derivations were confined to the case that both merging parties are equally restricted post-merger, our results can easily be extended to the more prevalent form of tying arrangement that offers physicians exclusivity rights but permits them to serve competing hospitals Žsee Frech and Danger, 1998, for some data related to one-sided exclusive contracts.. It can be demonstrated 12 that as with bilateral restrictions, the advantage of unilateral restrictions over unrestrictive mergers is more significant the larger the discrepancy between s and t. 5. Correlated providers’ distributions In this section, we relax the assumption that the distribution of preferences among hospitals is independent of the distribution among physicians. In fact, we make the opposing extreme assumption that those distributions are perfectly correlated. Specifically, patients use the same common criteria in choosing among hospitals and among physicians. This common criteria can be, for instance, the specialty of the provider, implying that the distribution of patients on the circle designates the type of diseases they suffer from and the location of the providers Žhospitals and physicians. on this circle indicates their specialty. We assume, once again, that providers partition the ex-post distribution into equal-sized segments, and as in Section 4, we restrict attention to the case that n s m s 2. Without any loss of generality consider the case that a given hospital–physician pair are located at the same point on the ex-post distribution 13 as demonstrated in Fig. 1. 12

The proof can be provided by the author upon request. With non-identical locations, a patient chooses the pair which is closest to each other and is most appropriate, therefore, in treating his disease. 13

644

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

It can be easily shown that in the absence of vertical integration the negotiated rates with providers remain identical to those derived when the distributions are independent. Hence, from Eq. Ž10. we obtain: tM sM yU s and zU s Ž 19 . 4Myu t 4Myu s In contrast to the case with independent distributions, with correlation a given hospital may strictly prefer to acquire one physician practice over the other. In Proposition 7, we indicate that this may be the case. Proposition 7 Ži. With an unrestrictive merger, a given hospital is indifferent as to which physician practice it decides to acquire. The negotiated rate post-merger that is secured by each of the merging partners is given by: M Ž t qs. tM sM yszs q q . 3Ž 4 M y u Ž t q s . . 6Ž 4 M y u t . 6Ž 4 M y u s . The rate negotiated with the independent hospital is given by: y Mt yys q , 2 Ž4Myu t .2 and that negotiated with the independent physician is: z Ms zys q . 2 Ž4n yu s. 2 Žii. With a restrictive merger, a given hospital strictly prefers to merge with the physician practice located closer to it than with the one located farther away. When merging with this closely located physician, the negotiated rate post-merger of each of the merging partners is given by: 5Ž t q s . M yszs , 8Ž 4 M y u Ž t q s . . and the rates secured by the independent providers are: 3Ž t q s . M yys zys . 4Ž 4 M y u Ž t q s . . The characteristics of the equilibria reported in Proposition 7 are very similar to those derived when the distributions are independent. The only exception being, that restrictive mergers are unambiguously preferred to unrestrictive mergers and that they always yield higher profits to the merging partners than prior to the merger. 14 Recalling the comparison in Section 4 between the restrictive and 14

In the region of M values that guarantee the existence of interior equilibria Ži.e., M ) u Ž t q s .r4..

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

645

unrestrictive mergers, we have identified both a cost and a benefit to the imposition of restrictions when the ex-post distributions are independent. The cost is the more limited choice among hospital–physician pairs imposed on subscribers and the benefit is the enhanced bargaining position of the independent providers. When the ex-post distributions are perfectly correlated, however, the above-mentioned cost disappears completely, since even when given the flexibility to ‘mix and match’ among different hospital–physician pairs, patients will always pick a commonly located hospital–physician pair. The pair selected is the one that is most appropriate Ži.e., closest to his address on the circle., given the specific disease the individual suffers from. Since the imposition of restrictions offers only a benefit in this case, the merged entity will find it advantageous to impose such restrictions following a vertical merger. The above results are consistent with the observation that exclusive contracts tend to overwhelmingly be with particular medical specialties closely tied to hospital practice such as pathologists, radiologists or anesthesiologists. The distribution of preferences of consumers among physicians belonging to such specialties is likely to be highly correlated with preferences among hospitals, implying from Proposition 7 the profitability of exclusivity contracts.

6. Concluding remarks and possible extensions We have demonstrated that the existence of incentives for vertical mergers between hospitals and physician practices crucially depends upon the relative degree of competitiveness of the two provider’s markets. We have distinguished between two types of vertical mergers. Unrestrictive mergers that do not prohibit the merging partners from offering their services in conjunction with outside, independent entities and restrictive mergers that require the hospital and physician who are parties to the vertical merger to offer their services exclusively as a ‘bundle’. In general, unrestrictive mergers are more likely to benefit the party who operates in the more competitive provider’s market. However, when both the hospital and the physician markets experience comparable degrees of competitiveness as measured by number of participants and degree of differentiation among them, both parties to a vertical merger can negotiate higher reimbursement rates with insurers. The imposition of restrictions on the merging partners introduces both a cost and a benefit in comparison to unrestrictive mergers. On the cost side, restrictions limit the choice of consumers among different hospital–physician pairs and may adversely affect, therefore, the negotiating power of the merged entity vis-a-vis ` insurers. On the benefit side, restrictions confer a positive externality on outside, independent providers who can negotiate higher reimbursement rates with insurers.

646

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

Since the reimbursement rates negotiated with the merged entity are positively correlated with the rates secured by ‘outsiders’, the merging partners can benefit from the existence of such an externality. We demonstrate that the cost of restrictions is relatively small when the two provider’s markets greatly differ in their degree of competitiveness. Hence when the hospital market is far more Žor far less. competitive than the physician market it is more likely that vertical mergers will be accompanied by the imposition of restrictions. In describing the preferences of consumers among hospitals and physicians, we have considered two different extreme cases. One in which consumers’ preferences among hospitals are determined independent of their preferences among physicians and the other where those preferences are perfectly correlated. In the former case, consumers use different criteria in selecting a physician practice than in choosing a hospital and in the latter case a single, common criterion guides the consumers’ choice either among physicians or among hospitals. The criteria for selection may include geographic location, the reputation of the provider in treating a specific disease, or the ‘bedside manners’ of the parties administering care. A most welcome extension of our analysis is to allow for an intermediate case, where the distributions of preferences among hospitals and among physicians are partially correlated. Our results concerning the implication of correlation on the desirability of restrictive mergers are likely to extend to such an environment. Specifically, increased correlation should increase the profitability of the imposition of restrictions on the merging partners. We have considered a very simple framework where differentiation among insurers or among providers is modeled as location on a circle and where the outcome of the negotiations between insurers and providers is determined by the Nash Bargaining Solution. Considering alternative models of differentiation or non-cooperative bargaining solution concepts is a worthwhile extension. We do not expect, though, that our qualitative results will be significantly affected. Our modeling does not permit us to conduct a very comprehensive welfare analysis, given our assumption that all subscribers find it optimal to acquire insurance irrespective of the level of premia established in the market Ži.e., the reservation price of consumers is always higher than such premia.. With a fixed size of the market served, higher reimbursement rates of providers yield a simple transfer of welfare from consumers to providers without affecting the aggregate level of social welfare. A useful extension of our analysis should incorporate the possibility that vertical mergers may reduce the total size of the insured population since it may result in higher compensation of providers and increased premia. In addition, in our analysis, the u parameter which measures the likelihood of requiring care is determined exogenously. In reality, this parameter is likely to be endogenously affected by patients, providers or both. Due to hidden information and hidden action issues great inefficiencies may be introduced by the parties’ attempts to manipulate the value of u . None of those issues in captured in our model.

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

647

Acknowledgements I wish to acknowledge the helpful suggestions of the editors and two anonymous referees.

Appendix A Proof of Proposition 1 Ži. The merging hospital can negotiate a higher rate if R k s yk y

mtM

) 0,

2

2Ž m M y u t .

and a merging physician can negotiate a higher rate if DÕ s z Õ y

nsM

) 0.

2

2Ž n M y u s .

After some manipulation, we obtain that: sgn  R k 4 s sgn  Ž 2 n y 1 . Mnm Ž ms y tn . Ž Mn2 m 2 y u Ž n2 t q m2 s . . qu ts Mn2 m2 Ž Ž 2 n y 1 . m q n . y u Ž n 2 t q m 2 s . Ž Ž 2 n y 1 . m yn Ž n y 1 . .

4,

Ž A.1 .

and sgn  DÕ 4 s sgn  Ž 2 m y 1 . Mnm Ž nt y ms . Ž Mn2 m 2 y u Ž n2 t q m2 s . . qu ts Mn2 m2 Ž Ž 2 m y 1 . n q m . y u Ž n 2 t q m 2 s . Ž Ž 2 m y 1 . n ym Ž m y 1 . .

4.

Ž A.2 .

By condition Ž16., the second terms included on the right hand side of Eqs. ŽA.1. and ŽA.2. are definitely positive. In contrast, the first term of each of the two equations have opposing signs. If this term is positive in Eq. ŽA.1., it is negative in Eq. ŽA.2. and vice versa. Hence, the only way that both the hospital and the physician can negotiate higher rates as a result of the merger is if the absolute value of the difference Ž nt y ms . is sufficiently small so that regardless of the sign of the first term in Eqs. ŽA.1. and ŽA.2. the entire expression of each equation is positive. Žii. If one market is much more competitive than the other, for instance if mrt 4 nrs, the sign of R k is positive and that of DÕ is negative. Hence, while

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

648

the merging party operating in the more competitive market can negotiate higher rates its partner from the less competitive market negotiates lower rates.

Proof of Proposition 2 Follows directly from Eqs. Ž13. – Ž15.. Proof of Proposition 3 The benefit from a vertical merger is given by:

P VI y P VS s

uM

= w AqBx,

2 2 mn Ž n q m . y Ž m2 q n 2 .

where

Ž n y m . mn w ms y nt x Mn2 m 2 y u Ž n2 t q m2 s .

A' and B '

u st  n 2 m 2 M w 2 mn Ž m q n . y Ž n y m . 2 x y m 2u s w n Ž n q m .Ž m q 1 . y Ž n 2 q m 2 . x y n 2u t w m Ž n q m .Ž n q 1 . y Ž n 2 q m 2 . x 4

w Mn2 m2 y u Ž n 2 t q m 2 s . x w n 2 M y u s x w m 2 M y u t x

While B is always positive, the sign of A depends upon the sign of the product Ž n y m.Ž ms y nt .. If it is positive the vertical merger is definitely beneficial. However, if it is negative and sufficiently small the merger may still benefit the merging partners. Proof of Lemma 1 Ži. Suppose Hospital 1 acquires Physician 1. Because of the pure bundling of the services of this pair of providers, subscribers have a choice between two different hospital–physician pairs H1 D 1 and H2 D 2 . Hence, if their insurer can reach an agreement with all providers, ex-post transportation costs can be computed as follows. When s G t 4

1r4ytr4 s

1r2

H0

Ž tx q sy . d xd z

1r4qtr4 s

1r4qsr4 ty Ž srt . y

1r4qtr4 s

1r2

H0

H1r4ytr4 s H0

q

1

1r2

1r2

H1r4qtr4 sH0

q

ž

1 2

1

ž / ž / / ž /

H1r4ytr4 s H1r4qsr4 ty Ž srt . y

q

Ž tx q sy . d xd y

2

yx tqs

tqs

1 2

2

d xd y

y y d xd y s

3s 2 q 6 ts y t 2 24 s

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

649

If the insurer fails to reach an agreement with the merged entity the subscribers have to obtain care from the single pair H2 D 2 , thus, experiencing ex-post costs amounting to Ž t q s .r4. The increase in cost is equal, therefore, to:

D'

3s 2 q 6 ts y t 2

tqs

3s 2 q t 2

y

s

4

24 s

24 s

.

The calculation for the case that s - t can be similarly derived. Žii. In case of disagreement between an insurer and either H2 or D 2 subscribers have to obtain care, once again, from a single remaining hospital–physician pair Ž H1 D1 ., since the merger between H1 and D 1 does not permit either party to offer its services in conjunction with independent providers. Hence, ex-post transportation costs increase by the same amount as in part Ži.. Proof of Proposition 4 Let H1 D 1 and H1 DU1 designate the agreement and disagreement payoffs of the U merged entity in the negotiation with insurer i and let JiH 1 D 1 and JiH 1 D 1 designate those payoffs for the insurer. Using the results of Lemma 1 when s ) t: JiH 1 D 1 s H1 D 1 s

ž ž

U

JiH 1 D 1 s H1 DU1 s

ž ž

1

Fj y Fi

q 2

/ž / Ž

Fi y u

M

Fj y Fi u

1 q 2

M

1 q

2

Fi y Fj

2

y

q

u Ž 3s 2 q t 2 . M 24 s

Fi y Fj

2

1

Ž y i q z1i . q 2 Ž y 2i q z 2i . 2 1

y 1i q z 1i . q

M

1

1

q

u Ž 3s 2 q t 2 .

M

M 24 s

ž

1 q

Fi y Fj

2

M

/Ž /Ž

/

u 2

/

Ž y1j q z1j .

Fi y u Ž y 2i q z 2i . .

u

2

y 1j q z 1j .

At the Nash Bargaining Solution, y 1i and z 1i maximize the product of the net U H D H D surplus to the merging parties Ž Ji y Ji .Ž H1 D 1 y H1 DU1 .. In the negotiation between insurer i and an independent provider Žeither Hospital 2 or Physician 2., the following agreement and disagreement payoffs apply: JiH 2 s JiD 2 s H2 s D2 s

ž ž

1 q 2

q 2

q

Fj y Fi

/ž / ž / ž M

Fj y Fi u M

1 2

ž

1

2

Fj y Fi u M

2

y 2i q z 2i q

Fi y u 1 q 2 q

1

Ž y i q z1i . q 2 Ž y 2i q z 2i . 2 1

Fi y Fj M

1 2

1

Fi y Fj M

/ /

u 2

u 2

y 2j z 2j

/

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

650

U

U

JiH 2 s JiD 2 s

H2U s

DU2 s

ž ž

1 q

ž

1 q

Fj y Fi

2

Fi y Fj

y

u Ž 3s 2 q t 2 .

M q

M 24 s

u Ž 3s 2 q t 2 .

2

M

M 24 s

1

Fi y Fj

u Ž 3s 2 q t 2 .

q 2

q

M

M 24 s

/ /

u 2

u 2

/Ž

Fi y u Ž y 1i q z 1i . .

y 2j

z 2j U

The Nash Bargaining Solution is obtained byUchoosing y 2i to max Ž JiH 2 y JiH 2 .Ž H2 y H2U . and choosing z 2i to max Ž JiD 2 y JiD 2 .Ž D 2 y DU2 .. In addition, simultaneously with negotiating reimbursement rates each insurer chooses its premia to maximize its profits. Solving for symmetric equilibrium where y k ' y ki s y kj , z Õ ' z Õi s z Õj and F ' F1 s F2 yields: y1 s z1 s

5 Ž 3s 2 q t 2 . M 8 12 sM y Ž 3s 2 q t 2 . u

and y2 s z2 s

Fs

M 2

3 Ž 3s 2 q t 2 . M 4 12 sM y Ž 3s 2 q t 2 . u

q u w y1 q y 2 x .

The derivations for the case s - t can be similarly obtained. Proof of Proposition 5 Ži. A comparison of Eq. Ž17. with Eq. Ž10. yields that the merging physician can negotiate higher rates post-merger only if: M-

3u s Ž 3s 2 q t 2 . 36 s 2 y 20 t 2

.

Ž A.3 .

Note that the RHS of the above inequality is bigger the bigger is the value of the parameter t. Hence, the merging physician can negotiate higher rates the closer t is to s. The independent physician can negotiate higher rates if: M-

u s Ž 3s 2 q t 2 . 12 Ž s 2 y t 2 .

Ž A.4 .

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

651

Fig. 2.

The RHS of Eq. ŽA.4. is increasing, once again, in t. Note that it is bigger than the RHS of Eq. ŽA.3., implying that the independent physician is more likely than the merging physician to negotiate higher rates post-merger. Žii. A comparison of y 1 with yU yields that the merging hospital can negotiate higher rates if:

Ž a . 60 s 2 y 96ts q 20t 2 G 0 or if Ž b . 60 s 2 y 96 ts q 20 t 2 - 0 and M -

3u t Ž 3s 2 q t 2 .

w 96 ts y 20 t 2 y 60 s 2 x

.

Ž A.5 .

A comparison of y 2 with yU yields that y 2 is always bigger. Žiii. A comparison of Eq. ŽA.3. with Eq. ŽA.5. yields that the range of parameter values that supports higher rates for the merging physician is a subset of the range of parameter values that supports higher rates for the merging hospital.

Proof of Proposition 6 Ži. From the expressions derived in Eqs. Ž13. and Ž17., the ‘pure bundling’ merger is dominant if: 5 Ž 3s 2 q t 2 . M 2

2

8 12 sM y Ž 3s q t . u

)

M Ž t qs. 3 4M y u Ž t qs. Ms q 6Ž 4 M y u s .

Mt q 6Ž 4 M y u t .

652

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

Fig. 3.

The above inequality holds if and only if the following is valid:  M 3 Ž 576 s 2 y 2304ts q 960t 2 . q 4u M 2 w63s 3 q 303s 2 t q 117t 2 s y 27t 3 x yMu 2 w 99 s 4 q 306 s 3 t q 324 s 2 t 2 q 38 st 3 q 33t 4 x qu 3 ts Ž t q s . Ž 3s 2 q t 2 . 4 ) 0 Ž A.6 . For t s 0, the LHS of Eq. ŽA.6. reduces to: M Ž 576 M 2 s 2 q 252 u Ms 3 y 99u 2 s 4 . ) 0, which is always positive for values of M that are required to support the interior solution Ži.e., M ) u Ž t q s .r4.. By continuity, therefore, Eq. ŽA.6. is still valid for small positive values of t close to zero, namely, when w F w1. Table 2 The two larger roots of the cubic expression Ž u s is normalized to equal to 1. w

0 F w F w1 w1 - w F w 2 w2 - w F w3

w 3 - w F1

0.03 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

All entries multiplied by u s M2

M3

Minimal value of M w u Ž t q s .r4x

0.000857 0.00137 0.0025 0.0026 0.3375 0.3704 0.4043 0.4384 0.4722 0.5409 0.5362 0.5655

0.257 0.262 0.27663 0.30599 22.3933 3.81458 2.45003 1.99357 1.80143 1.7312 1.7362 1.7993

0.2575 0.265 0.275 0.3 0.325 0.35 0.375 0.4 0.425 0.45 0.475 0.5

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

653

Žii. For larger values of w bigger than but close to the w1 , namely, for w 1 - w F w 2 , the graph of the cubic expression on the RHS of Eq. ŽA.6. takes the general shape illustrated in Fig. 2. Comparing the three roots of the graph with values of M that are consistent with an interior solution Ži.e., M G u Ž t q s .r4. yields that M2 - u Ž t q s .r4 - M3 . Hence, ‘pure bundling’ mergers dominate if M ) M3 , where M3 is increasing with w. Hence, the range of M values that support the dominance of ‘pure bundling’ mergers shrinks with w. For larger values of w´ Ž w 2 ,w 3 x, the graph of the cubic expression of Eq. ŽA.6. changes as in Fig. 3. In this range of w values, M1 - Ž t q s .r4 - M2 . Hence, ‘pure bundling’ mergers dominate if M2 - M - M3 . The root M2 increases and the root M3 decreases with w. Hence, once again, the range of M values that supports the dominance of ‘pure bundling’ mergers shrinks with w. For even larger values of w´ Ž w 3 ,1., the graph of the RHS of Eq. ŽA.6. still has the general shape described in Fig. 3. However, in this region, the two larger roots M2 and M3 both increase with w. Inspection of the calculations included in Table 2 Žnormalized to the case that u s s 1. indicates that our main conclusion remains unchanged, nevertheless. Proof of Proposition 7 Utilizing the Nash Bargaining Solution as in the previous propositions and solving for symmetric equilibria yields the stated results.

References Arrow, K., 1975. Vertical integration and communication. Bell Journal of Economics 6, 173–183. Bork, R.H., 1978, The Antitrust Paradox: A Policy at War with Itself. Basic Books, New York. Chen, Y., 1997. Equilibrium product bundling. Journal of Business 70, 85–103. Dranove, D., White, W., 1996. Specialization, option demand, and the pricing of medical specialists. Journal of Economics and Management Strategy 5, 277–306. Frech, H.E., Danger, K., 1998. Exclusive contracts between hospitals and physicians: the antitrust issues. Health Economics 7, 175–178. Gaynor, M., Haas-Wilson, D., 1998. Change, consolidation, and competition in health care markets. Working Paper. Grossman, S., Hart, O., 1986. The costs and benefits of ownership: a theory of vertical and lateral integration. Journal of Political Economy 94, 691–719. Hart, O., Tirole, J., 1990. Vertical integration and market foreclosure. Brookings Papers on Economic Activity, Microeconomics, pp. 205–276. Jaklevic, M.C., 1996. Buying doc practices often leads to red ink. Modern Healthcare 26, 39–44. Langley, M., 1997. M.D. vs. M.B.A.: Columbia Tells Doctors at a Hospital to End their Outside Practices. Wall Street Journal, May 2. McAfee, R.P., McMillan, J., Whinston, M.D., 1989. Multiproduct monopoly, commodity bundling, and correlation of values. Quarterly Journal of Economics 104, 371–384.

654

E. Gal-Orr Journal of Health Economics 18 (1999) 623–654

Ordover, J.A., Saloner, G., Salop, S.C., 1990. Equilibrium vertical foreclosure. American Economic Review 80, 127–142. Robinson, J., Casalino, L., 1996. Vertical integration and organizational networks in health care. Health Affairs 15, 7–22. Salinger, M.A., 1988. Vertical mergers and market foreclosure. Quarterly Journal of Economics 103, 345–356. Salinger, M.A., 1995. A graphical analysis of bundling. Journal of Business 68, 85–98. Williamson, O., 1979. Transaction—cost economics: the governance of contractual relations. Journal of Law and Economics 22, 233–261.