Organizational Form and Quality in Healthcare Markets∗ Mati Dubrovinsky The University of Winnipeg

Ralph A. Winter Sauder School of Business, UBC

September 29, 2011 Abstract This paper reexamines the relationship between organizational form and the provision of quality in health care markets. The Arrow-Hansmann theory of hidden action on the part of providers predicts higher quality for Non-Profit suppliers. This prediction has a puzzling lack of support in the empirical literature. We propose a theory that resolves the empirical puzzle and generates additional testable implications. The theory starts with the traditional assumptions of hidden action and supplier altruism and incorporates two additional features of health care markets: hidden information on supplier ability (to provide high quality) and a variation across buyers in the degree of informational asymmetry. Data from U.S. hospitals support four main implications of the theory, including the central prediction that the variance of quality is higher across For-Profit suppliers than across Non-Profit suppliers.

1

Introduction

Incentives to provide high quality health care are at the core of debates on health policy. To the extent that non-profit (NP) and for-profit (FP) organizational forms provide different incentives, it is important to understand the relationship between organizational form and the quality of services provided. This is especially so in light of the controversy over the on-going wave of conversions of NP health care providers to FP status in the US.1 In 2007, for example, some We thank Patrick Francois, Mariano Tappata, Ambarish Chandra, Robert Evans, Leemore Dafny, Jill Horwitz, Charles Weinberg, Xavier Martinez-Giralt, Nathan Schiff, Veikko Thiele, Linda Peritz, Alberto Romero, Pablo Moran, Isaac Holloway and seminar participants at the Sauder School of Business, The University of Winnipeg, the 8th AIIOC and the University of Manitoba for very helpful comments and suggestions. [email protected]; [email protected] 1 See Needleman, Chollet, and Lamphere (1997); Claxton et al. (1997); Robinson (2003); Schlesinger and Gray (2006). ∗

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nursing homes that converted to FP status were found to have abysmal quality.2 The same year, on the other hand, both FP and NP nursing homes were found to overuse anti-psychotic drugs.3 What have economists had to say about the relationship between organizational form and the quality of health care? The Arrow-Hansmann hypothesis is dominant. This theory is based on hidden action in quality provision on the part of health care suppliers. The theory attributes higher NP quality to the lower ability of NP managers to capture operating surpluses generated through shirking (Arrow, 1963; Hansmann, 1980; Hirth, 1999; Glaeser and Shleifer, 2001).4 Francois (2007), while focused on a different issue, offers a model that also yields the implication of higher quality at NPs, as a consequence of heterogeneity in the degree of altruism among doctors. More than 80 empirical studies,however, have left us with mixed evidence on the relationship between organizational form and quality.5 The failure of the evidence to support existing theory leaves us with a puzzle. This paper offers a theory that reconciles the existing evidence on quality and organizational form with the fundamental feature of information asymmetry in health care markets. The theory incorporates the two key assumptions of existing theories: 1) hidden action in quality decisions and 2) supplier altruism. We have homogeneous altruism to allow a focus on the element of heterogeneity that hat we hypothesize is important: supplier ability. Our theory adds to these a recognition of two additional features of health care markets: 3) hidden information on supplier 2

Duhigg, Charles (2007) “At Many Homes, More Profit and Less Nursing,” New York Times, September 23, 2007. 3 Lagnado, Lucette (2007) “Prescription Abuse Seen In US Nursing Homes: Powerful Antipsychotics Used to Subdue Elderly; Huge Medicaid Expense,” The Wall Street Journal, December 4, 2007. 4 Every dollar saved by a FP firm through reducing quality accrues to the owners of the firm. On the other hand, under section 501(c)(3) of the US Internal Revenue Code which prohibits outside parties from sharing in operating surpluses of NPs, it is more difficult for the managers or board of trustees to benefit from profits accruing from any shirking on quality. Hirth (1999), and Glaeser and Shleifer (2001) formalize this argument. Francois and Vlassopoulos (2008) develop the hierarchical implications more fully. In the Francois-Vlassopoulos model, altruistic employees are willing to provide a higher level of effort without incentive pay – but employees provide less effort (and quality) under the FP organizational form since they rationally anticipate that any extra effort will be met with a reduction in other inputs in order to save costs. Under NP status the incentive to reduce other inputs is weakened and the ability of owners to commit to higher quality is, therefore, stronger. 5 See Rosenau and Linder (2003) and Schlesinger and Gray (2006), also Dubrovinsky (2009) offers more evidence on cases where FP providers dominate NP ones in terms of quality.

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ability to set higher quality; and 4) a variation across consumers in the extent of informational asymmetry (in both the hidden action and hidden information dimensions). At first glance, a theory incorporating all four features would seem overly complex. In fact, the model generates a clear explanation of the inconsistency between existing evidence and theories, as well as a set of additional implications that are readily testable. The key to the tractability of the model is in the way we capture a variation in consumer information. Since the classic article by Salop and Stiglitz (1977), it has been standard to represent a variation in consumer information in a market by assuming that some portion of the buyer population is perfectly informed and the remaining buyers have zero information. Hirth (1999), in the one article that does introduce variation in patients’ information in health care markets, also adopts the Salop-Stiglitz formulation. This assumption is obviously not literally true for health care or any other market, but is the simplest route to investigating the consequences of a variation in information. In our theory, the informed consumers can observe and contract perfectly on supplier quality. In contrast with the literature’s focus on a comparison of average qualities between FPs and NPs, our central prediction is on the relative second moments of the distribution of quality within the NP and FP sectors. In our simple model, the prediction is stark. The equilibrium set of qualities is partitioned into three segments with FP providers supplying the lowest and the highest segments and the NP providing the middle segment. The highest ability suppliers in the market self-select into FP contracts which they write with informed consumers. These suppliers, having the lowest cost of providing high quality, generate the highest total surplus from the transaction when contracting with informed consumers over quality. Using these surpluses they can outbid lower ability suppliers and attract all of the informed patients. Among the remaining suppliers, which must serve uninformed buyers, suppliers adopting the NP organizational form have a greater commitment to quality than those adopting FP because the constraint on the distribution of profits leaves them with a lower incentive to shirk. (In this respect we formalize, as others have, the Arrow-Hansmann hidden-action perspec-

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tive.) Suppliers adopting the NP form are, in addition, able to reveal their type because of the tighter link between price and cost under the NP non-distributional constraint. Thus, suppliers adopting the NP form circumvent both the hidden-action and hidden-information problems, and derive altruistic enjoyment from the service they provide. (Altruism on the part of the suppliers is modelled in the spirit of Biglaiser and Ma, 2007.) On the other hand, suppliers adopting the FP organizational form benefit from the freedom to distribute profit. The impact of this trade-off for suppliers in providing the health care product to the uninformed consumers is that the better supplier types (of those types supplying uninformed buyers) self-select into NP contracts, leaving the lowest-ability segment of suppliers pooled into a common FP contract. The important prediction of our model is not the stark implication of an exact partitioning of supplier types by organizational form but rather the greater representation of FPs in the tails of the distribution of suppliers by quality, i.e., the greater variance in quality within the FP sector than within the NP sector. In contrast to this unambiguous prediction on the second moments in the equilibrium distributions of quality, we find that average quality may be higher or lower among FPs than among NPs – thus resolving the puzzling lack of consistent empirical support for the prediction of existing theories about the relative average quality supplied. Additional predictions about the distribution of quality emerge from our model. The share of informed patients initially increases mean FP quality and is consistent with the non-monotonic relationship found in the data, for higher shares of informed patients. Finally, the model generates predictions about the length of waiting time for procedures. After developing the theory, we test the set of predictions using U.S. hospital data. Following previous studies, we employ mortality rates for Heart Attacks (adjusted for patient characteristics) as a measure of hospital quality, high mortality rates indicating low quality. We compute means and standard deviations of mortality rates for each organizational form within markets (Metropolitan Statistical Areas). The paper documents empirical findings that support (to vary-

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ing degrees) all four implications. We begin the next section with a brief summary of existing theory and empirical evidence on organizational form and quality in health care markets. Section 3 sets up the model, derives the equilibrium and empirical implications. Section 4 then contains the empirical results and Section 5 concludes the paper. Proofs and select data plots are provided in the Appendix.

2

Existing Theory and Evidence

The central prediction of existing economic theory on the relationship between organization form and quality of service in health care is that NPs will provide higher quality than FPs. The ArrowHansmann theory postulates that certain aspects of service quality chosen by the producer are unobservable to the consumer. The NP organizational form involves severe constraints on the distribution of operating surpluses, compared to the FP form.6 Hence there is a lower incentive to raise operating surpluses by shirking on unobservable quality under the NP organizational form.7 The vast majority of empirical studies of health care quality and organizational form test the implication that (controlling for other factors) the average quality of NP providers is higher than that of FP providers.8 A typical study regresses the mortality rate for a certain procedure at a hospital, as a measure of hospital quality, on a set of hospital characteristics including an NP dummy. Rosenau and Linder (2003) reviewed studies of the relative quality of output between 6 Operating surpluses at FPs can be collected through dividends, while at NPs mainly through perquisites. Perquisites are, usually, valued less than cash, see Glaeser and Shleifer (2001). 7 The altruistic-employee approach, discussed in Francois and Vlassopoulos (2008), arrives at the same conclusion by noting that the costlier distribution of operating surpluses allows cheaper commitment not to substitute away from other costly inputs (which reduce quality) when employee effort is provided purely due to altruism. In Francois (2007) (summarized by Francois and Vlassopoulos, 2008), employees vary in their degree of altruism. The more altruistic ones self-select into voluntary provision (and being more altruistic, shirk less on quality). An application of his model to health care would again yield the prediction that the NP form (voluntary provision) offers higher quality. 8 Most of the empirical research on NPs comes from the US healthcare market due to availability of data and the importance of the sector socially and economically: in 2006 it accounted for 15.3% of the U.S. GDP (Chandra and Skinner, 2008).

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NP and FP providers. Studies based on data from the 1960s and 1970s fail to find any statistical difference in (average) quality between NP and FP providers. Studies based on data from the 1980s fall into the following three categories: 59 percent of these studies report that NPs (on average) have higher quality than FPs, in accordance with the Arrow-Hansmann hypothesis; 12 percent show higher (average) FP quality while the remaining 29 percent are unable to find a statistical difference in quality between the two organizational forms. Schlesinger and Gray (2006) list 38 empirical studies comparing quality of health care services provided by NP and FP institutions (21 of which overlap with Rosenau and Linder, 2003). Only 14 of those studies (36.84%) confirm the prediction of the Arrow-Hansmann hypothesis that NPs provide higher quality than FPs. 20 studies (52.63%) find no difference in quality of output between NPs and FPs. While 4 studies (10.53%) report higher FP quality. In short, the overall empirical evidence on the central prediction of the existing economic theory about the relationship between organizational form and quality is mixed and conflicting.

3 3.1

The Model Basic Assumptions

We consider a model of health care in which each supplier consists of one person (a doctor) who supplies one unit of the health care service to one buyer (a patient). Doctors vary in their ability θ, which determines the cost of providing quality q. Doctors are motivated in part by profit but are also altruistic, gaining utility from surplus derived by the patient (but valuing it less than profits). On the buyers’ side of the market, patients have homogeneous preferences for quality, but differ in the state of their information. A proportion of patients are informed, for simplicity perfectly so. These patients can observe and contract on q. The remaining patients are uninformed and can observe the price charged by a doctor, but cannot observe or contract on quality. In terms of organizational forms, FP suppliers (doctors) can earn profits, but NP suppliers earn utility only 6

through the altruistic benefit of providing positive quality service to patients. Like any useful economic model, our theory abstracts from many aspects of real markets. Since we are adding to existing theory both hidden information and a variation in the extent of the informational asymmetry across consumers, tractability of the model demands a higher level of abstraction than usual. Before proceeding with the formal assumptions, we delineate the main features of real markets from which we are abstracting. First, in making the assumption that each supplier is a one-person firm we abstract from all incentive issues within the firm. (These are the focus of Francois and Vlassopoulos, 2008.) Second, in reality NP firms earn positive surplus, surplus that cannot be distributed to any residual claimants. In our static model, as in other static models of NPs (see Newhouse, 1970; Weinberg, 1980;Liu and Weinberg, 2009), the nondistribution requirement is captured in an extreme assumption: NP firms are constrained to earn zero profit. This has the implication in our model that buyers can infer the ability of a doctor from the firm’s price, and thus know exactly the quality that is provided by an NP. This assumption captures in the simplest way the idea that buyers at an NP are more likely to “get what they pay for” because of a tighter link between costs and price. We make the assumption to reveal the logic of our theory most clearly but do not pretend that in reality the NP form allows such perfect inference.9 Third, our focus is on the comparison of FPs versus NPs, and therefore we abstract from a third organization form important in health care markets: government hospitals. Fourth, insurance intermediaries have no role in our model. Our theory relies on the assumption that patients have some scope in the choice of doctors and furthermore that they care about both quality and price. Insurance reduces the role of consumer choice but does not eliminate it: the more prevalent insurance schemes in the U.S. leave substantial scope for consumer choice among doctors.10 Fifth, as discussed in the introduction we capture variation in consumer information in 9

See Dubrovinsky (2009) for a more general model in which the inference about quality is not perfect. For example, the Preferred Provider Organizations (PPO) and Point of Service (POS) insurance contracts incentivize patients to be treated by particular doctors through discounts, but cover some of the costs incurred by visits to outside doctors and hospitals. PPOs account for 61 percent of U.S. employees in 2005 (Sultz and Young, 2009, p. 244). 10

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the standard way by assuming consumers are either perfectly informed or not informed at all (see Salop and Stiglitz, 1977; Hirth, 1999). In this static model reputational and word-of-mouth forces play no role. Furthermore, we abstract from imperfections in information except in the quality dimension, which is our focus. For example, consumers are assumed to observe and take into account the organizational form of the provider. Finally, we adopt abstractions common in the economic literature in general: consumers have homogeneous preferences, the market contains a single product and transactions costs are zero apart from the costs we introduce explicitly. This is a substantial list of basic assumptions.

We note that the articles in the existing

literature adopt many of the same abstractions, and that in fact our approach (in allowing for hidden information) is in some respects more general.11 To set out the model formally, assume that doctors’ types θ are uniformly distributed, denote this CDF G(θ), over an interval [θ, θ], of length D. The cost of providing quality at level q for a doctor of type θ is c(q; θ). Letting subscripts denote partial derivatives, we assume that c(q; θ) satisfies cθ < 0; cq > 0; cqq > 0; c(0; ·) = cq (0; ·) = 0 and cqθ < 0. We describe the model with a general cost function, but in deriving an equilibrium will rely on a quadratic form for the cost function, c(q; θ) = q 2 /4θ. That is, we assume that the marginal cost of providing greater quality is linear.12 Preferences on the buyers’ side of the market are homogeneous, with surplus given by q − F where F is the fee paid for a service. With respect to preferences on the supply side, doctors care about the welfare of their consumers. Define α ∈ (0, 1), the degree of altruism, to be the weight in doctor’s utility function on the welfare of a patient the doctor treats, with a weight of 1 11

Hirth (1999) offers a model of health care with hidden information about quality for a proportion of consumers, but does not adopt an explicit objective function for NPs. Hirth assumes an exogenous set of NPs that are not strategic players in the game analyzed; the supply of NPs is an exogenous function of price in his analysis. With respect to the assumption of altruism, the first paper in health care with this assumption is Newhouse (1970). The altruistic doctors assumption is also adopted by Biglaiser and Ma (2007) and Delfgaauw (2007). The assumption of altruism in the recent literature on theory of the firm is reviewed by Francois and Vlassopoulos (2008). 12 The reader familiar with asymmetric information models may ask why the selection arguments outlined in the introduction cannot be supported by a model with general costs, given that cqθ < 0. The additional tractability of the linear-marginal-cost assumption is required because the payoff functions over contract parameters are endogenous. The additional structure is needed to ensure the single-crossing property for these payoff functions.

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on profits. The parameter α is identical across doctors. A measure I of patients (“informed patients") can observe the quality of care and can enforce any contract over quality. A measure U of patients (“uninformed patients") cannot. The uninformed patients observe only the price (treatment fee), F , which is specified in any contract offered to them, as well as the organizational form that each doctor chooses for her clinic, FP or NP. An NP organizational form requires that the clinic earns zero profits, whereas for FP firms profits are unconstrained. To capture the idea that information is scarce in the market, we assume that the measure of informed consumers is smaller than the measure of doctors, I < D. Finally, it is well known that waiting times are common in the health care industry (see James, Bourgeois, and Shannon, 2005; Wilper et al., 2008). The existence of waiting times points to scarce capacity, since otherwise all patients could be treated the moment they seek care. We assume, therefore, that the number of doctors is smaller than the total number of patients: D < U + I. The recognition of scarce capacity leads to rationing in the equilibrium, allowing us to generate implications regarding relative waiting times across organizational forms.

3.2

Timing and Strategies

Doctors move first. After observing the realization of her type (the cost parameter θ) the doctor chooses a contract offer. The contract offered must be one of the following three contract types:13 • “Non-Profit contract”: a contract that specifies the fee, F , a patient pays if treated by the doctor. The contract includes a requirement (monitored by a regulator) to set the quality such that F = c(q; θ).14 We denote a contract of this type as [q, F ; N P ] • “Discretionary For-Profit contract”, denoted F P : a contract that specifies only the treat13

Note that if a doctor selects to stay out of the market, she can always choose a contract of type F P and set the fee high enough and quality low enough, that no informed patient would be willing to select her as the healthcare provider (e.g. F > q), while no uninformed patient is able to accept such contract. Therefore, there is no need to specify an additional action for doctors of staying out of the market. 14 Either the regulator observes θ from the doctor’s record or experience in the profession, or the regulator is able to determine ex-post whether the NP violated the regulatory constraint by making positive profits.

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ment fee F , and leaves the quality choice q to the discretion of the doctor. As usual in contract theory, we write the contract as including quality, [q, F ; F P ], but recognize that q must satisfy an incentive compatibility constraint. • “Full For-Profit contract”, denoted F P : a contract that specifies both fee F and quality q; compactly: [q, F ; F P ]. This contract is written only where it is enforceable. Each doctor’s strategy is thus a mapping from her type space θ into to a space of all contract offers. Let X = R2+ × {N P, F P, F P } be the space of possible contract offers, with a generic element of X being a vector [q, F ; τ ], where τ is the contract type: {N P, F P, F P }, q is quality ¯ → X. We focus on symmetric and F is the fee. A doctor’s strategy is a mapping sD : [θ, θ] equilibria: all doctors play the same type-contingent strategy sD . Patients move second. Patients observe the contract offers made by doctors, then simultaneously accept one contract among the ones doctors have offered, or choose not to be treated. Uninformed patients cannot accept a contract of type F P , as for them quality is noncontractable.15 An informed patient’s strategy is the choice of one contract offer out of the entire set of contract offers made by doctors in the previous stage of the game. An uninformed patient’s strategy is choice from the set of N P and F P contracts offered. For simplicity we assume that each doctor can treat only one patient. Given that multiple patients may choose the same doctor we must define a rationing mechanism. We adopt the simplest mechanism: Patients of the same type who choose the same doctor have an equal probability of being treated. If any informed patients choose a particular doctor, then no uninformed patient will be treated by that doctor.16 We assume that the patient’s condition is severe enough that she would prefer to be treated by the lowest ability doctor (at cost) rather than taking the chances of 15

Usually references on good doctors are passed through networks of acquaintances. Those who are not members of these networks will not be aware of the good doctors, who have enough business serving only the members (modelled as informed patients here). In our model, the acceptance of a contract of type F P by an uninformed patient makes this contract not incentive compatible for the doctor (as the patient cannot verify the quality she receives). Assuming that uninformed patients simply cannot accept these contracts significantly simplifies the model. 16 This feature proxies for informed patients’ relative advantage in access to health care.

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the rationing mechanism with the highest ability doctor. As will be clear below, this is captured in the following assumption: 1 qθF P − c(qθF P ; θ) > [qθ − c(qθ ; θ)] 2

(1)

where qθF P solves cq (q; θ) = α, and qθ solves cq (q; θ) = 1.

3.3

Payoffs

A patient receives zero payoff if she is not treated and surplus

S(q, F ) = q − F

(2)

if she receives a treatment of quality q at cost F . For a doctor of type θ, the payoff to treating a patient with quality q at a fee F is

v(q, F ; θ) = F − c(q; θ) + αS(q, F ) = F − c(q; θ) + α(q − F )

3.4

(3)

Equilibrium

We use the concept of Perfect Bayesian Equilibrium (PBE). A PBE consists of a strategy for each player and beliefs for the uninformed patients, conditional upon a set of contract offers, about the variable that is unobservable and payoff-relevant to them: quality. A PBE is a set of strategies and beliefs that satisfies sequential optimality for each player (for the uninformed, conditional upon beliefs) and rationality of the uninformed players’ beliefs. The PBE concept does not yield a unique equilibrium for this game, as is usual for this equilibrium concept. We describe one equilibrium, argue that it is a natural selection among possible equilibria, and use it as the basis for our predictions. This partition of doctor types into organizational forms, in the proposed equilibrium is depicted in Figure 1. 11

✲

FP

NP

FP

θ

Figure 1: Equilibrium Partition of Doctor-Types into Organizational Forms

We will construct the equilibrium by deriving the parameters of each offer, by type of doctor, and use two single crossing properties to demonstrate that the partition consists of intervals, as depicted.17 The figure describes the equilibrium contract offers; patients’ equilibrium acceptance strategies will involve multiple acceptances of the same contract offer (and therefore rationing) only for N P contract offers. We begin by characterizing the quality that must be contained in an equilibrium contract offer of each type F P , N P , or F P by a firm of type θ. A firm of type θ offering an N P contract will maximize its payoff, F − c(q, θ) + α(q − F ), subject to a zero profit constraint, F − c(q, θ) = 0. Incorporating the constraint yields an objective of α[q − c(q; θ)] and a first order condition cq (q; θ) = 1

(4)

This yields a one-to-one mapping between θ and q, to which we refer as qθ . The zero profit constraint on F then becomes F − c(qθ , θ) = 0, and this provides an invertible mapping between θ and F to which we refer as FθN P . Note that the two invertible mappings FθN P and qθ combine to yield an invertible mapping between F and q within the set of firms offering NP contracts. The quality provided by an NP firm will thus be inferred exactly from F by any uninformed consumer. An F P contract is between two informed parties and maximizes the firm’s payoff F − c(q, θ) + α(q − F ) subject to a minimum payoff for the patient, q − F . This problem again 17

It is in the derivation of the single-crossing properties that we impose the assumption of quadratic costs.

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yields the first-order condition (4) and a quality choice qθ . The quality set by a firm offering an F P contract (which contains no commitment to a quality level), simply maximizes the firm’s payoff F − c(q, θ) + α(q − F ). This yields a first order condition which provides a mapping from θ to q that we denote as qθF P . The quality qθF P is given by the solution to

cq (q; θ) = α

(5)

The quadratic cost function allows us greater specification of the contract parameters. Using c(q; θ) = q 2 /4θ and (4) yields qθ = 2θ. Inserting this into the zero profit constraint FθN P = qθ2 /4θ yields FθN P = θ and patient surplus from an NP contract with a doctor of type θ, qθ − FθN P = θ. Similarly, using (5) yields qθF P = 2αθ.

This completes the description of quality offers by

contract form and supplier type. Consider a strategy, for firms, of the following form. Firms of type θ ∈ [θ − I, θ] offer F P ˆ θ − I), for some θ, ˆ offer contracts with quality qθ and some fee FθF P ; firms in an interval [θ, ˆ offer an identical fee, N P contracts with quality and fee qθ and FθN P . And all firms in [θ, θ) denoted F F P , and choose quality qθF P . To complete the description of a specific strategy of this ˆ the fee F F P and the fee mapping F F P . The fees, however, depend on type we must specify θ, θ rationing. Accordingly, we note the following necessary property of any equilibrium: F P and F P contract offers are each accepted by one and only one patient. This follows simply from the fact that if a for-profit contract (of either type) offered by a particular doctor is accepted by more than one patient, then given the other contract offers, that doctor could raise her fee by a small amount ε and still have the contract accepted: if one of her patients were optimizing by accepting a fraction (at most 1/2) chance of gaining surplus through treatment at this doctor, then at least one patient will accept when the fee is raised by ε.18 With each for-profit contract being accepted by one patient, it follows that an equilibrium with a parameter θˆ must allocate ˆ θ) patients among θ − I − θˆ contracts of the N P type. (Recall that U is the measure of U − (θ− 18

This is a static version of the standard result of the queueing literature in economics: a customer utility loss due to waiting can be appropriated by the service provider through a higher price.

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uninformed patients). The fact that informed patients are not rationed allows us to determine the payoff, and hence fee charged, to the informed patients in the F P type contacts. Recalling that informed patients have the priority over uniformed patients in any rationing, it follows that an informed patient’s best alternative to the contract accepted in equilibrium is the highest quality contract offered within the N P set (recall assumption (1)); this is the N P contract offered by type θ − I. The fee FθF P is determined by the ability of any doctor offering an F P contract to raise the fee to the point where the patient is indifferent to moving to this alternative. Under the quadratic form for costs, the surplus earned by a patient from an N P doctor of type θ is θ.19 Therefore, the fee FθF P is determined by qθ − FθF P = θ − I, i.e. FθF P = qθ − (θ − I). Turning to the surplus earned by rationed patients in the N P sector, the only acceptance decisions among rationed patients that leave these patients with no incentive to deviate to another N P contact is the set of decisions that leaves the expected surplus (given the random allocation) equal across N P contracts. That is, the surplus achieved from treatment at an N P doctor of type θ must be inversely proportional to the probability of treatment. Given the quadratic form on costs, the realized surplus from a transaction with an N P doctor of type θ is equal to θ.19 In allocating the U − (θˆ − θ) patients among θ − I − θˆ contracts of the N P type, we must therefore select an allocation a(θ) that satisfies the following two conditions (for some common expected surplus level s for a patient choosing an N P contract): 1 θ=s a(θ) � 19

θ−I θˆ

=⇒

a(θ) = θ/s

a(θ)dθ = U − (θˆ − θ)

Given c(q; θ) = q 2 /4θ, (4), which defines qθ , yields qθ = 2θ. Inserting this into the zero profit constraint = qθ2 /4θ then yields FθN P = θ and surplus qθ − FθN P = 2θ − θ = θ.

FθN P

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These two conditions solve to yield a common expected surplus s given by

s=

(θ − I)2 − θˆ2 2[U − (θˆ − θ)]

(6)

The expected surplus s from an acceptance of an N P contract determines, in turn, the surplus levels of the (uninformed) patients accepting F P contracts. This follows from the fact that a forprofit firm will set its fee to render the patient indifferent to deviating to another contract. (Any lower fee could be raised by the for-profit firm without losing the patient.) ˆ This leaves two components of the proposed equilibrium strategy to be defined: F F P and θ. These are determined simultaneously by the following two relationships: 1) the expected surplus ˆ is s, defined by (6); and 2) the firm from an F P contract with F F P and qθF P from a firm in [θ, θ) at θˆ is indifferent between offering an F P contract (and being associated with the pooled set of firms in the F P interval) and offering an N P contract. Expressing these conditions formally: given the other parameters, F F P and θˆ must satisfy �

θˆ θ

qθF P

dG(θ) (θ − I)2 − θˆ2 − F FP = s = ˆ G(θ) 2[U − (θˆ − θ)]

(7)

and ˆ + α(q Fˆ P − F F P ) = α[q ˆ − c(q ˆ; θ)] ˆ F F P − c(qθFˆ P ; θ) θ θ θ

(8)

ˆ Using Using c(q; θ) = q 2 /4θ, the properties qθ = 2θ and qθF P = 2αθ, (8) yields F F P = αθ. ˆ = (θˆ − θ)/(θ − θ) yields the following characterizations of s these relationships in (7) and G(θ) ˆ and θ. Lemma 1 (a) s = αθ; (b) θˆ is characterized, in terms of exogenous parameters, by the following: αθ =

(θ − I)2 − θˆ2 2[U − (θˆ − θ)] 15

(9)

Where either the F P interval or the N P interval is empty, i.e. where θˆ = θ or θˆ = θ − I, equation (9) would not have an interior solution Simulation with the quadratic cost function, c(q; θ) = q 2 /4θ, however, shows that for a wide range of parameters, there is an interior solution in θˆ (and F F P ) to these equations. One such solution is depicted in Figure 1. Finally, having constructed a partition of types into intervals, and justified equilibrium strategies conditional upon the partition, we must verify the single-crossing properties, that the relative preference for the optimal (conditional upon θ) N P contract over the optimal F P contract is increasing in θ and similarly for the preference of the optimal F P contract over the the optimal N P contract. Lemma 2 follows immediately from the quadratic cost function assumption, and our characterizations of qθ and qθF P : Lemma 2 Under the linear marginal cost assumption, the payoff functions for θ conditional upon contract choices satisfy the following

π(θ|q, F ; N P ) = α[qθ − c(qθ , θ)] = αθ π(θ|q, F ; F P ) = F F P − c(qθF P , θ) + α(qθF P − F F P ) = α2 θ + (1 − α)αθˆ π(θ|q, F ; F P ) = FθF P − c(qθ , θ) + α(qθ − FθF P ) = θ − (1 − α)(θ − I) π(θ|q, F ; N P ) − π(θ|q, F ; F P ) and π(θ|q, F ; F P ) − π(θ|q, F ; N P ) are continuous and increasing in θ. With this property, we are assured that the F P , N P and F P sets are intervals, as depicted in Figure 1; and we have completed a description of a strategy on the part of doctors (as a function of their type θ) and an acceptance strategy by patients, defined as one patient accepting each for-profit (F P by uninformed and F P by informed) contract offer and a(θ) patients accepting the N P contract offered by type θ (the type can be inferred from the offer itself through the fee). Since all U patients receive the same expected surplus (and I patients receive a higher surplus equal across all I patients) in the configuration described, and any patient would be more tightly 16

rationed if she deviated to another choice, patients acceptance decisions are an equilibrium of the subgame following the offers. Moreover, given the beliefs of uninformed patients, the strategy has been constructed (with the two single-crossing properties) so that no doctor has the incentive to choose a different strategy. Finally, it is easy under the PBE concept to select beliefs on the part of uninformed patients conditional upon any F P offer that contains any fee other than F F P to deter such an offer: the belief that any such offer must signal the worst type. Since such an offer will not then be made, the beliefs satisfy Bayesian rationality. In sum, Proposition 1 In the model as specified, there are parameters for which an equilibrium exists in ˆ which the types of firms offering F P , N P and F P contracts are partitioned in intervals [θ, θ), ˆ θ − I) and [θ − I, θ] respectively. The equilibrium qualities are given by the solution to (4) for [θ, N P and F P firms of type θ and by the solution to (5) for F P firms, with quality being monotonic in θ overall. Rationing takes place only for N P contracts. This is the equilibrium that we take as the predicted outcome of the model. The first, and most important, implication that falls directly out of this equilibrium is that the variance of quality is higher among for-profit firms than among not-for-profit firms. The implication in the model is more stark than this, with for-profit firms represented only in the tails of the quality distribution of firms, but as discussed in the introduction, the implication selected is a more general and robust that is of interest for testing. The second implication is also direct: waiting times, reflecting rationing, should be greater at non-profit firms. Again, the literal implication is particularly stark in the model, with no rationing at all at for-profit firms.20 This brings us to the resolution of the empirical puzzle revealed in the existing literature, of the comparison of average quality between not-for-profit firms and for-profit firms. Simulations of the model show that average quality can be higher under either organizational form – 20

As explained above, the degree of rationing in the NP sector must be proportional to doctor’s type, and, hence, the equilibrium quality. This generates yet additional implication to be tested: higher quality non-profit firms should have longer waiting times that lower quality ones.

17

depending especially on the proportion of patients who are informed. If almost all patients are uninformed then the F P sector is much larger than the F P sector in the model, and the average quality of the for-profit sector is lower than that of the not-for-profit sector. With a dominance of more informed consumers (large I, keeping U + I fixed), the F P sector dominates and the comparison of qualities is reversed. For the final two predictions of the model, we move from a comparison of average quality within each sector, to the relationships between the proportion of informed patients and the average quality provided within each sector. The first of these predictions is the relationship between the mean quality in the FP sector (which is the combined F P and F P ) and the proportion I/(I + U ) of informed consumers. As I/(I + U ) rises, the average quality in the FP sector first rises and then falls. The average quality provided in the NP sector, on the other hand, is monotonically decreasing in the proportion of informed consumers. Proposition 2 (a) The mean equilibrium quality over the for-profit sector is initially increasing in I/(I +U ) and may be non-monotonic. (b) The mean equilibrium quality over the not-for-profit sector monotonically falls in I/(I + U ), for I in the relevant range. The core of the intuition for part (a) of the proposition is the basic economic principle that the average quality provided by a group increases with the addition of a new member to the group, if the new (“marginal”) member provides quality greater than the group average. When I is small, for-profit suppliers are dominated by F P -contract suppliers (as opposed to F P suppliers) and the average quality is low. The addition of a new I consumer induces the highest-quality supplier within the NP sector to switch to the F P segment, thus adding a high-quality supplier to the for-profit sector. When I is large, however, the for-profit sector is dominated by the F P group, with an average quality above the marginal entrant as I changes. The marginal versus average comparison changes and the addition of consumers to the I set reduces average quality within the for-profit sector. This simple intuition is reinforced by the fact that θˆ changes endogenously, in fact, falls with an increase in I. θˆ falls fast enough to increase the length of the N P interval, 18

thus leaving fewer and fewer doctors in the F P segment. This causes the for-profit sector to become dominated by F P suppliers faster. Part (b) of the proposition follows from the fact that when I/(I + U ) increases, both the ˆ and the upper limit of this sector, θ − I, fall.21 The average of lower limit of the N P sector, θ, the quality supplied, which is the average of qθ = 2θ over this segment, must fall.

4

Empirical Estimation

We test the implications of our model using data on U.S. hospital markets. The unit of observation in our cross-sectional regressions is a single hospital market, which we take to be a Metropolitan Statistical Area (MSA). The model above generates five testable implications. The first three are concerned with quality: 1. In each market, the variance of quality is higher across FP hospitals than across NP hospitals. 2. An increase in the share of informed patients increases the mean FP quality for small shares of informed, and may decrease the mean FP quality for large shares. 3. An increase in the share of informed patients reduces the average NP quality. As our model allows for rationing (which occurs only in the NP sector in equilibrium), two additional implications concerning waiting times follow: 4. NP hospitals have longer waiting times than FP ones. 5. Higher quality NP hospitals have longer waiting times than lower quality NP ones. Implications 4 and 5 are straightforward implications of the fact that NP hospitals (especially high-quality NP hospitals) cannot respond to higher waiting times by raising price. Accordingly, ˆ Although dθ/dI, given in (14) in the Appendix, becomes positive for large enough I, it is negative for all I ∈ [0, D). 21

19

the main interest is in the first three implications. In this section, however, we report the results of tests for all five implications.

4.1

Empirical Methodology and Data for the Analysis of Hospital Quality

Three main methodological issues arise in empirical tests involving hospital quality 1. How to measure the quality of a hospital. 2. How to identify hospital markets geographically. 3. What level of aggregation to apply to the data (as we observe hospital quality of care only though its impact on an individual patient). we examine these three issues below. The recent literature has converged toward measuring hospital quality in terms of mortality rates: higher mortality implies lower quality (McClellan and Staiger, 2000; Shen, 2002). We use 30-day post-admission risk-adjusted (or standardized, i.e. controlled for patient characteristics) mortality rates (RSMR) for Heart Attacks, obtained from the US Department of Health & Human Services, Hospital Compare.22 These RSMR were calculated by the Hospital Compare service using all admissions of Medicare and Medicaid insured patients between July 2006 and June 2007. Hospitals’ organizational forms and addresses were obtained from the same source.23 A number of characteristics of Heart Attacks are important to this study. First, this diagnosis group is severe enough such that hospital selection by patient is not likely to occur.24 On the one hand this contributes to the reliability of the measure; on the other hand, RSMR for Heart Attacks measures a quality aspect that lies outside of the model developed herein (recall that informed 22

http://www.hospitalcompare.hhs.gov/ accessed on 3 December 2008 at 13:07. For the details of RSMR calculation refer to “Medicare.gov - Hospital Compare: Information for Professionals”, http://www.hospitalcompare.hhs.gov/Hospital/Static/ InformationforProfessionals_tabset.asp accessed on 24 June 2009 at 11:46; For the details of the initial estimating procedure of mortality rates refer to Krumholz et al. (2006). 24 The patient needs to be transported in a timely manner to the nearest hospital after a heart attack. 23

20

patients choose a hospital based on its quality). One should interpret this measure, however, as a proxy for the quality of care the hospital offers for all the services it provides. Alternative outcome measures of quality (e.g. mortality for a less severe diagnosis group) are potentially biased by treatment of higher risk cases at higher quality hospitals.25 One may object to the notion that hospital’s performance in heart attacks is positively correlated with its performance in other types of procedures. Specifically, since exceptional performance in heart attacks does not bring more patients to the hospital (due to the urgent nature of this diagnosis group), it is possible that a hospital will find it more beneficial to invest resources in elective procedures at the expense of heart attacks. In this case, hospital’s performance in heart attacks will be negatively correlated with its quality of care in other diagnosis groups.As explained above, RSMR for Heart Attacks is a common measure of hospital quality, while performance in elective surgeries is a biased measure of quality due to doctor referrals and direct hospital choice by patients, for this reason many health analysts use RSMR for Heart Attacks to measure hospital’s overall performance. We use Metropolitan Statistical Areas (MSA) to bound geographical markets for hospitals. These boundaries correspond well to Hospital Referral Regions (HRR), and take into account any obstacles to travelling (see Horwitz and Nichols, 2007).26 From the US Census Bureau27 we obtained the demographic variables discussed below. We calculate market-level means and standard deviations of RSMR for each organizational form (NP, FP and Government owned)28 25

See Dubrovinsky (2009) for a discussion of alternative measures of quality, including process measures and their shortcomings. 26 See Dubrovinsky (2009) for a discussion of alternative market definitions for hospitals and their applicability to the current analysis. 27 www.census.gov American Fact Finder [download center] accessed on 4 December 2008 at 14:13. 28 The classification of hospitals by organizational form was done in the following manner. “Government - Federal”, “Government - Hospital District or Authority”, “Government - Local” and “Government - State” hospitals were all classified as government owned. All “Proprietary” hospitals we classify as FPs. Finally, all of the following ownership forms are classified as NP: “Voluntary non-profit - Church”, “Voluntary non-profit - Other” and “Voluntary non-profit - Private”. Studies that do not investigate the differences between religious NPs and non-religious ones (for an example of a comparison between religious and non-religious NPs see Hansmann, Kessler, and McClellan, 2003) tend to classify all of these institutions under one NP category. It is also common in the literature to treat NP and Government hospitals as separate categories (see McClellan and Staiger, 2000; Shen, 2002)

21

and use each MSA as one observation (recall that implications 1 through 3 are concerned with the first two moments of the quality distribution). Early empirical studies on hospital quality used patient-level data directly in the estimating equations (as discussed in Shen, 2002). Shen (2002) recognizes the advantages of estimating mortality rates for each hospital in the first stage and using the estimated values in the organizational form regressions in the second stage. This procedure treats each hospital as one observation. Our innovation (which follows closely the predictions of the model) comes from further aggregation of the unit of analysis to the market level. Our approach, which employs the marketlevel moments of quality distribution, has a closer correspondence between the theoretical model that generates the implications and the empirical analysis. Like essentially every economic theory of NPs, including the seminal papers of Glaeser and Shleifer (2001) and Hirth (1999), our model is concerned with only one market. For this reason a natural framework to test the predictions of the theory developed herein is by examining moments of quality distribution within markets while exploiting variation across markets. To implement this methodology we first compute the means and standard deviations of mortality rates for hospitals of the same organizational form within each MSA. One may object to this procedure on the grounds that the small number of hospitals within MSAs29 does not allow to estimate the moments of quality precisely at the market level. The imprecise estimation of the dependent variable has the potential to introduce a considerable amount of noise in the estimations. Market-level moments of quality distribution, however, should be viewed as population moments rather than sample moments. The dataset we use contains all the relevant hospitals (acute care hospitals treating Heart Attacks) that fall within MSAs (the MSAs, of course, are a sample of all US regions.) 29

See Table 2 and the discussion in Dubrovinsky (2009).

22

We estimate the following specification to test implication 1: In each market, the variance of quality is higher across FP hospitals than across NP hospitals � SDM ortmo = β0 + β1 F Pmo + β2 GOVmo + Xm β3 + ζmo

(10)

Where SDM ortmo is the standard deviation of RSMR in MSA m for hospitals of organizational form o. Dummy variables capture the effect of the organizational form. F P equals one if SDM ortmo corresponds to FP hospitals (in MSA m), and GOV equals one if it corresponds to government owned ones (NP category omitted). Xm is a vector of market characteristics, intended to control for forces that are not incorporated into the theory and that would render markets comparable. ζm is an error term coming from various idiosyncratic market-level shocks.30 A positive and significant coefficient on the FP dummy (β1 > 0) is consistent with implication 1. In order to test implication 2: An increase in the share of informed patients increases the mean FP quality for small shares of informed, and may decrease the mean FP quality for large shares, we specify the following regression � M eanM ortF Pm = γ0 + γ1 Gradm + γ2 Grad2m + Xm γ 3 + ηm

(11)

Here M eanM ortF Pm is the mean RSMR for FP hospitals in MSA m. Grad is the percentage of population in the MSA with graduate or professional degree. This variable proxies for the share of informed consumers in the population. We believe that higher level of education makes an individual more likely to belong to a social network that includes medical professionals, who are able to recommend the best hospitals and doctors. Additionally, higher level of education should improve an individual’s ability to make inferences about quality of hospitals from the information available. Following the potential non-monotonicity in implication 2, we include 30

The error terms may be potentially correlated at the MSA-level, as each MSA appears as an observation up to three times (once for each organizational form). To check for robustness we cluster the standard errors. Clustering does not seem to matter (see Table 3).

23

Grad2 in the regression. Xm are market-level controls and ηm is an error term capturing marketlevel shocks. A negative coefficient on Grad and a positive one on its square are consistent with implication 2, as high mortality rates imply low quality. Finally, implication 3: An increase in the share of informed patients reduces the mean NP quality, is tested by estimating � M eanM ortN Pm = δ0 + δ1 Gradm + Xm δ2 + ξm

(12)

Where M eanM ortN Pm is the mean RSMR for NP hospitals in MSA m. Grad is the percentage of population in the MSA with graduate or professional degree, again a proxy for the share of informed consumers. Xm are MSA-level controls and ξm is the error term. A negative coefficient on Grad is consistent with implication 3. We control for income, education and population differences between MSAs. The positive impact on health of the first two is well documented in the literature.31 Additionally, there are economies of scale to investments in health care.32 For this reason one would expect to observe higher investment in mortality-reducing technology in more populated MSAs (after controlling for any income and education differences). The vector Xm includes the following controls: MSA population, median household income in 1999 (a year prior to the remaining of the census sample) and “percentage of the population with high school degree or equivalent” or “percentage of the population with 9th to 12 grade and no high school diploma,” depending on the specification, as a measure of the overall level of eduction.33,34 31

Jones and Wildman (2008) report evidence on the impact of income on health status and DeWalt et al. (2004) offers a review of evidence on the impact of education. 32 Athey and Stern (2000) provides such evidence for enhanced 911 service. 33 The variable Grad is defined as the “percentage of MSA population with graduate or professional degree”, this variable proxies for the percentage of informed patients in the MSA (relevant for implications 2 and 3). Including a measure of overall level education enables to estimate the coefficient on the variable Grad more consistently, as it is correlated with the measure of general level of education (ρ = −0.627 for “percentage of the MSA population with 9th to 12th grade (no high school diploma)”, and ρ = −0.472 for “percentage of the population with high school degree or equivalent”). 34 It is common in the literature to control for per capita income and population size (McClellan and Staiger, 2000; Shen, 2002). Our paper seems to be the first to control for education in the studies of quality. For a discussion of

24

Table 1 presents the summary statistics for mortality rates. Each observation of a mortality rate corresponds to a hospital. The number of NP hospitals is almost four times as large as the number of FP hospitals and almost five times as large as the number of government owned ones. Both the means and the standard deviations of mortality rates averaged across markets are fairly Table 1: Risk Adj. Mortality Rates for Heart Attacks by Org. Form (estimated from 2006-2007 Medicare/Medicaid admissions) Org. Form Obs. FP 322 NP 1112 GOV 256

Mean Std. Dev. Min 16.072 1.097 12.5 15.968 1.208 12.4 16.11 0.996 12.7

Max 19.5 20 20.8

close between the NP and FP organizational forms. The NPs seem to have slightly lower average and slightly higher standard deviation of mortality. The remaining summary statistics for the variables used in the analysis of hospital quality appear in Table 2. Population size varies significantly across MSAs (standard deviation of over 2 Table 2: Summary Statistics for Hospital Quality Estimations Variable Mean MSA Population (mill.) 0.899 Med. HH Income 1999 (000s $) 39.175 Graduate or Professional Degree (%) 8.1 9th to 12th Grade (no high school diploma) (%) 11.4 High School Degree (%) 30.1 Number of FP Hospitals in MSA 1.298 Number of NP Hospitals in MSA 4.484 Total Number of Hospitals in MSA 6.815 No. of Obs.

Std. Dev. Min 2.06 0.058 6.755 11.385 2.9 2.9 2.8 3.4 6.2 17.8 3.693 0 10.571 0 14.347 1 N=248

Max 21.2 62.024 21 18.6 50 47 112 135

million inhabitants). This shows the importance of controlling for population size. The income dispersion between the highest and the lowest median income MSA is more than $50,000 a year. other controls used in hospital studies, reasons for their omission, and possible biases associated see Dubrovinsky (2009).

25

It is thus important to control for income differences. The percentage of population with high school degree or an equivalent as their highest level of education is the most variable among the three education measures used.35

4.2

Hospital Size and Weighting of RSMR

It has been established in the literature that larger hospitals (with higher volumes of patients) tend to have higher quality (or lower mortality).36 Controlling for hospital size is important to obtain consistent estimates when using quality data. This is especially so when comparing NP to FP hospitals, since NP hospitals tend to be systematically larger than FP ones.37 Studies that use individual hospitals as observations (e.g Shen, 2002) include hospital size (proxied by the volume of patients) as a control. This approach cannot be implemented under the methodology proposed in this paper, where the whole MSA enters the regression as one observation. We must address the issue of controlling for hospital size before computing the moments of the distribution of quality (means and standard deviations of RSMR within MSAs for NPs and FPs). Before calculating the market-level moments of interest, we weight the RSMR for each hospital by hospital’s share of patients within its MSA and within its organizational form. Formally, the weighting is done in the following manner: Fix hospital h. Let O(h) denote the set of all hospitals of the same organizational form as h (all across the US). Similarly, let M (h) be the set of all hospitals located in the same MSA as h. This allows us to define the set H(h) containing all hospitals that are of both the same organizational form as h and are located in the same MSA, � formally H(h) ≡ O(h) M (h). Let nh be the number of patients in hospital h treated for Heart

Attacks (from which the RSMR figure was calculated). Then each weighted RSMR for hospital h� is a product of the original RSMR of h� in the dataset (the descriptive statistics of which appear 35

As an average MSA has less than 7 hospitals, we do not phrase implication 1 in terms of the fourth moment. See Feldman and Scharfstein (2000) for a review of findings and Gowrisankaran, Ho, and Town (2006) for a discussion of the possible reasons for this regularity. 37 See the discussion in the Appendix. Figure 2 shows FP hospitals to have systematically fewer patients than NP ones. Figure 3 implies that these difference are observed within markets (MSAs) as well, i.e. the hope that hospitals of comparable sizes locate in one market has little ground. 36

26

in Table 1) and the following weight: nh� /(

�

h∈H(h� )

nh ).

In the weighting process each mortality rate is scaled by the overall number of patients treated in hospitals of the relevant organizational form in the MSA. A larger hospital receives a higher weight, thus relatively increases its mortality rate. On the other hand, RSMR that comes from a smaller hospital receives a lower weight, which relatively decreases the mortality rate of the hospital. As larger hospitals tend to have lower mortality rates than smaller ones (Feldman and Scharfstein, 2000; Gowrisankaran, Ho, and Town, 2006), when the mortality rate is adjusted relatively upward (downward) for larger (smaller) hospitals, the impact of the hospital size on mortality is reduced.38

4.3

Empirical Results for the Analysis of Hospital Quality

The main implication of the theory developed in this paper generates implication 1: In each market, the variance of quality is higher across FP hospitals than across NP hospitals. This implication is instrumental in the reconciliation of previous conflicting empirical results, as the explanation for finding higher quality for either NP or FP organizational form based on conditional mean (i.e. regression) analysis of quality (as in the previous studies) hinges on the main result of this paper of three pools of hospitals: high quality FP, medium quality NP and low quality FP. While the central implication of this explanation (in a world that is more complex than the stylized nature of the model) is that FP hospitals should have a higher variance of quality than NP ones. We estimate specification (10) to test implication 1.39 The results are reported in Table 3. 38

We replicated the analysis with unweighted RSMR (not reported here). Qualitatively the results remain unchanged, however, the standard errors on the coefficients are larger (most coefficients lose their statistical significance.) As this feature is true for all three quality related estimations, the weighting procedure seems to reduce the “noise” due to variation in hospital size. Surprisingly, in specification (11), for implication 2 predicting a nonmonotonic relationship between the share of informed patients and the mean quality of FP hospitals, the coefficient both on the first and second power of Grad are significantly different from zero at conventional levels even with unweighted RSMR. 39 We use the methodology developed in this paper to compare the mean quality of FPs and NPs. We estimate specification similar to (10) with mean quality instead of its standard deviation. The results obtained are consistent with the majority of the studies in the area: NPs dominate FPs in terms of quality in our dataset.

27

Column (4) includes all the relevant controls: population size, income and overall level of eduction. The coefficient of interest on the FP dummy has a positive sign with p-value of 8.7%. We interpret this result as modest support for implication 1 and the main result of the model: that FP hospitals have a higher variance (standard deviation) of quality than NP ones.40 Table 3: Organizational Form and the Variance of Quality (RSMR)

Dependant Variable: FP GOV

(1) SD Mort. 0.381 (0.433) 1.019* (0.556)

(2) (3) SD Mort. SD Mort. 0.685 0.649 (0.418) (0.417) 1.422*** 1.453*** (0.525) (0.523) -0.301*** -0.262*** (0.052) (0.052) -0.041* (0.023)

3.423*** (0.224) 232 0.02

3.858*** (0.228) 232 0.14

Population (mill.) Income (000s $) High School Degree (%) Constant Observations R-squared

5.488*** (0.931) 232 0.15

(4) MSA-Clustered S.E. SD Mort. SD Mort. 0.736* 0.736* (0.427) (0.426) 1.521*** 1.521*** (0.526) (0.515) -0.249*** -0.249*** (0.053) (0.071) -0.034 -0.034 (0.021) (0.022) 4.292 4.292 (3.515) (3.324) 3.935*** 3.935*** (1.389) (1.372) 232 232 0.16 0.16

Robust standard errors in parentheses * significant at 10%; ** significant at 5%; *** significant at 1%

As up to three observations potentially come from the same MSA, it could be that the error terms are correlated at the MSA level, generating biased estimates of the standard errors. Column (5) of Table 3 clusters the standard errors. None of the coefficients loses its significance. Table 3 indicates that Government owned hospitals also have a higher variance of quality than NP ones. One may be tempted to group the NP hospitals together with the government owned ones. Duggan (2000) finds, however, that Government owned hospitals, as oppose to NP 40

Observations are omitted, for each organizational form, when the number of hospitals of this form in the MSA is less than 2, since in this case the standard deviation cannot be calculated. When the regression is restricted to markets where both FP and NP firms number 2 or greater (not reported here), the estimated coefficient on FP increases to 0.80; the standard error also increases due to the smaller sample size.

28

ones, face a “soft budget constraint”. We believe that there is a high level of variation both in the funding of Government owned hospitals and the degree to which their budget constraint is indeed soft, these generate the high variation of quality across hospitals in the Government sector. Implication 2: An increase in the share of informed patients increases the mean FP quality for small shares of informed, and decreases the mean FP quality for large shares, is tested by estimating specification (11). The results are reported in Table 4. Column (4) of Table 4 presents Table 4: Informed Consumers and Mean FP Quality (RSMR) (1) (2) (3) (4) Dependant Variable: Mean Mort. FP Mean Mort. FP Mean Mort. FP Mean Mort. FP Informed (%) -255.446*** -343.519*** -240.629*** -226.546** (68.486) (77.485) (82.086) (91.035) Informed2 1,128.665*** 1,379.052*** 1,090.282*** 1,031.249*** (318.484) (326.711) (335.330) (374.987) 9th to 12th grade (%) -56.787** -26.447 -31.069 (28.552) (28.364) (30.232) Population (mill.) -0.672*** -0.640*** (0.185) (0.197) Income (000s $) -0.039 (0.094) Constant 23.016*** 35.192*** 26.293*** 27.630*** (3.332) (6.742) (6.988) (7.613) Observations 104 104 104 104 R-squared 0.09 0.12 0.22 0.22 Robust standard errors in parentheses * significant at 10%; ** significant at 5%; *** significant at 1%

the results with the entire set of the MSA characteristics as controls. The coefficients on the share of informed patients (“percentage of population with graduate and professional degree”) and its square are significantly different from zero and have the predicted signs (recall that lower mortality indicates higher quality.)41 The data support implication 2 rather strongly.42 41

One can calculate the extremum to be at 10.98% of the MSA population with graduate or professional degree, which falls within the range of the data: 2.9% to 21%, and above the mean of 8.1% (see Table 2). 42 Each market enters the dataset only once, therefore, there is no potential clustering of the residuals at the MSAlevel.

29

Table 5 reports the results of the test for implication 3: An increase in the share of informed patients reduces the mean of NP quality. We estimate specification (12) to perform this test. Column (4) presents a specification with the full set of MSA-level controls, the coefficient on the Table 5: Informed Consumers and Mean NP Quality (RSMR) (1) (2) (3) (4) Dependant Variable: Mean Mort. NP Mean Mort. NP Mean Mort. NP Mean Mort. NP Informed (%) -52.371*** -62.067*** -27.262 -21.725 (15.725) (20.088) (17.953) (15.169) 9th to 12th grade (%) -16.825 5.041 -20.380 (17.723) (16.915) (18.065) Population (mill.) -1.074*** -0.831*** (0.326) (0.303) Income (000s $) -0.219*** (0.081) Constant 13.245*** 15.927*** 11.706*** 22.522*** (1.275) (3.250) (3.041) (4.895) Observations 215 215 215 215 R-squared 0.07 0.07 0.22 0.26 Robust standard errors in parentheses * significant at 10%; ** significant at 5%; *** significant at 1%

share of informed patients (“percentage of population with graduate or professional degree”) has the wrong sign, however, is not significantly different from zero at conventional levels. The data does not support implication 3. Two out of the three predictions related to hospital quality find support in the data. The data shows higher variance of quality for FP hospitals relative to the NP ones (implication 1), which supports the explanation of this paper for previous conflicting empirical results on organizational form and quality. Implication 2, predicting a (potential) non-monotonic relationship between mean FP quality and the share of informed patients finds a rather strong support in the data.

30

4.4

Empirical Analysis of Waiting Times

The theory developed in this paper generates the following predictions regarding queues or waiting times: NP hospitals have longer waiting times than FP ones (implication 4); Higher quality NP hospitals have longer waiting times than lower quality NP ones (implication 5). Although the issue of waiting times for medical procedures is extremely acute in many OECD countries,43 surprisingly, economists have paid little attention to waiting times in the US hospital industry.44 Patient-level data on 2006 waiting times, measured as the difference in minutes between the time of patient’s arrival to the emergency department and her examination by a physician, was obtained from the National Hospital Ambulatory Medical Care Survey (NHAMCS) administered by the US National Center for Health Statistics.45 The dataset contains hospital characteristics, zip code-level demographics, patient characteristics,46 and the organizational form of each hospital (NP, FP and Government owned). We were not able to match hospitals in the NHAMCS sample with their mortality rates from the Hospital Compare database, as Medicare/Medicaid provider IDs were not available for hospitals in the NHAMCS dataset. Therefore, we employ for the regressions an alternative measure of quality: the average number of repeat visits of the emergency department within 72 hours. More repeat visits imply lower quality.47 One may claim that hospital selection by patients is likely to occur in this setting, with the result that the estimation will be biased. There are two possible directions of such selection: a) 43

See Fraser Institute 2008, “Waiting Your Turn: Hospital Waiting Lists in Canada 2008 Report”, by Nadeem Esmail and Maureen Hazel with Michael A. Walker, Studies in Health Care Policy, 18th Edition. for Canada, and Siciliani and Hurst (2005) for an OECD overview. 44 To the best of our knowledge there exists only one economics related empirical study (Wilper et al., 2008) and three in the medical field (see Richardson and Hwang, 2001; James, Bourgeois, and Shannon, 2005). 45 http://www.cdc.gov/nchs/about/major/ahcd/ahcd1.htm accessed on 08 July 2009 at 22:16. The documentation on survey design and variable coding can be obtained from ftp://ftp.cdc.gov/ pub/Health_Statistics/NCHS/Dataset_Documentation/NHAMCS/doc06.pdf accessed on 08 July 2009 at 22:10. 46 Refer to Dubrovinsky (2009) for a description and coding of these variables. 47 It is possible, however, that the reason for the repeat visit of the emergency department was a previous disease spell (potentially improperly treated at a different facility). We adjust the share of repeat visits in a manner that only those patients who were not hospitalized in any hospital within 7 days from the initial hospitalization are included in the calculations. We call this variable “adjusted repeat visits”.

31

hospitals which treat patients faster receive more patients, b) patients select hospitals on quality. In case a) there is a bias against finding significant differences between hospitals; hence, the bias is conservative. Case b), however, is modelled explicitly and the current study aims to test precisely for the presence of such mechanism.48 Therefore, for implication 5, it is important to allow such selection in the data. Table 6 presents the summary statistics for the variables used in the waiting times analysis.49 There are 364 hospitals in the dataset (as the value of the zip code level demographic variables is assigned to each patient observation, the number of patient observations and zip code characteristics are equal in the table). Only 347 of these hospitals enter the regressions due to missing observations. Table 6: Summary Statistics for Waiting Time Estimations Variable waittime NP GOV NP × Adj. Repeat Visit (%) Adj. Repeat Visit (%) Med. HH Inc. $32,794 to $40,626 Med. HH Inc. $40,627 to $52,387 Med. HH Inc. $52,388 or more Poverty: Below 5% Poverty: 5% to 9% Poverty: 10% to 19% Region: Northeast Region: Midwest Region: West Urban

Obs. Mean Std. Dev. Min 28391 58.387 88.89 0 28391 0.734 0.442 0 28391 0.179 0.383 0 28055 0.024 0.049 0 28055 0.031 0.049 0 27128 0.25 0.433 0 27128 0.214 0.41 0 27128 0.214 0.41 0 27124 0.144 0.351 0 27124 0.262 0.44 0 27124 0.363 0.481 0 28391 0.239 0.426 0 28391 0.215 0.411 0 28391 0.185 0.388 0 28391 0.883 0.322 0

Max 1430 1 1 0.75 0.75 1 1 1 1 1 1 1 1 1 1

Table 6 shows that the measure waittime is highly variable, which justifies the logarithmic 48

Recall that the uninformed patients infer the quality of NP hospitals perfectly (due to the non-distribution constraint). See Subsection 3.4. 49 To save space we do not report summary statistics or the coefficient estimates for the patient-level controls.

32

transformation, as suggested in the literature.50 Majority of the observations come from the South (the omitted category in the analysis) and from urban areas. The lowest share of the observations comes from the West region. Over 70% of the patients were treated at NPs, and only 9% at FPs. We estimate the following specification to test implication 4: NP hospitals have longer waiting times than FP ones, and implication 5: Higher quality NP hospitals have longer waiting times than lower quality NP ones. LN waittimep = φ0 +φ1 N Ph +φ2 GOVh +φ3 N P ×RepV ish +φ4 RepV ish +Zh� φ5 +Cp� φ6 +ϑp Where LN waittimep is the natural logarithm of the waiting time in minutes between patient p’s arrival and her examination by a physician. N Ph and GOVh are organizational form dummies (FP category omitted) for hospital h. RepV ish is the percentage of repeat visits of hospital h, omitting those who have recently undergone a hospitalization (a measure of quality). Zh is a vector of demographic characteristics of the population in the zip code where the hospital is located, and Cp is a vector of patient characteristics. ϑp is the error term that captures the impact of unobservable patient characteristics which influence waiting times.51 A positive coefficient on the NP dummy (φ1 > 0) supports implication 4. A negative coefficient on the interaction term (φ3 < 0) is consistent with implication 5 (more repeat visits implying lower quality). Table 7 reports the results. Column (1) estimates the regression only with the variables of interest and no controls. The coefficient on the NP dummy is positive and significantly different from zero. This is consistent with implication 4. The coefficient on the interaction between the adjusted percentage of repeat visits (a proxy for quality) and the NP dummy is negative and significant, which supports implication 5.52 Including hospital-, patient- and zip code-level controls (Columns (2) and (3)) does not 50

See Wilper et al. (2008) and James, Bourgeois, and Shannon (2005). ϑp s are potentially correlated within hospitals, clustering is employed to check for robustness. 52 It is interesting to note that in general (i.e. not for the NP group), higher percentage of repeat visits is associated with longer waiting times. 51

33

Table 7: Organizational Form, Quality of Care and Waiting Times (1) (2) (3) Hospital-Clustered S.E. Dependent Variable: LNwaittime LNwaittime LNwaittime LNwaittime NP 0.166*** 0.324*** 0.331*** 0.331*** (0.029) (0.030) (0.030) (0.096) GOV 0.164*** 0.227*** 0.302*** 0.302** (0.030) (0.032) (0.031) (0.117) NP × Adj. Repeat Visit (%) -2.193*** -4.277*** -3.275*** -3.275* (0.521) (0.519) (0.504) (1.986) Adj. Repeat Visit (%) 2.191*** 4.298*** 3.549*** 3.549* (0.506) (0.505) (0.487) (1.901) Income $32,794 to $40,626 0.105*** 0.088*** 0.088 (0.023) (0.023) (0.060) Income $40,627 to $52,387 0.175*** 0.170*** 0.170** (0.028) (0.029) (0.074) Income $52,388 or more 0.141*** 0.131*** 0.131 (0.034) (0.035) (0.096) Poverty below 5% -0.278*** -0.146*** -0.146* (0.038) (0.040) (0.084) Poverty 5% to 9% -0.237*** -0.134*** -0.134* (0.030) (0.032) (0.072) Poverty 10% to 19% -0.154*** -0.098*** -0.098* (0.023) (0.024) (0.055) Northeast -0.184*** -0.169*** -0.169* (0.019) (0.020) (0.086) Midwest -0.283*** -0.234*** -0.234** (0.020) (0.021) (0.091) West -0.199*** -0.113*** -0.113 (0.022) (0.024) (0.087) Urban 0.561*** 0.460*** 0.460*** (0.022) (0.024) (0.099) Patient level controls No No Yes Yes Constant 3.312*** 2.882*** 3.223*** 3.223*** (0.028) (0.038) (0.093) (0.215) Observations 27290 26067 22010 22010 R-squared 0.002 0.04 0.13 0.13 Robust standard errors in parentheses * significant at 10%; ** significant at 5%; *** significant at 1%

34

change the results qualitatively.53 The coefficient on the NP dummy remains significant, with clustering, at 1% level, which indicates strong support for implication 4. The coefficient on the interaction term, however, has the p-value of 10% exactly after clustering. This implies weaker support for implication 5. In sum, the data support (to varying degree) both predictions of the model regarding waiting times: patients at NP hospitals wait longer than at FP ones, while within the NP sector patients wait longer at higher quality hospitals.

5

Conclusion

In this study we reexamine the relationship between organizational form on the quality of health care. Previous empirical evidence on this issue is mixed, without strong support of the predictions of existing theory, the Arrow-Hansmann hypothesis. This paper argues that the lack of conclusive evidence on differences in first moments of quality between NP and FP organizational forms is entirely consistent with economic theory. The variance of quality, however, is predicted to be higher for FPs. This latter implication is supported by the data, along with three additional implications. In a model of information asymmetry we find that the following is an equilibrium: informed patients accept FP contracts that offer the highest quality of care in the market, uninformed patients accept both NP contracts that offer the second tier of quality levels, and FP contracts that offer the lowest quality of care. This generates three pools of hospitals: high quality FP, medium quality NP, and low quality FP. Hence, the average quality of one sector relative to the other will depend of the relative sizes of these pools. The main theoretical innovation of this paper enabling us to reconcile previous conflicting empirical results is the idea that doctors self-select between the NP and FP sectors based on ability rather than the degree of altruism. Altruism, on the other hand, is needed for NPs to arise. The differences in quality between the NP and FP sectors can be explained through differences 53

The coefficients on patient level characteristics, not reported here, are consistent with Wilper et al. (2008).

35

(arising endogenously) in the ability of doctors self-selecting between the two sectors. The empirical analysis of hospital quality involves a methodological innovation. We examine the relationship between organizational form and the market-level moments of the quality distribution directly, by using these moments as observations. This feature offers the most direct test of NP theories up to date. Previous empirical studies investigate the relationship between organizational form and conditional means of quality across the entire US territory, rather than within markets. The empirical results support to varying degrees four implications of our theoretical model. In particular, FP hospitals have a higher estimated variance of quality, consistent with the main implication. A new picture of health care markets emerges with for-profit providers tending towards the extremes of quality, relative to non-profit providers.

36

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Feldman, Sarah and David Scharfstein. 2000. “Managed Care and Provider Volume.” In The Changing Hospital Industry: Comparing Not-for-Profit and For-Profit Institutions, edited by David M. Cutler. NBER, The University of Chicago Press, 229–248. Francois, Patrick. 2007. “Making a difference.” RAND Journal of Economics 38 (3):714–732. Francois, Patrick and Michael Vlassopoulos. 2008. “Pro-social Motivation and the Delivery of Social Services.” CESifo Economic Studies 54:22–54. URL doi:10.1093/cesifo/ ifn002. Glaeser, Edward L. and Andrei Shleifer. 2001. “Not-for-Profit Entrepreneurs.” Journal of Public Economics 81:99–115. Gowrisankaran, Gautam, Vivian Ho, and Robert J. Town. 2006. “Causality, Learning and Forgetting in Surgery.” Department of Economics, University of Arizona. Hansmann, Henry. 1980. “The Role of Nonprofit Enterprise.” Yale Law Journal 89:835–901. Hansmann, Henry, Daniel Kessler, and Mark McClellan. 2003. “Ownership Form and Trapped Capital in the Hospital Industry.” In The Governance of Not-for-Profit Organizations, edited by Edward L. Glaeser. The University of Chicago Press, 45–69. Hirth, Richard A. 1999. “Consumer Information and Competition between Nonprofit and Forprofit Nursing Homes.” Journal of Health Economics 18:219–240. Horwitz, Jill R. and Austin Nichols. 2007. “What Do Nonprofits Maximize? Nonprofit Hospital Service Provision and Market Ownership Mix.” URL http://www.nber.org/papers/ w13246. NBER Working Paper 13246. James, Catherine A., Florence T. Bourgeois, and Michael W. Shannon. 2005. “Association of Race/Ethnicity with Emergency Department Wait Times.” Pediatrics 115 (3):e310–e315.

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APPENDIX This appendix provides a proof of proposition 2. Solving (8) for F F P and substituting the expression into (7) yields

40

�

θˆ θ

qθF P

2 ˆ2 dG(θ) α ˆ − 1 [c(q Fˆ P , θ) ˆ − αq Fˆ P ] = (θ − I) − θ − [qθˆ − c(qθˆ, θ)] θ θ ˆ 1−α 1−α G(θ) 2[U − (θˆ − θ)]

(13)

Into the left hand side of (13) we substitute the following expressions (which are derived in the ˆ q F P = 2αθ; c(q ˆ, θ) ˆ = q 2 /4θˆ = θ; ˆ c(q F P , θ) ˆ = α2 θ. ˆ The integral on the left text): qθˆ = 2θ; θ θˆ θˆ � 2 � α α ˆ The hand side solves to yield α(θˆ + θ); the remaining terms equal − θˆ = −αθ. 1−α 1−α left hand side thus equals αθ. Substituting this into (13) yields an equation that characterizes θˆ in terms of exogenous variables:

αθ =

(θ − I)2 − θˆ2 2[U − (θˆ − θ)]

Substituting U = N − I (N is the total number of patients, held fixed) and totally differentiating yields dθˆ θ − I − αθ = dI αθ − θˆ

(14)

ˆ Note that dθ/dI < 0 for I = 0.

The average quality in the F P segment is 2θ − I;54 the average quality in the F P segment is α(θˆ + θ),55 the average quality in the entire for-profit sector is the weighted average of these:

A≡

[θˆ − θ] · α(θˆ + θ) + I(2θ − I) α(θˆ2 − θ2 ) + 2θI − I 2 = θˆ − θ + I θˆ − θ + I

54

The quality provided by an F P firm of type θ is 2θ, with the quadratic cost function. Firms in the F P � θ dG(θ) segment fall into the interval [θ − I, θ], hence the mean quality in this segment is 2θ . Since 1 − G(θ − I) θ−I dθ θ−I −θ dG(θ) = , and G(θ − I) = , the value of the integral is 2θ − I. θ−θ θ−θ 55 ˆ The quality provided by an F P firm of type θ is 2αθ. All firms in the F P segment fall into the interval [θ, θ), � θˆ dG(θ) hence the mean quality in this segment is 2αθ = α(θˆ + θ). ˆ G(θ) θ

41

Differentiating this shows that dA/dI > 0, at I = 0 is equivalent to dA �I=0 > 0 dI

⇐⇒

dθˆ [2αθˆ − α(θˆ + θ)] + 2θ − α(θˆ + θ) > 0 dI �I=0

Rearranging yields dA �I=0 > 0 dI

dθˆ α(θˆ + θ) − 2θ �I=0 > dI α(θˆ − θ)

⇐⇒

(15)

Substituting (14) shows that the inequality on the right of (15) is met: dθˆ �I=0 dI

> ⇐⇒

α(θˆ + θ) − 2θ α(θˆ − θ)

θ − αθ α(θˆ + θ) − 2θ > αθ − θˆ α(θˆ − θ) (θˆ − αθ)[2θ − α(θˆ + θ)] > α(θˆ − θ)(θ − αθ) ⇐⇒

Rewriting the left hand side shows that this inequality is equivalent to ˆ − αθ) + (θˆ − αθ)(θ − αθ) ˆ > α(θˆ − θ)(θ − αθ) α(θˆ − θ)(θ − αθ) + (1 − α)θ(θ which always holds. Hence dA/dI > 0 at I = 0. To prove part (b) of Proposition 2, note that the average quality in the N P sector is the ˆ θ − I). Since dθ/dI ˆ average of qθ = 2θ over the interval [θ, < 0 for all I ∈ [0, D), mean quality in the N P sector θ − I + θˆ monotonically falls in I. Hospital Size by Number of Patients The distribution of hospitals by number of patients within each organizational form is reported in Figure 2. FP hospitals tend to be smaller than NP ones, if size is measured by the number of patients. The t-test for mean differences in the number of patients per hospital (admitted for a Heart Attacks) between NPs and FPs (H1 : NN P > NF P , where N is the number of patients) has the t-statistic value of 5.559 (322 FP observations and 1112 NP observations). 42

Figure 2: Distribution of the Number of (Heart Attack) Patients by Hospital for NPs and FPs (2006-2007 US Hospitals) Although FPs have systematically less patients than NPs, it is possible that within the same market one finds similar size hospitals. It turns out that this is not the case. Figure 3 plots the distribution of the mean number of patients per hospital by MSA (within organizational form). Even within MSAs NP hospitals have systematically more patients per hospital, on average, than FPs. The t-test for mean differences in the average number of patients per hospital admitted for a Heart Attack across MSAs between NPs and FPs (H1 : NN P > NF P , where N is the number of patients) has the t-statistic value of 4.097 (104 FP observations and 215 NP observations).

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Figure 3: Distribution of the Average Number of (Heart Attack) Patients per Hospital by MSA for NPs and FPs (2006-2007 US Hospitals)

44