Principal agency theory and health care utilization.

Schneider, Helen ; Mathios, Alan

I. INTRODUCTION

The way in which the health care industry is organized has undergone significant changes over the past 20 years, making it a particularly interesting arena for industrial organization analysis. There are currently two primary types of health insurance plans: traditional indemnity insurance (fee-for-service) and managed care organizations. Under fee-for-service (FFS), the provider is paid for each procedure or service dispensed to a patient. Managed care is more complex--health maintenance plans (or health maintenance organizations, HMOs) take many forms and health care providers are reimbursed in different ways. Of particular importance for this study is capitation. This form of reimbursement is one where the plan pays a fixed amount of income to the physician to care for a patient over a certain period of time. Physicians do not get additional payments, even if the cost of the patient's care is more than what was expected. Essentially, this fixed fee payment per patient transfers the financial risk of treatment from the insurer to the physician and is almost a textbook example of how to implement an incentive-compatible contract to contain excessive use of services. Principal agency theory, however, suggests that transferring the financial risk of treatment from the insurer to the physician can be costly if physicians are risk averse (Eeckhoudt et al. 1985). For example, levels of risk aversion vary across medical specialties and this has implications for medical malpractice (Danzon 1983). Also, incentive-compatible contracts may result in the physician not being a good agent for the consumer, leading to an underprovision of appropriate care. There is a significant literature documenting that managed care patients, on average, have significantly lower lengths of stay than FFS patients. (1) However, these effects appear to vary by diagnosis, and investigators have generally not attempted to systematically model why this is so. This is a key focus of our article.

Another mechanism for containing costs is for a third-party insurer to retain the financial risk of treatment but invest in directly monitoring the care provided by the physician. Some examples of monitoring include utilization review, mandatory preapproval of care, required second opinion options, and so on. Dranove and Satterthwaite (2000) report that utilization review has been widely adopted by U.S. health plans with 90% of indemnity plans and 100% of preferred provider organizations using this as a tool to control costs. The empirical studies by Wickizer and Lesser (1998) and Wickizer et al. (1989) report statistically significant reductions in inpatient utilization of 12-13% by employees enrolled in plans that conduct utilization review. Scheffler et al. (1991) reports a 4% reduction in the length of stay (LOS) by Blue Cross plans that adopt utilization management. Lindrooth et al. (2002) examine the effect of utilization management by managed care companies, finding that at least in mental health settings, utilization review accounts for 65% of the reduction in inpatient care under managed care contracting. However, little has been done to examine how monitoring performs relative to capitation and in what cases it is most effective at containing costs. From a social welfare perspective, the monitoring approach to cost containment is likely to be preferable if monitoring such decisions is low cost relative to the costs associated with introducing income risk to the physician and agency costs with respect to the physician consumer relationship. On the other hand, in situations where monitoring is difficult, incentive-compatible contracting would be a more efficient way to finance health services. (2)

Previous researchers have examined applications of the principal agent framework to health care markets. DeBrock and Arnould (1992) model the health care provider (the physician) as an agent who works for the principal (the insurer). They argue in favor of a risk-sharing arrangement, such as capitation, to mitigate the effect of moral hazard. Pauly and Redish (1973) regard physicians as the key decision makers who control hospital operations and hospitalization services. Ellis and McGuire (1986) develop a model in which the physician is the agent for two principals, the patient and the hospital. Empirical work by Manning et al. (1984) suggests that physicians are induced to place more importance on hospital profits compared with patient benefits, leading to a potential undersupply of services. There are, of course, other mechanisms that may serve to constrain this incentive to undersupply services, such as ethical codes, the probability of malpractice legal action, physician and hospital reputation, and so on. Pauly and Ramsey (1999) suggest patient's cost-sharing as an alternative way to minimize health spending. The authors advocate cost-sharing as a complement to utilization management, the greater the variation in illness severity and the smaller the degree of moral hazard.

This article expands on the application of principal agent theory to health services in several dimensions. First, the theoretical model explicitly considers the fact that an alternative to incentive-compatible contracting is for insurers to actually monitor the care prescribed by physicians under a FFS arrangement. It develops predictions for health care utilization for FFS arrangements relative to capitated arrangements in cases of both low and high monitoring costs. Second, we test the predictions of this theoretical model by examining health utilization (LOS in hospital) for a large sample of consumers where we can compare outcomes of those treated by physicians under FFS and those treated under capitation arrangements. Third, in our empirical work we take account of the self-selection issues related to whether consumers choose FFS or capitated physicians. Fourth, we develop a measure of monitoring costs and examine how differences in health care utilization across financial reimbursement arrangements interact with these measures of monitoring costs. Finally, we investigate whether capitation is utilized more in cases with high monitoring costs.

II. THEORETICAL MODEL

This section develops a model of physician behavior under different payment systems. Three players are involved: a patient, a physician, and an insurance company.

Patients

Patients are assumed to be fully insured and accept all the prescribed treatment their physician is willing to provide. Let the quantity of medical services provided and consumed by an individual patient be [q.sub.i]. Then B([q.sub.i]) denotes the patient's total benefit from health treatment during a single episode. The benefit function is similar to that used by Ellis and McGuire (1986); it is assumed to reach a maximum at [q.sub.i]' after which total benefits fall. The optimal utilization [q.sub.i]' varies by patient within treatment type (e.g., severity of health problem, recuperative powers of the patient's general constitution and health). Total benefits to the patient are assumed to fall after [q.sub.i]' because of the time cost of receiving treatment and possible negative consequences associated with a continued hospital stay or unnecessary procedures (e.g., unnecessary surgery). For simplicity we assume that benefit function is symmetric around [q.sub.i]'. This implies that extra health care is just as detrimental as the underprovision of necessary care. We assume that for individual patient i:

(1) [q.sub.i]' = [??] + [[epsilon].sub.i]

where [[epsilon].sub.i] ~ (0, [[sigma].sup.2]); [q.sub.i]' may vary among individuals, but the analysis in the article is made for the episode of illness. So, the optimal level of health services for a person i equals the mean health care utilization for the given procedure/diagnosis [bar.q] plus a random disturbance that has expected value of 0 and variance [[sigma].sup.2]. For example, for a person with above average health, [q.sub.i]' can be below the mean, whereas for a person with a poor health status [q.sub.i]' may be above the mean. Let benefits function have the form

(2) B([q.sub.i]) = B - [([q.sub.i] - [q.sub.i]').sup.2],

where subscript i denotes a patient, [q.sub.i] is the amount of health services consumed by patient i, and [q.sub.i]' the optimal level of health care services for that patient. In (2) B represents the initial health stock for patient i. In severe cases, when [q.sub.i]' is high, an underprovision of services (low [q.sub.i]) will substantially decrease benefits to the patient. If the optimal level of care [q.sub.i]' is small (as in a case of a trivial disease), benefits to the patient will not change much if the patient doesn't seek care (has a [q.sub.i] of 0). A significant overuse of services (e.g., unnecessary surgery) will also decrease total benefits to the patient by increasing [q.sub.i] relative to the optimal level of care. Although B may deteriorate with age, it is constant for a given episode. We also assume that health can be fully restored once a patient seeks treatment and receives the appropriate care.

Insurance Company

The insurance company is a profit-maximizing firm, and the profit function per episode is

(3) II = [SIGMA][[pi].sup.i](q.sub.i] = [SIGMA] {[P.sub.i] - [C.sub.i]([q.sub.i])} and [C.sup.i]' ([q.sub.i]) [greater than or equal to] 0, [C.sup.i]" ([q.sub.i]) [greater than or equal to] 0,

where [P.sub.i] is the premium revenue from enrollee i and [C.sup.i]([q.sub.i]) is the cost of treatment of person i (cost borne by the insurer) that depends on the amount of services rendered or the capitation payment. The cost function is nondecreasing in [q.sub.i]. The insurance company may choose one of the following alternatives to contain costs: (1) write an incentive-compatible contract (capitation), or (2) employ monitoring. Under capitation, profit for an episode is described by (4):

(4) [[pi].sup.i]([q.sub.i]) = P - a,

where a is the capitation payment to the provider (either per member per month or per episode). Under monitoring,

(5) [[pi].sup.i]([q.sub.i]) = P - F([q.sub.i]) + m([q.sub.i], [v.sub.i]),

where [v.sub.i] are monitoring costs, F([q.sub.i]) is the sum of total fees charged by a physician per episode, and m([q.sub.i], [v.sub.i]) denotes payment withheld from a physician due to monitoring (e.g., utilization management). Thus, m([q.sub.i], [v.sub.i]) can be viewed as a punishment for the overuse of services (net of the monitoring costs). The role that [q.sub.i] and [v.sub.i] play in determining monitoring costs is discussed in the next section.

Complexity/Severity of Diagnosis

We assume that complexity for a certain procedure/diagnosis determines the level of monitoring costs ([v.sub.i]). For diagnoses with little cross-patient variation in health inputs and health outcomes, the insurer can easily predict the optimal health care utilization. Consider a diagnosis where the LOS in a hospital is almost identical across all patients. Monitoring costs are low for such cases because the insurer can explicitly contract how many hospital nights will be covered for this procedure and have few exceptions that need to be investigated. For diagnoses/procedures with significant variation in the LOS (complex cases), monitoring is difficult to conduct because the optimal health care utilization is difficult to estimate. For example, if the insurer would contract for the average number of days there would be a large number of exceptions for which case-by-case monitoring would be required.

We assume that the physician perfectly observes the optimal level of services, [q.sub.i]', and prescribes the amount of treatment [q.sub.i]. The insurance company only observes health care utilization, [q.sub.i]. Complexity of the case, reflected by [v.sub.i], does not affect a capitated physician but makes it difficult to monitor utilization effectively in the FFS environment. Because high complexity makes it expensive for the insurer to deduce the actual [q.sub.i]', it affects the extent of moral hazard a physician may decide to engage in. To limit overutilization in the FFS system, the insurer may invest resources to estimate the optimal necessary amount of care [q.sub.i]'; this estimate, [q.sup.*]([v.sub.i]) is an increasing function of complexity, that is, [partial derivative][q.sup.*]([v.sub.i])/[partial derivative][v.sub.i] [greater than or equal to] 0. If a case is complex and the utilization is difficult to determine, the insurer will be inclined to make allowances for higher utilization. We assume that E[[q.sup.*]([v.sub.i])] = [q.sub.i]'. The monitoring function is assumed to be of the form:

(6) m([q.sub.i], [v.sub.i]) = [delta] [[([q.sub.i] - [q.sup.*]([v.sub.i]))/([v.sub.i] + 1)].sup.[gamma]] if [q.sub.i] [greater than or equal to] [q.sup.*]([v.sub.i]) and 0 otherwise, with [delta] [greater than or equal to] 1 and [gamma] [greater than or equal to] 1.

If utilization of services is below what insurer estimates as optimal, no punishment for overutilization will follow. If the health care utilization for a patient exceeds [q.sup.*]([v.sub.i], then the insurer may punish the physician by withholding a certain sum of money m([q.sub.i], [v.sub.i]) for overutilization. Note that m([q.sub.i], [v.sub.i]) increases in [q.sub.i] and decreases in complexity [v.sub.i]. The withheld payment increases in [q.sub.i] because the further [q.sub.i] is from the estimated optimal utilization [q.sup.*]([v.sub.i]), the higher the punishment m([q.sub.i], [v.sub.i]). It also decreases in complexity in a nonlinear fashion and can never be negative. As monitoring costs increase, the ability to effectively estimate and manage utilization decreases. Both [delta] and [gamma] indicate the toughness of the monitoring by the insurance company. We assume that monitoring increases at a nondecreasing rate as utilization provided falls beyond the estimated optimum. The functional form of monitoring costs in (6) is used as an illustrative example. All of the results that follow only depend on the sign of its derivatives.

Physicians

The physician is assumed to be interested in both his or her own profit, [[pi].sup.p]([q.sub.i]), and the benefits to the patient, B([q.sub.i]); Ellis and McGuire (1986) use a similar utility function. Therefore, we assume that the physician maximizes a utility function of the form:

(7) Max U[[[pi].sup.p]([q.sub.i]), B([q.sub.i])].

Although the physician may be modeled as a profit-maximizing agent only, we believe that physicians typically care about their patients' welfare (benefits). Also, health care providers are bound by their ethical code, and this will also put some weight on patients' benefits. Their profit-maximizing behavior is also constrained by the possibility of malpractice litigation and by the importance to a physician of his or her reputation. Reputation affects the flow of the new patients and the number of referrals, not to mention one's standing in the community.

To illustrate how a physician will behave, we select a separable utility function given by:

(8) U[[[pi].sup.p]([q.sub.i]), B([q.sub.i])] = [[pi].sup.p]([q.sub.i]) + B([q.sub.i]).

Physician Behavior under Capitation

We assume that under capitated reimbursement system, the insurer does not monitor physicians, because capitated contracts align (although imperfectly) physician incentives with those of the insurer. Alignment of incentives is not perfect because the physicians care about the welfare of the patients as well as their own profits.

Let [q.sup.c.sub.i] denote the amount of care provided by a capitated physician to patient i.

Claim 1: Under capitation, [q.sup.c.sub.i] [less than or equal to] [q.sub.i]'.

Under capitation, physician profits are given by the difference between fixed capitation payment and cost, or [[pi].sup.p]([q.sub.i]) = a - C([q.sub.i]). Therefore the utility function (8) can be written as

(9) U[[pi].sup.p]([q.sub.i]), B([q.sub.i])] = a - C([q.sup.c.sub.i]) + B - [([q.sup.c.sub.i] - [q.sub.i]').sup.2].

First-order conditions yield:

(10) C'([q.sup.c.sub.i]) + 2([q.sup.c.sub.i] - [q.sub.i]') = 0.

Equation (11) shows health care utilization for patient i under capitation:

(11) [q.sup.c.sub.i] = [q.sub.i]' - (1/2)C'([q.sup.c.sub.i]).

Because C'(q[sub.i]) [greater than or equal to] 0 we conclude that [q.sub.c.sup.i] [less than or equal to] [q.sub.i]'. Thus, under capitation, patient will receive a less than optimal amount of health care services, unless marginal cost to the physician is 0. Note, however, that from (10) we know that the physician does set marginal revenue to equal to marginal costs. Thus, if a physician weighs a dollar of benefit to a patient equally with a dollar of profit, and we define [q.sub.i]' as efficient health care utilization, then capitated contracts can result in the optimal amount of care. An interesting extension would be to consider whether physicians who enter into capitated contracts have different sets of preferences for patient benefits, which would then affect the degree to which there might be underprovision of service.

Physician Behavior under the FFS Reimbursement System

We break this analysis into two parts. First, we consider the case in which m([q.sub.i], [v.sub.i]) = 0 for all [q.sub.i]. That is, we examine what would happen with no penalties for excessive use of medical treatment. Let [q.sup.f.sub.i] denote the amount of care provided by a physician who is not at risk but works in a FFS environment that is not monitored by the insurance company.

Claim 2: Under a FFS system without monitoring, [q.sup.f.sub.i] [greater than or equal to] [q.sub.i]'

Under the FFS system, a physician's profit is given by the difference between fees and cost, or [[pi].sup.p]([q.sub.i]) = F([q.sub.i]) - C([q.sub.i]). Then the physician's utility function (8) can be written as:

(12) U[[pi].sup.p]([q.sub.i]), B([q.sub.i])] = F([q.sup.f.sub.i]) - C([q.sup.f.sub.i]) + B - [([q.sup.f.sub.i] - [q.sub.i]').sup.2].

First-order conditions are:

(13) F'([q.sup.f.sub.i]) - C'([q.sup.f.sub.i]) - 2([q.sup.f.sub.i] - [q.sub.i]') = 0.

From (13) health care utilization under the FFS system without monitoring [q.sup.f.sub.i] is:

(14) [q.sup.f.sub.i] = [q.sub.i]' + (1/2)[F'([q.sup.f.sub.i]) - C'([q.sup.f.sub.i])].

When the fee is greater than marginal cost, F'([q.sub.i]) > C'([q.sub.i], we find an over-utilization of services: [q.sup.f.sub.i] > [q.sub.i]'. Note that F"([q.sub.i]) - C"([q.sub.i]) - 2 [less than or equal to] 0 provides a necessary and sufficient condition for concavity.

Now consider the case of a physician when there is monitoring. Let [q.sup.m.sub.i] denote the amount of health services provided to patient i by a physician who is monitored by the insurer and is reimbursed on a FFS basis.

Claim 3. Monitoring decreases health care utilization, that is, [q.sup.m.sub.i] < [q.sup.f.sub.i], but the physician will still have an incentive to typically over-treat his or her patients, [q.sup.m.sub.i] > [q.sup.*]([v.sub.i]) where [q.sup.*]([v.sub.i]) is the insurance company estimate of [q.sub.i]'.

If the insurer monitors a physician, then the physician's utility function (8) can be written as:

(15) U[[pi].sup.p](q), B(q)] = F([q.sub.i]) - C([q.sub.i]) - m([q.sub.i], [v.sub.i]) + B - [([q.sub.i] - [q.sub.i]').sup.2].

Utility maximization yields:

(16) [q.sup.m.sub.i] = [q.sub.i]' + (1/2)[F'(q) - C'(q)] - (1/2)[partial derivative]m([q.sub.i], [v.sub.i])/[partial derivative][q.sub.i]

and m"([q.sub.i]) [greater than or equal to] 0 is sufficient condition. From (6) and (16) we get:

(17) [q.sup.m.sub.i] = [q.sub.i]' + (1/2)[F'(q) - (C'(q)] - (l/2)[delta][gamma]/([v.sub.i] + 1) x [([q.sub.i] - [q.sup.*]([v.sub.i]))/[([v.sub.i] + 1)].sup.[gamma]-1].

From (14) and (17) we have:

[q.sup.m.sub.i] = [q.sup.f.sub.i] - 1/2 [delta][gamma]/([v.sub.i] + 1) X [([q.sub.i] - [q.sup.*]([v.sub.i]))/([v.sub.i] + 1)][[gamma].sup.-1] [less than or equal to] [q.sup.f.sub.i]

since [v.sub.i] [greater than or equal to] 0, [delta] [greater than or equal to] 1, and [gamma] [greater than or equal to] 1. If [q.sub.i] < [q.sup.*]([v.sub.i]), then [q.sup.m.sub.i] = [q.sup.f.sub.i].

Now consider the value of [q.sup.*]([v.sub.i]). This is the insurance company's estimate of [q.sub.i]'. Suppose the insurance company's estimate happened to be equal to [q.sub.i]' (but the company cannot know this). Then, because we known [q.sup.f.sub.i] > [q.sub.i]', it must be the case that [q.sub.i]' < [q.sup.m.sub.i] < [q.sup.f.sub.i] (because the derivative of m([q.sub.i], [v.sub.i]) at [q.sub.i] = [q.sup.*]([v.sub.i]) is 0 and F'([q.sub.i]) > C'([q.sub.i])).

We can consider how the insurance company arrives at its expected [q.sup.*]([v.sub.i]). We have assumed E[[q.sup.*]([v.sub.i])] = q' where q' = E[[q.sub.i]'] for any procedure. If this is indeed the case, remembering that [partial derivative]m/[partial derivative][q.sub.i] = 0 for [q.sub.i] < [q.sup.*]([v.sub.i]), then physicians will always provide excess treatment to individuals with treatment below the average optimum, [q.sub.i]' < q' (less severely affected individuals). Because [partial derivative]m/[partial derivative][q.sub.i ]= 0 for [q.sub.i] = [q.sup.*]([v.sub.i]) = q', they will also overtreat individuals with [q.sub.i]' = q'. There will exist a range of [q.sub.i]' in which over treatment will occur, and this range will be in [q.sub.i]' [member of] [0, [q'.sub.max], where [q'.sub.max] > q'. More plausibly, one might suppose the insurance company would be more sophisticated. It might have, for example, E[[q.sup.*]([v.sub.i])] = [beta]q' + (1 - [beta])[q.sub.i]'. That is, its [q.sup.*]([v.sub.i]) might be the weighted average of the population mean q' and the true patient [q.sub.i]'. In this case, overtreatment of patients with lower [q.sub.i]' values would not be as great (but would still occur) and the value of [q'.sub.max] would rise (overtreatment would cover more patient types). The general result of overtreatment, but less treatment than the case with no monitoring, however will be the case for most patients under most plausible monitoring assumptions.

Monitoring versus Capitation

Claim 4: The difference between health care provided by a capitated physician and a physician who is monitored by the insurance company is lower for a simple diagnosis (when [v.sub.i] = 0) than for a complicated one (when [v.sub.i] is high). That is, [([q.sup.m.sub.i] - [q.sup.c.sub.i].sup.v=0] [less than or equal to ] [([q.sup.m.sub.i] - [q.sup.c.sub.i]).sup.v>0]. Equation (18) presents the difference in utilization between fee-for-service and a capitated physician:

(18) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

If [q.sub.i] [greater than or equal to] [q.sup.*]([v.sub.i]) then:

(19) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(because [gamma] [greater than or equal to] 1) and if [q.sub.i] > [q.sup.*]([v.sub.i]), then: [partial derivative]([q.sup.m.sub.i] - [q.sup.c.sub.i])/[partial derivative][v.sub.i] > 0.

The difference in health care utilization between a case that is reimbursed on FFS basis and a capitated case increases with the complexity of the procedure or diagnosis.

Summary of Predictions from Theoretical Model

The principal-agent model leads to three key predictions that we will test in our empirical model. The first is that LOS under capitation will be lower than under FFS. The second is that when monitoring costs are high, LOS will be higher. The third is that the positive relationship between monitoring costs and LOS will be largely accounted for patients under FFS insurance contracts. In other words, the difference in LOS between a FFS arrangement and a capitated arrangement increases with higher monitoring costs. This increase is due to the inability of the insurer to conduct utilization review, that is, estimate the optimal health care utilization in complicated cases, which leads to the higher LOS under the FFS system as monitoring costs increase.

III. EMPIRICAL MODEL

The Dependent and Key Independent Variables

Our empirical model focuses on differences in health care utilization as a function of insurance status and monitoring costs (as measured by the complexity of the diagnosis). We use LOS in a hospital as our measure of health care utilization. An alternative measure of resource use is charges by a physician or payments to a treating physician. Although both are available in the data set used in this study, they are not good indicators of the resource use due to variation in fees across specialties, geographic areas, health plans, and physicians. We utilize the variance in the LOS by surgical procedure as a measure of monitoring costs for that procedure. Conditions that vary greatly in LOS (such as heart surgery) make it difficult for a third-party payer to determine appropriate LOS in a hospital or develop some minimal coverage after which utilization will be scrutinized. In cases with low variance (even if the average LOS is large), there will be very few outliers, thereby minimizing the costs of reviewing these cases. The other key independent variable is insurance status which will be interacted with monitoring costs.

Regression Model

We estimate the following equation:

(20) [LOS.sub.i] = [[beta].sub.0] + [[beta].sub.1] x Capitation + [[beta].sub.2] x Variance + [[beta].sub.3](Capitation x Variance) + [[beta].sub.i] x [x.sub.i] + [epsilon].

In (20) subscript i denotes a person and [x.sub.i] is a vector of exogenous characteristics. Exogenous variables include demographic, socioeconomic, and geographic factors.

Based on the theoretical model we expect the coefficient on capitation, [[beta].sub.i], to be negative; the coefficient on Variance in the LOS across all patients for that diagnosis, [[beta].sub.2], to be positive; and the coefficient on the interaction term, [[beta].sub.3], to be negative. The negative coefficient on the interaction term would reflect the prediction that when monitoring costs are high FFS contracts start leading to even higher LOS relative to capitated contracts. Thus, the shorter lengths of stay associated with capitated contracts (captured by [[beta].sub.1]) will be enhanced when dealing with a high monitoring cost diagnoses. The other way to view the interaction term is that the positive relationship between monitoring costs and LOS, reflected by [[beta].sub.2] will not be relevant for capitated contracts--leading [[beta].sub.3] to be equal to - [[beta].sub.2].

Selectivity Problem

There is a potential for unobservable characteristics of enrollees to influence both utilization and the reimbursement arrangement choice. Besides age and health status, the two groups (capitation and FFS) may differ in characteristics that we cannot observe, such as preferences for longer hospital stay or for more aggressive medical intervention. We use a Heckman (1979) correction to account for the selectivity problem. Our identification strategy uses paid vacations and number of employees as variables that are included in the choice of insurance coverage equation but excluded from the LOS equation. One of the key identifying restrictions is the size of the employer, also used by Dranove et al. (2000). Many large employers offer their employees a choice of the FFS and managed care. However, small employers are much more likely to offer only managed care plans. Consequently, we expect this variable to be strongly correlated with choosing managed care because many employees will not have a choice and can only choose HMO-type plans. Moreover, we would not expect employee size to have a direct effect on LOS in a hospital, except through its effect on the insurance plan choice. In addition, we use an employer that offers paid vacations as an instrument. This variable is the proxy for the generosity of employer's benefits. We expect employers who offer paid vacations to offer more generous and less restrictive health care benefits.

Mean Preserving Spread

Because there may be a technical or behavior relationship between the variance in LOS and the average LOS independent of what we model, we also estimate our models for a set of diagnoses where the average LOS is very similar. Thus, we estimate (20) for the mean preserving spread conditions with the average LOS between 3.11 and 4.53 nights in a hospital. (3) Estimating the model for the mean preserving spread procedures is testing whether the results are robust. Although the mean is restricted, there is still a significant difference in the variance in the LOS (from 6.76 to 36.84).

IV. DATA: MEDICAL EXPENDITURE PANEL SURVEY (MEPS)

The project relies on the Medical Expenditure Panel Survey (MEPS) for 1996 and 1998; it provides nationally representative estimates of health care use and expenditures for U.S. households with additional data collected from the respondents' medical providers, employers, and insurance providers. MEPS contains detailed data on demographic characteristics, health conditions, health status, use of medical care services, charges and payments, access to care, health insurance coverage, income, and employment.

Descriptive Statistics

This study uses inpatient stay records for all insured survey respondents who reported at least one hospital inpatient stay and underwent a surgical procedure. The data set contains 2,207 hospital inpatient stay records. Of 2,207 stays, 884 were associated with a surgical procedure. Uninsured patients were excluded. In our selection equation we use a sample of all insured patients, whereas in our utilization equations we use a sample of insured patients who underwent a surgical procedure. For the mean preserving spread results, the sample was further reduced to eliminate procedures with very high or very low mean. Table 1 presents means for selected exogenous variables. Descriptive statistics for surgical procedures included in the analysis are presented in Table 2 and Table 3. Among all surgical procedures, the most frequent were hysterectomy (6.11% of all procedures), gallbladder surgery (5.77%), and cardiac catheterization (5.54%). Table 3 shows that common surgical procedures vary in average LOS: Average nights in a hospital vary from 0 for a cataract surgery to 11.84 for a joint replacement. Variance of the nights in a hospital fluctuates from 0 for cataract surgery to 275 for cardiac catheterization.

V. RESULTS

The Selection Equation

Table 4 provides the results of the equation that is used to control for selection. The dependent variable is whether the patient is covered on a capitated basis. Results in Table 4 show that among the insured population, men are more likely to be insured by an HMO than are women. This result may be due to higher overall health care utilization by women. Also, older and married individuals tend to avoid managed care arrangements. The probability of joining a managed care arrangement declines with age for all patients in the sample. Effects of perceived health status variables are both negative and only marginally significant. People with poorer perceived health are less likely to choose a more restrictive capitated arrangement.

The employer size variable has the expected negative effect. People who work for large companies are more likely to choose traditional FFS plans. People with higher income also have lower probabilities of being in a capitated arrangement. The negative effect of the West variable relative to South on the capitation choice is unexpected because HMOs are more established in the West, and thus a higher proportion of people are enrolled in capitated arrangements in those areas than elsewhere in the United States. Although tabulated data show that most HMO enrollees are located in the West, once we control for other characteristics, the effect of the West becomes negative. All three geographic variables have a generally significant impact on capitation; this suggests that geographic location is an important determinant of the health insurance plan. Monitoring costs are negatively correlated with capitation, and the variable is not significant. This indicates that at least for the diagnoses in this sample, capitation is not used more for diagnoses that have large variance in lengths of stay. This is relevant because the empirical results and theory suggest that this is precisely the type of situations where capitated contracts are likely to result in cost savings.

The LOS Equation

Table 5 presents regression estimates of the determinants of LOS by people who were admitted into a hospital and underwent a surgical procedure. The results in Table 5 support the hypotheses derived from our theoretical model. First, the coefficient on the variation in LOS for the diagnosis is positive and statistically significant, indicating that as our measure of monitoring costs increases so does an LOS in the hospital. Moreover, the coefficient on the interaction term of capitation and variance in LOS is negative and statistically significant. This suggests that differences in LOS between FFS and capitation increase as our measure of monitoring costs increases. When the variance was interacted with other demographic variables, there was no significant effect on these interaction terms, and they were dropped from the model. Thus, when we control for selection, as monitoring costs increase (i.e., as variance in the LOS increases), capitated arrangements decrease the LOS by 0.22 nights or 0.24 nights for the mean preserving spread procedures. Therefore, in difficult to monitor cases, incentive compatible contracts are more effective at keeping the costs down. A different measure of monitoring costs (the standard deviation in the LOS), does not change this conclusion. Despite the potential cost savings from using capitated arrangements for diagnoses that have high variation in LOS, our probit estimates in Table 4 show that people who have high variance procedures are not more likely to be covered by capitated rather than FFS plan.

It is important to note that patients covered by capitated arrangements also have shorter LOS in a hospital when monitoring costs are negligible (0). However, once we introduce the correction for selecting people into different health plans, the effect of this variable becomes insignificant. Heckman's [lambda] is the correction factor and was derived from the empirical results in Table 4. When the correction factor is added as a regressor, it has a significant negative effect. The negative sign indicates that people who join HMOs that use capitation stay fewer nights in a hospital if admitted. Significance of Heckman's [lambda] indicates that there is a strong correlation between the residual in the capitation equation and the residual in the LOS equation.

Other significant variables include geographic variables: West, Northeast, Midwest, and MSA. The West variable is negative and significant in both equations. HMOs are largely located and more established in the West; they are also more likely to employ incentive-compatible contracts. Because we control for the capitation effect (that may also be seen as toughness of the HMOs and their aggressiveness in controlling for costs), the significant negative effect of the Western region on health care utilization may indicate that hospitals with high HMO penetration tend to treat other patients in the same cost-effective manner. This was shown by Burchfield (1998).

VI. DISCUSSION

The goal of this study is to examine the differences in health care utilization between FFS and incentive-compatible contracts in the presence of varying monitoring costs. Whereas other studies have investigated differences in LOS across insurance status, there has been limited focus on characterizing the situations where these differences are most likely to occur. Principal agency theory provides insight into the types of situations where health care utilization is most effected by contract design. The theory suggests that capitation is more efficient at keeping health care utilization in situations where utilization review and other monitoring devices are likely to be costly. The empirical results of this article provide support for these theoretical predictions.

Despite the potential cost savings from using capitated arrangements in covering health costs associated with diagnoses for which monitoring is difficult, the empirical evidence suggests that this is not where capitated arrangements are used. Capitated arrangements are often used for primary care physicians and are less common among specialists who are treating very complex medical conditions. Based on the theory outlined herein, we should expect that health providers would realize the potential cost savings from using capitated arrangements in these situations. So why has this not occurred? There are several potential explanations. The first is that specialists in some areas do not realize the volume of caseload necessary for capitated arrangements to be effectively used. As mentioned, the capitated arrangements transfer the financial risk from the insurer to the physician. If the physician does not have a very large volume of cases, the income fluctuations associated with a capitated arrangement will have a large impact on the expected utility a physician would receive from such a contract. This would cause doctors to demand significantly higher fixed payments to participate, thereby raising the cost of incentive compatible contracts. Another potential explanation is that specialists may have some market power compared with primary care physicians. In this case it is difficult to predict in which situations capitated arrangements are likely to be used. In addition, differences in risk aversion across specialties might affect medical decision making. Although limited data exists on physician risk aversion, anxiety from uncertainty, and fear of malpractice litigation, several studies collected such data by directly surveying health care providers. Franks et al. (2000) and Baldwin et al. (2005) show that relatively little variation in utilization is explained by physician psychological factors. However, Gross et al. (2003) and Studdert et al. (2005) found that the perceived risks and fear of malpractice litigation affect physician's treatment choices. Finally, the limited use of capitated contracts for specialists treating complex diagnoses may suggest that our theoretical structure is not the correct way to view these markets. Certainly more research is needed to best understand why incentive-compatible contracts are used in some situations and not in others.

ABBREVIATIONS

FFS: Fee for Service

HMO: Health Maintenance Organization

LOS: Length of Stay

MEPS: Medical Expenditure Panel Survey

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(1.) For example, Welch (1985) showed that HMOs have about 3% fewer physician visits and fewer hospital days than conventional insurance though the latter results were not statistically significant. McCusker et al. (1988) found no difference between lengths of stay for HMO and FFS patients. Bradbury et al. (1991), Dowd et al. (1986), Rapoport et al. (1992), and Stern et al. (1989) found that there are significantly longer lengths of stay in hospitals for FFS patients. Johnson et al. (1989) found that in 6 of the 10 diagnoses studied, HMOs had significantly lower lengths of stay. Braveman et al. (1991), however, found no difference between insurance coverage and length of stay in a study of sick newborns.

(2.) It is also possible that incentive-compatible contracting might lead to changes in the optimal amount of quality monitoring. Insurers may use capitation to control costs and at the same time monitor the quality of care through utilization review. However, quality of care lies beyond the scope of this study.

(3.) Selection of a smaller interval with mean length of stay between 3.11 and 4.11 does not change the estimates.

HELEN SCHNEIDER and ALAN MATHIOS *

* An earlier version of this article was presented at the UC-Berkeley Health Policy seminar. We are grateful to all of the participants for their helpful comments and discussion. We are especially thankful to Prof. J. S. Butler and Prof. Rob Masson for their valuable suggestions that assisted us in improving our work. Masson provided significant assistance on the theoretical model. All remaining errors are our own responsibility.

Schneider: Technical Staff Member, Economist, Group D-3, Mail Stop K575, Los Alamos National Lab, Los Alamos, NM 87545. Phone 1-505-664-0643, Fax 505-667-5531, E-mail hschneider@lanl.gov

Mathios: Professor, Cornell University, Department of Policy Analysis and Management, Ithaca, NY 14820. Phone 1-607-255-2589, Fax 1-607-255-4071, E-mail adm5@cornell.edu

TABLE 1
Means for Selected Exogenous Variables

Variable Mean SD

Demographic variables

 Respondent's sex is male: 0.49 0.499
 Sex = 1 if male, 0 if female
 Respondent's age 46.32 17.80
 Respondent's race is white: 0.79 0.41
 Race = 1 if whitem 0 otherwise

Geographic variables

 SMSA area = 1 if SMSA, 0.79 0.41
 0 otherwise
 West = 1 if west, 0 otherwise 0.22 0.41
 Northeast = 1 if northeast, 0.20 0.40
 0 otherwise
 Midwest = 1 if Midwest, 0.22 0.41
 0 otherwise

Sociological variables

 Respondent is married 0.37 0.48
 Completed years of 12.53 3.22
 education
 Hourly wage, if employed 14.29 31.04
 Hours worked per week, if 37.36 14.05
 employed
 Wage income per weak 467.21 1074.71

Health status variables

 Respondent is in good 0.65 0.48
 health (= 1 if good,
 0 if other)
 Respondent is in poor health 0.31 0.47
 (= 1 if poor, 0 if other)
 Number of conditions 0.16 (0.66)
 associated with the event
 (secondary diagnoses)
 Employer offers paid 0.44 0.50
 vacations: vacations = 1 if
 offered and 0 otherwise
 Number of employees 85.71 156.86

TABLE 2
Number of Procedures and Capitation
Statistics for Selected Surgical Procedures

 Number of
 Procedures % of All Proportion
Surgical Procedure Performed Procedures Capitated

Appendectomy 24 2.71 0.33

Arthroscopic 9 1.01 0.22
surgery
(visual of joints)

Cardiac 49 5.54 0.31
catheterization

Cataract surgery 6 0.68 0.33

Coronary bypass 19 2.15 0.37

Dilation and 12 1.36 0.50
curettage

Dental surgery 1 0.11 0

Gallbladder surgery 51 5.77 0.27

Hernia repair 28 3.17 0.14

Hysterectomy 54 6.11 0.37

Joint replacement 33 3.73 0.21
surgery

Mastectomy/ 10 1.13 0.30
lumpectomy

Pacemaker insertion 15 1.70 0.47

Plastic/reconstructive 15 1.70 0.20
surgery

Prostate surgery 17 1.92 0.41

Spinal disk surgery 20 2.26 0.35

Surgical setting of a 27 3.05 0.33
broken bone

Thyroid surgery 5 0.57 0.40

Tissue biopsy 12 1.36 0.16

Tonsillectomy 4 0.45 0.50

Other 473 53.51 0.35

Total 884 100 0.39

TABLE 3
Descriptive Statistics for Selected Surgical Procedures

 Mean
 Length
Main Surgical Procedure of Stay SD Variance

Appendectomy 4.42 6.07 36.84
Arthroscopic surgery (visual of joints) 3.11 5.99 35.88
Cardiac catheterization 7.04 16.61 275.89
Cataract surgery 0 0 0
Coronary bypass 12 9.31 86.68
Dilation and curettage 1.08 1.38 1.90
Dental surgery 8 -- --
Gallbladder surgery 3.47 5.22 27.25
Hernia repair 5.57 11.27 127.01
Hysterectomy 4.30 5.63 31.67
Joint replacement surgery 11.84 12.92 164.87
Mastectomy/lumpectomy 0.8 1.14 1.23
Pacemaker insertion 4.53 4.66 21.72
Plastic/reconstructive surgery 6.47 11.43 130.64
Prostate surgery 3.47 2.60 6.76
Spinal disk surgery 3.65 3.94 15.52
Surgical setting of a broken bone 4.15 2.51 6.3
Thyroid surgery 6.4 7.96 63.36
Tissue biopsy 3.25 3.44 11.83
Tonsillectomy 0.75 0.75 0.25

 Min Max
 Length Length
Main Surgical Procedure of Stay of Stay

Appendectomy 1 30
Arthroscopic surgery (visual of joints) 0 19
Cardiac catheterization 0 100
Cataract surgery 0 0
Coronary bypass 2 31
Dilation and curettage 0 4
Dental surgery 8 8
Gallbladder surgery 0 35
Hernia repair 0 46
Hysterectomy 1 42
Joint replacement surgery 1 58
Mastectomy/lumpectomy 0 3
Pacemaker insertion 1 19
Plastic/reconstructive surgery 1 40
Prostate surgery 1 11
Spinal disk surgery 0 17
Surgical setting of a broken bone 1 11
Thyroid surgery 1 20
Tissue biopsy 0 9
Tonsillectomy 0 1

TABLE 4
Probit Estimates of the Determinants of
Capitated Reimbursement (Dependent
variable: Capitation)

Variable Estimates

Male 0.081 (1.07)
Age -1.11 (1.36)
Age squared 0.24 (l.94)
Perceived health status is good -0.22 (1.34)
(excellent health is excluded)
Perceived health status is poor -0.23 (1.38)
New health problem 0.0036 (0.11)
West (South is excluded) -0.19 (1.99)
Northeast -0.25 (2.76)
Midwest 0.17 (l.80)
Nonwhite -0.016 (0.18)
Education 0.05 (0.24)
[Education.sup.1/2] -0.13 (0.35)
MSA -0.34 (3.74)
Income -0.020 (0.99)
Fertility 0.19 (0.67)
Monitoring costs -0.44 (0.17)
Married -0.15 (1.88)
Number of conditions 0.022 (0.41)
Employer offers private vacations -0.014 (0.11)
Number of employees -0.077 (2.97)
Intercept 2.15 (1.62)
Log likelihood -966.52
N 12,366

Notes: Absolute values of t-statistics are in parenthesis.
All continuous variables are in the log form.

TABLE 5
Length of Stay in a Hospital

 Corrected for
Variable Uncorrected Selection

Intercept 0.28 (0.51) -0.13 (0.19)
Capitation -0.018 (1.94) -0.014 (0.48)
Monitoring costs 3.47 (2.47) 3.66 (2.39)
Interaction (Capitation x Monitoring) -3.65 (1.83) -3.88 (1.91)
Heckman's lambda -0.25 (7.31)
Male 0.022 (0.02) -0.017 (0.52)
Age -0.35 (1.96) 0.078 (1.79)
Age squared 0.070 (1.38) -0.031 (0.46)
Perceived health status is good 0.084 (1.26) 0.1 (1.50)
(excellent health is excluded)
Perceived health status is poor 0.090 (1.28) 0.11 (0.53)
New health problem 0.013 (1.01) 0.014 (1.07)
West (South is excluded) -0.018 (1.73) -0.046 (1.86)
Northeast -0.1 (2.62) -0.099 (2.60)
Midwest 0.085 (2.31) 0.082 (2.22)
Nonwhite 0.030 (0.77) 0.038 (0.97)
Income -0.022 (3.98) -0.019 (2.73)
Number of conditions associated 0.029 (1.31) 0.028 (1.26)
with the episode
Married 0.0048 (0.15) 0.0038 (0.12)
Fertility -0.046 (1.36) -0.12 (0.92)
Education -0.073 (0.83) 0.14 (0.85)
[Education.sup.1/2] 0.17 (1.12) -0.055 (0.59)
MSA -0.033 (0.92) 0.064 (1.25)
 4.70 4.34
[R.sup.2] 0.1527 0.1566
N 843 843

 Fixed Mean
 Procedures
 (3-4.5 Nights
Variable in a Hospital)

Intercept -0.14 (0.20)
Capitation 0.00283 (0.53)
Monitoring costs 3.81 (4.29)
Interaction (Capitation x Monitoring) -4.05 (3.23)
Heckman's lambda -0.09 (4.12)
Male -0.048 (8.31)
Age 0.26 (2.97)
Age squared 0.031 (2.47)
Perceived health status is good -0.0017 (0.13)
(excellent health is excluded)
Perceived health status is poor 0.0051 (0.37)
New health problem 0.0039 (1.50)
West (South is excluded) 0.017 (2.21)
Northeast -0.0042 (0.38)
Midwest 0.0036 (0.34)
Nonwhite 0.012 (1.80)
Income -0.0034 (1.46)
Number of conditions associated -0.019 (2.73)
with the episode
Married 0.0048 (0.15)
Fertility -0.11 (4.73)
Education 0.0013 (0.08)
[Education.sup.1/2] 0.054 (1.18)
MSA 0.0068 (0.84)
 0.12
[R.sup.2] 0.1670
N 675

Notes: Absolute values of t-statistics are in parentheses. All
continuous variables are in the log form.