Hospital technology in a nonmarket health care system.

Daniel Bilodeau (*)

Pierre-Yves Cremieux (*)(+)

Pierre Ouellette (++)

This article presents a quantitative analysis of the production of hospital services in a nonmarket environment based on production theory and a very complete data set on the hospital industry. It provides both insights into the optimality of the hospital industry structure and a useful framework to evaluate the impact of anticipated industry structural changes. We find that the industry structure is far from optimal; it is characterized by overcapitalization and would experience difficulty responding to increased demand for some types of services.

1. Introduction

The theoretical framework relating to the production of health services by hospitals is similar to that of any other firm. Economists are concerned with much the same issues in the measurement of output in the health sector as in other spheres of production. Foremost among these is the shape of the production function that underlies the transformation of inputs into outputs since it determines the optimal size and structure of the production unit, in this case hospitals.

Based on a 12-year panel of all short-term hospitals in Quebec covering 1981 through 1992, this research examines the health care production process. The approach is new in that it examines hospitals in a noncompetitive, socialized framework and relies on a very complete hospital sector data set. To avoid biases often present in previous work, all quasi-fixed inputs (physicians, equipment, and buildings), all variable inputs (labor, drugs, food for inpatients, supplies, energy, and an aggregate of other inputs), and all outputs (inpatient care, outpatient care, food, and laundry services sold to the public, laboratory services to outpatients or under contract, and teaching) are included in the estimation.

Determining the optimality of the hospital industry structure in Quebec is important for at least two reasons. First, hospital investment decisions in Quebec are centralized. Planners can determine the optimal hospital structure only if they have knowledge of the hospital production process. Second, the absence of a competitive market precludes the usual adjustments driven by competitive pressures from taking place. Diseconomies of scope or scale, highly unlikely in a competitive market, might be present, large, and persistent in a nonmarket structure. In Quebec, hospitals are most often private not-for-profit institutions. However, the Quebec government that controls the national health insurance system is their only payer except for very small revenues from hospital private foundations or uninsured services such as cosmetic surgery, some laboratory tests, etc. These private payments to hospitals represent negligible amounts. As a result, the system operates very much as if hospitals were in fact public enti ties. Collective bargaining occurs with the government, reimbursement rates are determined by the government, and major investment or merger decisions, equipment purchase, or new construction are approved by the government

The present analysis provides a framework to gather information valuable to planners in any publicly funded system as they restructure hospital health services delivery. In Quebec the government could also better respond to changes in relative input prices through changes in relative input use, review of its reliance on private laboratory analysis services, or toughening of its medical school admissions policies. In the early 1990s, and without the benefit of an analysis such as this one, the Quebec government froze health care spending, closed a number of hospitals, changed hospitals' role (from short-term care to long-term care), and decentralized its structure through regional boards (Regies regionales). Some of the unintended consequences included crowding in hospitals, a near breakdown of emergency care during the first months of each year since, and few, if any, gains in efficiency. Our analysis provides an exploration of the structure of hospital production in a nonmarket environment. In anticipation o f unavoidable restructuring of the industry in the years to come, it also suggests a management tool for planners to direct the industry toward greater economic performance through changes in hospitals' relative budgets, changes in the scope of services offered, or mergers between establishments. This article examines the optimality of size, diversification, capitalization levels, and technological change as well as the flexibility in the choice of inputs and outputs. It identifies the hospital and delivery structure characteristics associated with greater performance.

2. Hospital Productivity Analysis

Cost functions as a tool to examine the production process have been widely used to study various sectors, including hospitals (see Diewert 1971 on the use of cost function to recover technology characteristics). Econometric methods were the first ones used to assess the performance of hospitals and other entities (see Conrad and Strauss 1983; Cowing and Holtmann 1983; Cowing, Holtmann, and Powers 1983; Breyer 1987; Granneman, Brown, and Pauly 1986; Vitaliano 1987; Eakin and Kniesner 1988; Vita 1990; Dor and Farley 1996; Bilodeau, Cremieux and Ouellette 2000). This approach yields multiple measures of the firms' technology, their performance, and their cost minimizing behavior. However, like all econometric estimation, they have been criticized for their potential sensitivity to omitted variable bias and to the structure of the error term in general (cf., Jensen and Morrisey 1986a, b; Breyer 1987; Cremieux and Ouellette 2001).

Starting in the 1980s, other authors started applying nonparametric methods such as the data envelopment analysis (DEA) to the analysis of hospital performance (Grosskopf and Valdmanis 1987; Fare et al. 1997; Kooreman 1994; Grosskopf, Margaritis, and Valdmanis 1995). However, the DEA approach precludes the use of qualitative measures of output. These are important when estimating multioutput firms such as hospitals. Because qualitative variables can be included in a parametric cost function, this approach presents a significant advantage despite the need to impose a functional form. (1) On the contrary, the DEA method would require subsampling of hospitals into homogeneous groups. Substantial information would be lost, the comparison of hospital performances across heterogeneous establishments would be impossible, and the reduced sample size would require the elimination of many inputs and outputs. The DEA method also fails to generate confidence intervals for the various technology and performance measures.

Since our analysis is based on rather complete data, thereby reducing the likelihood of omitted variable bias in the context of an econometric analysis, we rely on parametric estimation to evaluate hospital performance.

Despite early progress in the underlying theory of productivity analysis, data constraints in the health care sector as well as other industries have led to the omission of some key variables. Most studies had to ignore some inputs (such as physicians or equipment), approximate capital (e.g., the number of beds), and ignore some of the multidimensional aspects of the output provided by hospitals (Vitaliano 1987; Eakin and Kniesner 1988; Ministere de la Sante et des Services Sociaux 1992; Koop and Carey 1994). In our analysis, the probability of bias resulting from such omissions is reduced since the data include a more comprehensive set of direct measures of inputs and outputs than most other work (Bays 1980; Jensen and Morrisey 1986a, b). Of course, differences in quality are only imperfectly measured since the actual output, namely better health, cannot be directly measured. However, differences in quality are likely to be less prevalent in the Quebec centralized setting than in the United States. For examp le, in the United States, health insurance coverage might limit the set of hospitals at which you can receive care. Poorer public hospitals might also provide lower quality care than hospitals in more affluent neighborhoods. However, the national health insurance system and the free access to virtually all hospital care in Quebec limits interhospital quality differences, at least for the overwhelming majority of the population living in areas where multiple hospitals are available to choose from.

The production function can be directly inferred from the estimation of a variable cost function of the following form:

[C.sub.ht] = C(y, w, k, MD, t; [theta]) + [[epsilon].sub.ht],

where C(*) is the cost function (in translog form), h indexes hospitals, [y.sub.hvt], is the vth output, [w.sub.hjt] is the jth variable input price, [k.sub.hmt] is the mth quasi-fixed input, and [MD.sub.hnt] is the nth type of physician of their corresponding vectors y, w, k, and MD. The trend t is introduced to account for technological change, [theta] is the vector of parameters to be estimated, and [[epsilon].sub.ht] is the error term. (2)

This specification distinguishes between variable inputs that are under hospital management's control and quasi-fixed factors (building, capital equipment, and physicians) that cannot be affected by management, at least in the short to medium run. This is done by introducing variable input prices as arguments in the regression (levels may vary) and quasi-fixed input levels (prices may vary). The cost function is hospital specific; however, the technology is the same for all hospitals since all employees are trained at the provincial level, their collective bargaining agreement is uniform across the province, and the management rules and the pooi of available equipment are similar.

3. Properties and Functional Form of the Variable Cost Function

Choice of the Functional Form

The performance of the translog function compared with other functional forms makes it most appropriate in this context (see Gagne and Ouellette 1998): (3)

In C = [[alpha].sub.0] + [summation over (i)] [[alpha].sub.i]ln [w.sub.i] + [summation over (j)] [[alpha].sub.j]ln [k.sub.j] + [summation over (m)] [[alpha].sub.m]ln [MD.sub.m] + [summation over (v)] [[alpha].sub.v]ln [y.sub.v] + [[alpha].sub.t]t

+ 0.5 [summation over (i)] [summation over (r)][[beta].sub.ir]ln [w.sub.i]ln [w.sub.r] + [summation over (i)] [summation over (j)] [[beta].sub.ij]ln [w.sub.i]ln [k.sub.j] + [summation over (i)] [summation over (m)] [[beta].sub.im]ln [w.sub.i]ln [MD.sub.m]

+ [summation over (i)] [summation over (v)] [[beta].sub.iv]ln [w.sub.i] ln [y.sub.v] +[summation over (j)] [summation over (s)] [[beta].sub.js]ln [k.sub.j] ln [k.sub.s] + [summation over (j)] [summation over (m)] [[beta].sub.jm]ln [k.sub.j] ln [MD.sub.m]

+ [summation over (j)] [summation over (v)] [[beta].sub.jv]ln [k.sub.j]ln [y.sub.v] + [summation over (j)] [[beta].sub.jt]ln [k.sub.j]t + 0.5 [summation over (m)] [summation over (n)] [[beta].sub.mn]ln [MD.sub.m]ln [MD.sub.n]

+ [summation over (m)] [summation over (v)] [[beta].sub.mv]ln [MD.sub.m]ln [y.sub.v] + [summation over (m)] [[beta].sub.mt]ln [MD.sub.m]t + 0.5 [summation over (v)] [summation over (u)] [[beta].sub.vu]ln [y.sub.v]ln [y.sub.u] + [summation over (v)] [[beta].sub.vt]ln [y.sub.v]t

+ 0.5[[beta].sub.tt][t.sup.2],

where C is total spending for each hospital each year. Hospital dichotomous variables are included as fixed effects that measure individual hospital performance. While this research does not focus on individual performance, it serves an important role since it embodies any time-invariant hospital characteristic. In particular, to the extent that differences in quality across hospitals remain despite free access to care and are persistent, they will capture these unmeasured quality differences. They might also capture systematic geographic or historical differences in the hospital or differences in population density or sociodemographics in the patient base. Finally, they might also capture any systematic differences in the type of care offered by teaching hospitals. Shephard's lemma yields the following share equations:

[S.sub.j] = [partial] ln C/[partial]ln [k.sub.j] = ([z.sub.j][k.sub.j]/C), for all j [S.sub.i] [partial] ln C/[partial] ln [w.sub.i] = ([w.sub.i][x.sub.i]/C), for all i,

where [S.sub.j] and [S.sub.i] are the ratios of the jth implicit capital spending and the share of spending in the ith variable factor over variable cost, respectively. The estimation is done using Zellner's iterated method. (4)

Given a standard set of hypotheses on the technology, the variable cost function C(w, y, k, t) is homogenous of degree one in w, nondecreasing in (w, y), and nonincreasing in k, concave in w, and convex in k. (5) If the cost function is differentiable, Shephard's lemma yields the conditional factor demands [partial]C/[partial][w.sub.i] = [x.sub.i] and the implicit prices of capital [partial]C/[partial][k.sub.j] = -[z.sub.j], where [z.sub.j] is the implicit price of the jth type of capital. In the remainder of the article, we will assume that the cost function is always twice differentiable. Hence, the variable cost function's Hessian is symmetric. (6)

Technology Measurement

The ultimate goal of production analysis is to derive various measures of performance such as economies of scale and scope, the various elasticities, and a measure of technological change. This is particularly important in the context of a centralized public health system implementing cost containment measures since centrally administered budgets must be distributed optimally within the system. This implies some administrative decisions on the fate of the worst performing establishments, on the overall structure of the network of hospitals, and on appropriate investment levels. This requires information not only on the individual hospital performance levels but also on the overall cost structure and the structural causes of the inefficiencies. (7) In this section, we analyze the technological measures that will yield information on the optimal hospital structure.

The impact of variations in variable and fixed inputs on outputs reveals the extent of scale economies, RTS = (1 - [[SIGMA].sub.j] [partial] ln C/[partial] ln [k.sub.j])/([[SIGMA].sub.v] [partial] ln C/[partial]ln [y.sub.v]). Comparing RTS to one indicates whether the firm could reduce its average cost by reducing (if RTS > 1) or increasing (if RTS < 1) all its inputs (variable and fixed) simultaneously. We also estimate the optimality of the overall size of the hospital by comparing the market price of capital with its implicit price [z.sub.j] (where [z.sub.j] = [z.sub.j] -[partial]C/[partial][k.sub.j] = [S.sub.j] C/[k.sub.j]). If the implicit price is below the market price, then the hospital is overcapitalized and should sell capital. The opposite is true if the implicit price of capital is above the market price.

The issue of economies of scope is a crucial one in the Quebec hospital industry. In a competitive market, firms experiencing diseconomies of scope will be excluded by market forces (Panzar and Willig 1975, 1980). However, in the centralized Quebec hospital system, a proper evaluation of the actions required to optimize the scope of services is necessary to modify the industry structure since market forces are not present to fulfill that role. Economies of scope that yield optimality measures of the diversity of services offered across inpatient, outpatient, laboratory services sold, teaching, hotel, and laundry services sold (between-diversity) can be assessed from a generalization of the usual measure of economies of scope as follows:

C([y.sub.1] + [DELTA][y.sub.1],...,[y.sub.1] + [DELTA][y.sub.t]) < C([y.sub.1] + [DELTA][y.sub.1], [y.sub.2],..., [y.sub.t] + ... + C([y.sub.1], ..., [y.sub.t-1], [y.sub.1] + [DELTA][y.sub.t])

where the [y.sub.i] represent the different types of outputs and [DELTA][y.sub.i]> 0 for all i. (8) This inequality yields a generalized evaluation of economies of scope. Setting [y.sub.i] to the observed level of output and letting [DELTA][y.sub.i] be infinitely small yields a local measure of economies of scope. The usual test for the presence of economies of scope, using [y.sub.i] = 0 for all i, would determine whether multioutput hospitals are preferable to single-output hospitals. However, a more relevant question for an existing hospital system is whether an increase in various types of services should be distributed across many establishments or each establishment should increase only one type of service, or whether a single hospital should increase its level of activity for all its services simultaneously; the latter is preferable if the inequality is satisfied. Furthermore, our proposed measure of economies of scope being local, it does not require any assumptions about the cost function's behavior o utside of the observed domain (Vita 1990). The preceding inequality is verified for [DELTA][y.sub.i] > 0 for all i if and only if [[summation over (i)] [summation over (j [not equal to] i)], [[partial].sup.2]C/([partial][y.sub.i][partial][y.sub.j][DELTA][y.sub .i][DELTA][y.sub.j])] < 0. A sufficient condition for the presence of economies of scope is that [[partial].sup.2]C/[partial][y.sub.i][partial][y.sub.j] < 0 for all i [not equal to] j. As mentioned by Vita (1990), this condition tests for the existence of weak cost complementarities. If this condition is verified, then the government should encourage further diversification of hospital production.

The Allen-Uzawa elasticity of substitution measures the effect of a variation in relative input prices on the ratio of the inputs used for a given quantity of output. It is expressed as [[sigma].sub.ir] = (C/[x.sub.i][x.sub.r]([[partial].sup.2]C/[partial][w.sub.i][partial][ w.sub.r]), where [[sigma].sub.ir] is the elasticity of substitution between variable inputs [x.sub.i] and [x.sub.r]. This elasticity of substitution measures the hospital's flexibility in input choices. The flexibility in outputs is measured using the curvature of the average cost function with respect to the five different outputs. The flatter the average cost function, the greater the flexibility.

Technological change is defined as the shift in the cost function that remains unexplained by variations in input prices, the stock of quasi-fixed inputs, or the level of output. We can express the dual measure of technological change as -[partial] ln C/[partial]t and compare technological changes across time and establishments.

4. The Data

Our data span all 121 Quebec short-term hospitals from 1981 to 1992 still in operation in 1992. Financial and output data were provided by the Quebec Ministry of Health (Ministere des Affaires Sociales, various years; Ministere de la Sante et des Services Sociaux, various years); data on medical staff expenditures were provided by the Quebec health insurance commission (Regie de l'Assurance-maladie du Quebec, various years). Statistics Canada provided us with the necessary price indices. All outputs and inputs are reported in the data and used in the study. (9) The variables' descriptive statistics are reported in Appendix A. Outputs include inpatient care, outpatient visits, laboratory exams (for nonhospitalized patients), laundry and cafeteria (except for hospitalized patients), and teaching. Variable inputs include labor, supplies, food for inpatients, drugs, energy, and an "other" category including all remaining variable inputs. Quasi-fixed inputs include equipment, building, and all types of physicians.

Some observations were lost because of new hospitals or change in the status of existing hospitals, and 10 observations have missing financial data. This leaves 1383 usable observations. The incompleteness of the panel was ignored based on the small and insignificant results of a test on the effect of post-1981 entry on the variable cost function.

Inputs

Total costs are available from the hospital financial reports for the six variable input categories (labor, medicine, food, supplies, energy, and other). (10) Quantities are also reported by hospital for energy and labor. (11) Statistics Canada's price indexes are used for all other inputs. (12)

A Fisher index for the physician quantity index was derived using price indexes from the RAMQ data set and the number of physicians from the hospitals' output reports (see Diewert 1992 for a survey on indexes, in which he identifies the Fisher indexes as a preferred measure). (13) While physicians are not paid by hospitals, they nevertheless enter into the hospital production function as inputs into the health care delivery process. The coefficient on the physician variable is, therefore, physicians' marginal impact on variable costs rather than physicians' price. The capital building stock is reported in square meters, and an index of equipment stock was calculated using the perpetual inventory method.

Outputs

If all outputs were incorporated in the analysis at a highly desaggregated level (e.g., one output measure per diagnosis related group [DRG]), no case-mix index would be required. However, the large number of outputs would not allow econometric analysis. Hence, outputs must be aggregated within and across departments and case-mix indexes must be included.

Many econometric analyses have focused on inpatients. Any study that omits outpatient services implicitly assumes that outpatient care and other services are proportional to inpatient care both in size and complexity. In some studies, outpatient visits are included, in part or in whole, but without a measure of the complexity of care (Cowing and Holtmann 1983; Granneman, Brown, and Pauly 1986; Eakin and Kniesner 1988; Vita 1990; Koop and Carey 1994; Gaynor and Anderson 1995; Dor and Farley 1996; Carey 1997; Koop, Osiewalski, and Steel 1997). This allows the proportion of outpatient services to vary but fails to correctly identify the simultaneous increase in case complexity resulting from increased reliance on outpatient surgery and outpatient care in general.

From the five hospital output categories (inpatient care, ambulatory care, laboratory services sold, hotel and laundry services sold, and teaching) available from the Ministry of Health's AS477 form, it is possible to account for a dimension of case mix never considered before. When focusing on inpatients exclusively, case mix can account for variations in the complexity of cases only within that category. This Omits the variation in types of care due to differences in the relative importance of the various output types across hospitals. On the contrary, we include two indicators of case mix for both inpatient and ambulatory care. (14)

Inpatient care is proxied by the number of inpatient days distributed into nine specialties (medicine, surgery, intensive care, gynecology and obstetrics, pediatrics, medicine and surgery, (15) active geriatrics [since 1988-1989], psychiatry, and other). The number of specialties offered in the hospital (within-diversity) and the complexity of cases indicators account for crosshospital case-mix variations. The complexity indicator must be consistent across time and usable across hospitals. This precludes the use of DRGs since they did not appear in Quebec until 1988 and have evolved over the years. For hospitals, the complexity indicator is computed as follows for any given year:

[summation over (9/i=1)] [[summation over (121/h=1)] total [cost.sub.ih]/[summation over (121/h=1)] number of patient [days.sub.ih] - number of patient [days.sub.is] * 100/total patient [days.sub.s]],

where i indexes the specialty and h the hospital. The indicator measures the intensity of resources used in hospital h based on average unit cost in each of the nine specialties across all Quebec hospitals.

Outpatient care is proxied by the number of outpatient visits including emergency and ambulatory psychiatric care. In the absence of DRGs, two case-mix indexes are constructed based on the method developed for inpatient care by replacing inpatient days with the number of clinic visits.

A teaching index is included to measure the extent of teaching activity within the hospital. Because residents provide care and receive training, they will be classified as inputs or outputs into the hospital production process based on the sign of the derivative of the cost function with respect to the teaching variable.

Laboratory, nuclear medicine, hemodynamics, X-ray, radiotherapy, electrocardiograms, electroencephalograms, inhalotherapy, audiology and orthophony, physiotherapy, ergotherapy, and hemodialysis were aggregated using a Fisher index.

A final Fisher index was performed for cafeteria and laundry services.

5. Hospital Technology and the Optimal Structure of Health Care Delivery

While the thrust of the article is to identify the individual hospital characteristics and health-providing structure associated with greater performance, our use of parametric methods requires that we first test the implicit theoretical assumptions underlying the use of such a method. This is generally necessary in U.S. hospital production analysis since hospitals are sometimes shown to have non-profit-maximizing motives. The testing is even more crucial in our analysis of Quebec hospitals since, as we mentioned earlier, the public provision of health care possibly reduces further any tendency to exhibit profit-maximizing behavior. Previous work based on this data set shows that theoretical properties are consistent with short-term but not long-term cost-minimizing behavior (Bilodeau, Cremieux, and Ouellette 2000). The function is monotonically increasing with respect to the six variable input prices and nondecreasing with respect to the five outputs and is concave in the variable input prices. However, the function is neither monotonically increasing with respect to the three quasi-fixed inputs nor convex in these stocks. Despite nonoptimal long-run behavior, the use of a parametric form to characterize production function is legitimate since only short-run cost-minimizing behavior is required. We do not report the estimation results since this would involve reporting 310 separate coefficients and their corresponding standard errors.

While the estimation of the cost function yields quite naturally a simple list of desirable technological characteristics, it also helps identify directions in which individual hospitals as well as the entire health care delivery structure should evolve in order to achieve greater performance. Again, because of the Canadian setting, the market mechanisms might not naturally lead the industry toward a more efficient structure. Furthermore, there is no unique structure likely to emerge from the forces of competition even though a unique structure might emerge from planners' decisions. In general, the results below do, in fact, show a great variety of technology characteristics across institutions. After discussing the hospitals' ability to respond to changes in health care demand, we report results that apply to the overall structure of the industry. Finally, we discuss results relevant for intrahospital decision makers.

Hospital Production, Changes in Relative Input Prices, and Variations in Demand

A health care system's ability to respond to changes in health care demand will depend in large part on its ability to substitute inputs in the face of increased or decreased demand for any given type of services. To evaluate the industry's ability to adapt to demand shifts, we measured the flexibility of inputs based on Allen-Uzawa elasticities of substitution. For each establishment, we computed the elasticities of substitution. While it would be tedious to report the results for each individual hospital, some trends emerged across the industry. We also calculated some correlation coefficients to identify hospital characteristics associated with greater input substitutability. Some industry trends are reported in Table 1.

Before discussing input-specific elasticities, it is worth noting that measures of input substitutability are notably unstable and should be interpreted with caution (Eakin and Kniesner 1988; Gagne and Ouellette 1998).

Some of the observed elasticities are consistent with expectations. Labor is a substitute for supplies, energy, or just about anything else except food, for which substitution is difficult. The substitutability of drugs and labor could be explained by the various possible approaches to a given illness (antiinflammatory drugs or chiropractic care for back pain). Similarly, the substitutability of supplies and energy for labor illustrate the hospitals' general ability to substitute capital for labor. For categories other than labor, the substitutability or complementarity of the various inputs is less clear. Unfortunately, it is the "other" category that shows the strongest link to other inputs (whether as a substitute or as a complement) but is also the least well defined. Beyond the individual substitutability results that might arguably be considered tenuous, a more remarkable trend of great substitutability among inputs appears.

Our results confirm previous U.S.-based evidence that inputs are relatively easy to substitute for one another in the provision of health care (Cowing and Holtmann 1983) and that hospitals have some leeway in their choice of inputs. Hence, the industry should be well positioned to respond to changes in relative prices due to greater availability of cheaper foreign supplies or changes in labor costs following changes in the government's bargaining position. They also imply, should the current trend toward lowered compensation for hospital employees (and all other provincial employees in Quebec) continue, a greater substitution of labor and an increase in employment opportunity in the sector.

The curvature of the average variable cost with respect to each type of output measures the flexibility in output choice. Since the results vary by hospital and by year, it is not possible to summarize them in a table. However, in general, the curvature of average variable cost with respect to inpatient days and outpatient visits is virtually flat. This implies that the hospital can adapt to great variations in demand without any effect on average variable cost. In contrast, the curvature with respect to teaching (number of residents), laboratories, and food and laundry (aggregated together) is great. Hence, hospitals would have difficulties in the face of variations in demand for any of these services. In the case of food and laundry (to outpatients), this is relatively unimportant since they represent an insignificant portion of a hospital's total output, but teaching and laboratory services could become bottlenecks or large financial burdens for the system if demand for these services increased. This might explain, in part, the government's intent to reduce or stabilize the number of students in medical school and to deal with increases in demand for laboratory exams with longer delays. This increase in delays has led to the emergence of private laboratories that, while opposed by public sector unions, might be an optimal response to increased demand.

Health Care Delivery Structure

Having examined results for individual hospitals, we now turn to the structure of the industry as a whole. We focus on the shape of the forest rather than that of the trees.

Beyond the various characteristics of the overall hospital delivery system such as average hospital size or scope of services, we examined the impact of technological change on hospital performance. The estimation of the variable cost function yields an index of technological change (-[partial] ln C/[partial] t) that varies over time and across hospitals. From that index, we can characterize the shift in the overall cost function over time. We find that the cost function has shifted differentially for large and small hospitals. Large hospitals, which tend to have high levels of quasi-fixed inputs, higher levels of equipment investment, lower flexibility in output (at least as far as inpatient days are concerned), and are more often teaching hospitals, experienced a 1.3% annual shift down in their cost function (the average hospital size of establishments experiencing a positive technological shift is 123,000 patient days). On the contrary, smaller hospitals with opposite characteristics have experienced a 1.3 % shift up of their cost function (average hospital size for establishments experiencing a negative technological shift is 56,000 patient days). There is no simple and obvious explanation for the smaller hospitals' shift, which has never been studied or even identified before. However, changes in regulations, the increased complexity of hospital management resulting from new technologies, and increased reliance on outpatient care in the last years of the panel examined here might make it harder for smaller hospitals to optimize their management practices.

Our results indicate that hospitals are well distributed around one in terms of economies of scale. Table 2 shows the results at various levels of significance.

The results are intuitively appealing since they show that roughly equal numbers of hospitals exhibit economies and diseconomies of scale while roughly 15% of hospitals show constant returns to scale. Unlike in the United States, the presence of strong diseconomies of scale for some establishments is not only possible but is likely to be persistent since no market mechanism will lead inefficient hospitals to alter their behavior. It might also be worth noting that, because of the wrong sign on two of the three partial derivatives of the cost function with respect to quasi-fixed inputs, long-term returns to scale are underestimated.

Appendix B shows simple correlation coefficients between various relevant variables. In particular, it shows that greater levels of technological progress (measured by the movement of the cost frontier) are associated with greater potential economies of scale. Similarly, teaching hospitals tend to enjoy higher economies of scale. Finally, larger hospitals, whether measured by the equipment level or the size of their capital plants, also benefit from greater returns to scale. This simply means that, for lower levels of capital, small hospitals are on the upward portion of the long-run average cost curves while larger hospitals with higher levels of capital are on the downward sloping part of their long-run average cost curve. In other words, the average cost function is shifting to the right in the output-cost plane as the stock of capital increases.

Our results also show that hospitals would benefit from increases in their scope of services. Specifically, while the usual test of a sufficient condition for the presence of economies of scope ([[delta].sup.2]C/[delta][y.sub.i][delta][y.sub.j] < 0 for all i, j) does not indicate economies of scope, a less restrictive yet necessary and sufficient condition ([summation over (i)] [summation over (j)], [[delta].sup.2] C/[delta][y.sub.i][delta][y.sub.j][DELTA][y.sub.i][DELTA][y.sub.j] < 0), indicates that, contrary to California hospitals (Vita 1990), a large majority of Quebec hospitals do show economies of scope. The relationship was tested based on the assumption that every output is increased by the same percentage. Again, the correlation matrix indicates that greater economies of scope are associated with greater levels of technological change as well as significantly less flexibility with respect to all outputs except inpatient days. (16)

A third dimension of hospital services is the complexity and within-diversity. As mentioned earlier, since DRGs are not available, we used measures of within-diversity and complexity based on the number of specialties offered within an output category (outpatient or inpatient) and weighted averages of relative specialty loads, respectively. We find that, for outpatients, increased within-diversity or complexity has virtually no impact on variable costs (average elasticities of variable cost is 0% and 0.08% with respect to complexity and within-diversity, respectively). This is consistent with the monotonicity test, which indicated that outpatient visits have little impact on variable costs. In fact, outpatient services are, overwhelmingly, a fixed cost for hospitals. However, both greater within-diversity and complexity of inpatient care lead to higher variable costs (average elasticities of variable cost is 4 and 1% with respect to complexity and within-diversity, respectively). This confirms that our measur es of within-diversity and complexity do, in fact, capture the impact of differential care structures from one hospital to the next. For inpatient care, the greater complexity and within-diversity lead, as expected, to higher variable costs.

Already, the results offer some preliminary insight into possible future changes in the hospital care delivery structure in Quebec. While there is no indication that the average hospital is too large, some specific establishments are clearly not of optimal size. This does not necessarily mean that hospitals should be merged or split. Population density and the local availability of care might require smaller or greater than optimal hospital sizes, but availability of services should be carefully balanced with efficiency considerations resulting from the indivisibility of quasi-fixed factors. It also seems clear that a greater between-diversity would be desirable at least from the standpoint of efficiency.

Another important issue is the level of quasi-fixed inputs such as physicians, building and equipment, and capital. To identify possible over- or undercapitalization, we compared the implicit price of the three quasi-fixed inputs with their corresponding market prices. In all cases, there is a clear and substantial overcapitalization as demonstrated by the relatively lower implicit value of the three quasi-fixed inputs compared with their market value. (17) This is not inconsistent with casual observation about inferior technology at Quebec hospitals compared with their U.S. counterparts. The Canadian hospitals might be overendowed in substandard equipment.

6. Conclusion

Limited data, a complex production process, and peculiar institutional structures have made it traditionally quite difficult to gain insights into the optimality of hospitals' production processes despite major advances in our understanding of the theoretical framework surrounding production analysis. Furthermore, traditional cost analysis of hospital production was usually limited to establishments operating within a U.S.-type semicompetitive framework. In this article, we combine a solid theoretical foundation with a rather complete data set to analyze hospital performance in a nonmarket environment. The data set includes all Quebec hospitals from 1981 to 1992. It provides reliable information on inputs, including quasi-fixed inputs such as physicians, equipment and building, and on all outputs including inpatient days, outpatient visits, laboratory services, teaching, and food and laundry. We account for the complexity and the range of services offered for inpatient and outpatient care. The inclusion of a more comprehensive set of direct measures of inputs and outputs reduces the probability of bias resulting from omitted variables often found in previous work using U.S. or Canadian data.

We find that the structure of the industry is far from optimal. Some of the results such as diseconomies of scale and scope would be hard to believe or even irrelevant in the context of an industry whose shape is determined by market forces. However, in a centralized and socialized system such as the health care system of Quebec or other Canadian provinces, such results are not surprising. They should also be important to government planners whose goal is to balance various concerns such as public access, equity, or medical research with economic efficiency when shaping the hospital industry structure. A correct understanding of current departures from optimality is a prerequisite to informed modification in the industry structure aimed at improving efficiency. In fact, many institutions exhibit nonoptimal size and diversification of services (between-diversity). For virtually all establishments, we observe economies of scope and overcapitalization. Only 20% of hospitals have constant returns to scale, while the remaining 80% are evenly divided between increasing and decreasing returns.

We also find that inputs in the Quebec hospital production function are remarkably substitutable (probably in part because of the multidimensional nature of the output). Similarly, flexibility in some outputs such as inpatients and outpatients, as measured by the curvature of the average cost with respect to each output, is great while flexibility with respect to laundry and cafeteria, laboratory services, and teaching is very limited. This implies that hospitals would have some difficulties adapting to an increase in demands for the latter services. Nevertheless, it appears that government planners and hospital administrators could easily adjust to relative and absolute variations in their most significant outputs--inpatient and outpatient care.

While the production frontier has shifted significantly over the 12 years covered in this sample, this technological change varies greatly from one hospital to the next. Not surprisingly, larger hospitals, which have higher levels of capital (whether building, equipment, or physicians) or are teaching institutions, show greater technological progress since they must remain at the forefront of technology to fulfill their mandate.

(*.) Department of Economics, C.P. 8888 Succursale Centre Ville, Universite du Quebec a Montreal, Montrea1, Quebec H3C 3P8, Canada; E-mail [e-mail].

(+.) Analysis Group/Economics, 1 Brattle Square, 5th Floor, Cambridge, MA 02138, USA; E-mail [e-mail].

(++.) Department of Economics, C.P. 8888 Succursale Centre Ville, Universite du Quebec a Montreal, Montreal, Quebec H3C 3P8, Canada; E-mail [e-mail]; corresponding author.

We thank the Ministere de la Sante et des Services Sociaux du Quebec for data and computer support. We also thank Susan Hoag for suggestions and comments.

Received March 1999; accepted June 2000.

(1.) The large existing body of literature on parametric cost functions with qualitative variables often refers to this class of functions as hedonic cost functions.

(2.) Despite the inclusion of all inputs and all outputs, the error term is necessary to capture possible random or measurement error.

(3.) Other functional forms such as the Barnett or the McFadden functions have been introduced in the literature (see Diewert and Wales 1987). Their main advantage is that they allow the imposition of particular curvature conditions. However, they perform quite poorly when such conditions are imposed. They also present little or no advantage when the data are reasonably complete.

(4.) A Box-Cox transformation is used when the output is zero.

(5.) For more details on duality theory, see Diewert (1982) and Fare and Primont (1995).

(6.) The symmetry of the Hessian implies that [[beta].sub.ir] = [[beta].sub.rl], [[beta].sub.ij], = [[beta].sub.ji], [[beta].sub.iv] = [[beta].sub.vi], [[beta].sub.js] = [[beta].sub.sj], [[beta].sub.jv] = [[beta].sub.vj], [[beta].sub.im] = [[beta].sub.ml], [[beta].sub.jm] = [[beta].sub.mj], [[beta].sub.mv] = [[beta].sub.vm], [[beta].sub.mn] = [[beta].sub.nm], and [[beta].sub.vu] = [[beta].sub.uv] for all I, j, v, m, r, s, sn, and u. To insure homogeneity of degree one in w, we impose the following necessary and sufficient linear constraints on the coefficients: [[SIGMA].sub.i] [[alpha].sub.i]= 1, [[SIGMA].sub.i][[beta].sub.iv] = 0, [[SIGMA].sub.i] [[beta].sub.it] = 0, [[SIGMA].sub.t] [[beta].sub.ij] = 0, [[SIGMA].sub.i] [[beta].sub.im] = 0 for all j, v, r, m.

(7.) This need for information on the overall structure of the hospital industry prevents the use of DEA methods. They would require subsampling by hospital type, thereby precluding a comparison of hospitals across broad categories (see Ferrier and Valdmanis 1996 for an example of such an analysis).

(8.) Our measure of economies of scope is a short-term one since the impact of output variations on the three types of quasi-fixed inputs is unknown (Cowing and Holtmann 1983).

(9.) None of the prices or costs need deflating since they are all expressed in relative terms because of the imposed linear homogeneity of the cost function in variable input prices.

(10.) Labor costs include salaries and fringe benefits. Note that differences in labor quality due to differences in ease mix will be captured by salary differences across hospitals. In the estimation equation, the [w.sub.i] will capture differences in labor quality and seniority across hospitals and across time rather than differences in prices since all hospitals' employees are covered under the same collective bargaining agreement.

(11.) A Fisher index is used to aggregate energy types.

(12.) Price indexes are Statistics Canada's medicine and medical products for drugs, restaurant food including nonalcoholic beverages for food, supplies and furniture for supplies, and GDP deflator for "other."

(13.) The Fisher index is the product of the square root of a Laspeyres and a Paasche index. As with all indexes, it is adimentional.

(14.) Potentially, one could consider an additional dimension of output related to the ability to offer space in an emergency since it might lead to high costs for empty beds (Gaynor and Anderson 1995). However, unlike their U.S. counterparts, virtually all Quebec hospitals are characterized by operations at or near full capacity.

(15.) When hospitals do not distinguish between medicine and surgery patients, both types of patients are aggregated into the "medicine and surgery" category.

(16.) The inverse relationship between economies of scope and flexibility in the choice of each output shown by the negative signs between scope of services and flexibility in outputs in the correlation table (Appendix B) is not inconsistent. It states that, while flexibility, measured by the curvature of the average cost function for each output (a function of the first and second own derivatives of the translog cost function with respect to each output) can be greater, economies of scope, measured by the second derivatives of the cost function with respect to two different outputs (a function of first and second cross-derivatives of the translog cost function) might very well be simultaneously smaller.

(17.) This might seem puzzling since we stressed earlier that strong economies of scope were present. However, it only emphasizes the strong underutilization of variable inputs.

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Table 1

Elasticities of Substitution

          Drugs  Food  Supplies  Energy  Other

Labor       +     -       ++       +      ++
Drugs            +++      --       ++     ---
Food                     ---       ++     +++
Supplies                           ++     +++
Energy                                    -?

- = complements (-1 < [[sigma].sub.ij] < 0);

+ = substitutes (0 < [[sigma].sub.ij] < 1);

-- = strong compl. (-10 < [[sigma].sub.ij] < -1);

++ = strong subst. (1 < [[sigma].sub.ij] < 10);

--- = very strong compl. ([[sigma].sub.ij] < -10);

+++ =very strong subst. ([[sigma].sub.ij] > 10);

? = indicates that the pattern varied across hospitals and across time.
Table 2

Number of Hospitals in Various Returns to Scale (RTS) categories

Level of
Confidence  RTS < 1  RTS = 1  RTS > 1

0.10          616      164      603
0.05          584      220      579
0.01          563      256      564
Appendix A

Descriptive Statistics for All Variables (1383 Observations)


Variable                 Unit             Mean

Total cost               $                32,945,613.1
Price of labor           $/hour                   19.514
Price of drugs           Index                   106.708
Price of food            Index                   105.71
Price of supplies        Index                   104.415
Price of energy          Index                     1.34
Price of other           Index                   102.476
Physicians               Index                     0.499
Equipment stock          Index                 6,821.695
Building stock           Square meters        28,856.513
Inpatient complexity     Index                  8945.11
Inpatient diversity      Index                     6.195
Total inpatient days     Days                 91,348.641
Time trend               1 to 12                   6.614
Outpatient complexity    Index                  2021.143
Outpatient diversity     Index                     9.826
Total outpatient visits  Number of visit      90,680.163
Labs, EEG, ECG, etc.     Index                     0.32
Laundry and cafeteria    Index                     0.168
Numbers of residents     Number                   20.097
Cost share of labor      Percentage                0.768
Cost share of drugs      Percentage                0.0254
Cost share of food       Percentage                0.0168
Cost share of supplies   Percentage                0.113
Cost share of energy     Percentage                0.0171
Cost share of other      Percentage                0.0593

                         Standard
Variable                 Deviation         Minimum

Total cost               31,967,290.5      1,307,387
Price of labor                    3.809           13.319
Price of drugs                   27.031           63.7
Price of food                    19.236           77.1
Price of supplies                14.895           81.8
Price of energy                   0.503            0.184
Price of other                   13.049           78.2
Physicians                        0.411            0.011
Equipment stock              42,490.543          136.707
Building stock               24,761.977         1526
Inpatient complexity           2964.227         1825
Inpatient diversity               2.2              1
Total inpatient days         76,482.911         2029
Time trend                        3.43             1
Outpatient complexity           858.697            0
Outpatient diversity              5.868            0
Total outpatient visits      99,487.123            0
Labs, EEG, ECG, etc.              0.291            0
Laundry and cafeteria             0.203            0
Numbers of residents             47.954            0
Cost share of labor               0.0519           0.141
Cost share of drugs               0.0101           0
Cost share of food                0.00566          0
Cost share of supplies            0.0336           0.0356
Cost share of energy              0.00598          0.00468
Cost share of other               0.0369           0.0119


Variable                 Maximum

Total cost               180,609,024
Price of labor                    30.646
Price of drugs                   146.1
Price of food                    138
Price of supplies                129.3
Price of energy                    3.99
Price of other                   121
Physicians                         2.139
Equipment stock              474,702.438
Building stock               110,531
Inpatient complexity          24,219
Inpatient diversity                9
Total inpatient days         463,511
Time trend                        12
Outpatient complexity           3741
Outpatient diversity              20
Total outpatient visits      544,086
Labs, EEG, ECG, etc.               2.114
Laundry and cafeteria              1.214
Numbers of residents             329
Cost share of labor                0.878
Cost share of drugs                0.0623
Cost share of food                 0.0459
Cost share of supplies             0.389
Cost share of energy               0.044
Cost share of other                0.81

Indices are either directly obtained from Statistics Canada or
calculated using Fisher's method.
Appendix B1

Correlation Coefficients for All Quebec Hospitals in the Sample


                 Performance  Returns   Tech.   Number  Flex.    Flex.
                   Measure    to Scale  Progr.  of MDs  Inpat.  Clinics

Returns             0.16
 to scale           0.00
Tech.               0.32        0.10
 progr.             0.00        0.00
Number              0.75        0.18     0.29
 of MDs             0.00        0.00     0.00
Flex.               0.01       -0.03    -0.31   -0.08
 inpat.             0.64        0.21     0.00    0.00
Flex.              -0.02       -0.02    -0.02   -0.03    0.01
 clinics            0.56        0.41     0.44    0.28    0.75
Flex.               0.01       -0.01    -0.07   -0.03    0.04    0.00
 labo.              0.77        0.59     0.02    0.24    0.19    0.96
Flex. laun.         0.13       -0.04    -0.13   -0.08    0.00    0.00
 + caf.             0.00        0.18     0.00    0.00    0.89    0.89
Flex.               0.02        0.02     0.05   -0.01   -0.01    0.00
 teach.             0.36        0.56     0.09    0.70    0.79    0.91
Econ. of           -0.05        0.01     0.08    0.02    0.00   -0.07
 scope              0.05        0.67     0.00    0.44    0.91    0.02
% Pat.             -0.19        0.00    -0.15   -0.14   -0.05    0.12
 over 65            0.00        0.88     0.00    0.00    0.07    0.00
Teaching            0.57        0.07     0.22    0.60   -0.04   -0.01
 status             0.00        0.01     0.00    0.00    0.11    0.81
Equip.              0.67        0.13     0.15    0.70   -0.03   -0.03
 stock              0.00        0.00     0.00    0.00    0.29    0.25
Equip.              0.57        0.10     0.13    0.59   -0.03   -0.02
 invest.            0.00        0.00     0.00    0.00    0.23    0.38
Building            0.80        0.17     0.39    0.83   -0.06   -0.03
 stock              0.00        0.00     0.00    0.00    0.03    0.26
Total               0.69        0.17     0.41    0.74   -0.08   -0.02
 pat.-days          0.00        0.00     0.00    0.00    0.00    0.54
Complex. index      0.30        0.07    -0.27    0.31   -0.05   -0.13
 inpatient          0.00        0.01     0.00    0.00    0.08    0.00
Diversity index     0.45        0.10     0.44    0.39   -0.10   -0.09
 inpatient          0.00        0.00     0.00    0.00    0.00    0.00
Complex. index      0.18        0.09    -0.36    0.22   -0.02   -0.02
 outpatient         0.00        0.00     0.00    0.00    0.48    0.43
Diversity index     0.63        0.15     0.24    0.61    0.03   -0.03
 outpatient         0.00        0.00     0.00    0.00    0.31    0.20
Number of           0.68        0.16     0.13    0.81   -0.06   -0.02
 visits             0.00        0.00     0.00    0.00    0.03    0.39

                        Flex.
                 Flex.  Laun.   Flex.   Econ. of  % Pat.   Teaching
                 Labo.  + Caf.  Teach.   Scope    Over 65   Status

Returns
 to scale
Tech.
 progr.
Number
 of MDs
Flex.
 inpat.
Flex.
 clinics
Flex.
 labo.
Flex. laun.       0.00
 + caf.           0.96
Flex.             0.00   0.03
 teach.           0.91   0.31
Econ. of         -0.91  -0.17   -0.01
 scope            0.00   0.00    0.73
% Pat.            0.00  -0.05    0.00     0.02
 over 65          0.89   0.06    0.88     0.39
Teaching         -0.02   0.03    0.17     0.00     -0.06
 status           0.52   0.23    0.00     0.88      0.04
Equip.           -0.02   0.04   -0.01     0.00     -0.11     0.48
 stock            0.51   0.17    0.82     0.99      0.00     0.00
Equip.           -0.02   0.02    0.00     0.01     -0.11     0.44
 invest.          0.54   0.58    0.86     0.67      0.00     0.00
Building         -0.02   0.02    0.05     0.00     -0.11     0.60
 stock            0.46   0.51    0.05     0.86      0.00     0.00
Total            -0.03   0.00    0.13     0.01     -0.02     0.47
 pat.-days        0.26   0.93    0.00     0.77      0.43     0.00
Complex. index   -0.01   0.06   -0.04    -0.01     -0.10     0.20
 inpatient        0.83   0.04    0.16     0.84      0.00     0.00
Diversity index  -0.03   0.02    0.05     0.03     -0.30     0.10
 inpatient        0.32   0.37    0.05     0.35      0.00     0.00
Complex. index    0.03   0.04    0.02    -0.06     -0.01     0.15
 outpatient       0.23   0.15    0.36     0.02      0.71     0.00
Diversity index  -0.04   0.02    0.01     0.05     -0.18     0.37
 outpatient       0.13   0.55    0.70     0.09      0.00     0.00
Number of        -0.02   0.02    0.00     0.00     -0.09     0.54
 visits           0.39   0.44    0.92     0.92      0.00     0.00

                                                        Complex
                 Equip.  Equip.   Building    Total      Index
                 Stock   Invest.   Stock    Pat.-Days  In-patient

Returns
 to scale
Tech.
 progr.
Number
 of MDs
Flex.
 inpat.
Flex.
 clinics
Flex.
 labo.
Flex. laun.
 + caf.
Flex.
 teach.
Econ. of
 scope
% Pat.
 over 65
Teaching
 status
Equip.
 stock
Equip.            0.72
 invest.          0.00
Building          0.73    0.62
 stock            0.00    0.00
Total             0.61    0.50      0.88
 pat.-days        0.00    0.00      0.00
Complex. index    0.30    0.23      0.19      0.07
 inpatient        0.00    0.00      0.00      0.01
Diversity index   0.36    0.28      0.47      0.52       0.29
 inpatient        0.00    0.00      0.00      0.00       0.00
Complex. index    0.16    0.12      0.14      0.10       0.61
 outpatient       0.00    0.00      0.00      0.00       0.00
Diversity index   0.46    0.40      0.58      0.53       0.31
 outpatient       0.00    0.00      0.00      0.00       0.00
Number of         0.69    0.62      0.76      0.68       0.42
 visits           0.00    0.00      0.00      0.00       0.00

                 Diversity    Complex     Diversity
                   Index       Index        Index
                 Inpatient   Outpatient   Outpatient

Returns
 to scale
Tech.
 progr.
Number
 of MDs
Flex.
 inpat.
Flex.
 clinics
Flex.
 labo.
Flex. laun.
 + caf.
Flex.
 teach.
Econ. of
 scope
% Pat.
 over 65
Teaching
 status
Equip.
 stock
Equip.
 invest.
Building
 stock
Total
 pat.-days
Complex. index
 inpatient
Diversity index
 inpatient
Complex. index     0.24
 outpatient        0.00
Diversity index    0.50         0.32
 outpatient        0.00         0.00
Number of          0.43         0.37         0.63
 visits            0.00         0.00         0.00

The second line in each correlation cell indicates the significance
level of the coefficient. The performance measure is an index that is
inversely related to actual performance and is defined as exp
([B.sub.i]) - 1.
Appendix B2

Correlation Coefficients for Teaching Hospitals Only


                 Performance  Returns   Tech.   Number  Flex.    Flex.
                   Measure    to Scale  Progr.  of MDs  Inpat.  Clinics

Returns             0.16
 to scale           0.00
Tech.               0.38        0.16
 progr.             0.00        0.00
Number              0.75        0.20     0.32
 of MDs             0.00        0.00     0.00
Flex.              -0.66       -0.17    -0.53   -0.52
 inpat.             0.00        0.00     0.00    0.00
Flex.              -0.01        0.00     0.03   -0.03   -0.02
 clinics            0.80        0.93     0.59    0.59    0.66
Flex.              -0.10       -0.04    -0.12   -0.09    0.18    0.00
 labo.              0.04        0.45     0.01    0.06    0.00    0.96
Flex. laun.         0.10       -0.05    -0.19    0.14   -0.02    0.00
 + caf.             0.05        0.31     0.00    0.01    0.67    0.93
Flex.              -0.16        0.01     0.02   -0.18    0.05    0.00
 teach.             0.00        0.88     0.69    0.00    0.33    0.94
Econ. of           -0.09        0.05     0.21    0.15    0.03    0.00
 scope              0.06        0.31     0.00    0.00    0.59    0.94
% Pat.             -0.17       -0.01    -0.23   -0.11    0.06   -0.02
 over 65            0.00        0.80     0.00    0.03    0.28    0.67
Equip.              0.73        0.17     0.15    0.74   -0.40   -0.03
 stock              0.00        0.00     0.00    0.00    0.00    0.51
Equip.              0.55        0.12     0.12    0.55   -0.30   -0.01
 invest.            0.00        0.01     0.02    0.00    0.00    0.79
Building            0.81        0.18     0.50    0.77   -0.56   -0.02
 stock              0.00        0.00     0.00    0.00    0.00    0.64
Total               0.66        0.18     0.54    0.68   -0.61    0.01
 pat.-days          0.00        0.00     0.00    0.00    0.00    0.91
Complex. index      0.24        0.00    -0.49    0.19    0.06   -0.03
 inpatient          0.00        1.00     0.00    0.00    0.27    0.52
Diversity index     0.45        0.14     0.49    0.50   -0.58    0.03
 inpatient          0.00        0.01     0.00    0.00    0.00    0.52
Complex. index     -0.06        0.02    -0.58    0.13    0.12   -0.04
 outpatient         0.22        0.75     0.00    0.01    0.02    0.39
Diversity index     0.71        0.18     0.46    0.69   -0.68    0.03
 outpatient         0.00        0.00     0.00    0.00    0.00    0.56
Number of           0.65        0.17     0.08    0.73   -0.42    0.01
 visits             0.00        0.00     0.09    0.00    0.00    0.77

                        Flex.
                 Flex.  Laun.   Flex.   Econ. of  % Pat.   Equip.
                 Labo.  + Caf.  Teach.   Scope    Over 65  Stock

Returns
 to scale
Tech.
 progr.
Number
 of MDs
Flex.
 inpat.
Flex.
 clinics
Flex.
 labo.
Flex. laun.       0.00
 + caf.           0.93
Flex.            -0.01   0.03
 teach.           0.85   0.59
Econ. of          0.17  -0.96   -0.06
 scope            0.00   0.00    0.24
% Pat.           -0.06  -0.08    0.01     0.10
 over 65          0.24   0.12    0.78     0.06
Equip.           -0.07  -0.03   -0.15     0.04    -0.01
 stock            0.17   0.61    0.00     0.46     0.78
Equip.           -0.06  -0.05   -0.10     0.06    -0.09     0.71
 invest.          0.27   0.28    0.05     0.24     0.10     0.00
Building         -0.08  -0.04   -0.08     0.05    -0.18     0.75
 stock            0.13   0.37    0.11     0.31     0.00     0.00
Total            -0.08  -0.05    0.08     0.06    -0.06     0.62
 pat.-days        0.12   0.34    0.12     0.21     0.27     0.00
Complex. index   -0.15   0.05   -0.12    -0.02     0.21     0.32
 inpatient        0.00   0.31    0.01     0.63     0.00     0.00
Diversity index  -0.16   0.02    0.07     0.02    -0.20     0.41
 inpatient        0.00   0.72    0.13     0.66     0.00     0.00
Complex. index    0.09   0.05    0.00    -0.04     0.29     0.15
 outpatient       0.09   0.28    0.95     0.40     0.00     0.00
Diversity index  -0.11  -0.04   -0.11     0.06    -0.14     0.54
 outpatient       0.03   0.44    0.03     0.21     0.01     0.00
Number of        -0.07  -0.03   -0.13     0.04    -0.07     0.73
 visits           0.14   0.59    0.01     0.43     0.17     0.00

                                               Complex    Diversity
                 Equip.  Building    Total      Index       Index
                 Invest   Stock    Pat.-Days  In-Patient  In-patient

Returns
 to scale
Tech.
 progr.
Number
 of MDs
Flex.
 inpat.
Flex.
 clinics
Flex.
 labo.
Flex. laun.
 + caf.
Flex.
 teach.
Econ. of
 scope
% Pat.
 over 65
Equip.
 stock
Equip.
 invest.
Building          0.55
 stock            0.00
Total             0.45     0.83
 pat.-days        0.00     0.00
Complex. index    0.21     0.07     -0.08
 inpatient        0.00     0.15      0.09
Diversity index   0.32     0.53      0.69       0.05
 inpatient        0.00     0.00      0.00       0.33
Complex. index    0.08     0.00      0.01       0.50        0.09
 outpatient       0.12     0.98      0.91       0.00        0.08
Diversity index   0.43     0.66      0.64       0.10        0.64
 outpatient       0.00     0.00      0.00       0.04        0.00
Number of         0.61     0.67      0.62       0.33        0.52
 visits           0.00     0.00      0.00       0.00        0.00

                  Complex     Diversity
                   Index        Index
                 Out-patient  Out-patient

Returns
 to scale
Tech.
 progr.
Number
 of MDs
Flex.
 inpat.
Flex.
 clinics
Flex.
 labo.
Flex. laun.
 + caf.
Flex.
 teach.
Econ. of
 scope
% Pat.
 over 65
Equip.
 stock
Equip.
 invest.
Building
 stock
Total
 pat.-days
Complex. index
 inpatient
Diversity index
 inpatient
Complex. index
 outpatient
Diversity index     0.07
 outpatient         0.16
Number of           0.32         0.65
 visits             0.00         0.00

The second line in each correlation cell indicates the significance
level of the coefficient. The performance measure is an index that is
inversely related to actual performance and is defined as exp
([B.sub.i]) - 1.