Are factor substitutions in HMO industry operations cost saving?

1. Introduction

As the number of HMOs increases, there is pressure on managed care entities, including mature staff-model HMOs, to reduce their costs ... For a managed care system, it is just as important to control such factors as inpatient hospitalization and the use of expensive diagnostic and therapeutic technologies. If (emphasis added) providing access to both generalist and specialist physicians is a substitute for the use of expensive technologies and hospitals, or if physicians are effective in their health promotion and disease prevention activities, investment in health professionals may actually reduce some downstream costs.

Hart et al. (1997, p. 68)

Coverage in traditional fee-for-service health insurance for private employees with group insurance fell significantly from 98% in 1979 to 15% in 1997. Managed care enrollment grew from 2 to 85% in the same period. More specifically, coverage in managed care (Kongstvedt 1997) grew from 19% in 1992 to 30% in 1997 in health maintenance organizations (HMOs), from 27% to 35% in preferred provider organizations (PPOs), and from 7% to 20% in point-of-service (POS) plans (Henderson 1999, p. 274). These health plans are "economically driven medical care models" (Etheredge, Jones, and Lewin 1996). Due to their increased dominance arising from cost-saving competitive features and production structures, managed care models such as open-access HMO systems offering the benefits of point-of-service products (Sachs 1997) are projected to play significant roles in future medical care delivery and related policy reforms in both the private and public health sectors. HMOs are entities that integrate the financing and delivery of health-care services to covered lives. In 1995, 89% of the HMO revenues derived from employee benefit plans, with the balance of 5% from Medicaid and 6% from Medicare enrollments. HMO expenses in 1995 (as percentage of total premiums) were comprised of physician and outpatient (41%), inpatient (31%), outside referrals (7%), emergency (3%), administrative (13%), and profit (5%). Private sector HMOs have become important prototypes for public sector managed care (Fox 1997). (1)

Recent studies of medical care in HMOs report about 15% cost savings compared with those under traditional indemnity insurance (Getzen 1997). These cost savings, achieved at an average quality of care level similar to the fee-for-service (FFS) arrangement (Miller and Luft 1997), have largely been attributed to (a) a huge reduction in the relatively expensive hospital days per enrollee (Etheredge, Jones, and Lewin 1996); (b) large volume discounts (e.g., provider networks) in acquiring hospital, physician, laboratory, and pharmacy services (Getzen 1997; Henderson 1999); and (c) cost-effective organizational strategies (e.g., use of more midlevel providers and generalists than specialists) that influence patient and provider behavior (Flood et al. 1998).

Cost studies of HMOs agree that specific economies characterize the multiple output production structure. Wholey et al. (1996) and Given (1996b) independently confirm substantial economies of scale and diseconomies of scope. They estimated differently specified multiproduct translog cost models using dissimilar data sets and time periods to arrive at remarkably consistent conclusions. Currently, there is no inquiry on whether the robust findings on economies of scale and scope extend to the scope for factor substitution possibilities implicit in the production technology. Past research is largely mute on the extent to which the HMOs are capable of reorganizing input ratios to contain operational costs when relative factor prices change, (2) all else equal. Because the HMOs offered a more diverse mix of products and reaped diseconomies of scope during the 1990s, there is also an interesting and unexplained phenomenon that an investigation of factor substitutions could help to resolve. For instance, if the core skill of HMOs is administrative efficiency, and administrative services complement physician services for Medicare patients but substitute for commercial patients, then adding Medicare product could thwart the substitution of administrative services for physician services. This makes the curvature of the isoquant critical to the degree of cost savings.

The relative factor prices in the health care industry, and particularly for the HMOs, have changed for the period analyzed in this study. These include health care inflation overall, which rose from 2.5% in October 1997 to 3.0% in April 1998 (Zelver 1998). The producer price index, or PPI, for all hospital care had a net deceleration from 1.2% in January 1997 to 0.2% in December 1997. Deceleration of the indexes was partly driven by general medical inpatient (from 1.2% to -1.0%), general Medicaid inpatient (from -0.1% to -0.8%), general Medicare outpatient (from 1.9% to 1.6%), and psychiatric Medicare inpatient (from 1.2% to 1.1%) care. The all-physician-care PPI inflation fell from 1.3% in January 1997 to 1.2% in December 1997. A stable 0.3% inflation in Medicare physician care and a non-Medicare physician inflation falling from 1.6% to 1.5% fueled the deceleration. Overall, the Medicare price indexes for internal medicine, surgery, pediatrics, and obstetrics and gynecology (OB/GYN) rose. Finally, the 12-mo nth PPI inflation rates (%) for December 1997 included hospital care (0.2%), physician care (1.2%), medical laboratories (0.9%), nursing homes (4.2%), and prescription drugs (3.6%).

Consequently, the goal of this study is to estimate the degree of factor substitution inherent in the structure of HMO production technology. That is, given the production technology structure of HMOs at constant output and the corresponding cost function, to what extent can cost savings be realized when relative factor prices change? Policy-driven estimates of the scopes for factor interchange exist for the health care services of general hospitals (Cowing and Holtmann 1983), physician practices (Escarce and Pauly 1998), hospital pharmacies (Okunade 1993, 2001), specialized hospital pharmacies (Okunade and Suraratdecha 1998), nursing (Eastaugh 1990), and outpatient dentistry (Okunade 1999). Despite the broad significance of the HMO industry, there is currently no similar study based on more recent data. Research on potentially cost-saving factor interchange has operational policy implications for the optimal reorganization of inputs in HMOs as the industry competition intensifies in geographic markets (Given 1996a). Therefore, findings of the current study are expected to augment the earlier conclusions on the economies of scale and scope technology aspects of HMOs and further provide a baseline set of factor substitution estimates with which to compare future substitution possibilities as HMOs continue their competitive evolution. The numerical estimates of pairwise factor substitutions and their informational contents (i.e., confidence interval bounds) could also aid in the understanding of whether inputs relate decidedly as complements or substitutes as competitive HMOs respond to relative input wage changes at a constant output set. How the HMOs react to the higher price of hospitals versus home health or outpatient pharmaceutical intervention for Medicare enrollees is, for example, a factor-factor substitution issue. (3) Other than the now-dated Bothwell--Cooley (1980) study, which used 1976-1977 data and a conceptually flawed elasticity of substitution concept, our present study utilizing the alternative c onceptual measures and more recent data sets is unique and timely in its approach to estimating the scope for cost-saving factor substitutions in HMOs.

Section 2 reviews the scant economic cost studies of HMO production and examines the different conceptual bases of the elasticity of factor substitutions and their implications for HMO isoquant shapes. Section 3 implements these concepts and discusses the findings using the translog cost model parameter estimates of each of the cost studies of HMOs published to date in peer-refereed economics journals. Section 4 concludes with the health policy and operational cost containment implications and advances the agenda for future HMO production studies.

2. Economic Cost Models of HMO Production Activities

The Appendix summarizes the regrettably anemic current literature (Given 1996b, p. 689) on the econometric models of HMO production cost behavior. With the exception of Schlesinger, Blumenthal, and Schlesinger (1986), whose methodology is not a translog economic cost model, the other three studies included at least four factor inputs and two or three intermediate outputs in their multiproduct translog cost representations of HMO operations in the United States. (4) The studies utilized data from different settings and operational periods to confirm positive scale economies and no economies of scope. Production characteristics have cost implications. Scale economies reduce unit costs with output expansion, economies of scope relate to the capacity of joint outputs to reduce costs compared with separate production, and potential cost savings from factor substitutions investigated here pertain to production economies arising from possible reorganization of input ratios at constant outputs when relative input prices change.

Translog Cost Model and the Alternative Concepts of Factor Substitutions

The translog cost models that Bothwell and Cooley (1980), Wholey et al. (1996), and Given (1996b) fitted to different HMO data sets rejected the statistical hypothesis test of a homothetic production structure. The model by Bothwell and Cooley (1980) is

ln C = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where C(*) is total cost, [Y.sub.i] (i = 1, 2, 3) are outputs, [w.sub.i] (i = 1, ... , 5) are input prices. Factor cost share equations are [M.sub.j] = [partial] log C/[partial][w.sub.j] = [w.sub.j][x.sub.j]/C = [[beta].sub.j] + [summation over (k)] [[gamma].sub.jk] log [w.sub.k] + [summation over (i)] [[rho].sub.ij] log [Y.sub.i] (j = 1,...,n). The theoretical restrictions imposed in statistical estimation are [summation over (i)] [[alpha].sub.i] = 1, [summation over (i)] [[delta].sub.il] = 0, [summation over (i)] [[rho].sub.ij] = 0. The model by Wholey et al. (1996) is

ln C = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where C(*) is total cost, [Y.sub.i] (i = 1,2) are outputs, [w.sub.j] (j = 1,...,5) are input prices, and X are specific operational characteristics affecting production costs but that do not affect substitution relations among inputs and do not influence the role of output on costs. The cost share equations are [P.sub.j][Q.sub.j]/C = [[beta].sub.j] + [summation over (5/k=1)] [[gamma].sub.ik] ln [w.sub.k] + [summation over (2/i=1)] [[rho].sub.ij] ln [Y.sub.i] and the theoretical constraints imposed in estimation are [summation over (j)] [[beta].sub.j] = 1 (j = 1, 2); [summation over (j)] [[rho].sub.ij] = 0 (j = 1, 2), [summation over (k)] [[gamma].sub.jk] = 0. The model by Given (1996b) is

ln TC = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where TC(*) is total cost, [Y.sub.i] (i = 1,) are outputs, [w.sub.i] (i = 1,...,4), [C.sub.h] the control variables, and [epsilon] an error term. Factor shares [S.sub.j] = [partial] log TC/[partial][w.sub.j] = [[beta].sub.j] + [summation over (k)] [[gamma].sub.yk] log [w.sub.k] + [summation over (i)] [[rho].sub.ij] log [Y.sub.i] + [summation over (h)] [[theta].sub.hj] log [C.sub.h] + [[epsilon].sub.j], and the theoretical restrictions for estimation are [summation over (j)] [[beta].sub.j] = 1; [summation over (k)] [[gamma].sub.jk] = [summation over (i)] [[rho].sub.ij] [summation over (h)] [[rho].sub.hj] = 0; [summation over (k)] [[gamma].sub.jk] = 0.

Conceptually, factor substitutions can be defined using any one of the Allen, Morishima, or shadow measures. Blackorby and Russell (1989) and Segerson and Ray (1989), however, prove that these alternative conceptual definitions are generally not equivalent when the production process is nonhomothetic and involves at least three inputs. As a results, we compute elasticity estimates for the different substitution concepts and also report the own-and cross-price elasticities of input demands. Their respective standard errors are also calculated (5) in order to asses the precise informational contents of substitution tendencies.

HMO production cost structure [C.sup.*] (y, w, z) has largely been approximated using a multiple-output (y), four- r five- input (w) total variable cost model of the form

C(w, y, z) = min {[summation over (i)] [w.sub.i][q.sub.i]) subject to y = f(q,z)}, (1)

where C(*) is operational cost (endogenous), y is the output set (exogenous), vector w contains (exogenously determined) competitive market input wages and q the associated factor quantities, and z is a set of nonprice, nonoutput HMO characteristics that impact production economies but leave invariant the scope for pairwise factor substitutions. C(*) is dual to x in Equation 1 under appropriate theoretical conditions (see notes 5, 6, and 7). The parent translog cost function C(*) is estimated jointly with all but one of the factor share equations ([partial] ln C(*)/[partial] ln [w.sub.i]) to add structural stability using iterative Zellner's (1962) SURE estimation method.

Taking a second-order, multiproduct translog cost approximation to C(*) in Equation 1 yields

ln C = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where the model variables, except dummies, are calibrated as log deviations from their sample means and the Greek symbols are the model parameters for econometric estimation. The translog technology properties implicit in the dual cost function C(*), inherited at the mean data expansion point, are also testable at each observed data point. The translog specification, most favored among the contending flexible functional forms for modeling costs and technologies, allows the factor substitution elasticities and economies of scale estimates to vary at each observation point.

If the operational budget constraints are strictly binding and there is a change in relative factor prices, possible cost efficiency gains in HMO production could arise from altering the input mix along a given production isoquant. (6) Different substitutability measures could yield disparate conclusions on the numerical size and sign of the substitution relationships, however. Different assumptions as to which factors are held constant underlie the different conceptual derivations of substitution elasticities (Davis and Gauger 1996). Therefore, the appropriate measure for a given situation depends on the research question and consistency of the particular conceptual measure with the underlying technology structure of production.

The classic Allen-Uzawa (hereafter, [[sigma].sup.AU.sub.ij]) partial elasticity of substitution is often misused among the different conceptual measures (Mundlak 1968) of pairwise factor interchange in flexible translog production cost models. Past researchers implicitly justified its use because it corresponds with the conventional comparative statics analyses, as it is proportional to [partial] ln [q.sub.i]/[partial] in [w.sub.j], when output and all other prices are held fixed but all other input quantities (e.g., [q.sub.k],) are allowed to adjust to a new equilibrium. Numerically, [[sigma].sup.AU.sub.ij] is a factor cost share-weighted proportionate change in the employment of an jth input arising from a proportionate change in jth input price (i.e., [partial]([q.sub.i]/[q.sub.j])/[partial]([w.sub.j]/[w.sub.i]) x ([w.sub.j]/[w.sub.i])/([q.sub.i][q.sub.j])). Although [[sigma].sup.AU.sub.ij] is fairly easy to calculate and independent of the magnitude of price changes, the [[sigma].sup.AU.sub.ij] concept is difficult to interpret, lacks an intuitive economic appeal, is inconsistent with the Hicksian definition, and unnecessarily imposes the invariance of input factor demands with respect to which one of the input prices changed (Blackorby and Russell 1989; Fleissig 1997). However, the Morishima measure, [[sigma].sup.M.sub.ij], a two-factor, one-price substitution elasticity concept, has a much stronger intuitive economic appeal because it captures how ([q.sub.i]/[q.sub.j]) adjusts with a change in input price by measuring the ease with which one factor can substitute for another along an isoquant.

Denoting [partial] ln C(*)/[partial] ln [w.sub.i] [q.sub.i][w.sub.i]/C(*) = ([partial]C(*)/[partial][w.sub.i]) X ([w.sub.i]/C) = [C.sub.i] as the first gradient of C(.) with respect to the ith variable input price (i.e., ith input share of total costs), the Allen-Uzawa elasticities of factor substitution (symmetric) are calculated using the expression

[[sigma].sup.AU.sub.ij] (=[[sigma].sub.ji]) = ([[beta].sub.ij] + [C.sub.i][C.sub.j])/[C.sub.i][C.sub.j], [for all]I [not equal to] j; and [[sigma].sup.AU.sub.ii] = ([[beta].sub.ii] + [C.sup.2.sub.i] - [C.sub.i])/[C.sup.2.sub.i], [for all]i = j, (3)

where [[beta].sub.ij], [for all] i [not equal to] j, is the estimated interaction effects between the prices of factor inputs i and j. The Morishima elasticity estimates (generally nonsymmetric except in a constant returns to scale technology) are calculated using the expression

[[sigma].sup.M.sub.ij] = [partial] ln ([q.sub.i]/[q.sub.j])/[partial ln [w.sub.j] = [w.sub.i][C.sub.ij]/[C.sub.j] - [w.sub.i][C.sub.ii]/[C.sub.i] = [C.sub.j]([[sigma].sup.AU.sub.ij] - [[sigma].sup.AU.sub.jj]), (4)

where [q.sub.i] and [q.sub.j] are, respectively, the physical quantities of inputs i and j, [C.sub.j] is the jth input factor cost share, and [C.sub.ij] is [[partial].sup.2]C(*)/[partial[w.sub.i][partial][w.sub.j]. Finally, a special form of Hicks two-factor, two-price elasticity of factor substitution, [[sigma].sup.TT.sub.ij] = [partial] ln([q.sub.i]/[q.sub.j])/[partial] ln ([w.sub.j]/[w.sub.i]), is the shadow elasticity of substitution ([[sigma].sup.S.sub.ij]). While [[sigma].sup.TT.sub.ij] captures how production input ratios respond to changes in factor price ratios, [[sigma].sup.S.sub.ij] is obtainable from [[sigma].sup.TT.sub.ij] by allowing input prices to vary at constant average cost (McFadden 1963). Definitionally, [[sigma].sup.S.sub.ij] is

[[sigma].sup.S.sub.ij] = ([C.sub.i][C.sub.j]/([C.sub.i] + [C.sub.j])[2[[sigma].sup.AU.sub.ii] - [[sigma].sup.AU.sub.jj]]. (5)

Finally, the own- and cross- price elasticities of factor demands, at the means, are obtained as cost-share weighted [[sigma].sup.AU] estimates, using the expression

[[gamma].sub.ii] = [[sigma].sup.AU.sub.ii] [C.sub.i] [for all] i = j(own); [[gamma].sub.ij] = [[sigma].sup.AU.sub.ij] [C.sub.j] [for all]i [not equal to]j(cross). (6)

3. Empirical Results and Discussion

Own-Price Elasticities of Factor Demands

Tables 1a, 1b, and 1c contain own- (diagonal entries) and cross- (off-diagonal cells) price elasticities of HMO factor demands, respectively, calculated from the translog cost parameter estimates in Wholey et al. (1996), Given (1996b), (7) and Bothwell and Cooley (1980). For the Wholey et al. model only, separate elasticities are computed for groups and independent practice associations (IPAs) because that study tabulated separate cost model parameter estimates for the differently organized HMOs.

Generally, the own demand elasticities are variously inelastic for all inputs across the models. Specifically, from Wholey et al.'s model, the highly statistically significant demand for non- Medicare inpatient and non-Medicare physician inputs are less inelastic for IPAs than for groups. This likely reflects the tendency for IPAs to respond relatively more swiftly to changing input market conditions than groups when servicing non-Medicare contracts. On the other hand, input demands, while appropriately signed, remain inelastic but not significantly sensitive to own-price in Medicare HMO production. Groups appear to be twice as sensitive as IPAs to factor price changes for Medicare products, however. The demand for hospital services input computed from the Bothwell--Cooley study is insignificant (-0.018), is highly significant in the Wholey et al. model for groups (-0.706) and IPAs (-0.720) when HMOs produce non-Medicare services, and is highly significant with a tendency toward unitary elasticity (-0.915) ba sed on computations using the coefficients in Given's model.

Administrative labor can be flexibly used for Medicare or non-Medicare HMO production. Its demand is more highly statistically significant in IPAs than groups and is almost equally inelastic in IPAs and groups. Regardless of the organizational form, administrative input demand is the most inelastic among the three statistically significant inputs for the Wholey et al. model. Remarkably, it remains the most inelastic but insignificant for computations based on the data of the Given and Bothwell-Cooley studies.

The "professional inputs" in HMOs as defined by Given approximates "medical professional staff services" in the Bothwell-Cooley study and "physician services" in the Wholey et al. model of Medicare (IPAs, groups) and non-Medicare (IPAs, groups) products. The respective estimates of own-price elasticities of demand are -0.668 (Given), -0.718 (Bothwell-Cooley), -0.532 and -0.641 (non-Medicare IPA and group, Wholey et al.), and -0.697 and -0.355 (Medicare IPA and group, Wholey et al.). The relatively more sensitive physician demand in IPAs than groups is consistent with the respective organizational contract conditions and incentives. While only that of Medicare is insignificant, the elasticity of demand for medical staff input appears remarkably stable at around -0.67 over time in HMOs, regardless of organizational structure. This stability may reflect the everpresent role of the gate-keeping physicians, largely general practitioners, and their indispensable extenders, largely physician assistants and nursing p ractitioners (Riportella-Muller, Libby, and Kindig 1995). Only Bothwell and Cooley (1980) and Given (1996b) included in their models some measure of variable capital input, variously defined. The own-price elasticity of demand for "capital and facilities price" of -0.51 (Given) is more than twice as large as the -0.239 for "health center expense and interest expense on loans" (Bothwell and Cooley). Because Given's data extended to 1992 and Wholey et al.'s to 1991, HMOs' capital input demands appear to have become more sensitive over time to variations in capital market prices.

HMO factor demands are variously inelastic across the three HMO cost studies used as bases for computation. Particularly, non-Medicare physicians (groups and IPAs in Wholey et al.), primary care professionals (in Given), medical professional staff, and the variously defined administrators are theoretically in a strong bargaining position for higher wages, ceteris paribus. The magnitudes of factor demand elasticities for the gate-keeping physicians and administrative labor accord generally with the theory that employers' responses to wage changes are smaller the larger the human capital embodied in particular groups of workers (Hamermesh and Rees 1988).

Cross-Price Elasticities of Factor Demands

The cross-price elasticities of factor demands (off-diagonal entries in Tables 1a, 1b, and 1c) at sample data means measure the response of HMO input use to a change in another factor price. The limited substitution of inpatient for physician inputs in non-Medicare production is higher in groups (0.127) than IPAs (0.084) when the relative price of physician input rises. However, the typical HMO is less capable of substituting inpatient for physician input when inpatient per diem rises relative to physicians' (0.07 in groups, 0.0571 in IPAs) in the production of non-Medicare products. The general pattern of the cross-price elasticities of demand in Table La reveals significant substitutions between inpatient and physician inputs for non-Medicare products in groups and IPAs. Perhaps due to HCFAimposed guidelines and a relative lack of variability in per diems for inpatient and physician inputs in Medicare HMO production, none of the pairwise factor substitutions are highly significant. Despite this, it is notew orthy that administrative labor seems to complement all other inputs in groups and IPAs in the production of non-Medicare products but substitutes for those inputs in the production of non-Medicare products.

Cross-price elasticities of demand between "hospital services" (inpatient) and "primary care" office visits (outpatient) in Table 1b are statistically significant (but inelastic, as expected). Because the primary goal of HMOs is to improve enrollee health status in cost-effective ways, for example, reducing inpatient utilization, they substitute more outpatient primary care inputs for inpatient services when hospitals become relatively more costly (0.296). This substitution is almost twice the substitution of hospital for physician inputs when the relative price of the gatekeepers rise (0.173). Despite statistical insignificance, administrative labor and hospital services are complements, while administrative labor, primary care visits, and capital facilities are substitutes.

All else equal, HMOs in their infancy operational years (Table 1c) generally substituted in place of the then more expensive medical professional staff, the relatively less costly inputs such as administrative services (0.19), hospital care (0.04), and health center capital (0.18). Interestingly, the HMOs used slightly more medical professional staff when administrative wages (-0.109), hospital services price (-0.126), or health center services price (-0.152) rose. Overall, the largest significant complementarity was between hospital services input and medical professional services (due to changed hospital services price), while the strongest and statistically significant substitution occurred between administrative input and health center capital services (when health center capital price changed). Significantly inelastic own- and cross- price elasticities of factor demands, coupled with the recently exhausted scale economies, suggest that HMO costs are likely to rise further as their input (hospitals, docto rs, drugs, ...) and product (non-Medicare, Medicare) markets get less competitive through mergers and acquisitions. How this hypothesis is reinforced by the alternative estimates of factor substitution tendencies is discussed next.

Alternative Measures of Pairwise Elasticities of Factor Substitutions

Allen--Uzawa Estimates

Tables 2a, 2b, and 2c contain estimates of the Allen--Uzawa partial elasticities of substitution. This symmetric (thus, unnecessarily restrictive) measure is inconsistent with the 4- to 5-input, nonhomothetic HMO production structure. Nevertheless, the [[sigma].sup.AU.sub.ij] estimates are presented for three reasons. (8) First, they form the basis for computing the preferred Morishima measures of factor interchange. Second, the flexibility of the [[sigma].sup.AU] concept allows producers to alter the usage of an input k other than input i or j when an input price changes, holding the output constant (Nicholson 1998). That is, if the "inpatient services price" increases, its use is expected to decline as HMOs use more of the now relatively cheaper "outpatient" input services. The [[sigma].sup.AU.sub.ij] concept, however, enables the HMOs to substitute a third factor for inpatient and outpatient inputs and so reduce their usage. Thus, depending on the relative size of these changes, the "inpatient-outpatient" inputs ratio might rise rather than fall, making them relate as complements rather than as substitutes. Third, in a k-factor production model, convexity of the isoquants is implied by negatively signed estimates of [[sigma].sup.AU.sub.ii] (I = 1,...,k), the own Allen elasticity of substitution.

The diagonal entries of Tables 2a, 2b, and 2c (elasticities of own-substitutions?) are rather uninteresting. However, the off-diagonals in Table 2a reflect a highly significant and an inelastic substitution between physician services and inpatient care (higher in groups [0.264] than IPAs [0.205]) for non-Medicare products. Administrative inputs neither substitute for nor complement other inputs. In Table 2b, primary care office visits and hospital services relate as significant but inelastic substitutes (0.51). Medical professional staff relates as highly significant and inelastic substitutes with administrative labor (0.240) and hospital services (0.279). Significant substitution also exists between health center services and administrative labor (0.257), hospital services (0.167), and medical professional staff (0.337) in Table 2c.

Morishima and Shadow Estimates

The Morishima elasticity of factor substitution, [[sigma].sup.M.sub.ij], is a two-factor, one-price concept for measuring the responsiveness of the input ratio due to a change in the jth input price (i.e., [[sigma].sup.M.sub.ij] = [partial] ln([q.sub.i],/[q.sub.j])/[partial] ln [w.sub.j]). This nonsymmetrical measure, unlike [[sigma].sup.AU.sub.ij], offers a uniquely richer insight into input substitution possibilities, particularly given that the HMO production structure is a non-constant elasticities of substitution (CES)-type technology with more than two inputs. Substitution between inpatient and physician inputs when the inpatient per diem changes (0.659 in groups vs. 0.725 in IPAs) is slightly lower compared with that arising from a changed price of physician services (0.777 in groups and IPAs) for non-Medicare products. Thus, with output constant, the ratio of these other inputs to physician services would rise in the bounds of 6.7% to 7.7% if the physician wages increased 10%. This illustrated asymmet ry of [[sigma].sup.M.sub.ij] is more pronounced in the production of Medicare HMO product (respectively, 0.697 in groups vs. 0.355 in IPAs and 0.724 in groups vs. 0.252 in IPAs).

The [[sigma].sup.M.sub.ij] entries in Table 3a classify the relationship of administrative labor with each of the remaining inputs as substitutes in the production of Medicare HMO product (e.g., 0.498 and 0.537 with "inpatient services" in groups and IPAs when Medicare inpatient per diem changed vs. 0.723 and 0.250 respectively, when "administrative hourly wage" changed). "Capital and facilities" and "medical professional labor" are also Morishima substitutes (Table 3b) in that, at constant output if the price of capital and facilities rise by 10%, the ratio of professional inputs to capital and facilities would go up about 5.12%. On the other hand, a 10% rise in the wages of professional inputs will raise the facilities/professional inputs usage by some 6.7%, assuming constant output.

Substitution possibilities in the Morishima context (non-Medicare products) are consistently the largest between inpatient services and other inputs (such as, roughly 0.78 with physician labor in groups and IPAs and, respectively, 0.712 and 0.73 6 with administrative labor in groups and IPAs) when these other input prices changed (Table 3a). Consistently, the largest elasticity in Table 3b is also the substitution of hospital services for professional medical inputs (1.088), administrative labor (0.901), and capital and facilities (0.916) when the respective prices of these other inputs changed. Substitution tendencies for the input pairs are consistently the largest between "medical professional staff services" and "administrative labor" (1.609), "hospital services" (1.591), and "health center services" (1.565) when the prices of these other inputs changed. During the late 1970s, the HMOs more easily substituted medical professional staff input when the price of another factor changed (Table 3c). This substi tution became more difficult during the late 1980s to early 1990s nationally (Table 3a) and in California (Table 3b) as the industry matured.

The direction and magnitudes of the Morishima elasticities of substitution of administrative services for other inputs between Tables 3a (using Wholey et al.'s data) and 3b (based on Given's data) differ when the input wage of any of the other factors changed. We conjecture that this arises mainly from a major difference in how the prices of these other inputs are defined in each study and the fact the Morishima substitutions are more complex because there are infinitely many directions to measure curvature. That is, how an HMO changes optimal factor quantity ratios ([q.sub.i]/[q.sub.j]) in response to changes in relative prices depends on whether the price change is in the ith or jth coordinate direction (Fleissig 1997, p. 692). The Morishima elasticities in the neighborhood of 0.5 using the Wholey et al. data classify administrative labor as substitutes with all other inputs. The corresponding estimates using Given's data are around -0.13 and reflect the complementarity of administrative services and other inputs in HMO production. However, if the input price of administrative services changed, the direction and numerical magnitudes of the pairwise [[sigma].sup.M.sub.ij] (i [not equal to] j) between administrative services and any other input do reflect the generally observed substitution tendencies in Tables 3a, b, and c.

The shadow elasticity of substitution (symmetric), theoretically approximating the Hicksian concept, is a special case of the two-factor, two-price measure. Tables 4a, 4b, and 4c present the shadow elasticities of substitution ([[sigma].sup.S.sub.ij]) estimates. They capture how the input use ratios respond to a change in factor price ratios (i.e., [partial] ln([q.sub.i],/[q.sub.j])/[partial] ln([w.sub.j]/[w.sub.i])) at constant average cost. The shadow measure in Table 4a classified all inputs as highly inelastic substitutes for non-Medicare and Medicare products in groups and IPAs. They imply sharply curved production isoquant shapes. Similarly, all input pairs in Table 4b relate as highly inelastic substitutes, with that between administrative labor and professional services (0.229) the largest. Finally, according to Table 4c, HMOs of the late 1970s operated with a production system in which the structure allowed for greater pairwise substitutions among inputs (e.g., 0.792 between hospital inputs and admin istrative services and 1.04 between medical professional staff services and health center services). There was, however, a hardly perceptible tendency toward complementarity (-0.06) between medical professional staff and hospital services.

How do the three conceptually different estimates of pairwise factor substitutions in HMO production compare? Foremost, they are not all equivalent. The shadow measure, a symmetric concept, consistently classifies all inputs as difficult substitutes when based on the Wholey et al. (Table 4a) and Given (Table 4b) model estimates but classify all but one pair of factors as substitutes with an estimate as high as 1.03 (Table 4c) when the Bothwell--Cooley cost model estimates are used. The Morishima substitutions implied by the translog cost estimates in Given classify some input pairs as complements (e.g., "administrative labor" complements each of the remaining inputs) and confirm others to be substitutes with substitutability sometimes at around unity (Table 3b). On the other hand, the Morishima estimates (Table 3a) from the Wholey et al. (1996) model classify all input pairs as substitutes, with the substitutability estimates ranging narrowly from around 0.5 to about 0.8. This indicates that the technology st ructure is neither Cobb-Douglas nor CES type. Consistent with their respective organizational incentive structures, these estimates also differ in magnitudes and sometimes directions for IPAs and groups. More specifically, there appears to be a greater scope for factor interchange (i.e., the degree of complementarity or substitutability when statistically significant and similarly classified) in non-Medicare than Medicare HMO production. This largely reflects the impact of government-imposed regulation as to how Medicare HMO care should be produced (an example is which facility or health care personnel should provide specific Medicare services to qualify for HCFA reimbursement). The [[sigma].sup.M.sub.ij] elasticities derived from the Bothwell-Cooley (1980) model classify all the input pairs as substitutes, with the substitution elasticities ranging widely and reaching as high as about 1.5 (Table 3c) in some cases.

4. Summary, Conclusion, and Implications

Past studies of HMO production cost economies confirmed the presence of scale economies and scope diseconomies in multiproduct HMOs. The latest operational data they modeled extended to 1992. Since then, however, industry analysts have consistently confirmed rising HMO premiums for reasons including the exhaustion of historical scale economies, increasingly costly new benefit offerings, and increased participation of private-sector HMOs in managed Medicare contracts. This third factor would worsen diseconomies of scope that already existed in the industry as far back as the early 1990s. Therefore, in search of unmeasured avenues for containing HMO costs in the literature on HMO cost economies, this article entertained hypotheses on the possible existence of cost-saving factor interchange (substitutability, complementarity) implied by the estimated translog production cost models of all the three major studies published in peer-refereed economics journals.

Because multiproduct HMOs employ at least four inputs and production is nonhomothetic, three alternative concepts of potential factor substitutions were investigated and implemented. These estimates were analyzed along with own- and cross-price elasticities of input demands. It was found that all of the inputs of HMOs exhibit highly inelastic demands and that significant but limited factor substitutions tend to exist when the preferred Morishima conceptual measure, consistent with the nonhomothetic underlying HMO technology structure, is implemented.

One of the major research questions in this article is whether the independent confirmation of positive scale economies and diseconomies of scope in Given (1996b) and Wholey et al. (1996) translates to similar conclusions about factor substitutions of the technology structure. Our analysis suggests different conclusions about the implied pairwise factor relationships in multiproduct HMOs. Across all of the studies used as the foundation for computing factor substitution estimates, the theoretically preferred Morishima measures are consistently larger; they reflect more convex production isoquants than those implied by the shadow and the Allen-Uzawa measures, given the HMO production technology structure.

Do the fairly recent declines in the producer prices of physicians and hospital services have implications for potential cost-saving factor substitutions in HMOs? The estimated Morishima factor substitution possibilities (Tables 3a, 3b, 3c) suggest increased utilization of inputs that have declining relative prices in non-Medicare and Medicare HMO production. Because the hospital services PPI recently declined faster than physician services, there could be a gradual rise in the ratio of inpatient to physician office services in HMO production, all else equal. However, the utilization of specialist physicians in general could continue its historical decline, as the PPI for specialists continues to rise and HMOs restrict patient access to specialist providers. There is one recent complicating factor, however. On August 2, 2001, the U.S. House of Representatives passed H.R. 2563, "The Bipartisan Patient Protection Act of 2001," sponsored by Representatives Ganske (R-IA), Dingell (D-MI), and Norwood (R-GA) by a v ote of 226 to 203 (American Benefits Council 2001). The Act, with the general effective date of October 1, 2002, defines patient rights for health insurance, with special emphasis on managed care. These rights include, among others, (1) guaranteed coverage of emergency care for conditions of sufficient severity as determined by a "prudent lay person," (2) assurance of better communication between doctors and patients, (3) patient appeals of their health care denials to internal and external independent review panels of medical experts, and (4) direct access of women to OB/GYNs and related primary care specialist providers without prior approval. On balance, implementing these rights would involve utilization of additional resources and raise HMO costs further. This would add to the recent increases in the PPI of specialist doctors and the resurgence of the growth in hospital costs reflecting retreats from tightly managed care and labor shortages (Strunk, Ginsburg, and Gabel 2001).

Finally, cost implications for multiproduct HMOs currently offering or anticipating an exit from the Medicare HMO markets are multidimensional. They include more intense competition among provider plans, rising substitution of the more cost-effective pharmaceutical treatments for expensive hospital care in many plans, and the expected increase in the compliance and monitoring costs of new rules for participating in Medicare HMO contracts. HMOs also operate with scope diseconomies and had nearly exhausted scale economies in 1997. Consequently, a broadened access to specialist providers in Medicare HMOs is likely to be cost-increasing, although Medicare HMOs traditionally reduced both the probability of hospitalization and the number of inpatient days when hospitalized (Mello, Stearns, and Norton 2002). Due to the inelastic factor demands, the somewhat sharply curved isoquant shapes detected in this study, and the input factor markets (e.g., hospitals, doctors, and possibly drugs) becoming less competitive thro ugh failures, mergers, and acquisitions (Feldman, Wholey, and Christianson 1996; Baker and Brown 1999; Okunade and Aronoff 2000), the cost-saving factor substitution tendencies are further predicted to become more limited when servicing Medicare HMO risk contracts in multiproduct HMOs in the absence of scale and scope economies.

Suggestions for insightful future research on HMO costs include (1) a richer analysis of more recent operational data (e.g., for capturing the potential cost-saving roles of alternative, auxiliary providers such as RNs [Merisalo l998] (9) and PAs versus the GPs when they become available); (2) investigating the relative cost efficiencies of established HMOs and the contending and rapidly growing PPOs; and (3) using more recent data for estimating multiproduct, generalized, flexible frontier cost models to assess provider-specific deviations from the cost efficiency frontier. (10) Finally, (4) a national sample or census of HMOs consisting of longer time-series and larger observations on Medicare, Medicaid, and private commercial products could yield improved estimates of economies of scope, scale economies, pairwise factor relationships, decomposed technical change effects, and other important attributes of the production technology structure in multiproduct HMOs. A timely assessment of the regulatory ineffic iencies in Medicare managed care plans is especially vital, as about 30% of the 38 million Medicare population is expected to enroll in managed Medicare HMOs (or other plans) in 2005. However, the profit margins of Medicare HMOs are likely to dwindle further as the Medicare program continues to mandate additional benefits (11) and cut provider payments (e.g., switch from FFS-based to HMO cost-based payments) at the same time when the pool of favorable risks from FFS Medicare is shrinking (Feldman and Given 1998).

Appendix

Summary of Published Econometric Cost Studies of HMO Production,
1980-1996


Study (Year)              Data and Study Methodology

Bothwell and Cooley       Firm-level, 1976 and 1977
(1980)                     sample of 106 quarterly
                           data from 20 (U.S.) federally
                           qualified staff and group
                           model HMOs, ranging in size
                           from 1131 to 37,000 members;
                           four input, two-output
                           translog total cost function
                           model (controlling for time
                           operation), estimated using
                           the iterative Zeliner joint
                           system estimation

Schlesinger, Blumenthal,  Firm-level, 1983 cross-section
 and Schlesinger (1986)    sample of from 80 and 173
                           investor-owned and private
                           not-for-profit HMOs, with
                           average enrollment of 42,000;
                           average revenue and cost
                           regressions on hospital
                           charges, doctor charge,
                           clerical wage, total
                           enrollment, Medicare
                           enrollment, and other
                           controls (ownership type,
                           organizational form); OLS
                           method, linear functional
                           form model of federally
                           qualified HMOs

Wholey et al.             Firm-level, U.S. time-series
(1996)                     (1988-1991) HMO data (598
                           groups, 1094 IPAs); a five-
                           input, two-output translog
                           cost function system model
                           estimated using the Zellner
                           method; controlle for other
                           production cost influences
                           (e.g., affiliation with
                           national organizations,
                           proportion of enrollees in
                           Medicaid, geographic market
                           size, federally qualified
                           status, etc.)

Given                     Firm-level sample data (1986-1992)
 (1996b)                   of California HMOs; A four-input,
                           two-output translog total cost
                           model, estimated using the Zellner
                           system; controlled for other cost-
                           influencing attributes of HMOs
                           (e.g., HMO model type, time trend
                           proxy, number of competing HMOs in
                           geographic service area)







Study (Year)                   Economies of Scale

Bothwell and Cooley       Output-specific economies of
(1980)                     scale for all HMOs; Positive
                           overall economies of scale
                           for all except one HMO









Schlesinger, Blumenthal,  For profit plans averaged 10%
 and Schlesinger (1986)    higher cost than not-for-
                           profit plans, largely due to
                           ambulatory costs; increased
                           plan size cut the average
                           total cost per enrollee due
                           to reduced administrative
                           and ambulatory costs









Wholey et al.             Scale economies are
(1996)                     exhausted at about 50,000
                           enrollees (group, IPA)












Given                     Economies of scale strongly
 (1996b)                   justify the mergers for small
                           HMOs (<115,000 enrollees)












                          Scope                 Pairwise Factor
Study (Year)              Economies              Substitutions

Bothwell and Cooley       No                        Yes (a)
(1980)











Schlesinger, Blumenthal,  No                          No
 and Schlesinger (1986)















Wholey et al.             Scope diseconomies          No
(1996)                     in production of
                           non-Medicare and
                           Medicare products











Given                     Diseconomies of             No
 (1996b)                   scope (all output
                           pairs) in
                           commercial,
                           Medi-Cal, and
                           Medicare enrollees;
                           scope
                           diseconomies
                           are largest in
                           the joint
                           production of
                           Medicare and
                           commercial
                           product

(a) Because the Bothwell--Cooley (1980) data set rejected a homothetic
production structure hypothesis and because their cost specification
included five inputs, their sole reliance on the conceptually flawed
Allen--Uzawa scheme for computing the elasticities of substitution
(Blackorby and Russell 1989) is erroneous. Moreover, the subsitution
elasticities in Bothwell and Cooley (Table IV, p. 983) are averages for
all HMOs for which estimates satisfy the concavity conditions in each of
the three time periods. (The excluded HMOs were not identified.)
Nonetheless, Bothwell and Cooley reported Allen--Uzawa elasticity
estimates showing that (1) the own-price demand elasticities are
inelastic for all inputs (administrative labor the least elastic), (2)
administrative labor complements all other inputs, (3) hospital service
and medical staff services are substitutes, (4) hospital services and
health center services are substitutes, (5) medical staff services and
health center services are substitutes.

Table 1a

Own-and Cross-Price Elasticities of Factor Demands in HMO Production
(1988-1991 Data) Computed Using Wholey et al.'s (1996) Translog Cost
Model Parameter Estimates (a)

                    [w.sub.1] (b)        [w.sub.2]
                  (Non-Medicare        (Non-Medicare
               Inpatient Per Diem)    Physician Index)

[w.sub.1]
  Groups (SE)        -0.706                0.1268
                     (0.064) *** (d)      (0.061) **
  IPAs (SE)          -0.720                0.084
                     (0.035) ***          (0.036) **

[w.sub.2]
  Groups (SE)         0.0713              -0.532
                     (0.034) **           (0.106) ***
  IPAs (SE)           0.0571              -0.6412
                     (0.024) **           (0.078) ***
[w.sub.3]
  Groups (SE)           0 (c)                0 (c)

  IPAs (SE)             0 (c)                0 (c)


[w.sub.4]
  Groups (SE)           0 (c)                0 (c)

  IPAs (SE)             0 (c)                0 (c)


[w.sub.5]
  Groups (SE)         0.007                0.018
                     (0.07)               (0.238)
  IPAs (SE)           0.016                0.033
                     (0.036)              (0.112)

                    [w.sub.3]          [w.sub.4]         [w.sub.5]
               (Medicare Inpatient     (Medicare      (Administrative
                    Per Diem)       Physician Index)   Hourly Wages)

[w.sub.1]
  Groups (SE)           0 (c)              0 (c)           0.0052
                                                          (0.056)
  IPAs (SE)             0 (c)              0 (c)           0.0172
                                                          (0.038)

[w.sub.2]
  Groups (SE)           0 (c)              0 (c)           0.0081
                                                          (0.104)
  IPAs (SE)             0 (c)              0 (c)           0.0243
                                                          (0.079)
[w.sub.3]
  Groups (SE)        -0.724              0.0001           -0.0159
                     (0.68)             (0.567)           (0.906)
  IPAs (SE)          -0.252             -0.0002           -0.0251
                     (0.417)            (0.381)           (0.667)

[w.sub.4]
  Groups (SE)        0.0001              -0.697           -0.016
                     (0.507)            (1.421)           (1.563)
  IPAs (SE)          -0.0001             -0.355           -0.012
                     (0.476)            (1.508)           (1.81)

[w.sub.5]
  Groups (SE)        -0.0013            -0.0015           -0.5138
                     (0.073)            (0.141)           (0.217) **
  IPAs (SE)          -0.0013            -0.0005           -0.562
                     (0.034)            (0.075)           (0.102) ***

(a) HMOs are assumed to produce a mix of Medicare ([Y.sub.1]) and
non-Medicare member months ([Y.sub.2]), using five major inputs
([Q.sub.1],[Q.sub.2], ....,[Q.sub.5]), Medicare inpatient days, Medicare
physician visits, non-Medicare impatient days, non-Medicare physician
visits, and administrative hours. The fitted cost shares of these inputs
in groups [IPA] HMOs are [w.sub.1] = 0.27 [0.28], [w.sub.2] = 0.48
[0.41], [w.sub.3] = 0.017 [0.015], [w.sub.4] = 0.019 [0.012], [w.sub.5]
= 0.21 [0.29].

(b) [w.sub.1] = non-Medicare hospital (inpatient) price, [w.sub.2] =
non-Medicare physician (outpatient) price, [w.sub.3] = Medicare hospital
(inpatient) price, [w.sub.4] = Medicare physician (outpatient) price,
[w.sub.5] = health personnel administrative services price.

(c) Wholey et al. (1996, p. 666) constrained second-order (i.e.,
interaction) terms between input wages of Medicare and non-Medicare
health care services to be zero (regardless of organization form)
because non-Medicare and Medicare enrollees are "mutually exclusive."
Therefore, the implied cross-price demand elasticities become
essentially zero.

(d) Statistical significance at the 0.01, 0.05, and 0.10 levels are
indicated as ***, **, and *, respectively.

Table 1b

Own- and Cross-Price Elasticities of Factor Demands in HMO Production
(1986-1992) Computed Using Given's (1996b) Translog Cost Model Parameter
Estimates (a)

                        [w.sub.1] (b)       [w.sub.2]
                        (Price of         (Professional
                    Hospital Services)    Inputs Price)

[w.sub.1] (SE) (c)    -0.915 (0.207) ***   0.296 (0.168) *
[w.sub.2] (SE)         0.173 (0.098) *    -0.668 (0.141) ***
[w.sub.5] (SE)        -0.015 (0.294)       0.0063 (0.35)
[w.sub.6]              0.0008 (d)         -0.0012 (d)

                       [w.sub.5]         [w.sub.6]
                    (Administrative    (Capital and
                     Labor Price)    Facilities Price)

[w.sub.1] (SE) (c)  -0.0078 (0.159)       0.00009 (d)
[w.sub.2] (SE)       0.0020 (0.110)      -0.00008 (d)
[w.sub.5] (SE)       0.129 (0.475)        0.00021 (d)
[w.sub.6]            0.001 (d)           -0.5125 (d)

(a) HMOs aare assumed to produce a mix of Medicare ([Y.sub.1]) and
Medi-Cal ([Y.sub.2]), and commercial ([Y.sub.3]) member months, using
four major inputs ([Q.sub.1], [Q.sub.2], [Q.sub.3], [Q.sub.4]), hospital
services, professional office visit inputs, administrative labor
(secretarial and other clerical) and capital and facilities. The fitted
translog cost shares of factor inputs are [w.sub.1] = 0.30, [w.sub.2] =
0.51, [w.sub.5] = 0.16, [w.sub.6] = 0.038.

(b) [w.sub.1] = hospital (inpatient services price, [w.sub.2] = average
price per primary care (outpatient) office visit, [w.sub.5] = index for
secretarial and other clerical hourly wages, [w.sub.6] = average
rental/other cost per square foot of general office space.

(c) Statistical significance at the 0.01, 0.05, and 0.10 levels are
indicated as ***, **, and *, respectively.

(d) Unable to compute approximate standard errors for factor demands and
substitution elasticities involving [w.sub.6] because the needed
translog cost regression model standard errors of the first- and
second-order input coefficients involving "capital and facilities" are
unavailable in Given (1996b). See text footnote 8 for the formula used
for obtaining the approximate standard errors of the elasticities.

Table 1c

Own- and cross-price elasticities of factor demands in HMO Production
(1976 Quarter 1-1977 Quarter 4 Data) Computed Using the
Bothwell-Cooley's (1980) Translog Cost Model Parameter Estimates (a)

                       [w.sub.5]           [w.sub.2]
                    (Administrative        (Hospital
                    Services Price)     Services Price)

[w.sub.5] (SE) (c)  0.0017 (0.008)       0.001 (0.01)
[w.sub.2] (SE)      0.0058 (0.031)      -0.018 (0.068)
[w.sub.3] (SE)      0.1870 (0.013) ***   0.037 (0.018) **
[w.sub.6] (SE)      0.1996 (0.011) *     0.022 (0.011) **

                          [w.sub.3]            [w.sub.6]
                    (Medical Professional   (Health Center
                    Staff Services Price)   Services Price)

[w.sub.5] (SE) (c)     -0.109  (0.008) ***   0.139  (0.007) ***
[w.sub.2] (SE)         -0.126  (0.061) **   -0.090  (0.045) **
[w.sub.3] (SE)         -0.718  (0.002) ***   0.1823 (0.013) ***
[w.sub.6] (SE)         -0.1523 (0.011) ***  -0.239  (0.019) ***

(a) HMOs are assumed to transform four major inputs, [Q.sub.1]
(administrative services), [Q.sub.2] (hospital services), [Q.sub.3]
(medical professional staff services), and [Q.sub.4] (health center
services hospital services), into three intermediate outputs, [Y.sub.1]
(ambulatory encounters with physicians), [Y.sub.2] (ambulatory
encounters with allied health care professionals), and [Y.sub.2]
(hospital discharges). The fitted translog factor cost shares are
[w.sub.1] = 0.778, [w.sub.5] = 0.133, [w.sub.3] = -0.452, and [w.sub.6]
= 0.541.

(b) [w.sub.5] = health plan administration expense per member month,
[w.sub.2] = hospitalization expense per hospital day, [w.sub.3] =
(medical group expense for direct service and outside referrals +
special services expense)/full-time equivalent medical care personnel,
including physicians, physician extenders.

(c) Statistical significance at the 0.01, 0.05, and 0.10 levels are
indicated as ***, **, and *, respectively.

Table 2a

Allen-Uzawa Partial Elasticities of Substitution in HMO Production
(1988-1991 Data) Computed Using Wholey et al.'s (1996) Translog Cost
Model Parameter Estimates (a)

                 [w.sub.1] (b)          [w.sub.2]
                 (Non-Medicare        (Non-Medicare
              Inpatient Per Diem)    Physician Index)

[w.sub.1]
 Groups (SE)        -2.613                0.264
                    (0.238) *** (d)      (0.127) **
 IPAs (SE)          -2.572                0.205
                    (0.128) ***          (0.087) **
[w.sub.2]
 Groups (SE)                             -1.108
                                         (0.221) ***
 IPAs (SE)                               -1.564
                                         (0.189) ***
[w.sub.3]
 Groups (SE)

 IPAs (SE)

[w.sub.4]
 Groups (SE)

 IPAs (SE)

[w.sub.5]
 Groups (SE)

 IPAs (SE)


                   [w.sub.3]          [w.sub.4]         [w.sub.5]
                   (Medicare          (Medicare      (Administrative
              Inpatient Per Diem)  Physicial Index)   Hourly Wages)

[w.sub.1]
 Groups (SE)         0 (a)              0 (c)             0.025
                                                         (0.27)
 IPAs (SE)           0 (c)              0 (c)             0.058
                                                         (0.13)
[w.sub.2]
 Groups (SE)         0 (c)              0 (c)             0.038
                                                         (0.50)
 IPAs (SE)           0 (c)              0 (c)             0.081
                                                         (0.27)
[w.sub.3]
 Groups (SE)        -42.61               0.0063          -0.076
                    (40.07)            (29.85)           (4.314)
 IPAs (SE)          -16.79              -0.0018          -0.086
                    (27.8)             (31.72)           (2.30)
[w.sub.4]
 Groups (SE)          0.0001           -36.67            -0.078
                     (0.507)           (74.79)           (7.44)
 IPAs (SE)           -0.0001           -29.36            -0.042
                     (0.48)           (125.7)            (6.24)
[w.sub.5]
 Groups (SE)                                             -2.447
                                                         (1.04) **
 IPAs (SE)                                               -1.937
                                                         (0.353) ***

(a) Fitted cost shares of groups [IPAs] are [w.sub.1] = 0.27 [0.28],
[w.sub.2] = 0.48 [0.41], [w.sub.3] = 0.017 [0.015], [w.sub.4] = 0.019
[0.012], [w.sub.5] = 0.21 [0.29].

(b) [w.sub.1] = non-Medicare hospital (inpatient) price, [w.sub.2] =
non-Medicare physician (outpatient) price, [w.sub.3] = Medicare hospital
(inpatient) price, [w.sub.4] = Medicare physician (outpatient) price,
[w.sub.5] = health personnel administrative services price.

(c) Wholey et al. (1996, p. 666) constrained second-order (interaction)
terms between input wages of Medicare and non-Medicare health care
services to be zero for groups and IPAs because non-Medicare and
Medicare enrollees are "mutually exclusive" groups. The implied factor
substitution elasticities thus become essentially zero.

(d) Statistical significance at the 0.01, 0.05, and 0.10 levels are
indicated as ***, **, and *, respectively.

Table 2b

Allen-Uzawa Partial Elasticities of Substitution in HMO Production
(1986-1992 Data) Computed Using Given's (1996b) Translog Cost Model
Parameter Estimates (a)

                     [w.sub.1] (b)        [w.sub.2]
                       (Hospital        (Professional
                    Services Price)     Inputs Price)

[w.sub.1] (SE) (c)   -3.081 (0.70) ***   0.581 (0.33) *
[w.sub.2] (SE)                          -1.311 (0.28) ***
[w.sub.5] (SE)
[w.sub.6] (SE)

                    [w.sub.5]            [w.sub.6]
                    (Administrative    (Capital and
                    Labor Price)     Facilities Price)

[w.sub.1] (SE) (c)  -0.049 (1.00)           0.0027 (d)
[w.sub.2] (SE)       0.012 (0.69)          -0.0024 (d)
[w.sub.5] (SE)       0.805 (2.97)           0.0062 (d)
[w.sub.6] (SE)                            -15.53 (d)

(abcd) See footnotes to Table 1b.

Table 2c

Allen-Uzawa Partial Elasticities of Substitution in HMO Production (1976
Quarter 1-1977 Quarter 4 Data) Computed Using the Bothwell--Cooley
(1980) Translog Cost Model Parameter Estimates (a)

                     [w.sub.5] (b)      [w.sub.2]
                    (Administrative     (Hospital

                    Services Price)  Services Price)
[w.sub.5] (SE) (c)   0.0021 (0.01)    0.0074 (0.039)
[w.sub.2] (SE)                       -0.131  (0.51)
[w.sub.3] (SE)
[w.sub.6] (SE)

                          [w.sub.3]           [w.sub.6]
                    (Medical Professionl   (Health Center

                    Staff Services Price)  Services Price)
[w.sub.5] (SE) (c)     0.2403 (0.017) ***   0.257 (0.014) ***
[w.sub.2] (SE)         0.279 (0.133) **     0.167 (0.083) **
[w.sub.3] (SE)         3.801 (0.005) ***    0.337 (0.025) ***
[w.sub.6] (SE)                             -0.4418 (0.034) ***

(abc) See notes to Table 1c.

Table 3a

Estimates of Morishima Elasticities of Substitution in HMO Production
(1988-1991) Groups Vesus IPAs, Computed Using Wholey et al.'s (1996)
Translog Cost Model (a)

              [w.sub.1] (b)        [w.sub.2]           [w.sub.3]
              (Non-Medicare      (Non-Medicare    (Medicare Inpatient
           Inpatient Per Diem)  Physician Index)       Per Diem)

[w.sub.1]
   Groups         0 (c)              0.659               0 (d)
   IPAs           0 (c)              0.725               0 (d)

[w.sub.2]
   Groups         0.777              0 (c)               0 (d)
   IPAs           0.777              0 (c)               0 (d)

[w.sub.3]
   Groups                                                0 (c)
   IPAs                                                  0 (c)

[w.sub.4]
   Groups         0 (d)              0 (d)               0.724
   IPAs           0 (d)              0 (d)               0.252

[w.sub.5]
   Groups         0.712              0.550               0.723
   IPAS           0.736              0.675               0.250

                [w.sub.4]          [w.sub.5]
           (Medicare Physician  (Administrative
                 Index)          Hourly Wages)

[w.sub.1]
   Groups         0 (d)              0.519
   IPAs           0 (d)              0.579

[w.sub.2]
   Groups         0 (d)              0.523
   IPAs           0 (d)              0.583

[w.sub.3]
   Groups         0.697              0.498
   IPAs           0.355              0.537

[w.sub.4]
   Groups         0 (c)              0.498
   IPAs           0 (c)              0.500

[w.sub.5]
   Groups         0.695              0 (c)
   IPAS           0.354              0 (c)

(a) Fitted cost shares of groups [IPAs] are [w.sub.1] = 0.27 [0.28],
[w.sub.2] = 0.48 [0.41], [w.sub.3] = 0.017 [0.015], [w.sub. 4] = 0.019
[0.012], [w.sub.5] = 0.21 [0.29].

(b) [w.sub.1] = non-Medicare hospital (inpatient) price, [w.sub.2] =
non-Medicare physician (outpatient) price, [w.sub.3] = Medicare hospital
(inpatient) price, [w.sub.4] = Medicare physician (outpatient) price,
[w.sub.5] = health personnel administrative services price.

(c) Conceptually, the Morishima own substitution elasiticities (i.e.,
diagnoal entries) are zero.

(d) Wholey et al. (1996, p. 666) constrained second-order (interaction)
terms between input wages of Medicare and non-Medicare health care
services to be zero for groups and IPAs because non- Medicare enrollees
are "mutually exclusive" groups. The implied factor substitution
elasticities thus become essentially zero.

Table 3b

Morishima Elasticities of Substitution in HMO Production (1988-1991
data) Computed Using Given's (1996b) Translog Cost Model Parameter
Estimates (a)

               [w.sub.1]         [w.sub.2]       [w.sub.5]
           (Price of Hospital  (Professional  (Administrative
               Services)       Inputs Price)   Labor Price)

[w.sub.1]          0               0.965          -0.137
[w.sub.2]        1.088               0            -0.127
[w.sub.5]        0.901             0.675             0
[w.sub.6]        0.916             0.667          -0.128

               [w.sub.6]
             (Capital and
           Facilities Price)

[w.sub.1]       0.5125
[w.sub.2]       0.5124
[w.sub.5]       0.5127
[w.sub.6]          0

(a) Conceptually, the Morishima own-substitution elasticities (i.e.,
diagnoal entries) are zero.

Table 3c

Morishima Elasticities of Substitution in HMO Production (1977 Quarter
1-1978 Quarter 4 Data) Computed Using the Bothwell-Cooley (1980)
Translog Cost Model Parameter Estimates (a)

              [w.sub.5]        [w.sub.2]           [w.sub.3]
           (Administrative     (Hospital     (Medical Professional
           Services price)  Services Price)  Staff Services Price)

[w.sub.5]         0             0.0184               1.609
[w.sub.2]      0.0041             0                  1.591
[w.sub.3]      0.185            0.545                  0
[w.sub.6]      0.198            0.0395               1.565

              [w.sub.6]
           (Health Center
           Services Price)

[w.sub.5]      0.378
[w.sub.2]      0.3292
[w.sub.3]      0.4213
[w.sub.6]         0

(a) Conceptually, the Morishima own substitution elasticities (i.e.,
diagonal entries) are zero.

Table 4a

Shadow Elasticities of Substitution in HMO Production (1988--1991 Data)
Computed Using Wholey et al.'s (1996) Translog Cost Model Parameter
Estimates (a)

           [w.sub.1] (b)    [w.sub.2]    [w.sub.3]  [w.sub.4]
           (Non-Medicare  (Non-Medicare  (Medicare  (Medicare
            Inpatient       Physician    Inpatient  Physician
             Per Diem)       Index)      Per Diem)   Index)

[w.sub.1]
  Groups       0 (c)          0.041        0 (d)      0 (d)
  IPAS         0 (c)          0.037        0 (d)      0 (d)

[w.sub.2]
  Groups                      0 (d)        0 (d)      0 (d)
  IPAs                        0 (d)        0 (d)      0 (d)

[w.sub.3]
  Groups                                   0 (c)     0.00013
  IPAs                                     0 (c)     0.00014

[w.sub.4]
  Groups                                              0 (c)
  IPAs                                                0 (c)

[w.sub.5]
  Groups
  IPAs

              [w.sub.5]
           (Administrative
               Hourly
               Wages)

[w.sub.1]
  Groups        0.023
  IPAS          0.031

[w.sub.2]
  Groups        0.040
  IPAs          0.046

[w.sub.3]
  Groups        0.000
  IPAs          0.001

[w.sub.4]
  Groups       0.0005
  IPAs         0.0004

[w.sub.5]
  Groups        0 (c)
  IPAs          0 (c)

(abd) See corresponding footnotes to Table 3a.

(c) Conceptually, the shadow own-substitution elasticities are zero.

Table 4b

Shadow Elasticities of Substitution in HMO Production (1988-1991 Data)
Computed Using Given's (1996b) Translog Cost Model Parameter Estimates
(a)

               [w.sub.1]         [w.sub.2]       [w.sub.5]
               (Price of       (Professional  (Administrative
           Hospital Services)  Inputs Price)   Labor Price)

[w.sub.1]          0               0.034           0.048
[w.sub.2]                            0             0.229
[w.sub.5]                                            0
[w.sub.6]

               [w.sub.6]
             (Capital and
           Facilities Price)

[w.sub.1]       0.0016
[w.sub.2]       0.0018
[w.sub.5]       0.0019
[w.sub.6]          0

(a) Conceptually, the shadow own-substitution elasticities (i.e.,
diagonal entries) are zero.

Table 4c

Shadow Elasticities of Substitution in HMO Production (1977 Quarter
1-1978 Quarter 4) Computed Using the Bothwell--Cooley (1980) Translog
Cost Model Parameter Estimats (a)

              [w.sub.5]     [w.sub.2]        [w.sub.3]
           (Administrative  (Hospital  (Medical Professional
              Services      Services           Staff
               Price)        Price)       Services Price

[w.sub.5]         0           0.792            0.325
[w.sub.2]                       0             -0.061
[w.sub.3]                                        0
[w.sub.4]

             [w.sub.6]
           (Health Center
              Services
               Price)

[w.sub.5]      0.335
[w.sub.2]      0.118
[w.sub.3]      1.024
[w.sub.4]        0

(a) Conceptually, the shadow own-substitution elasticites (i.e.,
diagonal entries) are zero.

Received August 1999; accepted February 2002.

(1.) Medicare and Medicaid are, respectively, government-sponsored health insurance programs for seniors and the poor. Medicaid managed care has strengthened in those demonstration states approved by the Health Care Financing Administration (Holahan et al. 1998; Okunade 1998). However. Medicare managed care only succeeded momentarily in selected markets because of cost savings from favorable selection. Medicare is the largest payer in the U.S. health care system, absorbing roughly 12% of the federal budget and 20% of all health care costs in 1999 (McClellan 2000). Since its 1965 inception, Medicare has allowed participants to enroll in HMOs. The rapid growth in Medicare HMO enrollment began with the 1985 implementation of the legislative changes under the Tax Equity and Fiscal Responsibility Act (or TEFRA) of 1982 (Blumberg and Evans 1998). These changes provided incentives for HMOs to enter into risk contracts with Medicare. Consequently, the roughly 4.0% Medicare risk plan enrollment as a percentage of tota l Medicare beneficiaries in 1992 rose to 11.7% in 1997 and was projected at 34.2% in 2007 (Lamphere et al. 1997). Medicare risk plans grew from 95 in 1990 to 241 in 1996. More recently, how. ever, many HMOs have dropped Medicare managed care coverage in counties where the adjusted average per capita cost, or AAPCC, failed to cover cost of care. During 1999, e.g., Humana, Inc., due to the rising medical expenses, embarked on benefit cuts, raised premiums, adopted a three-tier prescription drug benefit pricing for its Medicare HMOs for the year 2000, and reduced Medicare HMQ sales in 35 counties in order to retain only the profitable markets (Donaldson 1999). Currently, full implementation of the congressional health policy goals for Medicare Plus Choice plans is quite doubtful (http://www.cnn.com/HEALTH/9811/06/medicare.chaos/ accessed on February 1,2001). However, certain attractive features of managed Medicare, absent in traditional Medicare, such as expanded choices and prescription drug benefits, could sti ll make Medicare HMOs a good model of elderly health care in the future. Recent proposals to enhance the efficiencies of Medicare Plus Choice (M+C) plans often include financial incentives for the beneficiaries to select low-cost plans and competitive bidding among providers to establish payments or reimbursements to M+C plans (Thorpe and Atherly 2001).

(2.) Studies of HMO production cost economies omitted quantifying the potentials for cost savings, at constant output, from substituting among inputs (e.g., outpatient physician visits vs. in-hospital stays) due to a changed relative factor price. Past research on the economics of HMO activities implicitly hinted at the importance of the degree of pairwise factor substitutions. The conjectures of Wholey et al. (1997, pp. 79-81), Getzen (1997, p. 244), Hart et al. (1997, p. 68), Wholey et al. (1996, pp. 661, 666), Feldstein (1993, p. 326). and Henderson (1999), while highly suggestive, fall significantly short of yielding any estimates for potential cost-saving factor substitutions in HMOs.

(3.) In the United States, elderly persons are the largest per capita users of prescription medicines (Freund et at. 2000). on average, people age 50 in the United States who take six prescriptions a year will take 11 a year at age 60 and 15 a year at age 70. Prescription drugs also comprise the largest out-of-pocket expenses in elderly health care production. Traditional Medicare does not cover prescription drugs except when incidental to physician office visits. Some managed Medicare plans expanded prescription drug coverage and other benefits and consequently grew in popularity among the elderly. However, precise data on such benefits are not publicly available. Practically all of the health care production studies omitted pharmacy activities from consideration and, in the rare cases when data are available, pharmacy data are structured in ways that prevent their merging with other operational data. Consequently, researchers are unable to analyze pharmacy care inputs jointly with the other health care fact ors of production in a translog production cost econometric model that addresses input substitutions (Okunade 2001). However, an the elderly population grows and drug costs continue to soar unabated with the introduction and use of new, often more expensive drugs, the need to make publicly accessible the relevant data on drug utilization and costs is likely to gain rapid importance. This is because there are health policy implications, including access to drug insurance benefits coverage and cost control. President George W. Bush, in June 2001, proposed a voluntary private program to help Medicare beneficiaries obtain discounts on prescription drugs. In February 2003, a federal court issued an injunction barring implementation of this proposal.

(4.) One unpublished study (Born and Pacula 1998) utilized a single-output, four-intermediate input generalized translog cost methodology and 1991-1994 data of HMOs to investigate whether the cost savings achieved through enrollment growth and age of plan are shared with any of the factors of production. The authors, however, excluded from joint estimation the parent translog function with three of the factor share equations. The seemingly unrelated regressions estimates (SURE) were reported for the cost share equations of physician, other professional, and hospital. The parameter estimates of the input prices vary widely in magnitude, sign, and statistical significance across the factor shares. Because the study also omitted from the system estimation equations the parent translog cost equation, the second-order parameter estimates for input wages (i.e., interaction terms among input prices) are missing. Moreover, the definition of HMO output in the Born-Pacula study is unidimensional and was measured as "the number of enrollees" when it is generally known that the HMOs are multiproduct entities. Therefore, in addition to the possible misspecification of the output, the Born-Pacula estimates lack the necessary information for computing the pairwise elasticities of factor substitutions in the HMOs. Finally, our study focuses on the HMO production cost studies published in peer-refereed economies journals. The Born-Pacula study is an unpublished working paper and is no longer in public circulation.

(5.) The asymptiotic standard errors (SE) of the own- ([[gamma].sub.ii]) and cross-price ([[gamma].sub.ij]) elasticity of factor demands and pairwise substitutions ([[sigma].sup.AU.sub.ii], [[sigma].sup.AU.sub.ij]) are, respectively, approximated using

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(6.) Changes in input factor demands can be decomposed into those due Co the levels of the output set, factor interchange along the isoquant, and technical progress. Cross-sectional data at constant output can only investigate factor substitutions along a given isoquant.

(7.) As is standard practice, one of the factor cost share equations in a translog cost model must be dropped in the estimation of the Zellner ISURE (iterative seemingly unrelated regressions). (The estimated system comprises the parent trassslog cost function and all but one of the factor cost share equations to add structural stability.) The system parameter estimates obtained are invariant to which share equation is deleted from the full system of equations. Given (1996b), e.g., dropped the "capital and facilities" (i.e., [w.sub.6]) share equation. To recover the first-order coefficient of [w.sub.6], I appealed to the standard theoretical restriction of homogeneity of degree one in input prices ([SIGMA][[alpha].sub.i] = 1) condition. Dr. Given kindly supplied the translog cost estimates of the second-order interaction terms among inputs (excluding [w.sub.6] that was omitted from econometric estimation because Table 3, p. 700, in her published paper excluded them). Parameter estimates of the second-order in teractions of [w.sub.6] with the other inputs were also recovered by appealing to the translog symmetry conditions ([summation over (i)] [[beta].sub.ji] = [summation over (j)] [[beta].sub.ji] = [SIGMA] [summation over (ij)] [[beta].sub.ji] = 0. These recoveries enabled me to compute the full matrix estimates of factor demands and substitution elasticities arrayed here in Tables 1b, 2b, 3b, and 4b.

(8.) The [[sigma].sup.AU] estimates also permit hypothesis testing of the existence of a consistent aggregation index for the labor inputs (e.g., physician and administrative).

(9.) Hospitals arc no longer the sole employers of registered nurses (RNs); the diversifying economy ushered in alternative employment opportunities and managed care expansion fueled massive consolidations and mergers in the health care industry. Cost-cutting hospitals largely replaced nurses with less expensive auxiliaries, such as nursing assistants (NAs) and medical technologists (MTs). However, this may not generate long-term cost savings. Industry analysts observe that the recent increases in RN staffing in some hospitals are starting to save hospital costs. This they attribute partly to higher patient satisfaction with licensed health caregivers compared with their less trained substitutes. There are wide variations in the hiring and displacement of trained nurses among providers nationally. However, RN staffing is rising in mature managed care markets, as surveys tie patients' view of quality care to the presence of trained nurses (Merisalo 1998).

(10.) Technical change is one of the significant long-run drivers of health care cost (Okunade and Murthy 2002). Thus, future timeseries models ought to explicitly include a measure for the pace of technological change in managed care designs in order to yield deeper insights into the relative efficiencies and the shape of technical progress in different types of managed care.

(11.) On June 30, 1998, for instance, Medicare announced the addition of new benefits effective July 1, 1998 (e.g., osteoporosis screening and diabetes management such as glucose monitors, testing strips, lancets for enrollees who previously managed this disease through noninsulin therapies such as exercise, diet, or oral medications). Roughly 12% of the 38 million Americans eligible for Medicare are diabetics. Subject to the standard deductibles and copayments, these services will likely be standard benefits for managed Medicare enrollees. On June 29, 1999. U.S. President Clinton (D) proposed to extend prescription drug coverage to Medicare program enrollees, essentially making traditional Medicare compete with managed Medicare plans that have integrated low-cost drug coverage into their managed care offerings. The elderly "prescription discount card," recently proposed by the 43rd U.S. President George W. Bush (R), is a more market-based, modified version of the Clinton plan. During February 2003. opponents of this proposal won a federal court injunction against its implementation.

References

American Benefits Council. 2001. Summary of H.R. 2563, "The Bipartisan Patient Protection Act" as passed by the House of Representatives on August 2, 2001. Accessed on December 7, 2001. Available http://www.americanbenefitscouncil.org/documents/summary_hr2563.pdf.

Baker, Laurence C., and Martin L. Brown. 1999. Managed care, consolidation among health care providers, and health care: Evidence from mammography. RAND Journal of Economics 30:351-74.

Blackorby, Charles, and Robert R. Russell. 1989. Will the real elasticity of substitution please stand up? (A comparison of the Allen/Uzawa and Morishima elasticities). American Economic Review 79:882-8.

Blumberg, Linda J., and Alison Evans. 1998. Reform of the Medicare AAPCC: Learning from previous proposals. Inquiry 35:62-77.

Born, Patricia, and Rosalie Pacula. 1998. Does HMO spending on medical services change as HMOs grow and mature? NBER Working Paper No. 6423.

Bothwell, James L., and Thomas F. Cooley. 1980. Efficiency in the provision of health care: An analysis of health maintenance organizations. Southern Economic Journal 47:970-84.

Cowing, Thomas, and Alphonse Holtmann. 1983. A multiproduct short-run hospital cost functions: Empirical evidence and policy implications from cross-sectional data. Southern Economic Journal 49:637-53.

Davis, George C., and Jean Gauger. 1996. Measuring substitution in money-asset demand systems. Journal of Business and Economic Statistics 14:203-8.

Donaldson, G. 1999. Humans says higher medical costs hit profits; will hack off Medicare HMO sales. Managed Core Week 9:1.

Eastaugh, Steven R. 1990. Hospital nursing technical efficiency: Nurse extenders and enhanced productivity. Hospital and Health Services Administration 25:561-73.

Escarce, Jose J., and Mark V. Pauly. 1998. Physician opportunity costs in physician practice cost functions. Journal of Health Economics 17:129-51.

Etheredge, Lynn, Stanley B. Jones, and Lawrence Lewin. 1996. What is driving health system change? Health Affairs 15: 93-104.

Feldman, Roger, and Ruth S. Given. 1998. HMO mergers and Medicare: The antitrust issues. Health Economics 7:171-4.

Feldman, Roger, Douglas Wholey, and Jon Christianson. 1996. Economic and organizational determinants of HMO mergers and failures. Inquiry 33:118-32.

Feldstein, Paul J. 1993. Health care economics. 5th edition. New York: Delmar.

Fleissig, Adrian R. 1997. The dynamic Laurent flexible form and the demand for money. Journal of Applied Econometrics 12:687-99.

Flood, Ann Barry, Allen M. Fremont, Kinam Jin, David M. Bott, Jiao Ding, and Robert C. Parker, Jr. 1998. How do HMOs achieve cost savings? The effectiveness of one organization's strategies. Health Services Research 33:79-99.

Fox, Peter D. 1997. Applying managed care techniques in traditional Medicare. Health Affairs 16:44-57.

Freund, Deborah A., Don Willison, Grant Reeher, Jarod Cosby, Amy Ferraro, and Bemie O'Brien. 2000. Outpatient pharmaceuticals and the elderly: Policies in seven nations. Update. Health Affairs 19:259-656

Getzen, Thomas E. 1997. Health economics: Fundamentals and flow of funds. New York: John Wiley & Sons.

Given, Ruth S. 1996a. Ensuring competition in the market for managed care. In Competitive managed care, edited by J. D. Wilkerson, K. Devers, and R. S. Given. San Francisco, CA: Jossey-Bass, Ch. 8.

Given, Ruth S. 1996b. Economies of scale and scope as an explanation of merger and output diversification activities in the health maintenance organization industry. Journal of Health Economics 15:685-713.

Hamermesh, Daniel S., and Albert Rees. 1988. The economics of work and pay. New York: Harper & Row.

Hart, L. Gary, Edward Wagner, Sarmad Pirzada, Andrew F. Nelson, and Roger Rosenblatt. 1997. Physician staffing ratios in staff-model HMOs: A cautionary tale. Health Affairs 21:55-70.

Henderson, James. 1999. Health economics and policy. Cincinnati, OH: Southwestern.

Holahan, John, Stephen Zuckerman, Alison Evans, and Suresh Rangarajan. 1998. Medicaid managed care in thirteen states. Health Affairs 17:43-63.

Kongstvedt, Peter R. 199?. Essentials of managed care. Gaithersburg, MD: Aspen.

Lamphere, Jo Ann, Patricia Neuman, Kathryn Langwell, and Daniel Sherman. 1997. The surge in Medicare managed care: An update. Health Affairs 16:127-33.

McClellan, Mark. 2000. Medicare reform: Fundamental problems, incremental steps. Journal of Economic Perspectives 14:21-44.

McFadden, D. 1963. Further results on CES production. Review of Economic Studies 30:73-83.

Mello, Michelle M., Sally C. Steams, and Edward C. Norton. 2002. Do Medicare HMOs still reduce health services use after controlling for selection bias? Health Economics 11:323-40.

Merisalo, Laura J. 1998. The managed care payment advisor. Capitation and alternative compensation methods. Gaithersburg, MD: Aspen.

Miller, Robert H., and Harold S. Luft. 1997. Does managed care lead to better or worse quality of care? Health Affairs 16:7-25.

Mundlak, Yair. 1968. Elasticities of substitution and she theory of derived demand. Review of Economic Studies 35:225-36.

Nicholson, Walter. 1998. Microeconomic theory. Basic principles and extensions. 7th edition. Fort Worth, TX: Dryden Press.

Okunade, Albert A. 1993. Production Cost structure of US hospital pharmacies: Time-series, cross-sectional bed size evidence. Journal of Applied Econometrics 8:277-94.

Okunade, Albert A. 1998. Financing structure dynamics and other determinants of Medicaid pharmaceutical expenditures, 1993-996. Journal of Health Care Finance 25:59-71.

Okunade, Albert A. 1999. Will the real elasticity of substitution 'in Norwegian dentistry' please stand up? Health Economics 8:221-32.

Okunade, Albert A. 2001. Cost-output relation, technological progress, and clinical activity mix of US hospital pharmacies. Journal of Productivity Analysis 16:167-93.

Okunade, Albert A., and Aronoff, J. B. 2000. Determinants of specialty physician practice management integration. Managed Care Quarterly 8:61-71.

Okunade, Albert A., and V. N. R. Murthy. 2002. Technology as a 'major driver' of health care costs: A cointegration analysis of the Newhouse conjecture. Journal of Health Economics 21:147-59.

Okunade, Albert A., and Chutima Suraratdecha. 1998. Cost efficiency, factor interchange, and technical progress in US hospital pharmacies. Health Economics 7:363-71.

Riportella-Muller, Roberta, Donald Libby. and David Kindig. 1995. The substitution of physician assistants and nurse practitioners for physician residents in teaching hospitals. Health Affairs 14:181-91.

Sachs, Michael A. 1997. Managed care: The next generation. FRONTIERS of Health: Services Management 14:3-27.

Schlesinger, Mark, David Blumenthal, and Eric Schlesinger. 1986. Profits under pressure: The economic performance of investor-owned and nonprofit health maintenance organizations. Medical Care 24:615-27.

Segerson, Kathleen, and Subhash C. Ray. 1989. On the equivalence of alternative measures of the elasticity of substitution. Bulletin of Economic Research 41:207-21.

Strunk, Bradley C., Paul B. Ginsburg, and Jon R. Gabel. 2001. Tracking health care costs. Health Affairs 20. Available at http:// www.healthaffairs.org/.

Thorpe, Kenneth, and Adam Atherly. 2001. Reforming Medicare: Impacts of federal spending and choice of health plans. Health Affairs 20. Available at http://www.healthaffairs.org/.

Wholey, Douglas, Jon B. Christianson, John Engberg, and C. Bryce. 1997. HMO market structure and performance: 1985-1995. Health Affairs 16:75-84.

Wholey, Douglas, Roger Feldman, Jon B. Christianson, and John Engberg. 1996. Scale and scope economies among health maintenance organizations. Journal of Health Economics 15:657-84.

Zellner, Arnold J. 1962. An efficient method for estimating seemingly unrelated regressions and tests for aggregation bias. Journal of tire American Statistical Association 57:585-612.

Zelver, N. 1998. Health care price index. Update air monthly price changes hr medical care. Bozeman, MT: Price Index Communications.

Albert A. Okunade *

* Department of Economics, Room 450BB (The FCBE), Campus Box 526458, The University of Memphis, Memphis, TN 38152, USA; E-mail [e-mail].

The author is very grateful to Ruth S. Given, Arie Kapteyn, Joseph P. Newhouse, two anonymous referees, Kathy J. Hayes, the other editors of this journal, and many other individuals for their challenging discussions, careful readings, and critical comments on earlier drafts. He acknowledges partial funding for this work by The Fogelman Research Fund, a U.S. Department of Education research grant (P220A30035) at The Wang Center for International Business and Economic Research and a University of Memphis Faculty research grant. However, the author assumes full responsibility for any remaining errors. Portions of this revised work were undertaken during the author's research faculty sabbatical at Harvard School of Public Health in Boston, Massachusetts.