THE THEORY OF HOSPITAL MERGERS: MULTIPRODUCT SCOPE AND SCALE ECONOMIES
The impact of the prospective Payment System (PPS) and increased patient enrollment in HMOs and PPOs placed great pressures on hospitals for discounts. An increase in the number of hospitals involved in a merger suggests that merging is a way to become more efficient in health care delivery by coordinating services properly and allocating resources efficiently by eliminating waste and redundancies.
This study presents a theoretical framework and empirical analysis to test the existence of multiproduct scope and scale economies prior to the merger, one year after the merger and two years after the merger.
Using a hybrid translog cost function, merged hospitals along with control group hospitals are examined in two merger episodes; 1987-1988 and 1989- 1990. The control group hospitals are matched to merged hospitals with respect to their location, size, services provided and their system status in order to secure the study against a structural change in the market.
The first merger episode which includes hospitals involved in a merger in 1987 and 1988 display diseconomies of scale when the hybrid translog cost function is evaluated at variable means. On the other hand, the 1989-1990 mergers reveal the presence of ray economies of scale prior to the merger due to the differences in the relative size of hospitals contained in two samples. Past studies indicate that diseconomies are more likely to occur among large hospitals. Following the merger, merged hospitals show a worsening ray economies of scale while struggling to manage their labor and supply costs in both periods. Interestingly, they improve their ray economies of scale drastically twoyears after the merger which indicates that oneyear after the merger is not sufficient to achieve operational efficiencies. The control hospitals demonstrate stabilized scale and scope economies throughout the study which suggests that these hospitals are in long-run equilibrium. Finally, significant scope economies among different pairs of hospital services are found when the demand is weak for hospital services; otherwise, all scope economies detected are insignificant.
I am indebted to Mr. Allan Halfer, corporate Director, strategic Planning of the SSM Health Care System for his interest andsupport of this project and for his help in using the AHA data set.
I also would like to thank the members of my committee for their helpful comments, patience and encouragement. I especially benefitted a great deal from discussions with Prof. Campbell and Prof. Welch.
List of Tables……………………………………….v
Literature Review . . . . . . . . . . . . 8
Empirical Results: 1987-1988 Mergers •••.••• 51
Empirical Results: 1989-1990 Mergers••••••• 85
Appendix I •• e e e e e e e e • • e e e e e e • e • • • • • • e • • e • e e e • D •
Biography of the Author. …………………..
Table Table Table Table Table
Table Table Table Table Table Table
1: summary of Literature Review••••••••••••• 23 2: Anticipated Results, Pre-Merger Period ••• 40 3: Expected outcomes•••••••••••••••••••••••• 49
4: Descriptive statistics (1986-1987) ••••••• 51
5: Estimated Cost Function Parameters (1986
-1987) ..••••………••……………… 53
6:Ray Economies of scale (1986-1987) ••••••• 57
7: Estimated Scope Economies (1986-1987) •••• 58
8: Marginal Cost Estimates (1986-1987) •••••• 59
9: Estimated Price Elasticities (1986-1987). 61
10: Descriptive Statistics (1988-1989) ••••••• 62
11: Estimated Cost Function Parameters (1988
-1989) …………•…………………. 65
Table 12: Ray Economies of Scale (1988-1989) ••••••• 66 Table 13: Comparative Statistics of Control
Table 14: Estimated Scope Economies (1988-1989) •••• 69
Table 15: Marginal Cost Estimates (1988-1989) •••••• 70
Table 16: Estimated Price Elasticities (1988-1989). 71 Table 17: Descriptive Statistics of Merged
Hospitals….. o•••••••••••••••••••••••••• 72
Table 18: Descriptive statistics of Control
Table 19: Estimated Cost Function Parameters (1989
-1990) …………………………….. 75
Table 20: Ray Economies of Scale (1989-1990) ••••••• 77
Table 21: Estimated Scope Economies (1989-1990) •••• 79
Table 22: Marginal Cost Estimates (1989-1990) •••••• 80
Table 23: Estimated Price Elasticities (1989-1990). 80 Table 24: summary of Ray Economies of Scale•••••••• 81 Table 25: Summary of Marginal Costs•••••••••••••••• 83 Table 26: Summary of Significant Scope Economies ••• 84
Table 27: Descriptive Statistics (1988-1989) ••••••• 87 Table 28: Estimated Cost Function Parameters (1988
-1989) .•…………………………… 88
Table 29: Ray Economies of Scale (1988-1989) ••••••• 89 Table 30: Comparative Statistics of Merged
Table 31: Distribution of Merging Hospitals by Bed
Table 32: Estimated Scope Economies (1988-1989) •••• 95 Table 33: Comparing Marginal Cost Estimates •••••••• 97
Table 34: Estimated Price Elasticities (1988-1989). 98 Table 35: Comparative Statistics of Merged
Table 36: Comparative Statistics of Control
Table 37: Estimated Cost Function Parameters (1990
-1991). -: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Table 51: Summary of Estimated Price Elasticities. 120
|Table||38:||Ray Economies of Scale (1990-1991) ••••••||104|
|Table||39:||Estimated Scope Economies (1990-1991) •••||105|
|Table||40:||Comparing Marginal Cost Estimates•••••••||107|
|Table||41:||Comparing Price Elasticities ••••••••••••||108|
|Table||42:||Comparative Statistics of Merger ••••••••||109|
|Table||43:||Comparative Statistics of Controls ••••••||110|
|Table||44:||Estimated Cost Function Parameters (1991
|Table||45:||Ray Economies of Scale (1991-1992) •••••• 113|
|Table||46:||Estimated Scope Economies (1991-1992) ••• 114|
|Table||47:||Comparing Marginal Cost Estimates ••••••• 115|
|Table||48:||Estimated Price Elasticities (1991-1992) 116|
|Table||49:||Summary of Ray Economies of Scale••••••• 117|
|Table||50:||Summary of Marginal Cost Estimates•••••• 118|
INTRODUC IOH Chapter I
The last twodecades have witnessed an increase in the number of hospitals involved in mergers and consolidations. However, current merger activity is likely to be different from merger activity in the 1970s. Since 1983, the impact of the Prospective Payment System (PPS) changed the reimbursement method from cost-based to case-based for Medicare recipients, and increased patient enrollment in HMOs and PPOs placed great pressures on hospitals for discounts. In a market characterized by increased price competition, the most efficient firms will survive and others either fail or become more efficient. One way to become more efficient may be through mergers and consolidations.
This study tests the hypothesis that hospital mergers in the 1980s reduced production costs by achieving economies of scope and scale, thereby allowing hospitals to become more efficient in order to ensure long-run survival. It focuses on the cost advantages of merged hospitals located in or around the same metropolitan areas, and tests for the presence of operational efficiency at the service level within the hospital. It is assumed that
merging hospitals achieve scope and scale economies within three years following the merger. The three year span allows merging hospitals to identify and implement a cost efficiency program, and achieve scale and scope economies. If there is no evidence of the presence of unexploited scale and scope economies prior to the merger or the exploitation of these economies in the following three years, then
it is concluded that there must be different motivations for hospital mergers, like increasing market share and gaining competitive advantage in local markets.
Scale inefficiencies in the hospital industry may result from: (1) too small a hospital or service size which does not fully exploit economies of scale: (2) too large a hospital size or service associated with underutilization of overcapitalized hospital services (Cowing and Holtmann, 1983). A merger can also achieve scope economies by increasing the number of hospital services provided after the merger. Utilizing the plant and equipment of merged hospitals for an increased number of services should certainly help achieve economies of scope. Mullner and Anderson (1987) reveal that small-sized hospitals are likely to be involved in such mergers. If a small-sized hospital that
provided a very low level of a particular service or services, like maternity care, merges with another small hospital that provides the same service, then the result may be the closing of one of the duplicative units, increasing the size of other unit (product-specific scale effect), andconverting the closed unit to a new service or services (scope effect). It is a fact that the number of services typically increase following the merger (Manheim, Shortell, and McFall, 1989).
Mullner and Anderson also point out that most mergers involve a large hospital acquiring a small size hospital. In the case of underutilization of overcapitalized services in one of the merging hospitals or both, which results in higher production costs, utilization can be improved by the demand of other hospital for those particular services, and an inefficient unit or units can be converted to a new service or services, or closed to eliminate diseconomies of scale. Scope economies can also be achieved in this type of merger by the increased number of services.
Hospitals involved in a merger or consolidation may be more able to provide a full range of services in the market following the merger. As a result, the
possibility of obtaining HMO and PPO contracts may increase the utilization of all services and achieve ray economies of scale and multiproduct scope economies associated with the range of services provided.
In this dissertation, mergers throughout the United States are examined during the period 1987-1990.
This time period is viewed as one of disequilibrium, with movement toward to a new equilibrium path due to increased market competition in the hospital industry. During this time period, approximately
202 hospitals were involved in a merger or
consolidation1 • In this study, the term “merger” is generally used to explain both merger and
consolidations 2• In addition, the proportion of
mergers among system-affiliated and for-profit hospitals was 53 and 15 percent, respectively. Between 1987 and 1990, 283 hospitals were also closed, which indicates the adaptation of hospitals to changing market conditions.
- The number of hospitals involved in a consolidation is 173 in comparison to 29 hospitals involved in a merger in the 1987-1990 period.
- If one of the hospitals merging becomes a legal part of the other, taking on the other hospital’s name, this would be technically considered a merger. If two hospitals create a new entity with a new name, this is considered a consolidation according to Finkler and Harowitz (1985).
This study makes several contributions to the merger literature. Previous studies examined multihospital system affiliation, and differences in efficiency and profitability based on hospital ownership (Manheim, et al., 1989: Shortell, 1988: Mullner and Anderson, 1987). Poor empirical methods and different time periods of analysis resulted in conflicting results. Also, some models have not been well-grounded in economic theory. This dissertation is the first study employing multiproduct cost functions to test for the existence of unexploited pre-merger scope and scale economies. The study examines the post-PPS period when competition was at its peak, and operating efficiencies have become much more important for hospital survival. Using a multiproduct cost function to examine operational efficiencies introduces an economic flavor to the hospital merger literature. The model uses four output categories based on hospital services rather than a single output at the hospital level. This approach eliminates the most important weakness in past research.
This study also makes contributions to the antitrust literature. Although the Antitrust Division recognizes the efficiency-enhancing potential of
mergers, determining the relevant market has been the most important step in assessing the impact of hospital mergers. In 1988, two hospital mergers, in Roanoke, Virginia and Rockford, Illinois were challenged by the Justice Department (Werden, 1989). The hospitals in Roanoke were allowed to complete the merger: Rockford Memorial and Swedish-American Hospital were prevented from merging because of a significant increase in market concentration. After the Antitrust challenges in 1988, the number of mergers declined suggesting that hospitals feared antitrust challenges (Greene, 1992). If this study establishes, by clear and convincing evidence, that mergers achieved efficiencies in the 1980s, then the Antitrust Division should permit a merger that it
would otherwise challenge. Moreover, this study can be used to evaluate potential hospital mergers in
the future, whether they may achieve operational efficiencies or not.
The empirical analysis of this study consists of four parts: (1) the estimation of multiproduct cost functions for the pre-and post-merger period;
(2) the computation of ray economies of scale and scope economies: (3) the estimation of marginal costs along input price elasticities; and (4) the comparison of scope and scale economies for pre-and
post-merger periods. The hybrid translog cost functions of merged hospitals are estimated for the 1987-1988 and 1989-1990 periods by seemingly unrelated regression (Zellner, 1962). This study also includes a group of similar hospitals that did not merge to control for structural change in the market. The control group hospitals are matched to the merged hospitals with respect to location, size, system affiliation and ownership status. The data come from the American Hospital Association (AHA) annual survey of hospitals.
The remainder of the dissertation is organized as follows: Chapter II provides a review of previous research investigating mergers and outlines the use of multiproduct cost functions in analyzing hospital efficiency. Chapter III is divided into three sections. The first section describes the multiproduct cost concepts and the empirical model.
The second section explains the methods and expected outcomes of the study, and the final section analyzes the data and introduces variables used in the study. Chapters IV and V present the results of the analysis for the 1987-1988 and 1989-1990
periods, respectively. The final chapter assesses the findings and identifies areas for further research.
LITERATURE REVIEW Chapter II
In this chapter, the theoretical and empirical literature relevant to this study is reviewed. First, studies ranging from survivor analysis to multivariate regressions concerning hospital mergers are examined. The first section discusses the shortcomings of previous research and analytical problems related to hospital mergers. The second section explores the use of multiproduct cost functions in analyzing hospital efficiency. At the end of the chapter, the linkage between multiproduct cost functions and mergers is made, developing the methodology used in this study by bringing two separate literatures together.
Measure of Relative Efficiency
Previous studies explaining hospital merger activity have offered ambiguous findings. In addition, many suffered from a lack of support in economic theory and shortcomings in analytical procedures. These studies have focused on hospital-wide efficiency as measured by length-of-stay, occupancy, admissions per bed, and full-time equivalent staff per patient day rather than inter-hospital differences in
efficiency reflected by different services produced within the hospital (Shortell, 1988; Shortell and Hughes, 1988; Becker and Sloan, 1985). A considerable portion of the merger literature is devoted to describing, advocating, and empirically testing the benefits of multihospital system (MHS) affiliation, and comparing MHS hospitals and independent hospitals on hospital-specific economic performance outcomes such as profitability ratios, return on assets, staffing ratios and capital structure (Ermann and Gabel, 1984; Manheim and Shortell and McFall, 1989; Mullner and Anderson, 1987). Two empirical methods have been extensively used to measure relative efficiency: survivor analysis and traditional econometric models (multivariate analysis).
A. survivor Technique
The first method of assessing relative efficiency is the survivor technique introduced by Stigler (1958) and employed by Mobley (1990), Bays (1986), Marder and Zuckerman (1985), Blair and Vagel (1978), Williams and Gruebele (1976), and Frech and Ginsburg (1974). The survivor technique classifies the firms in an industry by size, and calculates the share of industry output coming from each size class over
time. If the share of a given class falls, it is relatively inefficient, and in general, is more inefficient the more rapidly the share falls. This is generally followed by a regression analysis to identify the determinants of optimum size, called multivariate survivor analysis. This technique was applied to the hospital industry by Mobley (1990)
and Bays (1986) to understand merger activity in the context of scale economies achieved by hospitals.
Mobley (1990) investigated the determinants of growth and the effects of various other factors in the hospital industry of California. Mobley focused on attaining scale economies at the hospital level, not the service or product level, and found that system affiliation was a determining factor in the analysis of survival. Scale economies were found to exist in hospitals up to about 300 beds in California from 1980 to 1986. The other survivor study by Bays (1986) used survivor analysis to analyze changes in the size distribution of U.S. short-term general hospitals from 1971 to 1977. A measure of survival size of non-profit hospitals by state was developed and its determinants were investigated in a multiple regression framework.
The analysis revealed that hospitals with beds size less than 100 and more than 500 declined. Also,
this study showed that increases in the market share of for-profit hospitals and HMOs lowered the
survival size. Medicare increased the survival size with substantial differences in survival size among geographic regions. However, the Mobley (1990) and Bays (1986) studies failed to identify the relevant markets and used instead the entire U.S. hospital industry and the California “market,” respectively, to determine survival size. Also, searching for the optimal minimum cost, survival size at the hospital level avoids the fact that hospitals compete at the service level. Most recent court cases brought against merging hospitals by the Antitrust Division addressed this issue (Wilder and Jacobs, 1987; Werden, 1989). Finally, survivor analysis is highly criticized because of the lack of an economic foundation to support the observed results.
B. Econometric Models
The second method is an econometric model, using some sort of the least squares or maximum likelihood technique. The econometric model approach is simply the estimation of single or multiproduct cost functions. These have varied from structural models to behavioral models, and the combination of the two
such as hybrid translog cost functions (Gillespie,
structural cost Functions
Structural cost functions have been used extensively since the theory of multiproduct firm behavior was developed by Baumol (1977), Panzar and Willig (1977), and Baumol and Panzar and Willig (1982), Bailey and Friedlaender (1982), and employed by cowing and Holtmann (1983), Conrad and Strauss (1983), and Caves and Christensen and Treatheaway (1980). The theory deals explicitly with the variety of outputs produced within the multiproduct
firm, and develops the concept of economies of scale and scope for these firms.
cowing and Holtmann (1983) used a translog cost function and analyzed the impact of several primary hospital characteristics on the short-run costs of
340 New York State hospitals in 1975. They reported falling marginal costs for various levels of each output while holding other outputs constant. They argued that scope economies are at least as important as economies of scale in the production of hospital services.
The other translog cost function study by Conrad and Strauss (1983) formed a multiple-output and multiple input model of the hospital industry in North Carolina using 1978 data for 114 hospitals. The results indicated that there were constant returns to scale. In addition, they reported that the marginal cost of child inpatient days was substantially greater than the marginal cost for the other types of inpatient days.
The other group of econometric models consists of behavioral models which have no clear functional form. The behavioral cost function was developed in the 1970s (Lave and Lave, 1970; Lave and Lave, 1978) and employed by Mobley (1990), Manheim et al.
(1989), Shortell and Hughes (1988), Mullner and Anderson (1987), Morrisey and Alexander (1987), Sloan and Morrisey and Valvona (1987), Becker and Sloan (1985), Levitz and Brooke (1985), Ermann and Gabel (1984), and Coyne (1982). This method recognizes that hospital production costs may be influenced by numerous factors such as non-profit status that have an independent effect on the equilibrium between input prices, outputs and costs.
Past merger studies using behavioral models investigated financial performance, cost, and productivity of independent versus system affiliated hospitals using descriptive statistics and multivariate analysis. Mobley’s (1990) study used two measures of hospital performance: cost per adjusted inpatient day and operating margin. The study employed a varying-parameter functional form estimated by Ordinary Least Squares (OLS), and used data for the California hospitals from 1980 to 1986. The study found no evidence that system affiliation enhanced hospital performance, and reported higher cost inflation, lower growth in operating margin and inpatient days.
Manheim et al. (1989) used multiple regression analysis to test the acquisition targets and the effects of acquisition on hospital costs and staffing. They compared a sample of acquired hospitals to their competitors (a control group) for the pre-and post-merger periods. Data included all short-term hospitals acquired by the Hospital Corporation of America (HCA) between 1973 and 1983. This study showed that acquired investor-owned chain hospitals had lower FTEs whereas independent acquired hospitals had lower depreciation, and lack of capital. Most importantly, increased expenditure
levels for both chain and independent acquisitions were found to be significant.
The Mullner and Anderson (1987) study described institutional, locational and environmental characteristics of US hospital mergers, and overall financial changes from the pre-merger to post-merger period. This study used descriptive statistics for the 1980-1985 period. Institutional characteristics included type of hospital, number of beds,
ownership, and occupancy rates. Environmental characteristics were the percentage of patients by Medicare, Medicaid, Blue Cross/Shield, and commercial insurance. Financial measures focused on three ratios: current ratio, total profit margin and net-to-gross patient revenue. Results indicated that community hospitals acquired specialty hospitals, and governmental and for-profit hospitals are more likely acquired by not-for-profit hospitals. They also reported that large hospitals with higher occupancy rates acquired small hospitals with lower occupancy rates. No financial troubles before and after were reported.
Morrisey and Alexander (1987) used data for 245 acquired or managed hospitals in MHSs and 745 freestanding hospitals. They used a Legit model to
analyze data obtained in 1982 and 1983, and reported hospitals that were acquired were fundamentally different from hospitals that were placed into management contracts. In other words, acquisition was a function of the market whereas management contracts were not. Medicaid share of hospital revenue and certificate of need (CON) regulation were found to increase acquisition.
Sloan and Morrisey and Valvona (1987) compared the cost of debt across hospital ownership and chain status, and analyzed differences in the cost of capital by using descriptive statistics and regression analysis. They found that investor owned hospitals (both system and independent hospitals) generated more revenue, and were more highly levered than non-profit hospitals. Investor owned hospitals relied on direct loans and non-profits on tax-exempt bonds. They concluded that the cost of capital issue was overemphasized because bond ratings have been more influenced by hospital characteristics than system status.
Becker and Sloan (1985) studied hospital ownership and performance using 1979 data, and found no conclusive evidence that systems were more efficient than independent hospitals. Shortell (1988)
reviewed past studies and made predictions concerning the hospital industry. He found no evidence that systems were better than freestanding hospitals. There were no significant differences among 13 out of 20 comparative performance measures. Of the seven items for which differences were found, six indicated freestanding hospitals outperformed system hospitals.
Levitz and Brooke (1985) studied significant differences in financial performance, cost, and productivity between system-affiliated and independent hospitals. Ninety-four hospitals located in Iowa were examined (74 freestanding and
20 affiliated) using 1981 data, a means-test and descriptive statistics. They found that system owned hospitals are more profitable, have better access to capital markets, charge higher prices and experience higher costs per discharge.
Coyne (1982) examined the hospital costs and productivity in multihospital systems versus those of independent hospitals. Comparisons of 100 system hospitals from 14 systems and four ownership categories with 50 independent hospitals showed that system hospitals realized both significantly higher cost and profitability levels. Strong evidence was
found that system affiliated hospitals employed more effective pricing policies as measured by markup and ratios between expenses and revenues from patient services. Also system hospitals had higher admissions per bed than their counterparts.
The behavioral models can be criticized for their lack of theoretical grounding and their additive linear specification. Also, marginal cost and the interaction between outputs are not represented in these models.
Hybrid cost Functions
Hybrid cost functions combine the features of structural and behavioral models (Goldberg et al. 1991; Hardwick, 1990; Akridge, 1989). Independent variables, in addition to input prices and outputs, are included to incorporate some of the richness of the behavioral model. The hybrid cost function was introduced to hospital industry research by Grannemann, Brown and Pauly (1986) and used by Fournier and Mitchell (1992), Eakin (1991), Gillespie (1991), Eakin and Kniesner (1988), and Vita (1990).
Grannemenn et al. (1986) provided a new approach to estimate cost functions for U.S. hospitals. Data came from a survey of 867 hospitals in the 1981-1982 period along with supplementary data from other sources. The results showed that the average incremental cost of emergency departments declined over all ranges of output, and no economies of scale were found for outpatient visits.
In the most recent study employing the hybrid translog cost function, Fournier and Mitchell (1992) used 1984-1985 Florida hospital data, and estimated the effects of market structure on hospital costs.
They found distinct scope and scale economies among Florida hospitals, and costs were substantially determined by service configuration. The study introduced market concentration measures by service type and reported only modest cost-increasing effects of the degree of competition. This is a rather unexpected result considering the fact that greater competition in a market leads to greater cost reductions and cost effectiveness. This could be explained by non-price competition among hospitals such as incentives to attract physicians, and the use of very expensive high-tech equipment which increase hospital costs dramatically.
Eakin (1991), and Eakin and Kniesner (1988) used a non-minimum hybrid translog cost function to obtain estimates of allocative inefficiency for 331 U.S. short-term hospitals. They found that hospitals overemployed capital and underemployed physicians. Allocative inefficiencies were estimated at about four to five percent, and the model was extremely sensitive to elasticity of substitution and factor demands. Even though the research revealed diseconomies for the whole sample, there is nearly an even split between hospitals with overall scale economies and those with overall diseconomies of scale in their sample. Eakin (1991) was a follow-up study that investigated variations in allocative inefficiencies in the short-term hospitals by regressing the allocative inefficiency estimates against hospital characteristics. He found that the regulatory environment was a critical factor for inefficiency: rate regulation reduced inefficiencies whereas the certificate of needs (CON) increased it. There was greater percentage inefficiency in larger hospitals with larger market share. He concluded that price competition would promote efficiencies.
Gillespie (1991) estimated quadratic and hybrid translog cost functions for the 159 Departments of Veteran Administration Medical Centers using 1987
and 1988 data. She showed that the hybrid cost function fit the data better and found modest scope and scale economies. She concluded that efficiency could be improved if the system was more diversified (scope effect), and smaller units were closed and converted to outpatient facilities (scope and scale effect).
Vita (1990) argued that estimated scale and scope values obtained from a short-run cost function did not represent the presence of scale economies as used by Cowing and Holtmann (1983): instead they measured only short-run returns to scale indicating a movement along the short-run average cost curve. Vita estimated a hybrid translog cost function for
296 California hospitals in 1983, and did not found strong evidence of either ray scale economies or cost complementarities.
This chapter reviewed the studies relevant to this dissertation. These studies were classified into two subgroups: merger studies measuring relative efficiency, and multiproduct cost functions.
Merger studies compared MHS hospitals with independent hospitals on measures of hospital specific performance using descriptive statistics and multivariate analysis. A brief summary of merger studies relevant to this dissertation is given in Table 1. In general, these studies found that multihospital system affiliation increased access to capital markets and lowered capital costs. However, cost per case was increased by system affiliation.
As opposed to multivariate regression analysis of performance indicators, multiproduct cost functions provide a theoretically grounded model for analyzing efficiency. This approach recognizes that hospital production costs are influenced by numerous factors, such as ownership, system and teaching status in addition to outputs and input prices. These studies use both translog and hybrid translog cost functions to measure relative efficiency among hospitals.
However, no study used these cost functions to test scope and scale efficiencies for merged hospitals. The relevant studies using translog or hybrid translog cost functions are given in the lower part of the Table 1, along with weakness and strengths. The next chapter describes the empirical model, data sources and variables used in the study.
Table 1. Summary of Literature Review
Early study (1975). Stepwise regression.
Ermann and Gabel (1984)
Tentative results Pre-PPS period.
Levitz and Brooke (1985)
Good descriptive analysis.
Pre-PPS and only Iowa hospitals.
Becker and Sloan (1985)
No conclusive results.
A complete survivor analysis except the role of market determination.
Sloan, Morrisey and Valvona (1987)
Only financial factors examined in system affiliation.
Descriptive statistics and regression analysis.
Mullner and Anderson (1987)
Good descriptive statistics. Lack of statistical analysis.
Morrisey and Alexander (1987)
Emphasis on management contracts and system differences.
Appropriate Logit model.
Excellent review of past studies. No statistical techniques used.
Manheim et al. (1989)
Examined only for-profit systems. Multiple regression analysis.
survivor analysis and varying parameter regression.
No conclusive results.
HOSPXTAL MULTZPRODUCT COST FUNCTXON STUDXES
cowing and Holtmann (1980)
Short-run cost function for scale
No merger study.
Grannemann, Brown and Pauly (1986)
First application of multiproduct cost functions to hospital industry. Pre-PPS period.
No merger study.
Eakin and Kniesner (1988)
Emphasize on inefficiencies. Different model specification. No merger study.
Long-run cost function discussion. No merger study.
OLS regression. Only VA hospitals. No merger study.
Good follow-up study. Source of inefficiencies. No merger study.
Fournier and Mitchell (1992)
A complete multiproduct cost function study with market concentration. measures.
Short-run cost function. No merger study.
METHODOLOGY Chapter III
This chapter first introduces multiproduct cost efficiencies such as product specific economies of scale, ray economies of scale and scope economies in a multiproduct setting. The second part of the chapter explains the hybrid translog cost functions and the empirical model used in this study. Short run and long-run cost functions are discussed in economic theory, and the set of equations with imposed restrictions is derived. This section also includes a discussion of the functional form used in this study along with the Box-cox transformation and the estimation technique-seemingly unrelated regression. The third and final section in this chapter discusses the methodology (pre-and post merger analysis), and the expected outcomes from the analysis. At the end of this section, the data sources and variables used to estimate hybrid translog cost functions are explained and transition to the next chapter is made.
- Multiproduct scope and scale Economies
Baumol (1977) and Panzar and Willig (1977) established the multiproduct cost concepts for scope
and scale economies. The analysis proceeds in much the same as that for a single output. They construct an output bundle, where the output proportions are fixed. This simplicity is achieved by focusing upon measures of cost variation as output proportions remain unchanged, permitting the resulting commodity bundle to be treated as a single (composite) good. These models primarily focus on measuring interrelations among goods in production, and declining average costs (ray average cost) in a multiproduct setting.
Hospitals may obtain cost advantages in increasingly competitive health care markets through product specific economies of scale, ray economies of scale and economies of scope. Product-specific economies
of scale 1 indicate the behavior of costs as one
output level is changed while the output levels of the other products are held constant. In a two product case, the degree of product-specific economies of scale for product one, S1, is
S1 = ———— (1)
Y1 orc / 0Y1
where Y1 is the output level of product one and Y2
is the output level of product two.
1 Baumol (1977) defines the product specific economies of scale as output-ray specific.
s1 is the ratio of average to marginal cost at Yi•
When s 1 is greater than one, average incremental
costs (AIC) are greater than marginal costs, and there are increasing returns to scale with respect to product one. Average incremental cost is defined as
Another way in which output may change is to move along a ray in output space, expanding or contacting all outputs proportionately. Following Baumol, Panzar and Willig (1982), ray economies of scale are a straight-forward extension of the concept of single-product scale economies. Ray scale economies are an overall return to scale measure, and are defined as the elasticity of output with respect to cost. At minimum average cost, marginal and average costs are equal, the weighted sum of marginal costs is equal to the weighted sum of average costs. This can be measured by
S = C (Y) / i Yi MCi (4)
i = 1, 2
Ifs is greater than one (less than one), it indicates that average costs exceed (is less than) marginal costs, and there are economies of scale (diseconomies).
savings from joint production are referred to as
economies of scope 2 • Economies of scope are present when the cost of producing two products jointly is less than the cost of producing them separately.
This is measured by equation (5).
A natural measure of the degree of economies of scope is given by the proportion of cost savings from joint production over the cost of separate production divided by the cost of joint production.
C (Y1, 0) + C (0, Y2) – C (Y1, Y2) C (Y1, Y2)
Several techniques exist for measuring scope economies. One obvious method is to evaluate
2 Panzar and Willig (1977) use the term “translog convexity” for economies of scope.
expression (6) with the estimated cost function. The other technique to measure scope effects is to use cost complementarities. Cost complementarities are present when the marginal cost of producing one product decreases when the quantity of the other product is increased. For a twice continuously
differentiable cost function, cost complementarities
exist if the expression
Cij = 0 2 C / o Yi Yj is negative. (7)
Willig (1979) argues that the production-specific scale economies and economies of scope can be combined into multiproduct scale economies using equation (8). If marginal costs are identical, the multiproduct measure of scale economies collapses into the conventional single output measure of scale economies. The measure of multiproduct scale economies can be shown as follows:
w (Si)+ (1 – w) Sj
Sij =- –1- —–
where Si and Sj are still product specific economies of scale, Sc is scope economies and
Yi (oC / oYi)
w = Yi (oC / oYi) +-Yj (oC /-OYj)
which represents the share of the variable costs of production incurred for product one. Thus, the overall degree of scale economies for both products is a weighted average of the degrees of scale economies pertaining to products one and two, weighted by economies of scope through the factor
1 / (1 – Sc)• An interesting application of this is that sufficiently strong scope economies can confer scale economies on an entire product set, that Sij can exceed one, even if there are constant returns or some degree of diseconomies of scale in the separate products (Bailey and Friendlaender, 1982).
B. The Empirical Model-Hybrid Translog cost Function
Short Run or Long-Run Decision
Analyzing the behavior of a firm’s costs requires an explicit assumption regarding the state of equil!brium among firms in the sample. If the firms are believed to be employing cost-minimizing levels of all inputs, given prevailing output levels and factor prices, it is appropriate to estimate a long run cost function:
C = C (Y, W) (10)
where C is the total cost function, Y represents output levels and W stands for factor prices.
In contrast, if firms cannot quickly adjust all inputs in response to changes in output levels or factor prices, they will employ at any given moment, optimal quantities of easily adjustable variable inputs (e.g., labor, and material), given the existing, possibly non-optimal levels of the fixed inputs (i.e., capital). Short-run total costs (Cs) are written as the sum of variable costs (Cv) and fixed costs (F)
Cs= Cv + F (11)
where Cv = Cv (Y, Wv, K) and F = wk.K, and Wv, Wk are the prices of the variable and fixed factors, and K is the quantity of the fixed factor. The
long-run cost function can be obtained by differentiating (11) with respect to Kand setting this derivative equal to zero, yielding
which can be solved for x*, the cost-minimizing level of x*. When x* is substituted into (11), which yields the long-run cost function (Vita, 1990).
Equation (12) implies that the long-run cost minimization is achieved when the variable cost saved by substituting the last unit of capital for variable inputs is equal to the marginal input cost
of that unit, wk 3 .
Given that there have been drastic changes in the demand for hospital services since the early 1980s, this study estimates the short-run variable cost function defined as
Cv = Cv (Y, W, BEDS, X) (13)
where Cv equals total variable costs, Y is a vector of outputs, Wis a variable vector of input prices, BEDS is the number of beds assumed to be fixed in the short-run and Xis the vector of independent variables affecting hospital cost, such as system membership, case-mix index, etc. To estimate (13),
- The case where 6Cv / 6K is less than wk and greater in absolute magnitude implies suboptimal capital, whereas the opposite case where 6Cv / 6K is larger than -wk implies excessive capital. It is even possible for 6Cv / 6K to be positive implying such an excessive amount of fixed capital that a reduction in K would lead to reductions in both fixed and variable costs.
one should select an explicit functional form. The following hybrid translog cost function is selected:
Ln Cv = ao + Ei ai Ln Yi + Ei Er air Ln Yi Ln Yr
+ Ej /3j Ln Wj+ Ei I:j /3ij Ln Wi Ln Wj
+ I:i I:j <Pij Ln Yi Ln Wj + ik Ln BEDS
+ ikk (Ln BEDS) 2 + I:i 1-‘i Ln Yi Ln BEDS
+ I:j &j Ln Wj Ln BEDS+ Bser SERVMIX
+ Bpro PROFIT+ Bsys SYSTEM+ e
where Cv is the total variable cost; Yi is a set of patient services-acute care, intensive care, subacute care and outpatient visits; Wj are the
input prices-average cost of labor and average price of supplies; BEDS is the number of beds in the hospital representing fixed capital; SERVMIX is an index of service mix offered by hospitals; PROFIT is a dummy variable of proprietary status andSYSTEM is another dummy variable indicating membership in a multihospital system.
Box-cox Transforma·tion and Restrictions
Many of the hospitals in this study have zero values for some of the output categories. Since the natural log of zero is undefined, a Box-cox transformation of the output variables is used to
permit zero outputs. With this transformation, the cost function becomes
+ Ej Pj Ln Wj+ Ei Ej Pij Ln Wi Ln Wj
+ Ei Ej ¢ij Yi*
Ln Wj + tk Ln BEDS (15)
+ ikk (Ln BEDS) 2 + Ei µi Yi*
+ Ej 6j Ln Wj Ln BEDS+ Bser SERVMIX
+ Bpro PROFIT+ Bsys SYSTEM+ e
where y* = (Yt – 1) / t and tis the Box-Cox transformation parameter. When t approaches zero, the Box-Cox transformation closely approximates the natural log transformation.
Before estimating this function, symmetry and homogeneity conditions are imposed on the model. Linear homogeneity in input.prices is a precondition for the existence of a duality relationship between the cost and transformation functions. Symmetry implies Pjs = Psj• The assumption of linear
homogeneity of degree one in factor prices requires
that the following restrictions are imposed on the cost function parameters.
Ej Pj = 1 Ej ¢ij = 0
Ej Pij = O
j Sj = O
The hybrid translog function contains a large number of parameters even for a relatively small number of inputs and outputs. As a result, estimation of Equation (15) via ordinary least squares (OLS) is likely to result in imprecise parameter estimates due to multicollinearity. Fortunately, Shephard’s Lemma (1970) can be used to derive factor demand equations for labor and supplies. Because this study has only two variable inputs and the two cost shares sum to unity, only one of the two equations is independent. Therefore, the labor demand equation is derived in the estimation as follows:
Mj = o Ln Cv / o Ln Wj
= Pj + Eij Pij Ln Wj + Ei Ej ¢ij Yi*
+ Ojk Ln BEDS (16)
These relationships increase the amount of information about the production structure in the model without increasing the number of parameters. Now, equations (15) and (16) comprise a multivariate system. The seemingly unrelated regression (SUR) method is used to estimate the cost equation along with the share equation.
Seemingly Unrelated Regression (SUR)
This technique was developed by Zellner (1962) which offers potential efficiency gains through the estimation of the contemporaneous covariance of the disturbances between each pair of variables. It is also called Generalized Least Squares (GLS).
GLS estimators are the best linear unbiased estimators (BLUE) of the basic linear regression model when the assumption of spherical disturbances is dropped, thereby allowing for both heteroskedasticity and serial correlation. Allowing both heteroskedasticity and serial correlation requires a new definition of the covariance matrix as follows:
Cov (u) = E (uu’) = a 2 n (17)
where n is a given symmetric positive definite matrix and a2 is an unknown variance. The estimators can be obtained using maximum likelihood technique. PA (n) is the GLS estimator given by
equation (18), which depends on the matrix n. It reduces to the ordinary least squares (OLS) if n = I, where I is the identity matrix.
In the nonspherical disturbances case (heteroskedasticity and serial correlation), in which the covarience matrix is given as in (17), the GLS estimator of (18) is the BLUE estimator; in particular, it is the efficient estimator. In case of heteroskedasticity, this method weighs both dependent and independent variables at each observation by the reciprocal of the standard deviation of the dependent variable at that observation. Thus GLS estimation in this case can be interpreted as OLS estimation for which the data Y and X are replaced by the transformed data, respectively. That is why the GLS estimators are interpreted as weighted least squares and efficient estimation in case of heteroskedasticity and serial correlation (Intriligator, 1978).
In this dissertation, nonlinear seemingly unrelated regression is used to estimate the hybrid translog cost functions. Estimating cost functions along with the demand function provides more efficient estimates, and corrects the possible multicollinearity among explanatory variables.
Within each hospital, the disturbances are assumed to be correlated because error involving one input
affects the cost shares of other inputs and total costs. The SUR algorithm permits the error covarience matrix to be augmented on each iteration such that nonzero terms can appear in the off diagonal elements (Goldberg, 1991).
The statistical validity of the model is assessed in
several ways. All regression models are estimated in a similar manner. The R2s for the models and the
number of statistically significant coefficients indicate the strength and the precision of the models. The Box-Cox transformation in the analysis provides two advantages. First, it tests whether the hybrid translog cost function is the best fit or not. If the hybrid translog cost function does not fit the data well, then linear, semi-log or quadratic functional forms can be tested for the best fit (S gaard, 1992). Two most recent comparisons of several functional forms-Gillespie (1991) with hospital based data and Hardwick (1990) with English building society data have reported that the hybrid translog model fits thedata better and provides a higher percentage of statistically significant coefficients. Secondly, the Box-cox transformation reduces heteroskedasticity because it is a form of log transformation which also reduces heteroskedasticity (Gujarati, 1988).
c. The Process of Analysis and Data
Pre-and Post-Merger Discussion
The analysis involves a two-step procedure. The first step is to estimate the variable cost functions for the merged and control hospitals for one year prior to the merger. These cost functions are used to test for the existence of scope and scale economies in the year prior to the merger.
The control group hospitals are matched to the merged hospitals with respect to their location, size, services provided, and system and ownership status. This way the analysis can be secured against a structural change in the industry that would cause the same effect on the regression parameters of merged and control hospitals.
The second part of the analysis is to apply this procedure to the post-merger period, and to estimate the variable cost functions of merged and control hospitals for one year and two years after the merger. The assumption is that operating efficiencies at the service level can be achieved within three years due to fast anddrastic changes in the hospital industry. Given the presence of economies in the pre-merger period, the post-merger
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