AN ANALYSIS OF

EFFICIENCY AND PRODUCTIVITY

IN SWISS HOSPITALS

Final Report to the:

Swiss Federal Statistical Office and

Swiss Federal Office for Social Security

June 2004

Authors:

Prof. Dr. Massimo Filippini

Dr. Mehdi Farsi

In collaboration with:

Dr. Luca Crivelli

Marika Zola

Department of Economics University of Lugano Via Maderno 24, 6900 Lugano, Switzerland

and

Swiss Federal Institute of Technology ETH Zentrum, WEC, 8092 Zurich, Switzerland

This project is sponsored by the Swiss Federal Statistical Office and the Swiss Federal Office for Social Security. The data are provided by the SFSO. We are grateful to Andr Meister for his general support throughout this work, and Luca Stger and Patrick Filipetto for their help to understand the data. We also thank Monika Romancyk and Diego Lunati for their assistance. The views expressed in this report are those of the authors and do not neceassrily reflect the positions of the sponsoring agencies.

Table of Contents

Summary.................................................................................................................... i

1 Introduction .............................................................................................................. 1

2 Methodology............................................................................................................. 4 2.1 Simple performance indicators....................................................................... 10 2.2 Indicators derived from cost frontier approach .............................................. 12 2.3 Total factor productivity growth .................................................................... 21

3 Data......................................................................................................................... 22 3.1 Outliers and reporting errors........................................................................... 30 3.2 Descriptive statistics ....................................................................................... 35

4 Simple indicators .................................................................................................... 44

5 Cost frontier analysis .............................................................................................. 56 5.1 Model specification and functional form........................................................ 56 5.2 Long-run analysis ........................................................................................... 62 5.3 Short-run analysis ........................................................................................... 69 5.4 Scale and cost efficiency and productivity ..................................................... 73

6 Regulation and ownership ...................................................................................... 79 6.1 Cost efficiency and regulation/ownership ...................................................... 80 6.2 Organization of hospital sector in Switzerland............................................... 81 6.3 Methodology and results ................................................................................ 88

7 Conclusions ............................................................................................................ 90

8 References .............................................................................................................. 93

i

Summary

In Spring 2002, the Swiss Federal Statistical Office in cooperation with the Federal Office for Social Security proposed a research project on the assessment of productivity and productive efficiency of Swiss general hospitals to our research group at the University of Lugano and Federal Institute of Technology in Zurich. The main goals of this study are defined as:

Development of simple indicators for measuring cost-efficiency and productivity in hospitals;

Estimation of more complex indicators on cost and scale efficiency and productivity;

Analysis of the impact of regulatory settings and ownership types on the efficiency of hospitals. This research has been carried out in several stages consisting of data

preparation, literature review, definition of some simple efficiency and productivity indicators, analysis of hospitals cost and scale efficiency using stochastic cost frontier models, and an analysis of different regulatory settings and their impact on efficiency.

The financial data of 214 general hospitals over the four-year period between 1998 and 2001 are used. Specialized clinics are excluded from this study. The main goal of this study is to analyze the cost-efficiency and scale-efficiency of the Swiss hospitals. We address this issue in two stages: First, based on the available data we propose some simple indicators of efficiency and productivity. By simple indicators we mean the ratio-type measures whose estimation does not require any mathematical or statistical analysis. These indicators have several limitations due to the fact that they do not capture the differences between hospital characteristics with regards to both outputs and operation conditions.

In the second stage, the efficiency of hospitals will be studied using more elaborate statistical methods. We focus on econometric approaches namely, stochastic cost frontier analysis. This method is based on the estimation of a cost frontier function that reprensents the minimum costs for producing a given level of output. The best or most cost-efficient hospital(s) observed in the sample are assumed to be on the cost frontier whereas other hospitals are located above the frontier with positive excess costs. However, in contrast with the deterministic approach the location of cost frontier varies across different production units by a stochastic shift. That is, not only does the model account for the observed differences among hospitals through explanatory variables, the unobserved random variations are also taken into account. Both cost and scale efficiencies will be studied. Given the rapid growth of medical expenditures in Switzerland, hospitals cost-efficiency is a very important policy issue. From a policy point of view it is also important to identify to what extent hospitals actually exploit the potential scale economies and if there is any possible improvement in this regard.

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The simple indicators of productivity and efficiency have two types of limitations. First, a hospital provides a great multitude of different services each of which requires different amounts of resources thus different costs. To the extent that different hospitals treat different patients, a single indicator cannot possibly provide a comparable measure of hospitals performance. Therefore, a simple indicator is based on an implicit assumption that on average different hospitals provide a similar mix of services regarding costs. This is not a realistic assumption because people in different locations are likely to have different health problems due to differences in socio-economic status, working environment etc. Secondly, different hospitals operate in different environments with different economic conditions. For instance: the price of labor varies from one region to another; there are relatively more physicians in large cities than rural areas; rents for buildings and medical equipment vary across different locations; etc. Therefore, simple indicators cannot be defined on a ceteris paribus basis that is, holding other relevant factors constant.

However, simple indicators can be useful in understanding the variation patterns of different factors among hospitals. They can give information about a hospitals cost structure and the partial productivity of its different input factors. When studied together, they can provide an overall picture of a hospitals functioning especially as compared to other hospitals. Moreover, a careful study of these indicators can provide some guidelines for a more elaborate analysis of efficiency. In particular, the model specification and the relevant factors can be identified using the proposed simple indicators. Finally, an analysis of such indicators can be useful to identify the potential reporting errors in the data and to introduce possible improvements.

An econometric analysis can provide great advantages regarding both types of limitations discussed above. The observed characteristics can be accounted for. Therefore, the estimated measures are comparable at least insofar as the observed characteristics are concerned. Moreover, with certain assumptions, an appropriate stochastic model can control for a part of unobserved characteristics. The econometric analysis is carried out with respect to three aspects of efficiency. First, a group of models are proposed to analyze the long-term efficiency by studying the hospitals total costs. Secondly, the short-term efficiency is analyzed using a variable cost function. Capital costs are excluded from this model. A log-linear (Cobb-Douglas) functional form is used for theses models. Finally, this econometric cost frontier is used to calculate the TFP growth and to identify its components.

In the last part of the project different regulatory systems and ownership types of general hospitals in Switzerland are analyzed and the distribution of different ownership/regulatory types across cantons and typologies is discussed. This descriptive analysis is followed by an analysis of inefficiency scores estimated from the cost frontier analysis. The main purpose of this analysis is to test whether hospitals with different ownership types and/or under different regulations have significantly different efficiencies.

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Our descriptive analysis of the data shows that the total number of hospitalizations has increased by about 10 percent over the study period (1998 to 2001). In the same period, the total expenditures of Swiss general hospitals have increased by about 15 percent in real terms. Our analysis also indicates that most hospitals while decreasing the average length of hospitalization have considerably increased the share of their ambulatory revenues. A selected set of simple indicators of productivity and efficiency has been compared across different typologies. This comparative analysis gives important insights to the different variations among hospitals. In particular, hospitals in different typologies show significant differences in many important aspects. The observed patterns in the data indicate that the small basic-care hospitals have the longest hospitalizations (on average about seven days longer than other hospitals) while university hospitals have the highest average costs (on average about 50 percent higher than other hospitals). However, university hospitals treat the most severe cases shown by the highest average AP-DRG cost weight (20% higher than the overall average), and have the highest nurse per bed ratio (about twice as the overall average). Different hospital types pay significantly different prices for their capital investments with the higher prices for larger hospitals. In particular the capital expenses per bed in a university hospital is typically three times higher than in a small basic-care hospital. Moreover, medical materials and physicians take a higher share of hospital costs in larger hospital types, while nursing staff have a higher share in smaller hospital types.

The variation patterns in the data and the outlier values have been studied. In general the quality of the available data is acceptable for an econometric analysis of cost-efficiency. However, because of the limited number of available years with non-missing data (three in most hospitals), some of the advanced panel data models could not be used. Therefore, the econometric analysis presented here is based on a cross-sectional model that treats the repeated observations of a same hospital as independent observations. This is not a realistic assumption and can probably be relaxed with an extension of the data by including a few more years of observation.

We contend that the data can be generally improved by minimizing the missing values and reporting errors and including more years. Such improvements can be helpful from a methodological standpoint in that they allow the application of more accurate econometric models and functional forms. Potential data improvements can particularly be considered in the quality of DRG coding, reporting the admission type (outpatient care, full and semi-hospitalization), and capital investment accounting. These improvements can be supported by regular or random independent monitoring combined with incentive mechanisms such as financial rewards for quality of reporting. Furthermore, additional quality measures such as information on the hospital structure and patients general satisfaction as well as the research and teaching activities can be useful for cost analyses.

A sub-sample of 459 observations corresponding to a total of 156 hospitals has been chosen for the econometric analysis of efficiency. The analysis

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has been carried out for the long-run and short-run performances separately. The long-run analysis using a stochastic total cost frontier estimation leads to the following results:

There are unexploited scale economies in the majority of Swiss general hospitals. Although we cannot clearly identify the optimal hospital size, our results along with the empirical evidence reported in the previous literature suggest that the scale economies are significant in hospitals with less than 200 beds.

Ignoring the severity adjustment by AP-DRG cost weights slightly biases the main coefficients. However, these differences are not significant for practical purposes, suggesting that most of the variation in DRGs among hospitals is random.

There are systematic cost differences among different typologies with larger hospital types being generally more costly. These differences remain considerable after controlling for severity through AP-DRG cost weights. In particular, the university and regional hospitals are the most costly hospitals (about 35% more costly than the small basic-care hospitals). This difference can be explained by the relatively wide range of medical specializations as well as research and teaching activities in those hospitals.

A one-day decrease in the average length of hospitalization can lower the hospitals total costs by about 4 percent. Given that the small basic-care hospitals have extremely long hospitalizations, considerable savings might be achieved by shortening the unnecessarily long hospitalizations.

Ambulatory care is much less costly than inpatient care. On average, each patient-day costs as much as 11 times more than an outpatient visit. To the extent that the insurers have more accommodating reimbursement plans for outpatient services, this result can explain the motivation behind the considerably growing share of ambulatory care in most hospitals.

Although our quality measures are limited the results suggest that the quality of medical services is an important factor in cost determination. Moreover, it should be noted that in this study we do not control for any outcome measure of quality and some of the estimated cost differences may be due to various levels of quality.

There exists a considerable cost variation among hospitals operating in different cantons. Part of these differences may be related to different regulatory systems implemented in different regions.

On average, the total costs of a typical general hospitals have grown by about 4 percent per year. This can be explained by

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technological progress in medical care, which enables the hospitals to provide more advanced services to more severe cases resulting in higher costs.

A variable cost frontier has been used to perform the short-run analysis. The results of this analysis indicate that the differences between hospital typologies are mainly due to their differences in capital expenditures. The inefficiency estimates obtained from this analysis are comparable to those obtained from the long-run analysis, suggesting that the inefficiency sources are mainly related to hospitals short-run decisions rather than long-term investment choices.

The cost-efficiency analysis using several models indicates that the inefficiency scores are not sensitive to the adopted model. The results generally suggest a mean inefficiency score of about 20 percent in Switzerlands general hospitals. The estimations also suggest that the cost-inefficiency has slightly but consistently decreased over the study period. Certain typologies show significantly different inefficiency estimates. In particular, the university hospitals the highest inefficiency estimates. However, these estimates are partly because of the special activities like advanced medical research and complex medical interventions in these hospitals. The inefficiency estimates are also relatively high in small basic-care hospitals, which is probably related to extremely long hospitalizations in these hospitals. Given the methodological and data limitations of this study, the individual hospitals efficiency scores should be considered with caution. In particular, these estimates should not be directly used as a basis for rewarding or punishing specific hospitals. Rather, the present analysis provides an overall picture of inefficiency situation in Switzerlands general hospitals.

In the last chapter, the effect of different regulatory systems and ownership types on the hospital efficiency has been analyzed. The general hospitals are divided into five groups based on their ownership (public, private non-profit and for-profit) and subsidy status (subsidized, not subsidized). A large majority of Switzerlands hospitals are owned by the State or benefit from government subsidies. Our data show that in 2001, 63 percent of general hospital beds were owned by the State, which together with the subsidized hospitals owned by the private sector, account for about 87 percent of the total general hospital beds in Switzerland. On average, both public and subsidized private hospitals are on larger and receive relatively more severe cases than non-subsidized hospitals. The data also point to considerable differences in average costs among hospitals with different ownership/subsidy types. However, some of these differences are related to differences in case mix severity and some others may be due to differences in operating costs that are not directly related to the actual hospitalizations. Such differences can be related to investment costs, excess capacity and the intensity of research and education activities.

Our analysis of inefficiency estimates obtained from the stochastic frontier analysis suggests that the efficiency differences across different ownership/regulation types are not statistically significant. This result indicates

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that our data do not provide any evidence of a significant efficiency advantage of one type over another. However, it should be noted that this result is restricted to our specific data and cannot be generalized. Moreover, because of the potential correlation between ownership/regulation types and other hospital characteristics such as typology and size, disentangling the actual ownership/regulation effects may be difficult. Therefore, the presented results cannot be considered as conclusive evidence that different regulation/ownership types induce similar cost efficiency.

1

An Analysis of Efficiency and Productivity in Swiss Hospitals

Final Report

June 2004

1 Introduction The health care expenditure is growing rapidly in Switzerland. During the

five-year period between 1997 and 2002, the national level of health care costs has grown with an average annual rate of about 4.5% attaining about 48 billion francs in 2002. In 2002, general hospitals (about 12.4 billion francs) and specialized clinics (4.0 billion francs) respectively accounted for about 25.8 and 8.3 percent of the total health care expenditures in Switzerland.1 In particular, the general hospitals sector shows an increasing growth rate rising form about 3.9 percent per year between 1997 and 1999 to an average of about 6.5 percent per year between 2000 and 2002. This increasing growth has raised the public interest in improving the performance of hospitals and determining the extent and identifying the sources of possible inefficiencies in this sector.

In Spring 2002, the Swiss Federal Statistical Office in cooperation with the Federal Office for Social Security proposed a research project on the assessment of productivity and productive efficiency of Swiss general hospitals to our research group at the University of Lugano and Federal Institute of Technology in Zurich. The main goals of this study are defined as:

Development of simple indicators for measuring cost-efficiency2 and productivity in hospitals;

Estimation of more complex indicators on cost and scale efficiency3 and productivity;

Analysis of the impact of regulatory settings and ownership types on the efficiency of hospitals. The project is organized in three phases: introductory phase, empirical

analysis, and writing of the final report. The present report is the final report anticipated for the project. In this report the main results of the project are presented. This research has been carried out in several stages consisting of data preparation, literature review, definition of some simple efficiency and 1 In Switzerland hospitals are divided into two categories: general hospitals and specialized clinics. While general hospitals provide short-term medical care in any field, specialized clinics are restricted to one of the following care categories: psychiatrics, rehabilitation, surgeries, gynecology/neonatology, pediatrics, geriatrics, and other specialties. See SFSO (2001) for more details. 2 Cost efficiency involves the least-cost method of producing a given output. As for productivity, it can be defined as the output produced by a given amount of one or several input factors. 3 Scale efficiency means that the production is performed at the optimal scale, that is, an increase in the output does not result in a decrease in the average cost.

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productivity indicators, analysis of hospitals cost and scale efficiency using stochastic cost frontier models, and an analysis of different regulatory settings and their impact on efficiency.

The financial data of 214 general hospitals over the four-year period between 1998 and 2001 are used.4 Specialized clinics are excluded from this study. The main goal of this study is to analyze the cost-efficiency and scale-efficiency of the Swiss hospitals. We address this issue in two stages: First, based on the available data we propose some simple indicators of efficiency and productivity. By simple indicators we mean the ratio-type measures whose estimation does not require any mathematical or statistical analysis. These indicators have several limitations due to the fact that they do not capture the differences between hospital characteristics with regards to both outputs and operation conditions.

In the second stage, the efficiency of hospitals will be studied using more elaborate statistical methods. We focus on econometric approaches5 namely, cost frontier analysis. Both cost and scale efficiencies will be studied. Given the rapid growth of medical expenditures in Switzerland, hospitals cost-efficiency is a very important policy issue. From a policy point of view it is also important to identify to what extent hospitals actually exploit the potential scale economies and if there is any possible improvement in this regard.

The simple indicators of productivity and efficiency have two types of limitations. First, a hospital provides a myriad of different services each of which requires different amounts of resources thus different costs. To the extent that different hospitals treat different patients, a single indicator cannot possibly provide a comparable measure of hospitals performance. Therefore, a simple indicator is based on an implicit assumption that on average different hospitals provide a similar mix of services regarding costs. This is not a realistic assumption because people in different locations are likely to have different health problems due to differences in socio-economic status, working environment etc. Secondly, different hospitals operate in different environments with different economic conditions. For instance: the price of labor varies from one region to another; there are relatively more physicians in large cities than rural areas; rents for buildings and medical equipment vary across different locations; etc. Therefore, simple indicators cannot be defined on a ceteris paribus basis that is, holding other relevant factors constant.

However, simple indicators can be useful in understanding the variation patterns of different factors among hospitals. They can give information about a hospitals cost structure and the partial productivity of its different input factors. When studied together, they can provide an overall picture of a hospitals functioning especially as compared to other hospitals. Moreover, a careful study of these indicators can provide some guidelines for a more elaborate analysis of 4 The data is also partly available for 1997. However, given the large number of missing values and the lack of DRG data for this year, our analysis is restricted to 1998 to 2001. 5 Econometrics is a discipline that mainly deals with the application of statistical techniques in economics.

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efficiency. In particular, the model specification and the relevant factors can be identified using the proposed simple indicators. Finally, an analysis of such indicators can be useful to identify the potential reporting errors in the data and to introduce possible improvements.

An econometric analysis can provide great advantages regarding both types of limitations discussed above. The observed characteristics can be accounted for. Therefore, the estimated measures are comparable at least insofar as the observed characteristics are concerned. Moreover, with certain assumptions, an appropriate stochastic model can control for a part of unobserved characteristics. The econometric analysis is carried out with respect to three aspects of efficiency. First, a group of models are proposed to analyze the long-term efficiency by studying the hospitals total costs. Secondly, the short-term efficiency is analyzed using a variable cost function. Capital costs are excluded from this model. A log-linear (Cobb-Douglas) functional form is used for theses models. Finally, this econometric cost frontier is used to calculate the TFP growth and to identify its components.

In the last part of the project different regulatory systems and ownership types of general hospitals in Switzerland are analyzed and the distribution of different ownership/regulatory types across cantons and typologies is discussed. This descriptive analysis is followed by an analysis of inefficiency scores estimated from the cost frontier analysis. The main purpose of this analysis is to test whether hospitals with different ownership types and/or under different regulations have significantly different efficiencies.

The rest of the report is organized as follows. General concepts of efficiency analysis in hospitals and the adopted methodology in this study are described in chapter 2. Simple performance indicators are introduced in section 2.1, and more elaborate measures of productivity and efficiency based on econometric methods are discussed in section 2.2. Chapter 3 describes the data and the methods to prepare the data for the analysis. The observed data problems such as reporting errors, missing variables and outliers are discussed in section 3.1. Section 3.2 provides a descriptive summary of the main variables used in the analysis and discusses the main trends and patterns observed in the data. In chapter 4, a series of simple indicators of efficieny and productivity are proposed and their variations over time and across hospital types are discussed. These indicators are introduced in two main groups: productivity and cost indicators, and indicators of hospital characteristics. Chapter 5 provides the results of cost frontier analysis. This chapter starts with a general discussion of model specification and functional forms used in this study. The long-run efficiency analysis with a total cost frontier analysis is presented next in section 5.2. The results are compared across several model specifications. Cost-efficiency and its potential driving factors are discussed. In section 5.3 the short-term efficiency analysis is presented. A variable cost frontier model is used in this section. The practical difficulties of measuring capital costs and capital stock used in hospital production are discussed. Section 5.4 provides a detailed discussion of scale and cost efficiency and hospitals productivity growth. Chapter 6 presents an analysis

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of regulation and ownership effects on hospitals efficiency. This chapter starts with a brief discussion of theoretical arguments for efficiency variation across different regulation/ownership types in section 6.1, followed by a general description of the Swiss hospitals organization in section 6.2. The chapter ends with section 6.3 presenting the adopted methodology and the empirical effects of ownership/regulation types. Chapter 7 concludes the report with a summary of the studys main results.

2 Methodology This chapter reviews the general concepts of efficiency analysis in

hospitals and discusses the adopted methodology in this project. A hospital can be considered as a production function with labor and capital as input and the medical care as output. Labor inputs can be classified in several groups such as services from physicians, nurses, administrative staff, etc. Capital stocks include buildings, hospital beds and medical equipment. A hospital output consists of medical services in different areas such as pediatrics, intensive care, internal medicine, obstetrics and so many others. There exist an extremely large number of diseases that call for different treatments and costs. Moreover, there is a great variation among patients treated in a hospital regarding the severity of illness thus the intensity of medical care. Medical care can also be in different forms with respect to the required time and hospital equipment: The treatments that require a hospital bed are usually referred to as inpatient care. Conversely, the treatments that are carried out without hospitalization of the patient, such as dialyses and X-ray sessions, are called outpatient or ambulatory care. Usually, the planned hospitalizations of less than 24 hours such as one-day surgeries are not considered as hospitalizations, but referred to as semi-hospitalizations.6

In order to construct any measure of productivity or efficiency, one needs to define relevant measures of outputs and inputs. A simple productivity indicator can be defined as the ratio of an output measure to an input measure. Therefore, the first requirement of any efficiency analysis is an appropriate measurement of inputs and outputs. Other characteristics of both inputs and outputs may also be used in a multivariate analysis. For instance, input factor prices are usually used to account for differences in access to input factors, or quality indicators are considered to control for different outputs.

In this chapter first, different measures of hospital outputs and inputs are introduced. A brief review of simple productivity measures follows. Finally, the stochastic cost frontier methods are discussed. Measuring hospital outputs

The ultimate output of hospital operation is the improvement of the patients health. However, the patients health status is difficult to measure and the improvements cannot be clearly attributed to the hospitals services. It is 6 See S.F.S.O. (1997) for detailed definitions of outpatient care, hospitalization and semi-hospitalization.

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therefore necessary to consider observable intermediary products as hospital outputs. Steinmann and Zweifel (2003) provide a discussion on this issue. These authors consider two levels of production for hospitals: the society level and the managerial level. They consider for instance the number of patient-days as an output at the managerial level but an input at the society level because it measures the costs incurred to patients. In this report, as the society-level output is difficult to measure, we focus on managerial output.

The measurement unit of output is usually considered as a patient or a patient-day, which is equivalent to one-day hospitalization of one patient. The number of cases is commonly accepted because it is closer to the true output (health improvement) especially if hospitals have different policies regarding the length of hospitalization. For instance, if certain hospitals keep their patients more than it is necessary, the patient-day measure of output will be distorted in favor of these hospitals, thus masking their inefficiency.7 However, if the monitoring system is strong and physicians make conscientious decisions especially when they are not subject to strong financial incentives to do otherwise, one can assume that all hospitals generally respect a normal stay as needed by medical reasons. Number of patients and patient-days can therefore be regarded as two dimensions of a hospitals output.8 Medical services like diagnosis, surgery, therapy, admission and discharge are best represented by the number of cases, whereas hotel services like nursing care and accommodation are reflected in the number of patient-days.9

It is commonly believed that initial days of a hospitalization are more costly than the following days. However, if medical services are captured by the number of cases, one can assume that the remaining services are uniformly distributed over a patients stay. Therefore, a complete measure of output should account for both dimensions. Some authors like Vita (1990) consider the number of cases and the average length-of-stay as two dimensions of output. In each of these output dimensions, several subgroups can be considered: Cases can be classified into diagnostic groups and patient-days can be distinguished by the care needs of a patient. Generally similar groups are considered for both dimensions. A commonly used grouping method is based on hospital departments. This approach is generally convenient because the data on hospital discharges by department are usually available in hospitals administrative records.

For instance, Vita (1990) considers five output categories based upon five departments: surgeries, obstetrics, pediatrics, emergency room and all others. Eakin (1991) has used four groups: general medicine, obstetrics, surgeries and outpatient visits while Steinmann and Zweifel (2003) have considered the number of discharges in five groups: medical, pediatrics, surgical, gynecological, and intensive care. Scuffham et al. (1996) on the other hand, consider three

7 This is especially important for the cost function analyses where it is generally assumed that the output is exogenous. 8 See Breyer (1987) for a discussion. 9 Breyer (1987) even regards the provision of hospital beds as an output to satisfy an option demand.

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aggregate outputs: total number of admissions, average length of hospitalization and the number of outpatient visits. Carey (1997) considers two outputs: discharges and outpatient visits, while controlling for the average length of stay and an aggregate case mix index based on Medicare patients. Folland and Holfer (2001) have considered patient days in five groups: general, surgical, pediatrics, obstetrics/gynecology and all others, in addition to outpatient visits. They applied an aggregate case-mix index to general and surgical patients.

Given that hospitals provide an extremely wide range of services. Any feasible measure of hospital output requires an aggregation of one sort or another. The more the output is disaggregated the higher is the precision of the analysis. However, for a disaggregated analysis more intensive data are required. A solution to this problem is to use aggregate measures but adjust them by a series of factors that represent the overall severity of the patient case mix. These factors, commonly known as case mix adjusters, can be the average characteristics of the patients and the proportion of patients in certain groups with respect to age, gender, disease etc. Zuckerman et al. (1994) used a series of hospital-level case-mix adjusters like the percentage of patient days in intensive care units, percentage of outpatient visits without surgery, ratio of births to admissions and inpatient surgical operations per admission.

An alternative commonly used approach is to consider a weighted sum of the medical care (in terms of cases) provided in more than 600 Diagnostic-Related Groups, the weights being the respective standard average cost for each DRG. DRGs are a system of patient classification based on primary and secondary diagnoses and procedures, age and length of stay. These groups are defined such that each category has more or less a uniform cost. Therefore, treating a patient in any given DRG can be considered as a single medical service with regards to costs. DRG system was first developed in the early 80s in the US. This system has been since used in the prospective payment system established by Medicare to contain medical expenditures. According to this system, hospitals are paid a similar amount per case for the inpatient care of one patient of each DRG.

Measuring hospital output based on DRGs is a common practice. Linna (1998), Rosko (2001) and Heshmati (2002) are three examples. These authors use the DRG-weighted number of admissions as a measure of hospitals main output.10 Other authors like Brown (2003) have used the DRG weighting system to classify the hospital output. This author for instance considers cases with DRG weight of lower than 1, between 1 and 2, and higher than 2 as three output categories.

Healthcare regulators in many countries use slightly different versions of DRG system to measure hospitals outputs. The UK equivalent of DRG classification is referred to as Healthcare Resource Groups (HRG). In Switzerland, a similar classification system, Swiss APDRG, has been

10 Rosko (2001) also controls for several case-mix adjusters such as the percentage of ER visits and outpatient surgeries out of all outpatient visits.

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developed.11 This system, administered by the Swiss Institute of Health and Economics, is used as a basis for cost reimbursement of hospitals in Switzerland. The DRG-based measures have also the advantage that the patients in one group can be considered approximately the same regardless of their length-of-stay (LOS) in the hospital. In fact an acceptable range of variation of LOS is given for each DRG. However, this interval is often quite wide and to consider a constant LOS for all patients in a given DRG is at best an aggregate approximation. Most regulators consider certain adjustments for cases with unusually long hospitalizations. For instance, Swiss APDRG version 4.0 considers a 70% reimbursement for each additional day if the LOS is greater than an extreme upper limit. However, this limit is only dealing with extreme outliers. In fact the within-DRG variation of hospital stays remains quite considerable even without these outliers.

Despite these shortcomings the DRG-adjusted number of cases is one of the best available simple measures of output. In any case it is more representative of costs than the number of patient-days. Outputs can also be approximated by an aggregate quantity index, consisting of the weighted sum of different outputs, weights being the revenue (or cost) shares of the respective outputs.12 For instance, the hospital output can be summed at the department level such as general, internal medicine, surgeries, gynecology etc. However, the revenue shares of departments are usually not available in administrative data.

Another aspect of hospital production function is that medical care can be provided with different levels of quality. Quality of medical care is a complex multi-dimensional concept. The measures of quality are classified in three main groups: Structural measures represent the quality of the provider in terms of physical amenities, administrative organization and staff qualification; Process measures are based on the evaluation of the medical procedures and practices against professional standards; Finally, outcome measures are associated with the patients health outcomes resulted from medical care.13 Hospital quality is difficult to measure for several reasons: First, appropriate data are usually not available, especially for outcome and process measures. Secondly, since the quality of care matters to the extent that it promotes the desirable health outcomes, process and structural measures cannot provide a direct measurement of quality. Finally, health outcomes, especially the relevant long-term outcomes, are affected by a large number of confounding factors that are beyond the hospitals control.

However, the evidence on the effect of quality measures on hospital costs is rather mixed. Referring to his previous empirical literature, Rosko (2001) conclude that the omission of quality indicators may not be as serious as commonly thought. For instance, Zuckerman et al. (1994) controlled for several outcome measures of quality such as 30-day post-admission mortality rates.

11 See Institut de Sant et dEconomie (2003) for more details. 12 This approximative approach is based on the assumption that hospitals are maximizing a Cobb-Douglas profit function with constant returns to scale. 13 See Donabedian (1980) for an extensive discussion of quality measures.

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Their analysis suggests that none of those measures have significant effects. Similarly Vitaliano and Toren (1996) report that most of their 12 quality measures showed insignificant effects on hospital costs. On the other hand, Folland and Hofler (2001) have considered two measures of structural quality (percentage of board-certified physicians and a measure of bed availability), both of which showed significant effects on total costs. In general the available evidence often points to a significant effect by structural quality measures, while outcome and process measures are more likely to appear unimportant. We contend that this may be explained by the fact that the structural quality is usually easier to measure whereas other quality indicators especially outcome measures are usually more prone to measurement errors and outside factors. For instance, the quality of the medical staff can be more or less clearly represented by the average level of their specialization whereas outcome measures like mortality rates and also process measures such as the rate of usage of an appropriate treatment procedure, are affected by a great deal of unobserved parameters.

Unfortunately, we do not have any data on the health outcomes or the treatment procedures used in the hospitals. With the available data no outcome or process measures of quality can be constructed. However, several structural measures are constructed using the information on the available amenities and staff qualification. These indicators will be discussed later.

Measuring hospital inputs

Most inputs in a hospital can be measured by physical quantities. For instance, labor can be measured by the number of workers or days worked or energy can be considered as the consumed fuel or its equivalent in energy. However, capital inputs are not as simply measurable. Capital is a stock that is usually used for several years. Capital stock depreciates and its monetary value is subject to annual inflation throughout its service. Therefore, all historical investments need to be converted to real monetary value (constant Francs) for each year by a relevant price index, and decreased for depreciation by a constant rate. The depreciation rate must include both physical deterioration and obsolescence. The rental or leased capital is also considered by the lease payments deflated to constant Francs similar to investments. The above method is referred to as the perpetual inventory method proposed by Christensen and Jorgenson (1969). Implicit in this method is the assumption that the flow of capital services in any given year is independent of the output produced in that year.

The method explained above requires inventory data on capital stock. Since such data are usually not available, simple proxies are commonly used to measure the capital stock. For instance, number of beds in a hospital has been used as an approximate measure of hospital capital stock.14 These proxies are

14 See Wagstaff (1989), Rosko (2001), Filippini (2001) and Crivelli et al. (2002) for examples.

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only indicative measures of capital and do not necessarily represent the actual capital stocks especially the medical equipment used in a hospital.

Different types of capital inputs have different roles in the production. For instance, compared to a pharmacy unit, a hospital bed has a relatively higher importance in the production process. Ideally, different capital types should be considered as separate input factors. This approach is however cumbersome. Moreover, the share of capital costs is usually low. According to our data on average, capital costs constitute less than 10 percent of a hospitals total costs. It is generally assumed that to the extent that they incur similar costs, different capital stocks have a uniform effect on production. The capital costs are however reported differently across hospitals. In particular, hospitals have different accounting procedures for amortization of their new investments.

Labor inputs also exist in different categories. Distinguishing these categories is fairly straightforward. Given that medical services are quite labor-intensive15, any refinement in labor inputs has a relatively high added value for the accuracy of the estimations. Especially, the physicians share of labor input is significantly different from other staff in both costs and type of activity. Physicians services are usually in the form of brief interventions and visits rather than continuous care. Moreover, in many cases physicians are not directly employed by the hospitals and are paid per case or per intervention. For instance, in the US only public hospitals are allowed to hire physicians. In Switzerland, hospitals usually have access to two types of medical staff: salaried physicians hired by the hospital, and private physicians who are authorized by the hospital to treat their patients. Both types may be paid per intervention. These fees can be an important part of physician costs in a hospital and can vary a lot across hospitals. For instance, large hospitals have more salaried physicians whereas small hospitals may use private affiliated physicians more frequently. A reasonable measurement of physician services requires data on the worked hours for each intervention. However, the hours of such services are usually not reported. The measurement of physicians productivity is therefore problematic. The labor price of physicians can however be approximated by the data on salaried physicians that exist in all Swiss general hospitals. The payroll data usually provides the information on salary and paid hours for the salaried physicians.

Many authors have considered labor inputs in two categories. For instance Eakin (1991) considers physicians and other staff and Folland and Hofler (2001) consider nursing staff and other employees in separate categories. Others like Scuffham et al. (1996) and Vita (1990) used four labor categories. Scuffham et al. considered medical staff, nurses, other health professions, and general staff as separate groups; and Vita considered management personnel and supervisors, non-physician and technical staff, nursing staff, and auxiliary personnel as separate inputs. Steinmann and Zweifel (2003) have considered three categories of labor (academic staff, nursing staff and administrative personnel) and non- 15 Our data show that labor costs constitute about 70 percent of total costs in a typical hospital in Switzerland.

10

labor expenses as separate input factors. Certain authors like Eakin (1994) and Scuffham et al. (1996) have also used materials as an input factor in addition to capital and labor inputs.

An aggregate input index can be constructed by dividing total expenditures by an aggregate input price index. This aggregate price index is an overall price of hospital inputs (including labor, capital and other inputs). Such aggregate price indices are usually estimated by regulation authorities and are available for certain industries.16 Hospital inputs however, have a relatively complex nature and cannot be measured with a single price index. Hospital aggregate input can also be measured by a weighted sum of all input indices, the weights being the respective cost shares of each input factor.17 2.1 Simple performance indicators Simple indicators are ratio-type measures that do not require a multivariate stochastic or deterministic analysis. Regulators use simple indicators to encourage cost-efficiency in hospitals. The cost-efficiency targets used by the UK National Health Services is one example.18 These indicators can be considered in four categories:

- Productivity indicators; - Indicators of hospital cost structure; - Output characteristics; - Other hospital characteristics.

Productivity indicators can be classified into two main groups: partial productivity indicators and total factor productivity indices. Oum et al. (1999) provide a survey of different productivity indicators.19 A partial productivity measure relates a firms output to a single input factor. These indicators are also called performance ratios. The performance ratios can be defined as the ratio of final output produced to a single input factor used in the production process. For instance labor productivity index can be defined as the number of patients treated in a hospital for every hospital employee. These measures can also be considered for any segment of the production process, that is the relation between an intermediary output and an intermediary input. For instance number of medical files handled for every administrative worker can be considered as a partial productivity measure.

The advantage of partial indicators is that they are easy to construct and understand. The problem is the fact that the productivity of a single input factor

16 See Waters and Tretheway (1991) for an example related to railway industry. 17 This measure is based on the assumption that hospitals take the input prices as given and maximize profits based on a Cobb-Douglas production function with constant returns to scale. 18 The reference cost index in this case was chosen as an activity-weighted average cost of each HRG (health resource group) relative to the national average. 19 Although Oum et al. (1999)s paper is not related to hospitals its definitions are general and apply to any industry.

11

may depend on the level of other inputs used in the production. This implies that high productivity of one input factor may be because of a relatively low productivity of some other inputs. Partial productivity factors can however give useful insights for identifying productivity problems. In this study we consider several indicators of labor and capital productivity. Separate labor productivity indicators are considered for all hospital employees and nursing staff. These indicators will be presented in chapter 4.

Total factor productivity (TFP) can be defined as the ratio of a total output quantity measure to an index of total input quantity, that is: output index

input indexTFP = . TFP

measures are generally used as relative measures between at least two firms or one firm in two different years. Several procedures have been proposed in the literature. These methods are generally referred to as index number procedures. Tornqvist index and Fisher ideal index are two of the most commonly used measures.20 The results are however, sensitive to the adopted weights and the measurement units of input factors, thus difficult to interpret. Given the high sensitivity and unrealistic variation of these measures we decided to exclude simple TFP indicators from this chapter.21 Instead, we focus on partial productivity indicators that are clearly defined and thus can be easily interpreted.

Jacobs and Dawson (2003) propose a hospital-specific cost indicator for the UK hospitals, defined as the hospitals total costs divided by an output index. This input index is defined as the weighted sum of hospitals outputs that is; HRG-adjusted number of inpatient cases, outpatient visits, and the number of accident and emergency visits, with the weights for each output being the national share of expenditure of that output.

The hospitals cost structure can be characterized by simple indicators such as average unit costs and the cost share and price of different input factors. Average unit costs are considered for an output based on the DRG-adjusted number of cases. Several input factors are considered in the analysis: capital, physicians, nursing staff, and other categories of hospital personnel. Capital stock can be proxied by the number of hospital beds, that is, capital price is approximately defined as the capital costs per bed. Price of labor can be calculated as the ratio of salaries and wages to the total number of remunerated days for each category.

Output characteristics can be considered in two groups: The first set of indicators measure the quality of hospital output. All these indicators represent hospitals structural quality in the Donabedian (1980)s sense. Quality of labor can be measured by the percentage of certified physicians (physicians with FMH), proportion of qualified and teaching nurses, number of physicians per bed, and number of nursing staff per bed. Seven indicators are considered for the provision of hospital amenities such as emergency room, operating room, waking 20 See Coelli et al. (2003, 1997) and Oum et al. (1999) for surveys of TFP measurement with index numbers. 21 However, we will use the cost frontier analysis to estimate measures of TFP growth. The advantages of these measures over simple TFP indicators will be discussed in section 2.2.

12

room, computer tomography, MRI (magnetic resonance imaging) facility, chemical laboratory and pharmacy.

Note that the structural quality measures are only indicative of the hospitals potential ability in provision of high-quality care. The second set of output characteristics are directly related to hospitals actual activities. This set consists of indicators such as: the average length of a hospitalization; percentage of ambulatory care revenue22 over total revenue from all medical services; percentage of semi-hospitalization cases over all admissions; proportion of private and semi-private insurance patient-days; and proportion of private and semi-private insurance semi-hospitalizations.

Other hospital characteristics considered in this study are three binary indicators respectively for public and subsidized hospitals, private for-profit hospitals, and private not-for-profit hospitals. Finally, an indicator is considered for the access to outside private physicians. This variable is defined as the number of private affiliated physicians per hospital bed, who are not directly employed by the hospital but are allowed to treat their patients in the hospital.

Although all the above indicators are legitimate measures of hospital performance, the main characteristics can be summarized in a relatively small number of indicators. As we see later the Swiss general hospitals are classified into five categories that represent relatively uniform groups of hospitals in terms of size and services. In fact many of the above indicators especially those that represent structural quality are similar within these categories. Therefore, we have decided to focus on a selected set of simple indicators that represent the main performance aspects of a hospital while avoiding lengthy lists of numbers.

2.2 Indicators derived from cost frontier approach

Cost frontier analysis can be used to estimate indicators of cost-efficiency, scale efficiency and total factor productivity growth. The main focus of this study is on the cost-efficiency indicators and estimates of scale economies. The TFP growth is also studied and decomposed in three components driven by scale efficiency, cost efficiency and technical change.

There are several cost frontier methods to estimate the cost efficiency of individual firms. Two main categories are non-parametric methods originated from operations research, and econometric approaches namely stochastic cost frontier models.23 In non-parametric approaches like Data Envelopment Analysis (DEA), the cost frontier is considered as a deterministic function of the observed variables but no specific functional form is imposed.24 Moreover, non-parametric approaches are generally easier to estimate. Parametric methods on the other

22 The number of cases in outpatient or ambulatory services is not reported in our data. However, the information on the revenue of these services is available. 23 See Kumbhakar and Lovell (2000) for an extensive survey of parametric methods and Coelli et al. (1998), chapter 6, and Simar (1992) for an overview of non-parametric approaches. 24 See Coelli et al. (2003) for more details on DEA. See also Steinmann and Zweifel (2003) for an application of DEA to estimate the efficiency of Swiss hospitals.

13

hand, allow for a random unobserved heterogeneity among different firms but need to specify a functional form for the cost function. The main advantage of such methods over non-parametric approaches is the separation of the inefficiency effect from the statistical noise due to data errors, omitted variables etc. The non-parametric methods assumption of a unique deterministic cost frontier for all hospitals is unrealistic. Another advantage of parametric methods is that these methods allow statistical inference on the significance of the variables included in the model, using standard statistical tests. In non-parametric methods on the other hand, statistical inference requires elaborate and sensitive re-sampling methods like bootstrap techniques.25 Given the above discussion we decided to focus on the stochastic cost frontier models in this report.

Many authors have used cost frontier models to evaluate hospitals efficiency. Zuckerman et al. (1994), Linna (1998) are two examples. The former paper used a translog functional form while the latter used a Cobb-Douglas cost function. Rosko (2001) has also used the frontier approach with a translog cost function and with instrumental variables to account for the potential endogeneity of capital and labor prices. The use of cost frontier models to evaluate efficiency in the health-care sector has been criticized by Newhouse (1994) and Skinner (1994). The main arguments against these models are related to the unobserved heterogeneity due to differences in case-mix and quality and the errors committed by aggregation of outputs as well as non-testable assumptions on the distribution of efficiency.

Folland and Hofler (2001) provide a discussion on the reliability of hospital efficiency estimates obtained from stochastic cost frontier models. These authors show that the individual efficiency estimates are rather sensitive to the adopted model specification and functional form. However, the results are robust when the comparisons are performed between hospital group mean inefficiencies. This finding is consistent with the results reported by Hadley and Zuckerman (1994) suggesting that the stochastic frontier analysis of hospitals efficiency is of practical use when applied for comparing group means. Farsi, Filippini and Kuenzle (2003) reached a similar conclusion in their study of the Swiss nursing homes.

The concept of cost frontiers is illustrated in figure 1. The output and total cots are respectively given in horizontal and vertical axes. A frontier cost function defines minimum costs given output level, input factor prices and the existing production technology. Generally, a cost frontier model can be presented as: TC = f (Y, P)+ , where TC is the total cost; Y is its output vector; and P is the vector of input factor prices. Theoretically the perfectly efficient firms are located on the cost frontier f (Y, P). However, the observed costs of other firms can be higher than their corresponding frontier costs. The difference () represents the firms excess cost, which is shown as the vertical distance of the observed costs from the cost frontier (i in figure 1). Part of this excess cost may 25 These methods are available for rather special cases and have not yet been established as standard tests. See Simar and Wilson (2000) for an overview of statistical inference methods in non-parametric models.

14

be related to differences in external factors that are not related to the firms inefficiency. For instance hospitals that treat sicker patients have higher costs. Assuming that our cost frontier already accounts for the observed differences among hospitals, the firm is excess cost (i) can be decomposed into two parts. The first part is due to the unobserved differences between firms (shown as vi in the figure) and the second component is related to the inefficiency of the firm (shown as ui).

Here we focus on stochastic cost frontier models, that is, the deterministic frontier models like Corrected OLS26 are excluded. In the deterministic methods, it is assumed that all the relevant factors are observed and accounted for, which means that the term vi is zero. The main shortcoming of deterministic models is that they do not distinguish inefficiency from statistical noise. In these models there is only one stochastic term (ui) that represents the relative inefficiency. The cost frontier is therefore identical for all observations, thus deterministic.

In stochastic frontier models on the other hand, the cost frontier is specific to each firm. Therefore, the cost frontier (as shown in figure 1) represents the expected locus of the minimum costs of all firms. With certain assumptions on the distribution of the two error components (ui and vi) stochastic cost frontier methods can distinguish between these two components.27 The inefficiency measure of a given firm is therefore the ratio between its observed total cost and

its corresponding frontier cost that is: frontier

observed

TCTC , where TC represents the total

costs. Cost frontier models also allow an estimation of scale efficiency. Scale efficiency indicates the degree to which a company is producing at optimal scale. The optimal size of a firm is defined as the amount of output that minimizes the average cost of producing one unit of output. This concept is illustrated in figure 2. If a given firms output is less than this optimal level, there are unexploited scale economies, whereas for firms larger than the optimal size there are diseconomies of scale. Frisch (1965) defines the optimal scale as the level of operation where the scale elasticity is equal to one. The degree of returns to scale (RS) is defined as the proportional increase in output (Y) resulting from a proportional increase in all input factors, holding all input prices and output characteristic variables fixed (Caves et al., 1981). The RS degree may also be defined in terms of the effects on total costs resulting from a proportional increase in output (Silk and Berndt, 2003). This is equivalent to the inverse of the elasticity of total cost with respect to the output.28 26 This frontier model has been developed by Greene (1980) based on Richmond (1977)s Corrected Ordinary Least Squares method. See Wagstaff (1989) and Filippini and Maggi (1993) for some applications of this method. 27 Notice that in deterministic models like COLS, there is no need for any distribution assumption. 28 The inverse of cost elasticity of output is referred to by Chambers (1988), as the economies of size rather than economies of scale, which are defined in regards to production function. Scale and size economies are equivalent if and only if the production function is homothetic (see Chambers, 1988, page 72). However, as for the purpose of this study we are more interested in the cost effects of output, we define the returns to scale in terms of cost elasticity.

15

Figure 1: Stochastic cost frontier and cost efficiency

TC

Y

Frontier cost function

TCobs

TCfro

frontier

observedi TC

TCEFF =

vi

ui i

Frontier cost (firm i)Observed cost (firm i)

Yi

Figure 2: An illustration of scale economies

Average costs (AC)

Output (Y)

Economies of scale Diseconomies of scale

Y* optimal size

AC*

16

The returns to scale can therefore be obtained from:

=Y

TCRSln

ln1 , (1)

where TC and Y represent the total cost and output respectively. There are increasing returns to scale if RS is greater than 1, and conversely, there are decreasing returns to scale if RS is below 1. In the case of RS = 1 we have a constant returns to scale situation. Economies of scale exist if the average costs of a nursing home decrease as output increases. Returns to scale parameter can be readily obtained from the estimated cost function.

Notice that a similar methodology (as shown in figure 1) can be applied to variable costs, that is total costs net of fixed or quasi-fixed costs such as capital costs. In this case the fixed input factors are considered as given. The cost efficiency indicators based on variable costs represent the short-run efficiency, because they do not include the inefficiencies caused by quasi-fixed input factors that could change over relatively long periods of time. As for the scale efficiency both long-term and short-term indicators can be obtained at least theoretically, from a variable cost frontier model. The following equations give respectively, the short-term and long-term returns to scale based on variable costs:

ln11 lnln lnln ln

s h o r t l o n g

V CKR S R S

V C V CY Y

= =

(2)

In these equations the variable costs (total cost net of capital expenditures) and the capital stock are respectively denoted by VC and K. Theoretically, the scale economies in the long run should be greater than those obtained in the short run.29 This is implied by the theoretical condition that the variable cost function is decreasing in capital stock. However, the empirical results documented in the literature show that this condition is not satisfied in many cases.30

29 See Caves et al. (1981) for an extensive review of scale economies estimated from variable cost functions, and Sung (2002) for a recent application. 30 See Gagn and Quellette (2002) and Filippini (1996) for examples.

17

Functional form The cost frontier is a function of output and input factor prices. Other

hospital and output characteristics like quality indicators can also be included as independent variables. A general cost frontier model with M outputs, N inputs and K output characteristics can be defined as:

1 1 1( , . . . , ; , . . . , ; , . . . , )M N KT C f Y Y P P Z Z= (3)

where TC is the total costs; Ym (m=1,.., M) are the outputs; Pn (n=1,N) are the input factor prices; and Zk (k=1,.., K) are output characteristics and other exogenous factors that may affect costs.

There are several functional forms that can be used for a cost function. Griffin et al. (1987) provide a comprehensive list of alternatives. These authors have also proposed a series of criteria for selecting the functional form in cost and production analyses. These criteria can be grouped in four categories corresponding to hypotheses, estimation methods, data and application. The first category concerns the restrictions imposed by the maintained hypotheses. In the absence of such hypotheses the unrestrictive forms are more appropriate. Second, the availability of data may restrict the choice of statistical estimation procedures. As the number of variables increase, most functional forms require a geometrically increasing number of parameters to be estimated, thus necessitate much larger samples. The third criterion concerns the conformity of the functional form to the data. Finally, in some applications, some properties are desired in the functional form, because for instance they might be used in simulations.

In this study the most important restrictions are related to the sample size and the estimation method. The best choice is therefore a functional form that can be estimated with available estimation procedures and limits the number of parameters while using as many relevant variables as possible. In the first step of this analysis, we focused on two models, Cobb-Douglas and translog, which are most commonly used in the literature. These models are linear in coefficients and can be estimated, with some distribution assumptions, using a reasonably well-behaved likelihood function.31 As we will explain later, at the end we used only the Cobb-Douglas form.

Cobb-Douglas (log-linear) model is one of the most commonly used functional forms. A Cobb-Douglas cost function can be written as:

01 1

l n ln lnM N

m m n n k km n k

T C Y P Z = =

= + + + (4)

31 See Greene (2002a) for more details on the maximum likelihood estimation method applied to cost frontier models.

18

The main advantage of this model is its simplicity. Thanks to its limited number of variables the Cobb-Douglas form has a practical advantage in statistical estimations over more complicated forms. The interpretation of the results is also easier because it does not include any interaction term. Another interesting characteristic of this function is self-duality. Namely, the corresponding production function of a Cobb-Douglas cost function is also log-linear. The main shortcoming of this model is that the returns to scale (RS as defined in equation 1) are assumed to be constant. One can expect that the scale economies change with the output level. Using the same proportional increase in output, small companies usually gain more than large firms, by saving in their fixed costs. However, in some industries, it might be the case that the scale economies do not vary much in the range of observed data. The potential changes in scale economies with output can be analyzed using more flexible functional forms. One of the main flexible forms is transcendental logarithmic (translog) model. This model is a second-order Taylor approximation of any arbitrary function and can be written as:

0l n ln ln

1 1ln ln ln ln2 21 ln ln2

m m n n

p q p q r s r s

p r p r k kk

T C Y P

Y Y P P

Y P Z

= + ++ +

+ +

(5)

Translog form can give a local approximation to any general functional form. However, it is not as powerful as it appears at the first impression. From a practical point of view, a translog model requires the estimation of a large number of parameters that can substantially reduce the efficiency of the statistical method. Furthermore, the interaction terms included in the translog model may cause multicollinearity, which can reduce the models statistical performance. A special case of the translog model can be obtained by imposing homotheticity to the cost function that is, by excluding the interaction terms between prices and outputs (lnYplnPr). This alternative has a practical advantage over the original model in that it has fewer parameters. It is generally assumed that the cost function given in equation 3 is the result of cost minimization given input prices and output. Cost functions should therefore satisfy certain properties.32 Mainly, the cost function must be non-decreasing, concave, linearly homogeneous in input prices and non-decreasing in output. The linear homogeneity in input prices implies that the coefficients of factor prices (n in equation 4 or 5) add to one.33 This constraint is usually 32 For more details on the functional form of the cost function see Cornes (1992), p.106. 33 Linear homogeneity in prices means that if all input prices increase proportionally, the costs will increase with the same proportion. As a result of this property, the coefficient of any given factors price in the cost function represents that factors share of total costs. The sum should naturally be one if all the factor prices are included.

19

imposed by dividing total costs and input prices by one of the factor prices. However, as we see later in chapter 5, we do not impose this constraint because our models do not include all input factors. The other theoretical restrictions are usually verified after the estimation. In particular, the concavity of the estimated cost function reflects the fact that the cost function is a result of cost minimization.

As we will see later there are at least 15 important variables that are essential for our cost models. Compared to the sample size that is limited to about 500 observations, the number of parameters in more general functional forms can be excessively high. For instance the adopted specification with a general (non-homothetic) translog model could easily have more than 30 parameters. Moreover, the primary purpose of this study is hospitals cost efficiency and the scale economies come only as secondary results. We therefore decided to focus on the Cobb-Douglas model as our main functional form. Because of its simplicity, this functional form is commonly used in recent papers on cost-efficiency measurements such as Greene (2003, 2004) and Linna (1998)

In addition, we have estimated several specifications with translog form. The results (not reported here) indicate that the cost frontier estimations with translog form appear to be numerically unstable when applied to our data. In fact these models tend to converge to a degenerate solution34 in which the inefficiency term cannot be identified. Therefore, we decided to restrict our presentation to the models based on Cobb-Douglas form, which have a reasonably general form and at the same time require a limited number of parameters to be estimated.

Econometric specification

There are a number of econometric approaches to estimate stochastic cost frontier models. Kumbhakar and Lovell (2000) provide an extensive survey of these methods. A general form of a stochastic cost frontier can be written as:

1 1 1( , . . . , ; , . . . , ; , . . . , )i t i t M i t i t N i t i t K i t i t i tT C f Y Y P P Z Z u v= + + (6)

where subscripts i and t represent the firm and year respectively; uit is a positive stochastic term representing inefficiency of firm i in year t; vit is the random noise or unobserved heterogeneity; and other variables are similar to equation 3. Typically, it is assumed that the heterogeneity term vit is normally distributed and that the inefficiency term uit has a half-normal distribution that is, a normal distribution truncated at zero:

2 2 ~ (0, ) , ~ (0, ).it u it vu N v N (7)

34 The variance of one of the stochastic components degenerates to zero. The numerical problems are probably due to the fact that this solution locates at the boundary of the parameter space and do not necessarily maximize the likelihood function with the given specification.

20

The above model with a half-normal/normal error structure is actually an extension of Aigner et al. (1977)s model for panel data. In this model all the observations are pooled together regardless of whether they belong to the same firm or not.

An important variation of the pooled model is Pitt and Lee (1981)s model in which the inefficiency term uit is assumed to be constant over time, that is:

2~ (0, )i uu N . There is also another version of this model (proposed by Schmidt and Sickles (1984)), that relaxes the distribution assumptions on both ui and vit, and estimates the model using Generalized Least Squares (GLS) method. Both models are versions of random-effects model.35 The advantage of these models is that they use the panel aspect of the data to estimate the parameters, thus should be more efficient.36 In cases where the individual firm effects (ui) are correlated with the explanatory variables, the estimated parameters may be biased. Schmidt and Sickles (1984) proposed a fixed-effects approach to avoid such biases. In this model the inefficiency term is not random and is estimated as an intercept for each company.

There is however, an important practical problem with the fixed-effect model in that it requires the estimation of a large number of parameters, which limits its application to reasonably long panels with sufficient within-firm variation. Generally, in short panels the fixed effects are subject to considerable estimation biases, which directly reflect in the inefficiency scores.37 Given that our data is a rather short panel of four years, the fixed effects model is not a quite feasible approach. Moreover, our preliminary analysis shows that in virtually all the main variables, the between variations are dominant and the within variations are comparatively insignificant.38

Another important issue is that in both fixed and random effects models discussed above, the inefficiencies are assumed to be constant over time. This is an unrealistic assumption in most practical cases, where the driving forces of cost-inefficiency are not generally persistent. In fact firms constantly face new problems39 and revise their strategies. Moreover, there exist incentive mechanisms (either through regulation and monitoring or through profit and career incentives) that induce managers to correct their past suboptimal decisions.

Greene (2004, 2002b) proposes a new approach that integrates the random and fixed effects approaches into the original Aigner et al. (1977)s model. These

35 In panel data models random-effect approach is referred to models that take individual effects (here ui) as identically independent distributions (iid). This is in contrast with the fixed-effect approach that considers the individual effects as constants. 36 Efficient in statistical terms means more accurate. 37 See Greene (2004, 2002b) for more details. This author considers a panel of 5 years as a short panel. 38 In contrast with between variations that are related to the differences across companies, within variations correspond to the changes in a given company over time. 39 These problems may emerge from the implementation of new techniques, or from dealing with new regulation systems, or other external constraints.

21

models are labeled as true random effects and true fixed effects models.40 These models can be written as an extension to equation 6:

1 1 1( , . . . , ; , . . . , ; , . . . , )i t i t M i t i t N i t i t K i t i i t i tT C f Y Y P P Z Z u v= + + + (8)

where i is a firm-specific stochastic term that could be an i.i.d. random component in random-effects framework, or a constant parameter in fixed-effects approach. These models have an important advantage over all other models in that they not only allow for time-variant inefficiency while controlling for firm-level unobserved heterogeneity through fixed or random effects. The main difficulty of these models is that they are numerically cumbersome. In particular, our experience suggests that in cases where the within variation in the data is low, these methods are numerically unstable. In our data, our analysis shows that these models were not numerically feasible. This can be explained by the small number of periods in our sample and its relatively low within variations. As we see later in the chapter 3, our sample is an unbalanced data with maximum 4 periods but on average it has about three periods. Moreover, our experience shows that such models can substantially reduce the inefficiency estimates especially in cases like hospitals, where the heterogeneity is considerable.41 The data constraints and also the numerical restrictions bring us back to the original pooled frontier model in line with Aigner et al. (1977) as in equation 6. However, we also estimated Pitt and Lee (1981)s model and checked if the results are consistent. Our analysis (not reported here) indicates that in terms of scale economies the two models provide comparable results. In terms of efficiency estimates the results show a quite high correlation. However, the results estimated from Pitt and Lees model were systematically higher than those of the pooled model. This difference can be explained by the fact that the inefficiency estimates from Pitt and Lees model capture other sources of heterogeneity across hospitals that are not necessarily related to inefficiency. In fact our analysis suggests that the firm-specific effects capture a significant part of between variations in costs and reflect them as inefficiency. Given that there may be a great amount of unobserved heterogeneity among hospitals, we contend that these estimates are likely to be exaggerated. Therefore, we restricted our analysis to the pooled model as shown in equation 6.

2.3 Total factor productivity growth

The measures of the TFP growth can be divided into three groups: price-based index numbers, indicators based on cost frontier analysis, and measures derived from production frontier analysis. The price-based index numbers are simple TFP indicators that were briefly discussed in the previous section.42 An important shortcoming of these measures is that they can only give an overall

40 See Farsi, Filippini and Kuenzle (2003) for an application in Switzerlands nursing homes. 41 See Farsi, Filippini and Kuenzle (2003) for a detailed discussion. 42 See Coelli et al. (2003) for an extensive discussion of price-based index numbers.

22

estimate of total growth that could be driven by changes in efficiency, scale economies as well as technical progress. The decomposition of growth into different components is only possible using a cost or production frontier model. Here, we focus on the stochastic cost frontier approach.

The general formula to estimate the TFP growth of firm i between periods 0 and 1 in a single-output production is given as:43

( ) ( ) ( )

1 0

0 10 1

0 1 1 0

l n ( / )l n ln

ln ( / ) 0 . 5

0 . 5 1 1 . l n ln

i i

i ii i

i i i i

T F P T F PT C T C

C E C Et t

Y Y

= +

+ +

(9)

where CEis is the cost-inefficiency estimate of firm i in period s, given as exp(uis), with uis being estimated from cost frontier model in equation 6 or 8. TC represents the estimated total cost function; Y is the output; t denotes the time; and is defines the output elasticity given by: lnln i si s

T CY

which can be calculated

from the estimated total cost function. The terms on the right-hand-side are respectively the growth components

resulted from changes in cost efficiency, from technical progress, and from changes in scale efficiency. This formula gives a logarithmic measure of change in TFP over one period with a single output using a total cost function. However, the method is readily extensible to more periods, multi-output functions and variable cost functions. If the changes in TFP are sufficiently small the logarithmic measure is conveniently interpretable as a proportional change, that is: l n T F P T F P

T F P .

3 Data In this chapter we present the data used in this project. A discussion of the

main patterns and trends observed in the data is also included. The data sets used in this study are extracted from the annual data reported by Swiss hospitals to the Federal Statistical Office from 1997 to 2001.44 These data consist of the financial information of about 420 hospitals that operated in Switzerland during this period. These hospitals include both general hospitals and specialized clinics. In this study we focus on general hospitals. These hospitals that provide short-term general medical care form a relatively uniform sample regarding the production process. The specialized clinics which constitute about half of Swiss hospitals are therefore excluded. These clinics are specialized in a single type of medical care varying from psychiatric care and rehabilitation to surgeries and obstetrics. The financial data are merged with another set of data that consists of the medical 43 See Coelli et al. (2003) for more details and the equations for multi-output cases. 44 The 1997 data are not complete.

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data on the number of cases in each APR-DRG classification.45 The DRG data are available for 1998 through 2001. Since in our main estimations, we use the DRG data to adjust the number of cases in a hospital, we decided to focus on the 1998-2001 data. Another reason for excluding the 1997 data is the relatively low quality of the data in this year, suggested by a great number of missing values and outliers.46 Furthermore, the data are not complete in 1997. For instance out of 161 general hospitals with records for 1997, only 54 hospitals have all the variables used in the regressions studied in this report.

The final sample (after excluding specialized clinics) consists of an unbalanced panel with 747 observations from 1998 through 2001. According to these data, overall 214 general hospitals have operated in Switzerland during this period. Only for 158 general hospitals, the data are available for all four years. The number of general hospitals reported in the data is different in every year. Year 1999 with 195 observations has the highest number of general hospitals. In 1998, 2000 and 2001 the information is available respectively for 191, 184 and 177 general hospitals. These missing observations may be related to missing reports or may as well represent hospitals that have closed or started to operate in a year during the study period. Each hospital is identified by a unique identification number. We do no have access to hospital names or addresses.

The variables are presented in six subsets in Microsoft Access format. The general data like hospital ownership and legal status, and the types of medical services offered by the hospital are respectively given in the first and second subsets. The third subset consists of information about the working days of the hospital employees by profession. This data was later completed using a complementa