The specification of a hospital cost function. A comment on the recent literature

Estimating health care costs at scale in low- and middle-income countries: Mathematical notations and frameworks for the application of cost functions

Appropriate costing and economic modeling are major factors for the successful scale-up of health interventions. Various cost functions are currently being used to estimate costs of health interventions at scale in low- and middle-income countries (LMICs) potentially resulting in disparate cost projections. The aim of this study is to gain understanding of current methods used and provide guidance to inform the use of cost functions that is fit for purpose. We reviewed seven databases covering the economic and global health literature to identify studies reporting a quantitative analysis of costs informing the projected scale-up of a health intervention in LMICs between 2003 and 2019. Of the 8725 articles identified, 40 met the inclusion criteria. We classified studies according to the type of cost functions applied-accounting or econometric-and described the intended use of cost projections. Based on these findings, we developed new mathematical notations and cost function frameworks for the analysis of healthcare costs at scale in LMICs setting. These notations estimate variable returns to scale in cost projection methods, which is currently ignored in most studies. The frameworks help to balance simplicity versus accuracy and increase the overall transparency in reporting of methods.

Estimation of a physician practice cost function

OBJECTIVE

The goal of the present paper is to provide evidence on the behavior of physician practice cost functions.

DATA SOURCES

Our study is based on the data of 3686 physician practices in Germany for the years 2006 to 2008.

STUDY DESIGN

We apply a translog functional form and include a comprehensive set of variables that have not been previously used in this context. A system of four equations using three-stage least squares is estimated.

PRINCIPAL FINDINGS

We find that a higher degree of specialization leads to a decrease in costs, whereas quality certification increases costs. Costs of group practices are higher than of solo practices. The latter finding can be explained by the existence of indivisibilities of expensive technical equipment. Smaller practices do not reach the critical mass to invest in certain technologies, which leads to differences in the type of health care services provided by different practice types.

CONCLUSIONS

This is the first study to use physician practices as the unit of observation and to consider the endogenous character of physician input. Our results suggest that identifying factors that influence physician practice costs is important for providing evidence-based physician payment systems and to enable decision-makers to set incentives effectively.

Has Price Competition Changed Hospital Revenues and Expenses in New York?

This study analyzes the factors that influenced hospital expenses and revenues prior to and following the enactment of the New York State Health Care Reform Act of 1996 (HCRA)—the period from 1994–1999. HCRA was expected to encourage price competition which in turn was anticipated to lower hospital revenues and expenses. We measured the differential effects on hospital revenues and expenses in markets with varying degrees of competition. We also measured the relationship between hospital revenues and expenses and the increased concentration resulting from the formation of local hospital systems. We found that revenues and expenses both grew more slowly for hospitals located in more competitive markets; hospital systems that increased concentration tended to have higher revenues. In the short run at least, price competition induced by HCRA did constrain both hospital expense and revenue growth, although the increase in hospital mergers countered this trend.

Effects of Specialty Hospitals on the Financial Performance of General Hospitals, 1997–2004

Hospital specialization has become a controversial topic, culminating in a moratorium issued in 2003 by Congress directing the Centers for Medicare and Medicaid Services to cease payments to new physician-owned specialty hospitals for those Medicare and Medicaid patients referred by physicians with a financial interest in the facility. This paper focuses on one important economic question: does the presence of specialty hospitals in a market affect general hospitals' financial performance? We estimate longitudinal fixed-effects models for a national panel of short-term acute care hospitals for the period 1997 though 2004; models are estimated for general hospital patient-care revenue, costs, and operating margins. We find that the presence of one or more new or established specialty hospitals in a market has a negative effect on general hospital costs and a positive effect on general hospital operating margins. Results, which were consistent across several different modeling approaches, imply that the presence of specialty hospitals encourages greater efficiency on the part of incumbent general hospitals, and the existence of profits attracts market entry. Our findings question the contention that competition from specialty hospitals harms general hospitals financially.

The Economies of Scale for Nursing Home Care

Using a modified hybrid short-term operating cost function and a national sample of nursing homes in 1994, the authors examined the scale economies of nursing home care. The results show that scale economies exist for Medicare postacute care, with an elasticity of –0.15 and an optimal scale of around 4,000 patient days annually. However, more than 68 percent of nursing homes in the analytic sample produced Medicare days at a level below the optimal scale. The financial pressures resulting from the implementation of a prospective payment system for Medicare skilled nursing facilities may further reduce the quantity of Medicare days served by nursing homes. In addition, the results show that chain-owned nursing homes do not have lower short-term operating costs than do independent facilities. This indicates that the rationale behind recent increasing horizontal integration among nursing homes may not be seeking greater cost efficiency but some other consideration.

Demand uncertainty and hospital costs: an application to Portuguese public hospitals

In this paper, we evaluate the effect of demand uncertainty on hospital costs. Since hospital managers want to minimize the probability of not having enough capacity to satisfy demand, and since demand is uncertain, hospitals have to build excess capacity and incur the associated costs. Using panel data comprising information for 43 Portuguese public hospitals for the period 2007-2009, we estimate a translog cost function that relates total variable costs to the usual variables (outputs, the price of inputs, some of the hospitals' organizational characteristics) and an additional term measuring the excess capacity related to the uncertainty of demand. Demand uncertainty is measured as the difference between actual and projected demand for emergency services. Our results indicate that the cost function term associated with the uncertainty of demand is significant, which means that cost functions that do not include this type of term may be misspecified. For most of our sample, hospitals that face higher demand uncertainty have higher excess capacity and higher costs. Furthermore, we identify economies of scale in hospital costs, at least for smaller hospitals, suggesting that a policy of merging smaller hospitals would contribute to reducing hospital costs.

Do waiting times reduce hospital costs?

Using a sample of 137 hospitals over the period 1998-2002 in the English National Health Service, we estimate the elasticity of hospital costs with respect to waiting times. Our cross-sectional and panel-data results suggest that at the sample mean (103 days), waiting times have no significant effect on hospitals' costs or, at most, a positive one. If significant, the elasticity of cost with respect to waiting time from our cross-sectional estimates is in the range 0.4-1. The elasticity is still positive but lower in our fixed-effects specifications (0.2-0.4). In all specifications, the effect of waiting time on cost is non-linear, suggesting a U-shaped relationship between hospital costs and waiting times. However, the level of waiting time which minimises total costs is always below ten days.

Converting to critical access status: how does it affect rural hospitals' financial performance?

To improve rural access to care, the Balanced Budget Act of 1997 allowed eligible rural hospitals to convert to critical access hospitals (CAHs), which changed their Medicare payment from a prospective payment system (PPS) to a cost-based system. The objective of this paper is to examine the effects of CAH conversion on rural hospital operating revenues, operating expenses, and operating margins using an eight-year panel of 89 rural hospitals in Iowa. Ad hoc hospital revenue, cost, and profit functions were estimated using panel data fixed-effects linear models. We found that rural hospital CAH conversion was associated with significant increases in hospital operating revenues, expenses, and margins.

Capacity utilization and the cost of primary care visits: implications for the costs of scaling up health interventions

Objective

A great deal of international attention has been focussed recently on how much additional funding is required to scale up health interventions to meet global targets such as the Millennium Development Goals (MDGs). Most of the cost estimates that have been made in response have assumed that unit costs of delivering services will not change as coverage increases or as more and more interventions are delivered together. This is most unlikely. The main objective of this paper is to measure the impact of patient load on the cost per visit at primary health care facilities and the extent to which this would influence estimates of the costs and financial requirements to scale up interventions.

Methods

Multivariate regression analysis was used to explore the determinants of variability in unit costs using data for 44 countries with a total of 984 observations.

Findings

Controlling for other possible determinants, we find that the cost of an outpatient visit is very sensitive to the number of patients seen by providers each day at primary care facilities. Each 1% increase in patient through-put results, on average, in a 27% reduction in the cost per visit (p < 0.0001), which can lead to a difference of up to $30 in the observed costs of an outpatient visit at primary facilities in the same setting, other factors held constant.

Conclusion

Variability in capacity utilization, therefore, need to be taken into account in cost estimates, and the paper develops a method by which this can be done.

Examining variation in treatment costs: a cost function for outpatient methadone treatment programs

OBJECTIVES

To estimate a hybrid cost function of the relationship between total annual cost for outpatient methadone treatment and output (annual patient days and selected services), input prices (wages and building space costs), and selected program and patient case-mix characteristics.

DATA SOURCES

Data are from a multistate study of 159 methadone treatment programs that participated in the Center for Substance Abuse Treatment's Evaluation of the Methadone/LAAM Treatment Program Accreditation Project between 1998 and 2000.

STUDY DESIGN

Using least squares regression for weighted data, we estimate the relationship between total annual costs and selected output measures, wages, building space costs, and selected program and patient case-mix characteristics.

PRINCIPAL FINDINGS

Findings indicate that total annual cost is positively associated with program's annual patient days, with a 10 percent increase in patient days associated with an 8.2 percent increase in total cost. Total annual cost also increases with counselor wages (p<.01), but no significant association is found for nurse wages or monthly building costs. Surprisingly, program characteristics and patient case mix variables do not appear to explain variations in methadone treatment costs. Similar results are found for a model with services as outputs.

CONCLUSIONS

This study provides important new insights into the determinants of methadone treatment costs. Our findings concur with economic theory in that total annual cost is positively related to counselor wages. However, among our factor inputs, counselor wages are the only significant driver of these costs. Furthermore, our findings suggest that methadone programs may realize economies of scale; however, other important factors, such as patient access, should be considered.

Effects of ownership, subsidization and teaching activities on hospital costs in Switzerland

This paper explores the cost structure of Swiss hospitals, focusing on differences due to teaching activities and those related to ownership and subsidization types. A stochastic total cost frontier with a Cobb-Douglas functional form has been estimated for a panel of 148 general hospitals over the six-year period from 1998 to 2003. Inpatient cases adjusted by DRG cost weights and ambulatory revenues are considered as two separate outputs. The adopted econometric specification allows for unobserved heterogeneity across hospitals. The results suggest that teaching activities are an important cost-driving factor and hospitals that have a broader range of specialization are relatively more costly. The excess costs of university hospitals can be explained by more extensive teaching activities as well as the relative complexity of the offered medical treatments from a teaching point of view. However, even after controlling for such differences university hospitals have shown a relatively low cost-efficiency especially in the first two or three years of the sample period. The analysis does not provide any evidence of significant efficiency differences across ownership/subsidy categories.

A micro-costing approach to estimating hospital costs for appendectomy in a cross-European context

This paper aims (a) to determine whether variations in the hospital costs of appendectomy in EU member states are larger within individual countries or between different countries and (b) to explore causes for variations in costs between hospitals and countries. To do so, hospitalisation costs and reimbursement rates for appendectomy were obtained from 54 hospitals in nine European member states based on 1786 cases using a standardised methodology. Regression analysis was performed using hospital characteristics, treatment characteristics, and purchasing power parities (PPP) as explanatory variables in a multilevel framework. The within-country standard error was estimated to 294 euros (27%), whereas the between-country standard error was 796 euros (73%). Excluding hospitals in Spain, Hungary, and Poland, which had significantly lower costs than hospitals in the other countries in our analysis, the within-country standard error was 331 euros (57%) and the between-country standard error dropped to 248 euros (43%). Regression results show that the treatment decision for open surgery was associated with significantly lower costs, whereas a greater number of beds and a higher staff per bed ratio were associated with significantly higher costs. PPP explained a major part of the between-country variance.

Variations in hospitalisation costs for acute myocardial infarction - a comparison across Europe

The aim of this study was to determine whether between-country variations in hospital costs are larger than within-country variations and, furthermore, to explore reasons for this variability. For this purpose, we chose the primary treatment of patients with acute myocardial infarction (AMI) as an episode of care. We obtained hospitalisation costs and reimbursement rates from 45 hospitals in nine different EU member states (i.e. Denmark, England, France, Germany, Hungary, Italy, Netherlands, Poland, and Spain) for the year 2005. To further analyse the variations in hospital costs, we employed a hierarchical random effects model based on treatment and hospital characteristics and using purchasing power parities (PPPs) as a proxy for country-specific price levels. The between-country standard error was estimated at 2473 euros, whereas the within-country standard error was estimated at 1242 euros. Our regression analysis showed that percutaneous coronary intervention was associated with significantly increased hospitals costs compared to other treatment strategies. We were able to distinguish between three groups of countries with different cost levels based on the number of hospitals that were able to provide these services (i.e. percutaneous transluminal coronary angioplasty (PTCA) with intracoronary stenting). Excluding Hungary, Poland, and Spain, where none of the participating hospitals were able to provide these procedures, the between-country standard error decreased to 1632 euros, whereas the within-country standard error increased to 1416 euros. Finally, we observed exogenous price-level effects between countries and within countries for hospitals located in urban areas.

Health service costs in Europe: cost and reimbursement of primary hip replacement in nine countries

This paper assesses variations in the cost of primary hip replacement between and within nine member states of the European Union (EU). It also compares the cost of service with public-payer reimbursements. To do so, data on cost and reimbursement were surveyed at the micro-level in 42 hospitals in Denmark, England, France, Germany, Hungary, Italy, The Netherlands, Poland, and Spain. The total cost of treatment ranged from 1290 euros (Hungary) to 8739 euros (The Netherlands), with a mean cost of 5043 euros (STD +/- 2071 euros). The main cost drivers were found to be implants (34% of total cost on average) and ward costs (20.9% of total cost on average). A one-way random effects analysis of variance model indicated that 74.0% of variation was between and only 26% of variation was within countries. In a two-level random-intercept regression model, purchasing-power parities explained 79.4% of the explainable between-country variation, while the percentage of uncemented implants used and the number of beds explained 12.1 and 1.6% of explainable within-country variation, respectively. The large differences in cost and reimbursement between Poland, Hungary, and the other EU member states shows that primary total hip replacement is a highly relevant case for cross-border care.

Scale and scope efficiencies through hospital consolidations

The hospital sector in the Province of Ontario has recently completed a large scale restructuring marked by wide ranging hospital closures, mergers and program transfers. Given a generally inconclusive economics literature, regulators used an accounting, as opposed to an economic, approach when predicting gains to consolidations. This paper uses an economic cost function to examine economies of scale and scope in the years preceding restructuring, where there was little doubt that economies were possible. Issues relating to output aggregation, functional form, and scale and scope testing are addressed and an equilibrium cost function is derived from an estimated short run function to measure the cost concepts of interest. Using index and direct approaches, we examine a variety of potential reconfigurations and conclude that there were indeed large scale unexploited gains to strategic consolidation in the hospital sector. Furthermore, these gains may not have been detected using standard approaches in the literature.

Determinants of variation in the cost of inpatient stays versus outpatient visits in hospitals: A multi-country analysis

Information on hospital costs is key to many types of economic and financial analyses, yet many countries lack reliable estimates due partly to the time and resources required to undertake detailed costing studies. Accordingly, some analysts have used simple rules of thumb to estimate hospital unit costs, e.g., total hospital costs are allocated between departments assuming that the cost of an inpatient day equals a fixed number of outpatient visits. This paper first explores the extent to which these simple rules apply within and across countries. It then identifies determinants of variation in the relationship between the cost of outpatient visits and inpatient days, then uses the estimated relationship to calculate average costs of inpatient and outpatient stays for countries where data are not yet available. Cost information from 832 hospitals in 28 countries are used. We show that simple rules of thumb do not prove to be an accurate basis for cost estimates. The ratio of inpatient to outpatient unit costs varies with GDP per capita, hospital size, ownership, and occupancy rate. We show how the estimated relationship can be used to calculate a mean cost of inpatient stays and outpatient visits, taking into account differences in the levels of key determinants, and argue that, in the absence of a representative sample of hospital costing studies, this method can be used to estimate unit costs in the interim. Moreover, we suggest that the observed great variation in unit costs for similar hospitals in the same country means that this method might well be preferable to basing policy advice on the results of costing studies that cover only one, or a few hospitals, which might well be outliers.

Marginal Cost of Emergency Department Outpatient Visits

OBJECTIVE

We sought to clarify the importance of time frame in the measurement of marginal cost and to provide marginal cost estimates for outpatient emergency department (ED) visits that better reflect current economic conditions.

DATA SOURCES

Analyses are based upon data that California hospitals report to the Office of Statewide Health Planning and Development (OSHPD). The time period covered was 1990 through 1998. Hospitals without EDs, or hospitals designated as trauma centers, were excluded from the analysis.

STUDY DESIGN

Nine years of panel data were used to estimate hospital cost functions, which were then used to test for economies of scale and to derive estimates of both short- and long-run marginal costs (excluding the physician expense component).

PRINCIPAL FINDINGS

We found only weak evidence in favor of scale economies and, in that context, we argue that long-run marginal costs should be the preferred metric for judging the cost of treating outpatient ED visitors. We estimate these long-run costs (in 1998 dollars) to be roughly 348 dollars per visit for large urban hospitals, 288 dollars for other urban hospitals, 203 dollars for rural hospitals, and 314 dollars overall.

CONCLUSIONS

Our results suggest that the marginal cost of an outpatient ED visit is larger than is commonly believed. A key implication of this finding is that hospital administrators need to think more carefully about their nonurgent care policies, especially as they pertain to ED operations.

The cost of an emergency department visit and its relationship to emergency department volume

STUDY OBJECTIVE

This article addresses 2 questions: (1) to what extent do emergency departments (EDs) exhibit economies of scale; and (2) to what extent do publicly available accounting data understate the marginal cost of an outpatient ED visit? Understanding the appropriate role for EDs in the overall health care system is crucially dependent on answers to these questions. The literature on these issues is sparse and somewhat dated and fails to differentiate between trauma and nontrauma hospitals. We believe a careful review of these questions is necessary because several changes (greater managed care penetration, increased price competition, cost of compliance with Emergency Medical Treatment and Active Labor Act regulations, and so on) may have significantly altered ED economics in recent years.

METHODS

We use a 2-pronged approach, 1 based on descriptive analyses of publicly available accounting data and 1 based on statistical cost models estimated from a 9-year panel of hospital data, to address the above-mentioned questions.

RESULTS

Neither the descriptive analyses nor the statistical models support the existence of significant scale economies. Furthermore, the marginal cost of outpatient ED visits, even without the emergency physician component, appear quite high--in 1998 dollars, US295 dollars and US412 dollars for nontrauma and trauma EDs, respectively. These statistical estimates exceed the accounting estimates of per-visit costs by a factor of roughly 2.

CONCLUSION

Our findings suggest that the marginal cost of an outpatient ED visit is higher than is generally believed. Hospitals thus need to carefully review how EDs fit within their overall operations and cost structure and may need to pay special attention to policies and procedures that guide the delivery of nonurgent care through the ED.

Does case management matter as a hospital cost-control strategy?

Using an evidence-based model for management research, we examine the relationship of case management adoption and the expected nonclinical outcomes in nationwide hospitals operating continuously between 1994 and 2000. Although case management may be beneficial for certain populations, institution-wide effects in the form of decreased costs or decreased length of stay do not appear to be present in the study hospitals.

Within-year variation in hospital utilization and its implications for hospital costs

Variability in demand for hospital services may have important effects on hospital costs, but this has been difficult to examine because data on within-year variations in hospital use have not been available for large samples of hospitals. We measure daily occupancy in California hospitals and examine variation in hospital utilization at the daily level. We find substantial day-to-day variation in hospital utilization, and noticeable differences between hospitals in the amount of day-to-day variation in utilization. We examine the impact of variation on hospital costs, showing that increases in variance are associated with increases in hospital expenditures, but that the effects are qualitatively modest.

How much confidence should we place in efficiency estimates?

Ordinary least squares (OLS) and stochastic frontier (SF) analyses are commonly used to estimate industry-level and firm-specific efficiency. Using cross-sectional data for English public hospitals, a total cost function based on a specification developed by the English Department of Health is estimated. Confidence intervals are calculated around the OLS residuals and around the inefficiency component of the SF residuals. Sensitivity analysis is conducted to assess whether conclusions about relative performance are robust to choices of error distribution, functional form and model specification. It is concluded that estimates of relative hospital efficiency are sensitive to estimation decisions and that little confidence can be placed in the point estimates for individual hospitals. The use of these techniques to set annual performance targets should be avoided.

Econometric estimation of country-specific hospital costs

Information on the unit cost of inpatient and outpatient care is an essential element for costing, budgeting and economic-evaluation exercises. Many countries lack reliable estimates, however. WHO has recently undertaken an extensive effort to collect and collate data on the unit cost of hospitals and health centres from as many countries as possible; so far, data have been assembled from 49 countries, for various years during the period 1973-2000. The database covers a total of 2173 country-years of observations. Large gaps remain, however, particularly for developing countries. Although the long-term solution is that all countries perform their own costing studies, the question arises whether it is possible to predict unit costs for different countries in a standardized way for short-term use. The purpose of the work described in this paper, a modelling exercise, was to use the data collected across countries to predict unit costs in countries for which data are not yet available, with the appropriate uncertainty intervals.The model presented here forms part of a series of models used to estimate unit costs for the WHO-CHOICE project. The methods and the results of the model, however, may be used to predict a number of different types of country-specific unit costs, depending on the purpose of the exercise. They may be used, for instance, to estimate the costs per bed-day at different capacity levels; the "hotel" component of cost per bed-day; or unit costs net of particular components such as drugs.In addition to reporting estimates for selected countries, the paper shows that unit costs of hospitals vary within countries, sometimes by an order of magnitude. Basing cost-effectiveness studies or budgeting exercises on the results of a study of a single facility, or even a small group of facilities, is likely to be misleading.

Cost characteristics of hospitals

Modern hospitals are complex multi-product organisations. The analysis of a hospital's production and/or cost structure should therefore use the appropriate techniques. Flexible functional forms based on the neo-classical theory of the firm seem to be most suitable. Using neo-classical cost functions implicitly assumes minimisation of (variable) costs given that input prices and outputs are exogenous. Local and global properties of flexible functional forms and short-run versus long-run equilibrium are further issues that require thorough investigation. In order to put the results based on econometric estimations of cost functions in the right perspective, it is important to keep these considerations in mind when using flexible functional forms. The more recent studies seem to agree that hospitals generally do not operate in their long-run equilibrium (they tend to over-invest in capital (capacity and equipment)) and that it is therefore appropriate to estimate a short-run variable cost function. However, few studies explicitly take into account the implicit assumptions and restrictions embedded in the models they use. An alternative method to explain differences in costs uses management accounting techniques to identify the cost drivers of overhead costs. Related issues such as cost-shifting and cost-adjusting behaviour of hospitals and the influence of market structure on competition, prices and costs are also discussed shortly.

Striving towards efficiency in the Greek hospitals by reviewing case mix classifications

In order to verify the efficiency level of Greek public hospitals, this paper evaluates the most recent indicators. Relevant data were collected from the two following databases: (a) hospitals' utilisation data generally and per clinical speciality [Ministry of Health, Athens, (Data based) 1995]; (b) Patients' and hospitals' characteristics per diagnosis [National Statistical Office, Athens, (Data based) 1993]. As explanatory variables, the study examines supply and demand factors following case mix classifications. Firstly, average length of stay (ALOS) and secondly, cost per case were regressed as dependent variables. The study highlights the extent of variability across hospitals for different groups of patients with the same condition. The results specify the most important factors that affect ALOS and cost pertaining to efficiency. Per speciality analysis shows occupancy, size-type of the hospital, beds and doctors per speciality, access and use of outpatient services, and surgical operations, etc. as the most significant factors. Per disease-diagnosis analysis shows age of over 65 years, gender, residence, marital status, surgical operation and insurance as the most important factors. General cost analysis in all National Health Systems (NHS) hospitals shows that economies of scale appear in: (a) district and/or specialised hospitals of 250-400 beds; (b) regional and/or teaching hospitals of over but near to 400 beds. Consequently, the author determines the 'Greek' Diagnostic Related Groups (DRGs), based on the cost per clinical speciality in the nine basic specialities and on the cost per diagnosis of the top 15 diagnoses. Further to the scientific results, such studies will enhance much necessary discussions on the organisation of service delivery and financing, by following case mix classification.

Does prospective payment really contain nursing home costs?

OBJECTIVE

To examine whether nursing homes would behave more efficiently, without compromising their quality of care, under prospective payment.

DATA SOURCES

Four data sets for 1994: the Skilled Nursing Facility Minimum Data Set, the Online Survey Certification and Reporting System file, the Area Resource File, and the Hospital Wage Indices File. A national sample of 4,635 nursing homes is included in the analysis.

STUDY DESIGN

Using a modified hybrid functional form to estimate nursing home costs, we distinguish our study from previous research by controlling for quality differences (related to both care and life) and addressing the issues of output and quality endogeneity, as well as using more recent national data. Factor analysis was used to operationalize quality variables. To address the endogeneity problems, instrumental measures were created for nursing home output and quality variables.

PRINCIPAL FINDINGS

Nursing homes in states using prospective payment systems do not have lower costs than their counterpart facilities under retrospective cost-based payment systems, after quality differences among facilities are controlled for and the endogeneity problem of quality variables is addressed.

CONCLUSIONS

The effects of prospective payment on nursing home cost reduction may be through quality cuts, rather than cost efficiency. If nursing home payments under prospective payment systems are not adjusted for quality, nursing homes may respond by cutting their quality levels, rather than controlling costs. Future outcomes research may provide useful insights into the adjustment of quality in the design of prospective payment for nursing home care.

Estimating hospital costs with a generalized Leontief function

This paper estimates a long-run hospital cost function with multiple outputs and inputs using a panel data set from Washington State hospitals during 1988-1993. We find that with our data the generalized Leontief function is more appropriate than a translog for estimating hospital cost functions. With respect to hospital costs, we find that hospitals readily adjust the use of intermediate products. Radiology, therapies and surgery, and other inpatient days, all serve as substitutes for core inpatient days. Outpatient services are found to be complementary to core inpatient services, indicating that the growth of stand-alone outpatient clinics might increase the costs of providing healthcare services. Our analysis finds that hospitals show significant economies of scale, but there is a limited amount of evidence of scope economies. Also, there is some evidence that profit-seeking hospitals achieve some of their goals by controlling costs, and that diagnostically related groups (DRG)-based Medicare services are effective in getting hospitals to control costs.

Omitted variable bias and hospital costs

This research examines the impact of omitted variables on the accuracy of parametric hospital cost function estimations based on Québec hospital level data. We assess the effect of omitted variables resulting from incomplete data on technology and performance measurement and on tests of the cost minimizing behavior of the institution. Our results show that important characteristics of hospital technology, such as returns to scale, are extremely sensitive to omitted variable bias. Similarly, estimates of hospital performance are poor indicators of actual performance when data are incomplete.

Research without billing data. Econometric estimation of patient-specific costs

OBJECTIVES

This article describes a method for computing the cost of care provided to individual patients in health care systems that do not routinely generate billing data, but gather information on patient utilization and total facility costs.

METHODS

Aggregate data on cost and utilization were used to estimate how costs vary with characteristics of patients and facilities of the US Department of Veterans Affairs. A set of cost functions was estimated, taking advantage of the department-level organization of the data. Casemix measures were used to determine the costs of acute hospital and long-term care.

RESULTS

Hospitalization for medical conditions cost an average of $5,642 per US Health Care Financing Administration diagnosis-related group weight; surgical hospitalizations cost $11,836. Nursing home care cost $197.33 per day, intermediate care cost $280.66 per day, psychiatric care cost $307.33 per day, and domiciliary care cost $111.84 per day. Outpatient visits cost an average of $90.36. These estimates include the cost of physician services.

CONCLUSIONS

The econometric method presented here accounts for variation in resource use caused by casemix that is not reflected in length of stay and for the effects of medical education, research, facility size, and wage rates. Data on non-Veteran's Affairs hospital stays suggest that the method accounts for 40% of the variation in acute hospital care costs and is superior to cost estimates based on length of stay or diagnosis-related group weight alone.

Investigating hospital efficiency in the new NHS: the role of the translog cost function

The reforms to the United Kingdom's National Health Service (NHS) of recent years have greatly increased the role of economic incentives in the hospital sector. Hospitals now have to compete for the business of GP and health authority purchasers and are assumed to have an incentive to minimise costs. This makes the analysis of cost functions much more relevant than has previously been the case. The objective of this paper is to assess the potential usefulness of the translog cost function applied in the NHS internal market. Three main issues are identified that limit the role of this type of cost function in the internal market: the adequacy of the econometric model (including data quality); the assumptions underlying the model, and; the interpretation of economies of scale, marginal costs and economies of scope that can be derived from such a cost function. It is concluded that at present the application of translog cost function analysis in the NHS is of limited usefulness, but that it does indicate areas for further methodological research.

Uncertain demand, the structure of hospital costs, and the cost of empty hospital beds

In this paper we reformulate the theory of cost and production to take account of uncertain demand facing a firm. In the reformulated theory the duality between cost and production no longer obtains, and demand distribution parameters enter the cost function as well as the traditional outputs and input prices. We then estimate a short run cost function for a hospital facing uncertain demand using data from a national sample of over 5000 hospitals for the years 1983-1987. The traditional cost model is strongly rejected in favor of the reformulated model. This model is used to calculate the cost of empty hospital beds, controlling for the effect of uncertain demand on the structure of hospital costs. The cost of an empty hospital bed is calculated as $36,443 in 1987 dollars. We estimate that a one percent decrease in the number of hospital beds would decrease hospital costs by slightly over one-third of one percent. Increasing the occupancy rate from the average 1992 level (65 percent) back to the average 1980 level (76 percent) is estimated to save the average hospital over $2 million, or 9.5 percent of costs.

A cost function analysis of residential services for adults with a learning disability

Successive UK governments have pursued a policy of community care for people with learning disabilities which, in the past ten years, has led to a marked change in the nature of residential provision. Research evidence on the costs and quality of alternative forms of community provision is inconclusive and contradictory. It is therefore timely to consider whether or not community residential facilities have delivered the expected quality of service at appropriate cost. The paper presents the results of a cost function analysis of a random stratified sample of staffed community facilities in England excluding London. Both costs and quality of care were found to vary greatly amongst community residential facilities. The most important factors explaining differences in cost were case-mix factors relating to client age, dependency and length of stay. Facility characteristics such as the type of building, the internal layout and the structural quality were not significant. Quality of service measures such as the extent to which care-regimes were client orientated and made use of local community services were positively and significantly associated with costs. Type of provider had no impact on costs independent of differences in case-mix and quality of care with the exception of the private for profit sector which appeared less expensive than other agencies. The shortcomings of the methods and implications of these findings for policy makers are discussed.

A simple objective method for determining a percent standard in mixed reimbursement systems

In a mixed system for hospital rate setting, reimbursement is set at the weighted average of provider-specific and standard unit costs. With one or more explanatory variables, forward and reverse regression is used to motivate the simple but objective choice of one minus the squared correlation coefficient as the proportion standard. Special treatment is given to nuisance variables that help explain cost but not reasonable cost. Efron's bootstrap provides confidence intervals for the proportion standard. This regression approach is contrasted with the conventional use of the coefficient of variation, and with economic models for the optimal proportion.

Exploring hospital production relationships with flexible functional forms

This paper estimates a multiproduct variable cost function using data on a sample of California hospitals. The results provide useful insights into the advantages and disadvantages of flexible functional forms for cost analysis. The translog function appears to provide reasonable estimates of marginal costs when evaluated at or near the approximation point of the function. The estimated function performs less satisfactorily, however, when evaluated outside this range. The paper's results do not provide strong evidence of either ray scale economies or of weak cost complementarities. There is some evidence, however, that the degree of scale economies may be underestimated.

An evaluation of Medicaid selective contracting in California

This study used 1982-1986 data on 262 private community hospitals to evaluate the effects of selective contracting for inpatient services by California's Medicaid program. Selective contracting by Medicaid significantly reduced the rate of inflation in average costs per admission and per patient day, while slightly increasing average lengths of patient stays. Private sector contracting also reduced cost inflation rates significantly and caused small, non-significant, reductions in lengths of stays. Hospital savings in 1986 due to Medicaid selective contracting were $836 million, 7.6% of what hospital expenditures would have been in the absence of contracting.

The marginal cost of nursing home care, New York, 1983

Many believe that nursing homes exclude heavy-care Medicaid patients because their costs exceed the Medicaid reimbursement rate. This paper tests whether this was true in New York in 1983 by calculating the marginal costs of a day of nursing home care and comparing them with the per diem Medicaid reimbursement rate. Contrary to popular beliefs, the marginal cost of the most dependent SNF patient was found to be between $9 and $12 less per patient day than the average Medicaid reimbursement rate for SNF patients. This suggests that excess demand, rather than lower-than-cost reimbursement rates, was creating the heavy-care access problem in New York in 1983. Policy solutions differ depending on the cause of the access problem. The strengths and weaknesses of the different policy solutions are compared.