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Hospital Cost Analysis.

by James R. G. Butler (Dordrecht: Kluwer Academic Publishers, 1995), xxii + 393 pp., ISBN 0 7923 3247 4.

Hospitals are multiproduct firms that provide an intermediate product for a spectrum of health-related conditions through a wide range of services. Costs and efficiencies may be altered by changes in both the quantity and mix of inputs or the quantity and mix of outputs. Identifying the right balance between input and output mix and quantities of both, to achieve the most efficient bundle, is the goal of analysing hospital behaviour. Over the last three decades, hospital behaviour has become of increasing interest and concern to health service funders, providers and researchers. Juxtaposed with this interest in hospital behaviour, developments in econometrics have led to a number of flexible functional forms being proposed to estimate cost functions. However, flexible functional forms require a large number of parameters to be estimated for each additional output. Butler, in his book Hospital Cost Analysis, trades flexibility in functional form in favour of a large number of homogeneous hospital output categories.

Hospital Cost Analysis is the third of five volumes to date in the series Developments in Health Economics and Public Policy, edited by P. Zweifel and H. E. Frech III. This book, based on the author's doctoral thesis, encompasses many issues surrounding the economics of hospitals as multiproduct firms. Particular attention is focused on the estimation of multiproduct cost functions for hospitals. The book is divided into three sections. Part A covers the theoretical background to the analysis of cost functions and the measurement of hospital output. In part B, the bulk of the book, empirical analyses of restricted cost functions are presented, and in part C the book concludes with a discussion on various hospital and health care service funding options and mechanisms.

Chapter 2 is grounded in the economic theory of the multiproduct firm and swiftly moves into explaining the concepts of "jointness" (i.e., the cost of producing outputs together is less than the sum of the cost of producing them independently), separability of inputs and outputs (i.e., the mix of outputs in the output set is independent of the mix of inputs in the input set), and returns to scale. After describing flexible forms, including the generalised linear-generalised Leontief cost function and a brief note on the translog cost function, the fundamental dilemma in estimating hospital cost functions is highlighted, namely the trade-off between flexibility in functional form and parsimony in the number of parameters to estimate. In favour of parsimony, Butler argues that flexibility of functional form should be sacrificed in favour of allowing for greater disaggregation of output types.

Defining, classifying and measuring hospital output is the focus of Chapter 3. This entails defining the role of the hospital and arguing that measurable hospital output is the number of treated cases, as opposed to changes in health status or the number of treatments given. Case-mix classification schemes and case-mix indices of output are discussed at the end of the chapter.

The empirical section of the book, Part B, is where a variety of analyses are presented for Australian (mainly Queensland) hospitals, using data from 1978 to 1982. A succinct history of the development of the public hospital system in Queensland is given in Chapter 4, and some of the characteristics of Queensland hospitals are compared to hospitals in other Australian states. The most notable difference between the Queensland public health system and those in the other states is the highly centralised control over hospitals in Queensland. This chapter is perhaps too succinct as, for later years, especially from the 1970s onwards, the description comprises two sentences and part of a table. This leaves the reader wondering if, and how, the current system has changed compared to the early 1970s, and asking questions such as what changes have occurred to the services provided, access to the system, rationing, and how the system is funded. It is unlikely that the findings from an analysis of late 1970s data will be relevant in relation to the present structure.

In Chapter 5, the effect of case mix on costs is analysed using multiproduct cost functions for two different sets of output classifications. Initially the 18 chapter headings from the International Classification of Diseases (World Health Organisation, 1977) arc used, followed by a more disaggregated case mix of 47 output categories. Features of this section are the restrictions of "non-jointness", input/output separability, and overall constant returns to scale imposed on the functional form. Hospitals are treated not as a true multiproduct firm but as a collection of single-product firms. The specification of the cost function necessitates, therefore, that marginal cost equals average cost, and economic phenomena such as economies of scope, cannot exist. Unfortunately, the "true" functional form was not tested by relaxing the restrictions and many of the following analyses are beset with problems.

A problem that arose with the empirical application of the restricted cost function was that some of the estimated parameters were negative. This indicated negative average and marginal costs. The attempts to reduce this problem, thought to be caused by multicollinearity, included a principal components analysis (that failed to remedy the problem), followed by an information theory approach to construct a weighted case mix index. Although this gave well-behaved parameter estimates, it had poor explanatory power in relation to the variation in the average cost per case. Butler concludes the chapter with the comment "... that the problem of misbehaved parameter estimates arises because of misspecification of the underlying cost function" (p. 155).

The restriction of constant economies of scale is relaxed in Chapter 6. Tests for scale and utilisation effects failed to find evidence of long-run scale economies. This was not a surprising result as the maintained hypothesis of non-jointness and input/output separability restricted scale effects to be equal in all output groups. Differences in input prices was noted in this section but, unfortunately, the potential for substitution between inputs was disregarded. This is the main area in which hospital administrators may use their influence to purchase the cost-minimising mix of inputs to produce a given set of outputs. There is no doubt that the different proportions of inputs are a substantial source of the variation in hospital costs.

In Chapters 7, 8 and 9, Butler applies the cost function to test for differences between teaching and non-teaching hospital costs, public and private hospital costs, and Queensland hospital costs versus New South Wales hospital costs respectively. These three chapters are heavily focused on casemix differences as the source of cost variation between hospitals. Although the issues raised in these chapters may contain lessons for New Zealand, the results are tenuous given the restricted specification of the cost function. Chapter 10, the first of two chapters in Part C, addresses hospital performance. This is an interesting chapter, in which Butler develops a "costliness index" as a measure of relative performance. Instead of comparing hospitals on an average cost per case basis, Butler argues that the costliness index (a ratio of the actual to the predicted average cost per case) should be used. The predicted costs are derived from an estimated cost function. Therefore, for the costliness ratio to be a valid measure of performance, the estimated model should be a good fit. The empirical results in this section should be treated as indicative of the approach, as the model estimated by Butler explained only 55% of the variance in costs. Butler shows how the index can be used to estimate costliness per day and relative length of stay and then disaggregate these by input categories. This method could be useful but the competing econometric developments for measuring performance and efficiency of multiproduct firms, such as the stochastic cost and production frontiers (e.g., Wagstaff, 1989; Bums and Weyman-Jones, 1996) and the non-parametric data envelopment analysis approach (e.g., Valdmanis, 1992), are more appealing. Unfortunately, these contemporary methods get little more than a mention by Butler.

A discussion of prospective payment schemes and hospital incentives is provided in Chapter 11. It is argued that payment by "Diagnostic Related Group" (DRG), of a fixed amount adjusted for case mix, may give hospitals "an incentive to treat larger numbers of some case types which increase `profits' and treat a smaller number of other case types which incur `losses'" (p. 352). Hospital output, therefore, becomes endogenous to the hospital (and the economic production-cost duality is lost). Prospective payment raises the issue of predicting future demand for hospital services and case mix by DRG. Forecasting demand, disaggregated by DRG, is almost impossible for individual hospitals due to small cell sizes. Therefore, the usefulness of the DRG system is questionable.

What is the usefulness of the book? Sections of the book will be of interest to economists and health policy advisors working in this area. In addition to well described and illustrated explanations given to the economic concepts, the strengths of the book are the sections on measuring hospital output, case mix indices and output classification schemes. However, key aspects of analysing hospital costs, such as measuring hospital efficiency, are only partly addressed. Furthermore, the empirical results are derived from data almost two decades old; hence, their relevance is highly questionable.

References

Burns, P. and Weyman-Jones, T. G. (1996), "Cost functions and cost efficiency in electricity distribution: a stochastic frontier approach", Bulletin of Economic Research, 48, 41-56.

Valdmanis, V. (1992), "Sensitivity analysis for DEA models: an empirical example using public vs. NFP hospitals", Journal of Public Economics, 48, 185-205.

Wagstaff, A. (1989), "Estimating efficiency in the hospital sector: a comparison of three statistical cost frontier models", Applied Economics, 21, 659-672.

World Health Organisation (1977), Manual of the International Classification of Diseases, Injuries, and Causes of Death, Ninth Revision, London: HMSO.
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Author:Scuffham, Paul
Publication:New Zealand Economic Papers
Article Type:Book Review
Date:Dec 1, 1997
Words:1626
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