Objective. To compare the results of scoring hospital efficiency by means of two new types of frontier models, Data Envelopment Analysis (DEA) and stochastic frontier regression (SFR).
Study Setting. Financial records of Florida acute care hospitals in continuous operation over the period 1982-1993.
Study Design. Comparable DEA and SFR models are specified, and these models are then estimated to obtain the efficiency indexes yielded by each. The empirical results are subsequently examined to ascertain the extent to which they serve the needs of hospital policymakers.
Data Collection. A longitudinal or panel data set is assembled, and a common set of output, input, and cost indicators is constructed to support the estimation of comparable DEA and SFR models.
Principal Findings. DEA and SFR models yield convergent evidence about hospital efficiency at the industry level, but divergent portraits of the individual characteristics of the most and least efficient facilities.
Conclusions. Hospital policymakers should not be indifferent to the choice of the frontier model used to score efficiency relationships. They may be well advised to wait until additional research clarifies reasons why DEA and SFR models yield divergent results before they introduce these methods into the policy process.
Key Words. Hospital efficiency, Data Envelopment Analysis, stochastic frontier regression, hospital cost containment
Until recently, the efficiency of hospitals has been measured by estimating cost or production functions by means of ordinary regression methods. Cost studies, for instance, typically regressed operating expenses against various measures of hospital "output," input prices, and control variables such as case mix of the patient population to draw inferences about efficiency differentials across hospitals (Cowing, Holtmann, and Powers 1983). Although these regression studies produced many useful insights, they were unavoidably subject to the limitation that the estimated equation represented the average as opposed to the best-practice cost-output relationship. The error term in such regressions has a mean of zero, so deviations from the estimated "line" (hyperplane) are not only as likely to raise costs as reduce them, but are assumed to be entirely attributable to chance factors. It is intuitively clear that some observations below the regression "line" in cost equations are systematically more efficient in the sense that, for a given set of factor prices and patient characteristics, they produce more output per unit of input. However, ordinary regression methods cannot distinguish between these systematic variations and those truly due to statistical noise. In an industry where inefficiencies are thought to be widespread, this methodological gap seriously limits the use of such statistical inferences for policy purposes.
Recent years have witnessed technical developments in the field of management science and econometrics that hold out the promise of enabling analysts to identify best-practice output-input (cost) relationships as well as to gauge how much efficiency levels of given decision-making units or providers deviate from these frontier values (Bauer 1990). One of these developments is Data Envelopment Analysis (DEA), a nonparametric programming technique that pieces together an efficiency frontier by maximizing (a seriatim) the weighted output/input (cost) ratio of each provider, subject to the condition that this ratio can equal, but never exceed, unity for any other provider in the data set (Charnes, Cooper, and Rhodes 1978). DEA then yields several measures of the relative distance of any provider's efficiency ratio from the piecewise linear frontier, the most common being the proportional reduction in input or cost levels that could be achieved were the provider delivering services in the most efficient manner po ssible. Another was the development of stochastic frontier regression (SFR) methods. Unlike its classical OLS counterpart, SFR models the error term in two parts, one reflecting systematic deviations from a frontier (cost or output) level and the other from more conventional statistical noise (Aigner, Knox Lovell, and Schmidt 1977). SFR uses this composable error, as it is called, to estimate the overall efficiency level across any sample of providers and then, in what may be characterized as a second step, computes efficiency deviations of each sample observation from the industry frontier by taking the expected value of the disturbance of each observation, conditional on the estimated parameters of the underlying distribution of the composable error (Jondrow et al. 1982; Greene 1992). Like DEA, these SFR provider-specific efficiency values are also cast as the proportional difference between the costs (output) of any provider and the frontier level of costs (output).
Not surprisingly, the efficiency vectors yielded by DEA and SFR techniques find ready uses by policymakers, nowhere more so than in the hospital sector. Indicators of the relative efficiency of hospitals are needed to gauge whether hospital cost-containment efforts are succeeding; they are also needed to evaluate the effect of more extensive managed care arrangements in local healthcare markets and to prepare "report cards" and other quality assessments of hospital service delivery. Such indicators may also have a prescriptive role to play in establishing criteria for selective contracting purposes and in pegging reimbursement levels in hospital rate-setting programs; see Batavia et al. (1993), Hadley and Zuckerman (1994), and Newhouse (1994) for differing views on these potential uses. Yet, whether frontier methods actually live up to their policy promise is untested at the moment. The recent literature includes a number of DEA hospital applications but only one published SFR study. [1] The knowledge base m ust be expanded before we can judge if, and how well, frontier methods serve the needs of hospital policymakers.
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