STOCHASTIC FRONTIER ESTIMATION OF COST MODELS WITHIN THE HOSPITAL.

Publication: Review of Economics and Statistics

Publication Date: 01-MAY-01

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COPYRIGHT 2001 MIT Press Journals

I. The Basic Problem

THE healthcare sector is characterized by an extraordinary degree of innovation. Unlike many other areas, however, innovation in this sector is generally perceived as substituting newer technologies that require increased--rather than decreased--resource use. Clearly, we wish to begin the process of determining whether this common perception is accurate. To do so, we must first understand the basic relationship between the medical-care decisions required of existing and innovative technologies, and how medical innovation affects the cost relationships we observe.

In addition to considering the underlying theoretical model of hospital-based treatment decision making, we must also consider the nature of the empirical approach used to address this question. Particularly when we seek to estimate the difference in the costs between a newer and an older technology, the usual assumptions that underlie ordinary least-squares estimation may be inappropriate. Clinical evidence clearly indicates that there are substantial learning curves in the provision of certain kinds of medical care. Numerous studies have shown that the success rates of procedures such as angioplasty depend on the frequency with which hospitals and individual doctors treat patients with this tool. (See, for example, Jollis et al. (1997).) Similarly, one would expect a learning curve as new technologies are introduced into the hospital. In this case, using OLS to estimate the difference in cost between the two technologies may produce biased estimates if the entire difference in observed cost is attributed to true resource requirements, rather than to a combination of different resource needs and different levels of inefficiency. We will utilize a statistical technique, stochastic frontier estimation via generalized methods of moments, which has the potential to disentangle these factors.

Here we address these issues by comparing the costs for two competing technologies for the treatment of coronary artery disease: coronary bypass surgery (CABG) and balloon angioplasty (PTCA). Utilizing data from a large Southern hospital, we examine costs at the patient level, allowing estimation of the cost savings that would be available if technological innovations in the less expensive PTCA procedure made that treatment available to all the patients currently undergoing CABG. This approach is in contrast to previous cost-frontier studies, which typically employed data at the hospital level.

Section II addresses several issues in the estimation of cost functions for hospital services. In section III, we present our estimation technique, data, and specification. Section IV reports our cost-estimation results. Section V presents the estimated costs savings that would be available as the result in innovation in PTCA technology, and section VI contains our conclusions.

II. Estimating Costs in the Hospital: A Return to the Physicians' Workshop Model

A. The Appropriate Level of Aggregation

Several articles (for example, Conrad and Strauss (1983), Menke (1990) and Zuckerman, Hadley, and Iezzoni (1994)) have assumed one "global" production function for the hospital. These papers posit a relationship between broad classes of inputs (such as numbers of nurses, numbers of employees, and numbers of beds) and a small set of outputs--typically discharges or bed-days. Alternatively, a second widely used approach is based upon Newhouse (1970), which assumes that there is a utility function for the hospital. This utility function leads to behavioral relationships between inputs and some output measures. Examples of this (larger) branch of the literature include Granneman, Brown, and Pauly (1986), Thorpe (1988), Wagstaff (1989), Thorpe and Phelps (1990), Carey and Stefos (1992) and Bradford and Craycraft (1996).

These approaches have led to models that are estimated with a high level of aggregation. For example, in Zuckerman et al., total costs for the hospital are estimated as functions of such variables as percentage of intensive-care beds, average Medicare casemix, and the share of admissions from out of state and the like. This introduces a potentially serious problem with aggregation bias. In general, estimating production functions is problematic when using traditional data sources that pool observations from a large number of hospitals in widely dispersed geographic regions.

In this work, we will appeal to a different model of the hospital. On a conceptual level, many health economists have considered hospitals to be "physicians' workshops" since Pauly (1980). This model asserts that hospitals exist to provide capital equipment for physicians who each create their own team within the institution to treat patients. Each hospital is therefore not appropriately considered a "firm" in the traditional neoclassical sense. Rather, it is a collection of "virtual firms," each defined by a unique provider team and production function.

One can extend this analogy further by recognizing that, in most circumstances, the actual team utilized will be unique for each patient. Thus, when a patient is admitted to the hospital, he travels through a treatment process that is tailored to his particular medical needs. This implies that a production function of in-patient services is best defined using the patient as the unit of analysis. Note that this framework is fairy far removed from the notion of one production function for hospitals which can be estimated by examining behavior across a large number of institutions.

We can formalize these notions in a simple model of the hospital. Assume that each patient enters the hospital and faces a production function that depends not only on resources used, but also on patient-specific characteristics, such that

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] represents the intermediate healthcare outputs (for example, PTCA or CABG) supplied to the [j.sup.th] patient, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is an M-dimensional vector of inputs supplied to the [j.sup.th] patient to produce the [i.sup.th] intermediate output and, [[Theta].sup.j] reflects patient-specific characteristics.

In addition to the patient intermediate-service production functions, each patient is assumed to possess a utility function. Patients enter the hospital to have their health raised, which is accomplished by the consumption of the vector of intermediate services [x.sup.j], thus the [j.sup.th] patient's level of utility is:

(2) [U.sup.j] = U([x.sup.j])

The hospital seeks to maximize the joint welfare of all patients, subject to a break-even constraint. Hospitals receive revenue, E, which depends upon the resources they...

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