Shawna Grosskopf

Chapter 10 Profitability and productivity changes: An application to Swedish pharmacies

The relationship between Malmquist productivity change and profitability is developed in this paper. Our theoretical construct is applied to Swedish pharmacies.

Chapter 12 Evaluating Health Care Efficiency

The purpose of this chapter is to suggest a general framework for assessing the efficiency of health care in general, and health care interventions specifically. We begin with a three-pronged overview of assessing performance in health care which begins with what we call the budget or cost side model relating budgets and costs to treatments. Next we proceed to describing an intermediate outputs specification which relates hospital resources to medical outcomes, and we conclude with a final outcomes model which relates the medical outcomes to patient health outcomes. The third model is illustrated with an application to data from Swedish cataract patients.

Modeling pollution abatement technologies as a network: Counting the Environment and Natural Resources

One approach used to calculate the costs and productivity changes associated with pollution abatement involves modeling the joint production of good and bad outputs. The joint production model treats the process of transforming inputs into good and bad outputs as a black box. We investigate the consequences of generalizing the transformation process by introducing a network technology that looks inside the black box, which consists of a set of sub-technologies or sub-processes. Both models are operationalized using a panel dataset of coal-fired power plants to compare empirical results generated by the two specifications of the production technology.

Production Frontiers: Input-Based Efficiency Measurement

Introduction In Chapter 3 we modeled technology in terms of the input correspondence and measured efficiency relative to the input set, i.e., output quantities were taken as given and inefficiency identified by feasible reductions in input quantities or cost. In this chapter we measure efficiency relative to the output set P ( x ), i.e., we take input quantities as given and judge performance by the ability to increase output quantities or revenue. As such the topic of this chapter is very much in the spirit of the neoclassical production functions defined as maximum achievable output given input quantities and technology, although we generalize here to the case of multiple rather than scalar output. In Section 4.1 output-based measures which are independent of prices, i.e., technical in nature, are introduced, and we show how overall technical efficiency can be decomposed into three component measures – scale, congestion, and purely technical efficiency. All of these measures of technical efficiency take input quantities as given and measure efficiency as feasible proportional expansion of all outputs. In Section 4.2 we turn to output price-dependent measures of efficiency, the goal being to maximize revenue rather than to proportionally increase outputs. Here it becomes relevant to alter the output mix in light of existing output prices. In particular, we show how to decompose overall revenue efficiency (defined as the ratio of maximum to observed revenue) into technicaland allocative components. Sections 4.1 and 4.2 focus on what we call radial measures of output efficiency. One of the drawbacks of these radial measures is that they project an observation onto the isoquant of the output set, and not necessarily onto the efficient subset of the output set.

Toward Empirical Implementation

In this brief concluding chapter we offer a summary of where we have been, where we are going, and how we might get there. In Section 9.1 we summarize the essential elements of efficiency measurement gleaned from the core of the book, chapters 3–8. In Section 9.2 we suggest two ways in which our work might be extended, to the development of dual efficiency measures, and to the measurement of dynamic efficiency. In Section 9.3 we provide a brief reader’s guide to the various extant approaches to empirical implementation. This guide condenses and updates earlier surveys of Forsund, Lovell and Schmidt (1980) and Lovell and Schmidt (1983).

A Comparison of Input, Output, and Graph Efficiency Measures

In the three previous chapters we established some relationships among various radial input measures of efficiency (chapter 3), among various radial output measures of efficiency (chapter 4), and among various hyperbolic graph measures of efficiency (chapter 5). In this brief chapter we establish some relationships among input, output, and graph measures of various types of efficiency. Our motivation for so doing is that we seek answers to questions such as (1) Under what conditions, if any, do input, output, and graph measures of a certain type of efficiency attach the same efficiency value to a given input-output vector? (2) Under what conditions, if any, can the three measures of a certain type of efficiency be ordered? And, (3) If an input-output vector is labeled efficient by one measure, when, if ever, is it labeled efficient by the other two measures?

Nonradial Efficiency Measures

In chapters 3 and 4 we introduced radial input and output efficiency measures. The hyperbolic graph efficiency measure introduced in chapter 5, though not a radial measure in the strict sense, nonetheless possesses many of the characteristics of the radial input and output efficiency measures. Among the virtues of this family of efficiency measures are their consistency with the original formulations of Farrell (1957), their ease of computation, their straightforward cost or revenue interpretation, and their consequent decomposability. That is, measures of overall (input, output, and graph) efficiency each have a multiplicative decomposition into technical, congestion, and allocative components.

Radial Output Efficiency Measures

In chapter 3 we modeled the technology of a production unit with an input correspondence uL(u) ⫅ R + n , and we developed various measures of the efficiency with which inputs are used to produce a certain output vector ∈R + m . Three of these measures are technical, and so are input price-independent, while one is allocative and input price-dependent. Thus the overall measure of input efficiency is also input price-dependent, having the cost minimizing set CM(u, p) as its reference set, and so the behavioral assumption underlying the construction of the overall measure of input efficiency is one of minimizing input cost in the production of a certain output vector.

Hyperbolic Graph Efficiency Measures

In chapter 3 we developed a series of measures of the efficiency with which a production unit uses variable inputs to produce a given output vector. These measures are appropriate under a behavioral assumption of constrained cost minimization. In chapter 4 we developed an analogous series of measures of the efficiency with which a production unit produces variable outputs from a given input vector. These measures are appropriate under a behavioral assumption of constrained revenue maximization. In this chapter we drop the assumption that either outputs or inputs are given, and develop a similar series of measures of the efficiency with which a production unit uses variable inputs to produce variable outputs. That is, the production unit is assumed to be able to freely adjust all inputs and all outputs, subject only to the constraints imposed by the production technology. These measures are appropriate under a behavioral assumption of profit maximization. Since all inputs and all outputs are freely variable, we model technology with the graph rather than with the input correspondence or the output correspondence.

Radial Input Efficiency Measures

Consider some feasible production plan {(u, x) : x ∈ L(u)}. It is natural to inquire as to whether there exists some smaller input vector 0 ≤ y ≤ x that remains feasible for output vector u, i.e., y ∈ L(u). A different, but related, question involves the existence of a less expensive, though not necessarily smaller, input vector z : pz < px, given input prices p ∈ R ++ n , that remains feasible for output vector u, i.e.,z ∈ L(u). If either y or z exists, then x is clearly inefficient for u, and the efficiency of x can be calculated relative to y or z respectively.