Introduction

In this chapter, we consider cases where outputs are exogenously given to a firm. Recall that, in Chapter 4, we introduced the cost frontier, which gives the minimum cost of producing any exogenously given level of output. A cost-minimizing firm chooses the levels of inputs in order to produce the given level of output with the lowest possible cost. When output and input prices are exogenously given to a firm, cost minimization is equivalent to profit maximization. Because inputs are endogenous in the cost minimization framework, input-oriented (as opposed to output-oriented) technical inefficiency is usually chosen as the preferred approach to model technical inefficiency.

In the standard neoclassical context, Christensen and Greene (1976) proposed using a system approach, consisting of the cost function and the cost share equations, to estimate the cost function parameters. Here we consider a similar system, but we allow producers to be technically inefficient. That is, compared to the cost function introduced in Chapter 4, which consists of only the cost function adjusted for technical inefficiency (see, for example, equation (4.15)), here we include the cost share equations and form a system to estimate the cost function parameters. The use of these share equations does not require any additional assumption, and the share equations do not contain any new parameter that is not in the cost function (other than the parameters associated with the errors in the cost share equations). Thus, the additional information provided by these share equations helps in estimating the parameters more precisely. (As such, this chapter does not provide new tools to answer additional questions; the questions that can be answered are the same as those set out at the start of Chapter 4. However, we use a different empirical example in this chapter: the examples used throughout this chapter examine U.S. commercial airlines.)

In addition to the efficiency gain in the parameter estimates, the inclusion of the share equations in the estimation has one important advantage in the current context: Residuals of the share equations may be interpreted as allocative inefficiency (or functions of them).