Introduction

In modeling and estimating the impact of technical inefficiency on production it is assumed, at least implicitly, that inputs are exogenously given and the scalar output is a response to the inputs. By contrast, in modeling and estimating the impact of technical inefficiency on costs, it is assumed that output is given and inputs are the choice variables (i.e., the goal is to minimize cost for a given level of output). However, if the objective of producers is to maximize profit, both inputs and output are choice variables. That is, inputs and outputs are chosen by the producers in such a way that profit is maximized.

In this chapter, we derive the stochastic profit frontier model when both inputs and output are endogenous. In deriving the model, we assume that producers are maximizing their profit. However, although they may not be fully efficient technically, we assume, in this chapter, that they are allocatively efficient. Models with both technical and allocative inefficiency will be discussed in Chapter 9.

In the long run, profits are zero for producers operating in a competitive market and producers with negative profits exit the industry. Similarly, if there are positive profits, then new firms will enter the market, which will drive profits down to zero. In this chapter, we do not take such a long-term perspective. The long run can be viewed as a sequence of short runs, in which firms can operate with positive as well as negative profit. Our focus here is to model profit efficiency (in particular, profit loss due to technical inefficiency). We consider profit maximization in the short run and argue that differences in profits are due to quasi-fixed inputs (i.e., inputs that are not chosen optimally in the short run) and technical inefficiency. However, the existence of quasi-fixed inputs is not necessary for modeling technical inefficiency in a profit maximizing framework.