Linear Programming Models for Firm and Industry Performance

Abstract

Programming models of technology are enjoying a revival in several strands of literature. One such strand is the growing literature devoted to the assessment of firm performance based on the work of Farrell (1957) and the later popularized by Charnes, Cooper and Rhodes (1978) under the name of data envelopment analysis (DEA); for an early programming model, see Boles (1966). A second strand of literature seeks to model the industry production function and is associated with Johansen (1972), Fbrsund and Hjalmarsson (1987) and Aigner and Chu (1968). A third strand of literature uses programming techniques such as nonparametric tests of regularity conditions in production; see Afriat (1972), Hanoch and Rothschild (1972), Diewert and Parkan (1983) and Varian (1984). One of the purposes of this paper is to examine the relationship between the first two areas, i.e., analysis of firm and industry programming models of technology and performance. In order to compare the industry and firm models, we restate them in a general programming form, and ignore issues of functional form. Examination of these models in primal and dual form reveals that the industry approach constructs technology from firm data but allows (hypothetical) reallocation of aggregate resources across firms to yield an industry function. The firm models also construct technology from the data on all firms in the sample/industry, but do not allow for reallocation of inputs across firms. This suggests a natural hybrid: an industry model which allows for both firm specific inputs and inputs which can be reallocated across firms.' The paper unfolds as follows. We begin by presenting a stylized version of the Aigner and Chu and Johansen models of industry production. We