The purpose of this chapter is to introduce the indexed quadratic (IQ) function and to examine its applications to empirical problems in the econometrics of production, with particular attention to the problem of modeling network technologies. The function in its most general form is a slight modification of a proposal by Baumol, Panzar, and Willig (1982) to construct cost functions as quadratic functions of outputs and to regard the resulting coefficients as concave independent homogeneous functions of input prices. Baumol et al. demonstrated that this formulation is well suited for modeling the technologies of multiple-output firms.

While the techniques developed in this chapter are applicable to a wide variety of industries characterized by network technologies – telecommunications, the postal system, most public utility systems (water, electricity) – the most obvious application is to transportation systems. A leading issue in transportation economics has been the appropriate measurement of output, since most transportation networks are sufficiently complex that an enumeration of outputs by origin–destination combination yields a very high number of ostensibly different outputs, possibly thousands. To distinguish these outputs for the statistical estimation of cost or production functions is infeasible. Moreover, it is not clear that such a treatment would be entirely desirable, since prior information concerning the nature of the relations among the outputs could not be easily incorporated in the estimation procedure; nor would the important network aspects of the technology – which induce the economies of scale and scope that are of primary interest – be perspicuous in the resulting representation.