Analyzing inefficiency using a frontier search approach

Abstract

Efficiency measurement naturally requires the definition of a frontier as a benchmark indicating efficiency. Usually a measure reflecting the distance of a data point to the frontier indicates the level of efficiency. One of the crucial characteristics to distinguish efficiency measurement tools is the way in which they construct the frontier. The class of deterministic and non parametric tools of constructing the frontier mainly comprises of tools associated with Data Envelopment Analysis. Coming in various flavors all DEA frontiers suffer of their piecewise construction giving rise to numerous vertices. Those vertices do not allow convenient analysis of the frontier properties such as computing elasticities and the like. In this paper we want to contribute to the class of deterministic and non parametric tools of constructing the frontier in an one output and n input setting. We suggest a new empirical approach drawing on functional search in the fashion of Koza's (1992) genetic programming. The frontier search algorithm employed evolves the functional form of the frontier and the parameters simultaneously. The frontier exhibits the neat property that it is smooth and differentiable enabling the computation of elasticities,for example. In particular we introduce both the idea and the algorithm of the frontier search procedure. We discuss the advantages and shortcomings with respect to empirical problems. The arguments brought forth in the preceding sections are illustrated by the investigation of an artificial example.