The Nonparametric Approach

Abstract

The nonparametric approach to the measurement of productive efficiency can be specified either through a flexible form of the production function which satisfies the efficiency hypothesis, or a set-theoretic characterization of an efficient isoquant. In the first case the production frontier can be of any general shape satisfying some very weak conditions like quasi-concavity or monotonicity, although in most empirical and applied work piecewise linear or, log-linear functions have been frequently used. Thus both Farrell and Johansen applied linear programming models in the specification of the production frontier. Farrell’s efficiency measure is based on estimating by a sequence of linear programs (LPs) a convex hull of the observed input coefficients in the input space. Two features of Farrell efficiency make it very useful in applied research. One is that it is completely data-based i.e., it uses only the observed inputs and outputs of the sample units while assuming production functions to be homogeneous of degree one. Hence it has many potential applications for the public sector units, where for most of the inputs and outputs the price data are not available. For example consider educational production functions for public schools, where outputs such as test scores in achievement tests are only proxy variables for learning; inputs such as average class size, experience of teachers or ethnic background of students do not have observed market prices. Secondly, Farrell’s method uses a set of LP models to estimate the efficiency parameters, so that the production frontier appears as piecewise linear functions. Nonnegativity conditions on the parameter estimates can therefore be easily incorporated.