Maximum Likelihood Estimation of Econometric Frontier Functions*

The estimation of production functions has been one of the more popular areas of applied econometrics. Recent work in duality theory which has linked production and cost functions has made this topic even more attractive. Typically, least squares (or some variant, such as two stage or generalized least squares) is used to estimate the model of interest in accordance with the assumption of a normally distributed disturbance in the model. However, definitions of a production function are given in terms of the maximum output attainable at given levels of the inputs. Similarly, a dual cost function gives the minimum cost of producing a given level of output at some set of input prices [See Christensen and Greene (1976).] It has thus been argued that the disturbances specified in these models, and techniques used to estimate them should account for that fact. These considerations have motivated the recent literature on frontier functions. Numerous studies have been devoted to the respecification of empirical production and cost models to make them more compatible with the underlying theory, and to the derivation of appropriate estimators. In some cases, this has amounted to minor modifications of least squares results. The remaining estimators are based on two distinct specifications. The very recent work on composite disturbances has relaxed somewhat the orthodox interpretation of the underlying function as a strict frontier with all observations lying on one side of it, and has produced well behaved maximum likelihood estimators with all of the usual desirable properties. Other authors, following the more strict interpretation, have employed what we shall call full frontier estimators which allow only one sided residuals. It