Properties of Technical Efficiency Estimators in the Stochastic Frontier Model

The estimation of frontier cost and production functions has been given impetus by the introduction of the stochastic frontier.’ This model is distinguished by a disturbance term composed of two parts a one-sided component, non-positive for production functions and non-negative for cost functions, representing the degree of inefficiency, and a symmetric component representing the usual statistical noise (reporting and measurement error, for example) that characterizes any relationship. This formulation has proven to alleviate some of the statistical and practical shortcomings of earlier attempts at measuring frontiers, such as linear programming methods. A serious drawback of this procedure is the inability to measure individual effects. This was the original motivation for the introduction of production isoquants in the pioneering work of Farrell (1957). Instead, all that is available is an estimate of the overall or industry level of inefficiency. In an attempt to rectify this shortcoming, Jondrow et al. (1982) proposed estimating the firmlevel inefficiency with an estimate of the conditional expectation of the one-sided component conditional on the total disturbance. This is an interesting suggestion for an estimator, but the account of its statistical properties is limited to the observation that the sampling error disappears asymptotically. Since the total disturbance contains only imperfect information regarding the one-sided disturbance, the proposed estimator has a certain ‘intrinsic’ variability [Jondrow et al. (1982, p. 235)].