Production Frontiers and Panel Data

TLDR: In this article, the authors consider the estimation of a stochastic frontier production function, which is the type introduced by Aigner, Lovell, and Schmidt (1977) and Meeusen and van den Broeck (1977).

Abstract: This article considers estimation of a stochastic frontier production function-the type introduced by Aigner, Lovell, and Schmidt (1977) and Meeusen and van den Broeck (1977). Such a production frontier model consists of a production function of the usual regression type but with an error term equal to the sum of two parts. The first part is typically assumed to be normally distributed and represents the usual statistical noise, such as luck, weather, machine breakdown, and other events beyond the control of the firm. The second part is nonpositive and represents technical inefficiencythat is, failure to produce maximal output, given the set of inputs used. Realized output is bounded from above by a frontier that includes the deterministic part of the regression, plus the part of the error representing noise; so the frontier is stochastic. There also exist socalled deterministic frontier models, whose error term contains only the nonpositive component, but we will not consider them here (e.g., see Greene 1980). Frontier models arise naturally in the problem of efficiency measurement, since one needs a bound on output to measure efficiency. A good survey of such production functions and their relationship to the measurement of productive efficiency was given by F0rsund, Lovell, and Schmidt (1980).