Dissections of input and output efficiency : A generalized stochastic frontier model

This paper considers a model that accommodates both output and input-specific inefficiency components (inputslacks). We use a translog function to represent the underlying production technology in which the input slacksare generalized to have both deterministic (functions of exogenous variables) and stochastic components.Consequently, the composed error term becomes a nonlinear function of several error components, viz., a onesidedinput slack vector (the dimension of which depends on the number of inputs), a one-sided output technicalinefficiency and a two-sided random noise. Identification of two sets of one-sided errors is possible in a translogmodel because the vector of one-sided input slacks appears in additive form as well as interactively with the (log)inputs. Distributional assumptions on technical inefficiency and slacks also help in identification. Bayesianinference techniques are introduced, organized around Markov Chain Monte Carlo, especially the Gibbs samplerwith data augmentation, to estimate these inefficiency components. For an empirical application we use a largeunbalanced panel of the U.K. manufacturing firms. Slacks associated with labor and capital are found to be2.35% and 10.74%, on average. Output (revenue) loss from technical inefficiency is, on average, 2.43%, whilerevenue loss from input slacks is, on average, 9.2%