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

Abstract

This paper considers a model that accommodates both output and input-specific inefficiency components (input slacks). We use a translog function to represent the underlying production technology in which the input slacks are 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 one-sided input slack vector (the dimension of which depends on the number of inputs), a one-sided output technical inefficiency and a two-sided random noise. Identification of two sets of one-sided errors is possible in a translog model 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. Bayesian inference techniques are introduced, organized around Markov Chain Monte Carlo, especially the Gibbs sampler with data augmentation, to estimate these inefficiency components. For an empirical application we use a large unbalanced panel of the U.K. manufacturing firms. Slacks associated with labor and capital are found to be 2.35% and 10.74%, on average. Output (revenue) loss from technical inefficiency is, on average, 2.43%, while revenue loss from input slacks is, on average, 9.2%.