Posterior analysis of stochastic frontier models using Gibbs sampling
The authors investigate a basic stochastic frontier model of the form \(y_i={x'}_i \beta+\nu_i-z_i,\) where \(y_i\) is the log of output or the negative of log cost for the firm \(i\;(i=1,\dots,N);\) \(x_i\) is a vector of \(K\) exogenous variables; \(v_i\) is a symmetric disturbance capturing measurement error in the stochastic frontier; \(z_i\) is a nonnegative disturbance capturing the level of firm inefficiency. It is assumed that \(v_i\) is \(N(0,\sigma^2).\) Three different specifications for \(z_i\) are considered corresponding to different Gamma distributions with integer shape parameter \(j=1,2,3.\) Bayesian methods are used to analyse this stochastic frontier model. It is shown that Gibbs sampling methods greatly reduce the computational difficulties involved in analyzing such models. The main interest in the empirical illustrations is concentrated on making marginal posterior inference on the parameters and \(z\) and, in particular, on firm efficiency given by \(r_i=\exp (-z_i).\)
scientific article; zbMATH DE number 1409708