On the distribution of estimated technical efficiency in stochastic frontier models

We consider a stochastic frontier model with error epsilon = v - u, where nu is normal and it is half normal. We derive the distribution of the usual estimate of u, E(u vertical bar epsilon). We show that as the variance of v approaches zero, E(u vertical bar epsilon) - u converges to zero, while as the variance of v approaches infinity, E(u vertical bar epsilon) converges to E(u). We graph the density of E(u vertical bar epsilon) for intermediate cases. To show that E(u vertical bar epsilon) is a shrinkage of u towards its mean, we derive and graph the distribution of E(u vertical bar epsilon) conditional on u. We also consider the distribution of estimated inefficiency in the fixed-effects panel data setting. (C) 2008 Elsevier B.V. All rights reserved.