On the distribution of estimated technical efficiency in stochastic frontier models

We consider a stochastic frontier model with error ε=v−u, where v is normal and u is half normal. We derive the distribution of the usual estimate of u,E(u|ε). We show that as the variance of v approaches zero, E(u|ε)−u converges to zero, while as the variance of v approaches infinity, E(u|ε) converges to E(u). We graph the density of E(u|ε) for intermediate cases. To show that E(u|ε) is a shrinkage of u towards its mean, we derive and graph the distribution of E(u|ε) conditional on u. We also consider the distribution of estimated inefficiency in the fixed-effects panel data setting.