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.