The wrong skew problem in stochastic frontier models when inefficiency depends on environmental variables

A well-known result due to Waldman (J Econom 18:275–279, 1982) states that, in the standard normal/half-normal SFA model, estimated technical inefficiency will be zero if the OLS residuals are positively skewed. It is not clear how much this result generalizes. In this paper, we consider the normal/half-normal model in which the distribution of the half-normal error depends on explanatory variables. We consider estimation by nonlinear least squares and maximum likelihood. In both cases, we find a stationary point (zero derivatives) at parameter values that indicate zero inefficiency, a result similar to Waldman’s. However, both for nonlinear least squares and for MLE, we show that in general the stationary point is neither a local minimum nor a local maximum.