On asymmetry and quantile estimation of the stochastic frontier model

Quantile regression has become common in applied economic research. Recently, these methods have been adapted for use with the stochastic frontier model. However, the composed nature of the error term is ignored, drawing into question if a “stochastic” quantile frontier is actually estimated. Here we demonstrate that a particular distributional pair is consistent with the intent of these earlier proposals but is not in fact a quantile estimator. An interesting feature of this distributional pairing is that both distributions can be asymmetric. We further discuss the identification and practical issues associated with this framework.