Quantile estimation of stochastic frontiers with the normal-exponential specification

There has been increased interest in estimation of the stochastic frontier model via quantile regression. Two main approaches currently exist, one that ignores distributional assumptions and selects arbitrary quantiles and another that attempts to estimate the frontier by recognizing that it aligns with a specific quantile of the conditional distribution of output. We add to this second vein of literature by developing the necessary tools to estimate the quantile which is consistent with the location of the frontier under the Normal-Exponential distributional setting. We show that this can be accomplished by evaluating the Normal-Exponential cumulative distribution function at the expected value of OLS residuals to directly estimate the stochastic frontier model parameters. Both simulations and an empirical illustration showcase the performance of the method.