The noise error component in stochastic frontier analysis

With a little help from a handful of scholars, the noise component of the composed error in a production model created the stochastic frontier analysis field. But after that glorious moment, it was confined to obscurity. We review what little research has been done on it. We present two cases where it torments us from the shadows, by sabotaging identification, and by distorting the sample skewness. We examine the relation between predicted noise and predicted inefficiency. For the Normal-Half Normal and the Normal-Exponential error specification, we provide its conditional expectation as predictor and we examine its distribution in relation to the marginal law. We also derive the conditional distribution of the noise and we compute confidence intervals and the probability of over-predicting it. Finally, we present a model where the noise, as the carrier of uncertainty, induces directly inefficiency. We conclude by showcasing our theoretical results through an empirical illustration.