The “wrong skewness” problem: a re-specification of Stochastic Frontiers.

Abstract

In this paper, we study the so-called “wrong skewness” anomaly in Stochastic Frontiers (SF), which consists in the observed difference between the expected and estimated sign of the asymmetry of the composite error. We propose a more general and flexible specification of the SF model, introducing dependence between the two error components and asymmetry (positive or negative) of the random error. This re-specification allows us to decompose the third moment of the composite error in three components, namely: i) the asymmetry of the inefficiency term; ii) the asymmetry of the random error; and iii) the structure of dependence between the error components. This decomposition suggests that the “wrong skewness” anomaly is an ill-posed problem, because we cannot establish ex ante the expected sign of the asymmetry of the composite error. We report a relevant special case that allows us to estimate the three components of the asymmetry of the composite error and, consequently, to interpret the estimated sign. We present two empirical applications. In the first dataset, where the classic SF displays wrong skewness, estimation of our model rejects the dependence hypothesis, but accepts the asymmetry of the random error, thus justifying the sign of the skewness of the composite error. In the second dataset, where the classic SF does not display any anomaly, estimation of our model provides evidence of the presence of both dependence between the error components and asymmetry of the random error