Indirect inference estimation of stochastic production frontier models with skew-normal noise

In this paper we consider a stochastic frontier model in which both the noise and inefficiency components are asymmetric, viz., the noise term is skew normal and the inefficiency term is half-normal. This formulation avoids the criticism that skewness of the composite error term (sum of the noise and inefficiency) cannot be an indicator of inefficiency because skewness can also arise from the noise term. Our estimator of inefficiency does not depend on skewness of the one-sided error alone; it controls for skewness in the noise term as well. We further generalize the model by introducing determinants of skewness of the noise term as well as determinants of inefficiency. Additionally, we test hypotheses that the noise term is either symmetric (normal) or has a constant skewness parameter. Instead of using the standard ML method, we use the indirect inference (II) approach to estimate the parameters of the proposed model. Formulae for predicting (in)efficiency are also provided. Finally, we provide both simulation and empirical results using the II estimation approach to showcase workings of our model.