Closed-form solution for a bivariate distribution in stochastic frontier models with dependent errors

Abstract

This paper proposes a bivariate continuous model based on normal–half normal distributions for testing the independence of idiosyncratic and inefficiency terms in the stochastic frontier model in a maximum likelihood framework. This model allows us to construct a closed-form of the marginal distribution of the composite error term dependent on a parameter which gives a flexible covariance structure (positive and negative correlations are possible), but also nests classical models utilised in stochastic frontier studies. In addition, we obtain the point estimator for technical efficiency using the Battese and Coelli (J Econom 38:387–399, 1988) expression.