<p>Production costs are often evaluated beforehand by engineers, given the main characteristics of the output and using the decomposition of the production process in elementary tasks. The economist usually observes ex post the cost and the characteristics of the product. In this paper we propose to take advantage of the situation where we have information from both approaches. We consider a system of two equations, one being a standard regression model (for the technical cost function) and one being a stochastic frontier model for the economic cost function where a positive part is explicitly introduced to model the difference between the two costs. We derive estimators of this joint model and derive its asymptotic properties. The models are presented in classical parametric approach, with few assumptions on the stochastic properties of the joint error terms. We also suggest a way to extend the model to a nonparametric approach, the latter provides an original way to model and estimate nonparametric stochastic frontier models. The techniques are illustrated in the case of the cost function for the distribution of gas in France.</p>