Reconciling Engineers and Economists: the Case of a Cost Function for the Distribution of Gas

The analysis of cost functions is an important topic in econometrics both for scientific studies and for industrial applications. The object of interest may be the cost of a firm or the cost of a specific production, in particular in case of a proposal to a procurement. Engineer methods evaluate the technical cost given the main characteristics of the output using the decomposition of the production process in elementary tasks and are based on physical laws. The error terms in these models may be viewed as idiosyncratic chocs. The economist usually observes ex post the cost and the characteristics of the product. The difference between theoretical cost and the observed one may be modeled by the inefficiency of the production process. In this case, econometric models are cost frontier models. 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 inefficiencies are explicitly introduced. 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 suggest also 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.