The econometric estimation of cost functions has been proposed in the literature as a suitable approach in order to obtain estimations of marginal costs, efficiency levels and scale elasticities for transport industries. However, regarding the airport industry, no significant attention has been paid in developing an airport-specific estimation methodology rather than adapting the procedures applied to other industries. The lack of comparable airport data is one of the causes which could explain the scarcity of this literature in the past, as well as the use of very limited approaches to explain airport technology. This paper tries to overcome these limitations by developing an airport-specific methodology to estimate a multi-output long-run cost function using an unbalanced pooled database on 161 airports worldwide. The specification of hedonically-adjusted aircraft operations, domestic and international passengers, cargo and commercial revenues in the output vector, as well as the calculation of input prices are discussed. Both technical and allocative inefficiencies are specified in the model using a Stochastic Frontier method that has been estimated through Bayesian Inference and Markov Chain Monte Carlo methods.