This paper tackles specification searches in bayesian production analysis. A two step procedure is set up to determine posterior probabilities for completely regular cost functions. First a set of models with homogeneity, symmetry and adding up is compared with naive models. Both are linear in parameters and bayes factors with diffuse and proper priors can be easily computed. Decomposition of factors with informative priors is carried out too. Then inequality constraints, such as monotonicity and concavity, are imposed through a Monte Carlo Composition method that takes into account both parameter and predictive uncertainty. Monte Carlo methods allow to approximate probability about these constraints and derive posterior probability for completely regular specifications. The procedure is applied to Italian regional translog cost functions. A strong empirical result is obtained. Rankings between almost and completely regular models are different and cast doubts on standard specification searches. Finally model uncertainty is addressed and mixtures of price and substitution elasticities over the regular cost function family are derived.
