We propose a methodology for modelling and influence diagnostics in a Cobb–Douglas type setting. This methodology is useful for describing case-studies from economics. We consider stochastic restrictions for the model based on auxiliary information in order to improve its predictive ability. Model errors are assumed to follow the family of symmetric distributions and particularly its normal and Student-t members. We estimate the model parameters with the maximum likelihood method, which allows us to compare the normal case with a flexible framework that provides robust estimation of parameters based on the Student-t case. To conduct diagnostics in the model, we use two approaches for studying how a perturbation may affect on the mixed estimation procedure of its parameters due to the usage of sample data and non-sample auxiliary information. Curvatures and slopes used to detect local influence with both approaches are derived, considering perturbation schemes of case-weight, response and explanatory variables. Numerical evaluation of the proposed methodology is performed by Monte Carlo simulations and by applications with two data sets from economics, all of which show its good performance and its further applications. Particularly, the real data analyses confirm the importance of statistical diagnostics in the data modelling.