This paper aims to provide a flexible methodological framework to estimate import demand models, which explicitly considers the stochastic properties of data and the endogenous/exogenous nature of some variables. The French imports of virgin olive oil have been used as a case study with Spain, Italy and the Rest of the World as main suppliers. The methodological framework starts by the specification a reduced-form VAR. Appropriated exogeneity tests show the exogeneity of Total Real Imports, indicating the appropriateness of estimating a conditional model. Two cointegration relationships have been found. Several restrictions have been tested in order to identify them as AIDS equations. From structural coefficients of the restricted cointegrated vectors expenditure, own- and cross-prices elasticities are computed. Results show the leadership of Spanish exports to the French market. Italian exports compete in the French market with the Spanish exports, being highly dependent on Spanish domestic production conditions.