Price elasticities of demand for public transport are a key determinant in evaluating the impact of changes in fares on user flows, yet in many integrated fare transit systems, estimating these indicators is often hampered by two realities: the fare changes for different modes are implemented simultaneously and their magnitudes are highly correlated. This strong collinearity is particularly problematic in linear or log-linear models, commonly used for elasticity estimation, and in a case study of Santiago, Chile, robust results with such specifications proved elusive. This paper presents a method based on discrete choice models to estimate the elasticities in an integrated fare system that overcomes these econometric problems, generating results that are both robust and consistent with those reported in the literature. The proposed models are also easy to update and evaluate.