In this study, a nested multivariate Tobit model is proposed to model activity and travel time use jointly. This proposed model can handle: (1) The corner solution problem; (2) time allocation trade-offs among different types of activities; and (3) travel being treated as a derived demand of activity participation. The model is applied to the Swedish national travel survey (NTS). Evidence of the potential positive utility of travel time added on non-work activity time allocation in the Swedish case is also found. The proposed model is compared to an MDCEV model specification. The results show clear differences in marginal effect estimates. In terms of prediction, the nested multivariate Tobit model shows a slightly worse performance on the hit rate measure than the MDCEV model combined with a stochastic frontier model, but shows a slightly better performance on the SMAPE measure.