Modeling sequences of discrete and continuous variables over time with an application to the vehicle ownership and usage problem

The problem of modeling individual decisions repeatedly over time is important to study dynamics in travel behavior, changes in preferences, and adoption of new services or technologies. Although different methods have been proposed to account for dynamics in pure discrete choice contexts, the case where both continuous and discrete decision variables evolve dynamically has not been fully solved. In this paper, we develop a methodology for the problem of vehicle ownership and usage in a finite time horizon, but the formulation is general and can be easily transferred to other contexts where discrete-continuous decision variables are modeled in time. The model specification is based on a recursive binary probit model that maximizes instantaneous and future utility components of discrete choices, and on a linear regression that models the continuous decision variable. Empirical results are obtained using simulated data; validation tests attest that trends in demand are correctly recovered.