A new flexible multiple discrete–continuous extreme value (MDCEV) choice model

Traditional multiple discrete–continuous (MDC) models generally predict the continuous consumption quantity component reasonably component well, but not necessarily the discrete choice component. In this paper, we propose, for the first time, a new flexible closed-form MDCEV model that breaks the tight linkage between the discrete and continuous choice dimensions of the traditional MDC models. We do so by (1) employing a linear utility function of consumption for the first outside good (which removes the continuous consumption quantity of the outside good from the discrete consumption decision, and also helps in forecasting), and (2) using separate baseline utilities for the discrete and continuous consumption decisions. In the process of proposing our new formulation, we also revisit two issues related to the traditional MDC model. The first relates to clarification regarding the identification of the scale parameter of the error terms, and the second relates to the probability of the discrete choice component of the traditional MDC model (that is, the multivariate probability of consumption or not of the alternatives). We show why the scale parameter of the error terms is indeed estimable when a γ-profile is used, as well as show how one may develop a closed-form expression for the discrete choice consumption probability. The latter contribution also presents a methodology to estimate pure multiple discrete choice models without the need for information on the continuous consumptions. Finally, we also develop forecasting procedures for our new MDC model structure.