Allowing for non-additively separable and flexible utility forms in multiple discrete-continuous models

Many consumer choice situations are characterized by the simultaneous demand for multiple alternatives that are imperfect substitutes for one another, along with a continuous quantity dimension for each chosen alternative. To model such multiple discrete-continuous choices, most multiple discrete-continuous models in the literature use an additively-separable utility function, with the assumption that the marginal utility of one good is independent of the consumption of another good. In this paper, we develop model formulations for multiple discrete-continuous choices that allow a non-additive utility structure, and accommodate rich substitution structures and complementarity effects in the consumption patterns. Specifically, three different non-additive utility formulations are proposed based on alternative specifications and interpretations of stochasticity: (1) The deterministic utility random maximization (DU-RM) formulation, which considers stochasticity due to the random mistakes consumers make during utility maximization; (2) The random utility deterministic maximization (RU-DM) formulation, which considers stochasticity due to the analyst’s errors in characterizing the consumer’s utility function; and (3) The random utility random maximization (RU-RM) formulation, which considers both analyst’s errors and consumer’s mistakes within a unified framework. When applied to the consumer expenditure survey data in the United States, the proposed DU-RM and RD-DM non-additively separable utility formulations perform better than the additively separable counterparts, and suggest the presence of substitution and complementarity patterns in consumption.