The Generalized Multiple Discrete-Continuous Extreme Value (GMDCEV) Model: Allowing for Non-Additively Separable and Flexible Utility Forms

Many consumer choice situations are characterized by the simultaneous demand for multiple alternatives that are imperfect substitutes for one another. A simple and parsimonious Multiple Discrete-Continuous Extreme Value (MDCEV) econometric approach to handle such multiple discreteness was formulated by Bhat (2005) within the broader Kuhn-Tucker (KT) multiple discrete-continuous economic consumer demand model of Wales and Woodland (1983). However, the MDCEV model, and other extant multiple discrete-continuous models, use an additively-separable utility function, with the assumption that the marginal utility of one good is independent of the consumption of another good. The implication is that the marginal rates of substitution between any pair of goods is dependent only on the quantities of the two goods in the pair, and independent of the quantity of other goods, thus substantially reducing the ability of the utility function to accommodate rich and flexible substitution patterns. Also, the specification of a quasiconcave and increasing utility function with respect to the consumption of goods in extant models, when coupled with the additive utility across goods, immediately implies that goods cannot be inferior and cannot be complements. In this paper, we develop a closedform model formulation for multiple discrete-continuous choices that allows a non-additive utility structure, and accommodates rich substitution structures and complementarity effects. As importantly, the utility functional form proposed here remains within the class of flexible forms, while also retaining global theoretical consistency properties (unlike the Translog and related flexible quadratic functional forms). The result is also clarity in the interpretation of the model parameters. The proposed Generalized Multiple DiscreteContinuous Extreme Value (GMDCEV) model is easy to estimate, and should represent a substantially more accurate representation of the underlying behavioral process for many multiple discrete-continuous choice situations.