A multiple discrete continuous extreme value choice (MDCEV) model with a linear utility profile for the outside good recognizing positive consumption constraints

A variant of the traditional multiple discrete-continuous extreme value (MDCEV) model that obviates the need to have budget information, labeled as the Lγ-profile MDCEV model, has been proposed recently. This new model structure breaks the strong linkage between the discrete and continuous choice dimensions of decision-making. But recent studies show that this Lγ-profile model may not work well in situations when, even if the budget is unobserved, the budget is known to be finite and small in magnitude. The reason is that the formulation, while ensuring the positivity of consumptions of the inside goods (that may or may not be consumed), does not guarantee, within the model formulation and estimation itself, the positivity of the consumption of the essential outside good. In this paper, we develop a formulation based on a reverse Gumbel structure for the stochastic terms in the utility functions of alternatives that develops a closed-form probability expression, while also accommodating the positivity requirement for the outside good. The ability of our proposed Budget-based Reverse Generalized Lγ-profile model (labeled the BR-GLγ-profile model) to recover true underlying model parameters is assessed. Our results clearly point to the benefit of employing the proposed model (relative to extant linear outside utility profile models in the literature) in empirical contexts when there is reason to believe that a finite ceiling applies to the budget (even if the budget is unobserved) or if the budget is actually available. In the latter case when the budget is available, our proposed model is a serious contender to the traditional γ-profile-MDCEV model and will generally outperform the traditional γ-profile-MDCEV when the consumption share of the outside good is high.