A new closed-form two-stage budgeting-based multiple discrete-continuous model

Abstract

In this paper, we propose a multiple discrete-continuous (MDC) model approach that (a) does not need the total budget to be observed or predetermined, (b) allows for any finite or not-so-finite budget over the entire set of inside and outside goods, and (c) preserves a strong endogenous utility-theoretic link between inside good consumptions and the budget allocated to the inside goods (that is, to the product group of interest). We show that our proposed model, including a fractional MDC model at the lower level linked up to a Tobit model for the budget allocation to the inside goods, is strictly consistent with a two-stage budgeting utility theoretic structure. As importantly, by using reverse Gumbel distributional assumptions for the stochastic terms in the model system, we derive an incredibly simple closed-form model that, to our knowledge, is a first of its kind in the econometric literature. In doing so, we formally introduce a new distribution, which we label as the minLogistic distribution, to the statistical literature, and derive the properties of the distribution that is then used in the forecasting stage of the proposed model. An application of the proposed model to investigate the household vehicle fleet composition and usage demonstrates its potential relative to an unlinked and exogenously developed budget for the inside goods. The proposed model has the potential to open up a whole new world of MDC applications in general, and particularly for those cases with an unobserved total budget over the inside and outside goods.