A multiple discrete–continuous extreme value model: formulation and application to discretionary time-use decisions

Abstract

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). This paper examines several issues associated with the MDCEV model and other extant KT multiple discrete-continuous models. Specifically, the paper proposes a new utility function form that enables clarity in the role of each parameter in the utility specification, presents identification considerations associated with both the utility functional form as well as the stochastic nature of the utility specification, extends the MDCEV model to the case of price variation across goods and to general error covariance structures, discusses the relationship between earlier KT-based multiple discrete-continuous models, and illustrates the many technical nuances and identification considerations of the multiple discrete-continuous model structure through empirical examples. The paper also highlights the technical problems associated with the stochastic specification used in the KT-based multiple discrete-continuous models formulated in recent Environmental Economics papers.

An empirical investigation into the time-use and activity patterns of dual-earner couples with and without young children

“…The model used in the analysis is based on Bhat's (2005Bhat's ( , 2008 Multiple Discrete Continuous Extreme Value (MDCEV) model, which recognizes that time-decisions entail the choice of participating in one or more activity purposes along with the amount of time to invest in each chosen activity purpose (see Habib and Miller, 2008, Xia et al, 2009, 8 Eluru et al, 2010 The survey collected time use information at a very fine activity purpose level.…”

A joint model for the perfect and imperfect substitute goods case: Application to activity time-use decisions

“…A simple and parsimonious econometric approach to handle multiple discreteness was formulated by Bhat (2005) based on the use of a non-linear utility structure with a multiplicative log-extreme value error term. The non-linear utility structure used in Bhat's approach was employed originally by Kim et al (2002) as a specific satiation-based formulation within the broader Kuhn-Tucker multiple-discrete economic model of consumer demand proposed by Wales and Woodland (1983).…”

“…Thus, in the context of time-use in many different kinds of leisure activity purposes, the time investment in all the consumed leisure activity purposes is such that the marginal utilities are the same across purposes at the optimal time allocations. Also, for an activity purpose in which no time is invested, the marginal utility for that activity purpose at zero time investment is less than the marginal utility at the consumed times of other purposes (Bhat, 2005). However, there are many instances where the real choice situation is characterized by a combination of imperfect and perfect substitutes (perfect substitutes correspond to the case where consumers prefer to select only one discrete alternative at any choice occasion; see Hanemann, 1984).…”

“…In any given day, an individual, if s/he chooses to participate in recreation, may participate in only one of these recreational activity categories. The MDCEV model, as formulated in Bhat (2005), needs to be modified to handle such a combination of a multiple discrete-continuous choice among alternatives, as well as a single choice of one subalternative within one or more of the alternatives.…”

“…To our knowledge, this is the first consideration of such a unified utility-maximizing framework for joint imperfect-perfect substitute goods analysis in the economic literature. As discussed earlier, previous studies of the imperfect substitute goods case include Wales and Woodland (1983), Kim et al (2002), and Bhat (2005), while previous studies of the perfect substitute goods case include Hausman (1980), Dubin and McFadden (1984), Hanemann (1984), Mannering and Winston (1985), Train (1986), Chiang (1991), Chintagunta (1993), and Arora et al (1998).…”