A multiple discrete extreme value choice model with grouped consumption data and unobserved budgets

In this paper, we propose, for the first time, a closed-form multiple discrete-grouped extreme value model that accommodates grouped observations on consumptions rather than continuous consumptions. For example, in a time-use context, respondents tend to report their activity durations in bins of time (for example, 15-minute intervals or 30-minute intervals, depending on the duration of an activity). Or when reporting annual mileages driven for each vehicle owned by a household, it is unlikely that households will be able to provide an accurate continuous mileage value, and so it is not uncommon to solicit mileages in grouped categories such as 0–4,999 miles, 5000–9,999 miles, 10,000–14,999 miles, and so on. Similarly, when reporting expenditures on different types of commodities/services, individuals may round up or down to a convenient dollar value of multiples of 10 or 100 (depending on the length of time in which expenditures are sought). In some other cases, a product itself may be available only in specific package sizes (such as say, instant coffee, which is typically packaged in fixed sizes). In this paper, we use the so-called linear outside good utility MDCEV structure of Bhat (2018) to show how the model can be used for grouped consumption observations. Of course, this is also possible because the linear outside good utility does not need a continuous budget value, and allows for unobserved budgets. We discuss an important identification issue associated with this linear outside good utility model, and proceed to demonstrate applications of the proposed model to the case of weekend time-use choices of individuals and vehicle type/use choices of households.