Dynamic Transactions Models

As identified by De Jong and Kitamura (1992), most discrete choice models of household vehicle ownership are vehicle holdings models that describe the likelihood that a household of given attributes will hold a particular set of vehicles. These models quantify the effects on vehicle demand of various vehicle attributes (e.g. price, running costs, make, type, etc.) and household socio-demographic attributes (e.g. income, household size, etc.). On the other hand, dynamic vehicle transactions models view the household vehicles ownership status as a result of a series of transaction decisions to acquire, replace and dispose of household vehicles. They represent changes in a household’s vehicle ownership status, such as buying and/or selling of a car. In this way, household car ownership is modeled as a dynamic behaviour process over time.

The transactions choice model for alternative-fuel vehicles in California (Bunch et al, 1995; Brownstone et al 1996) used micro-simulation methods to model dynamics. The household simulation module updated (aged) household by simulating births, deaths, divorces, children leaving home, etc. The transaction timing module took the updated (aged) household and current vehicle holdings as inputs and decided whether or not a vehicle transaction took place during the simulation period, which was set to 6 month to limit the number of transaction to 1. The vehicle transaction was defined to include disposal, replacement and new purchase. If the transaction time module predicted that a vehicle transaction had taken place, the module of transaction type determined exactly what type of transaction took place. The transaction type module used a number of multinomial logit model after the test on the Independence of Irrelevant Alternatives confirmed its suitability. Finally, the household’s vehicle holdings were updated after the transactions, and they became the starting values for the next period’s simulation.

A more common type of dynamic transactions models is duration models (e.g. Hensher and Mannering, 1994; Gilbert, 1992; De Jong, 1996; Ramjerdi et al. 2000). For example, De Jong (1996) described a disaggregate transactions model system developed and tested by Hague Consulting Group between 1993 and 1995 for the Netherlands. The core of the model system was a duration model which explained the time which elapsed between purchase of a vehicle and its replacement. The Duration decision can be influenced by a number of factors including attributes of the previous car, socio-economic attributes of persons and households, macro-economic development and attributes of the car market. In a duration model, exit from a state is a realization of a stochastic transition process. This process is characterized by a hazard function h(t), which gives the probability of exit from the state immediately after time t, given that the state is still occupied at t. Besides the core duration model, the model system also contained other modules including vehicle type choice models, regression equations for annul use of the present vehicle and module on fuel efficiency.

The simple duration model considers the duration of ownership of vehicle(s) until its replacement (disposal). More recent models consider three types of vehicle transactions: replacing one of the vehicles in the household fleet (replacement), disposing one of the vehicles (disposal) and acquiring a vehicle to add to the fleet (new purchase). The model used is a competing-risks-duration model, where several “latent” hazard

functions describe different ways of exit from the state. The latent hazard that ends the state first will prevail, and other hazards will remain latent. The examples of competing-risks-duration model include De Jong and Pommer (1996), Yamamoto et al (1999) and Mohammadian and Rashidi (2007).

The duration models rely on statistical hazard functions and are not consistent with the micro-economic theory of utility maximization. A small number of studies attempt to bridge this gap and have been developed based on utility maximization theory. A notable example is Golounov et al (2002) and Golounov et al (2004), which used revealed preference data and stated preference data respectively. Their models are based on the intertemporal utility theory (Deaton, 1992), where the decision maker maximizes the intertemporal utility function, which is represented by a discounted sum of utilities in every period. The latter study used the mixed logit model to model random discount rate across individuals, thus accounting for heterogeneity in intertemporal decisions. The major shortcoming of these studies, however, lies in their failure to model the impacts of current choice on future utilities so they can not be regarded as a genuine dynamic model.

Dynamic random utility model explicitly accounts for state dependence. For example, Mohammadian and Miller (2003) used exponentially smoothed weighted average of past choices (Guadagni and Little, 1983) to capture the dependence of current utility evaluations on past transaction choices. This followed the idea that a vehicle transaction itself may have effects on household needs and motivations for automobile ownership level and each transaction can potentially affect the timing and type of the transaction that followed. Heterogeneity across decision makers, on the other hand, was handled by mixed logit formulation. Another truly dynamic theoretical model of car transactions is Adda and Cooper (2000), which used dynamic optimization to investigate the effect of government subsidy on vehicle scrapage. It will be discussed in Chapter 7 with other dynamic models of state dependence so no further details are given here.