How Long to Own and How Much to Use a Car? A Dynamic Discrete Choice Model to Explain Holding Duration and Driven Mileage
G Cernicchiaro, M de Lapparent, INRETS, FR
This paper formulates a dynamic discrete choice model under uncertainty to describe the behavior of French households as it regards car holding duration and its driven mileage while accounting for the evolution of fuel prices.
The defining characteristic of a durable good, here a car, is that it yields productive services over multiple time periods but it wears also out with age and use.The average holding duration of a car has increased over the last decades. It is often explained by an overall improvement in quality of its features that extends its lifecycle and that gives therefore the possibility to use it over a longer period of time. It is also characterized by a higher initial budget expenditure that may imply to need a longer period of time to return on investment. On the other hand, as the cost of using a car increases with its age because of its physical depreciation, there may therefore be temptation to use it more intensively to return on investment more quickly. All the same, the scrap value of the asset is also higher in this latter situation.Anyway, car use depends on fuel prices. The rising cost of petrol contributes to people cutting back on car use. We expect therefore a variation of fuel prices to have two effects: one on the amount of driving with a car and one on its holding duration. It acts like a leverage effect on the holding duration as it becomes more expensive to operate a car.All in all, households have to balance the costs and benefits of owning a car and using it over a period of time. Each has to optimize a related expected discounted utility with respect to future evolution of fuel prices and anticipated car mileage over that horizon and to choose when to dispose it.This paper formulates a finite-horizon optimal stopping problem under uncertainty to describe the behavior of a household as it regards car holding duration and its driven mileage accounting for the evolution of fuel prices. In the present approach, the decision to dispose a car coincides with an optimal stopping problem and the optimal stopping rule is the solution to a stochastic structural dynamic programming problem. The solution to such a problem is rather standard. It is characterized by a threshold-type of rule: the household chooses to dispose a car at some date if the expected discounted future flows of satisfaction it obtains falls below the expected discounted future flows of holding and use costs at this moment.The proposed model belongs to the class of discrete Markov decision processes. It is specified as a dynamic discrete choice model of a forward-looking economic agent with two observed state variables and one decision variable. The observed state variables model beliefs about the evolution of fuel prices and anticipated driven mileage. The decision variable models the decision to either dispose the owned car or to keep it. The stochastic aspect of the problem comes from the modeler?s lack of knowledge about beliefs and preferences of the observed decision maker.We demonstrate the model by drawing data from the French ?Parc Auto? (Car Fleet) panel survey, the most comprehensive database about car ownership and use that is available in France. We focus on the population of households that owned only one car and that disposed it over the period 2003-2007. The panel nature of the data force to account for individual-specific unobserved components that may affect the modeled beliefs and decisions. As the problem is finite-horizon, it is therefore solved by backward induction. The parameters of the structural model are estimated using the Nested Fixed Point algorithm. Once estimated the model, one is able to advise decision-makers about the effects of different policies that may affect car holding and car use behaviors.
Association for European Transport