Using a large household panel we estimate demand for car ownership by means of a dynamic multinomial model with correlated random effects. Results suggest that the persistence in car ownership observed in the data should be attributed to both true state dependence and to unobserved heterogeneity (random effects). It also appears that random effects related to single and multiple car ownership are correlated, suggesting that the IIA assumption employed in simple multinomial models of car ownership is invalid. Relatively small elasticities with respect to income and car costs are estimated. It should, however, be noted that the level of state dependence is considerably larger for households with single car ownership as compared with multiple car ownership. This suggests that the holding of a second car will be more affected by changes in the socioeconomic conditions of the household and by economic policy shocks