We study smoking persistence in ten countries using data from the European Community Household Panel. Such persistence may be due to true state dependence but may also reflect individual unobserved heterogeneity. We distinguish between the two by using semi-parametric dynamic panel data methods applied to both the decision to smoke or not and to the decision on the number of cigarettes smoked. Our model allows for correlation of the two time-varying error terms, i.e. for selectivity. We find that for both smoking decisions true state dependence is in general much smaller when unobserved individual heterogeneity is taken into account, and we also uncover large differences in true state dependence across countries. Finally, we find that taking into account heaping in the reported number of cigarettes smoked considerably improves the fit of our model.