This paper models health insurance choice in Chile (public versus private) as a dynamic, stochastic process, where individuals consider premiums, expected out-of pocket costs, personal characteristics and preferences. Insurance amenities and restrictions against pre-existing conditions among private insurers introduce asymmetry to the model. We confirm that the public system services a less healthy and wealthy population (adverse selection for public insurance). Simulation of choices over time predicts a slight crowding out of private insurance only for the most pessimistic scenario in terms of population aging and the evolution of education. Eliminating the restrictions on pre-existing conditions would slightly ameliorate the level (but not the trend) of the disproportionate accumulation of less healthy individuals in the public insurance program over time.