Regulations to design private yet publicly sponsored health insurance markets are increasingly adopted in many OECD countries. Here I combine data and economic theory to analyze the interaction between insurers’ competition and the design of premium subsidies in determining equilibrium outcomes. My empirical model includes adverse selection, rich heterogeneity in preferences for vertically and horizontally differentiated plans and accommodates alternative assumptions on pricing conduct. In the context of the Affordable Care Act in the US, I estimate the joint distribution of preferences and expected cost using Californian administrative records on 3.7 million plan choices between 2014-2017, combined with plan and survey data on medical claims. An empirical horse race between conduct assumptions favors oligopoly pricing over perfect competition. Considering alternative subsidy designs shows that, in equilibrium, shifting subsidy generosity toward the young invincibles would lower premiums for all enrollees while increasing enrollment and profits.