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This paper develops and estimates a model of a regulated health insurance exchange, in which insurers' ability to adjust prices across buyers with different observed risk or preferences is restricted. I show conditions under which the joint distribution of risk and preferences is identified, even when the econometrician does not observe any information on individual risk. These primitives can then be used to simulate equilibrium under alternative regulations. I estimate the model with data from the first year of the Californian exchange under the Affordable Care Act, where age-rating restrictions and a subsidy program determine the way in which insurers' decisions translate to expected profits. For this market, I investigate alternative designs of the subsidy program. Compared to the subsidy formula mandated by the healthcare reform, the adoption of a voucher program – providing buyers with a lump-sum equal to 70-80% of their expected expenditure – would transfer welfare away from insurers, favoring consumers and/or taxpayers. Simulations of equilibrium under this alternative policy result in total coverage between 100-115% of the levels achieved by the current regulations, while also reducing government expenditure, average premiums, and markups, by 0-20%, 12-15%, and 22-27%, respectively.