Policymakers subsidizing health insurance often face uncertainty about future market prices. We study the implications of one policy response: linking subsidies to prices, to target a given post-subsidy premium. We show that these price-linked subsidies weaken competition, raising prices for the government and/or consumers. However, price-linking also ties subsidies to health care cost shocks, which may be desirable. Evaluating this tradeoff empirically using a model estimated with Massachusetts insurance exchange data, we find that price-linking increases prices 1-6%, and much more in less competitive markets. For cost uncertainty reasonable in a mature market, these losses outweigh the benefits of price-linking.