We study whether to auction or to freely distribute emissions allowances when some firms participating in emissions trading are subject to price regulation. We show that free allowances allocated to price-regulated firms effectively act as a subsidy to output, distort consumer choices, and generally induce higher output and emissions by price-regulated firms. This provides a cost-effectiveness argument for an auction-based allocation of allowances (or equivalently an emissions tax). For real-world economies such as the Unites States, in which about 20 percent of total carbon dioxide emissions are generated by price-regulated electricity producers, our quantitative analysis suggests that free allowances increase economy-wide welfare costs of the policy by 40-80 percent relative to an auction. Given large disparities in regional welfare impacts, we show that the inefficiencies are mainly driven by the emissions intensity of electricity producers in regions with a high degree of price regulation.