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Evaluating shadow prices is critical in devising environmental regulatory policies for pollutants. Compared to traditional frontier estimation methods, this paper uses a recently developed data-driven approach named convex quantile regression, taking both the noise and inefficiency into account and estimating the shadow prices locally. This paper is the first work applying convex quantile regression to jointly evaluate shadow prices of CO2, SO2, and NOx produced by U.S. coal power plants from 2010 to 2017. During this period, five major regulatory provisions were implemented for U.S. coal power plants. We find that the shadow prices of CO2, SO2, and NOx increased from 2010 to 2017. The increase in the shadow price of CO2 is mainly due to the increase in electricity prices, while the increase in shadow prices of SO2 and NOx is mainly due to the successful emission reductions. Moreover, the results show that the CSARP and CSARP Update have significantly increased the shadow prices of SO2 and NOx. However, the relatively lower market allowance prices compared to the shadow prices indicate that society could benefit more if the government could increase the market prices of the pollutants to be more close to the shadow prices. [ABSTRACT FROM AUTHOR]