The European Union Emission Trading System (EU ETS) is the world's largest trading system for emissions. It has a crucial role to play in meeting the goals of the Paris Agreement. However, there has been debate over its effectiveness. This thesis examines how the EU ETS impacts methane emissions. The study uses Swedish emission data from 2005 to 2021 and employs a fixed effect model with two exogenous and two endogenous variables. While the test produced significant results for carbon dioxide emissions, it could not do so for methane emissions. The thesis concludes that EUA prices have a negative effect on carbon dioxide emissions, while electricity prices have a positive effect. The impact on methane emissions could not be determined. Previous research is divided, suggesting that financial solutions like a cap and trade system can have varying effects depending on the sector and perspective. A new model with interaction variables, more control variables, or a different data set could yield significant results.