European Union has launched its Emissions Trading Scheme (ETS) in 2005, creating the first and one of the biggest international carbon markets, with the aim of reducing CO2 emissions of the Member States. Forming a part of the EU Climate Action plan, composed by a broad set of policies, as well as belonging to a complex interrelated energy system, the assessment of the ETS system effectiveness is not straight forward. Policy-makers tend to use emission levels or CO2 prices as indicators, even though both measures are affected by other policies, energy market fundamentals, and speculative shocks. This paper develops an empirical VAR model that connects the energy sector (oil, natural gas, coal and electricity prices, as well as a share of fossil fuels in electricity production), economic activity and CO2 permit prices. We use frequency domain analysis to study how the parts of this system impact each other and how these impacts evolve over time. The model can be used as a monitoring tool for CO2 price dynamics and for the effectiveness of the ETS system. Our empirical results indicate that up to 90% (65% on average) of the variation in CO2 prices, adjusted by supply effects, is explained by the variations in fundamental market variables; however, the individual contributions of them have changed over time. For example, the importance of the economic activity, used to be a major source of CO2 price variations in the past, is vanishing recently, while the opposite occurs to the coal prices, which have gained in importance in recent periods. The impact of CO2 prices on a share of fossil fuels in electricity production is limited, pointing towards the still low contribution of the ETS system for renewable energy penetration.