The debate on the capacity of the European Union Emissions Trading System (EU ETS) to effectively induce CO2 emissions reduction is still ongoing. This is particularly noteworthy in the case of the power sector, where numerous decarbonization policies overlap. This paper contributes to this discussion by leveraging a methodological approach that circumvents the challenges of constructing credible counterfactuals for causal inference and allows for disentangling the impact of the EU ETS from other policies on the power sector's abatement efforts, alongside influencing factors such as weather. Specifically, we employ a Bayesian structural time series (BSTS) model to assess the effectiveness of the three completed phases of the EU ETS (2005-2020) in reducing CO2 emissions in the power sector across 24 Member States. We analyze the policy implementation effect over the course of each phase by comparing actual power sector emissions with counterfactual estimates derived from contemporaneous predictors related to such emissions. The results indicate a statistically significant emissions reduction in the second and third phases, with no significant reduction in the first phase. The power sector's centrality to the EU ETS, and its critical role in our economies emphasize the importance of our findings in evaluating emissions reduction objectives.