The European Union Trading Scheme gives emission allowances a market price and are a marginal cost factor for power plants that run on polluting fuels. Power plants include these costs while determining the selling price of their output. Sold on a market place, it is sensible to expect that electricity market prices do reflect the prices of emission rights. The pass-through rate measures the fraction of the price of an emission right passed through to the electricity market price and is often assumed to be constant. Depending on different demand levels between and over days, we expect that the pass-through rate should vary and not be constant as the market clearing price is determined by different marginal producers who differ in terms of emission intensity. We therefore test the hypothesis that pass-through rates are constant and find strong support, using futures prices from the U.K. and Germany, for rejecting this hypothesis against the alternative that pass-through rates are non- constant and vary over time. From a policy perspective, the finding that the internalization of the costs of carbon emission allowances is not fully and time-varying implies that policy makers should be careful analyzing the effectiveness of the EU ETS policy.