International carbon markets are an appealing and increasingly popular tool to regulate carbon emissions. By putting a price on carbon, carbon markets reshape incentives faced by firms and reduce the value of emissions. While a price constitutes the mechanism by which carbon becomes less appealing, observers have tended to infer the effectiveness of a carbon market from the price of its permits. The general belief is that a carbon market needs a high price in order to be effective. As a result, many observers remain skeptical of initiatives such as the European Union Emissions Trading System (EU ETS) whose permit price remained low (compared to the social cost of carbon). In this paper, we assess whether the EU ETS reduced CO2 emissions despite low prices. We motivate our study by documenting that a carbon market can be effective if it is a credible institution that can plausibly become more stringent in the future. In such case, firms might cut emissions even though permit prices are low. In fact, low prices are a signal that the demand for permits weakens and can therefore suggest that the institution is successful. To assess whether the EU ETS reduced carbon emissions even as permits were cheap, we estimate counterfactual carbon emissions paths using an original sectoral emissions data set. We find that the EU ETS saved about 1.2 billion tons of CO2 between 2008-2016 (3.8%) relative to a world without carbon markets, or almost half of what EU governments promised to reduce under their Kyoto Protocol commitments. Emission reductions within regulated sectors were higher.