Mitigating climate change requires reducing overall greenhouse gas (GHG) emissions. International climate treaties, such as the Kyoto Protocol and the Paris Agreement, are negotiated and signed in order to distribute mitigation burdens among different countries. But before we can decide which countries should reduce GHG emissions and by how much, we need to know who emitted how much. The most prominent carbon emissions accounting mechanisms are production-based (PBEA), and consumption-based emissions accounting (CBEA). PBEA assigns emissions based on the production of goods and services while CBEA assigns emissions based on the consumption of those goods and services. One way of deciding between emissions accounting mechanisms is based on fairness considerations. We call this ‘fair emissions accounting’. In this paper, we present a common approach to fair emissions accounting (Common Approach) and argue that it is misguided. Instead, we offer our Moral Responsibility Approach as an alternative. We argue that the primary consideration from a fairness perspective ought to be who ought to take moral responsibility for emissions. We provide some criteria for moral responsibility in the context of climate change and present a moderate defense of CBEA as the mechanism that, on balance, best meets these criteria.