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We analyze how different ways of allocating emission quotas may influence the electricity market. Using a large-scale numerical model of the Western European energy market with heterogeneous electricity producers, we show that different allocation mechanisms can have very different effects on the electricity market, even if the total emission target is fixed. This is particularly the case if output-based allocation (OBA) of quotas is used. Gas power production is then substantially higher than if quotas are grandfathered. Moreover, the welfare costs of attaining a fixed emission target are significantly higher. The numerical results for OBA are supported by a theoretical analysis, which offers some new results.