**2. Related Work**

This section reviews related works concerning the influence of carbon prices on the price of electricity.

#### *2.1. Long Run vs. Short Run Relationship*

Previous works have analyzed the relationship between carbon prices and the price of electricity as part of an empirical study. These reveal statistical evidence of such a relationship across several markets in both the long and short run ye<sup>t</sup> not for phase III of the EU ETS.

In regard to the long run, Bunn and Fezzi [7] find a positive relationship between the carbon price and the price of electricity in the U. K. during phase I of the EU ETS. Their analysis reveals that a 1 % change in the carbon price results in an increase in electricity prices by 0.42 % in the equilibrium case. In the short run, this study observes a visible shock in electricity prices after a few days. A similar, positive relationship in the long run is observed in the Spanish market [8,9]. However, the effect here is of a lesser magnitude; i.e., a 1 % change in the carbon price yields a 0.24 % increase in the long run during phase II and in the first year of the third phase [9]. In addition, the findings sugges<sup>t</sup> a smaller impact for a lower carbon price than for a higher one.

On the other hand, there is also strong evidence in favor of a short-run relationship. For example, in the Nordic electricity market, the price of EUA tends to considerably influence the electricity price in the short run [10,11]. Cotton and Mello [5] examined the Australian approach to reducing greenhouse gas emissions. The authors found no impact in the long run but did in the short run. Analogously, our analysis is concerned foremost with the short-run relationship, since we not only investigate the day-ahead market but also the price setting mechanism in the intraday market, where empirical evidence is especially limited.

According to Bannoer et al. [12], the relatively small impact may result from the almost constant carbon price, at least during the period from 2010 until 2013, and conclude, therefore, that the carbon price has only a very small effect. However, this work only studies phase II and cannot assess whether the additional adjustments from phase III have been effective.

## *2.2. Asymmetric Pass-Through Rate*

The ratio of costs passed on to customers has been extensively discussed in the literature. From a theoretical point of view, this pass-through rate should account for 100 % in perfect markets [3]. However, the condition of perfect markets seldom holds in reality, thus resulting in a lower pass-through rate [4]. The pass-through rate depends on additional factors, such as the energy mix, the demand, as well as the supply of energy [13]. In addition, recent works [14,15] find a less than 100% but asymmetric pass-through of costs in the German market. In particular, a pass-through rate of at least 84%, ranging from 98% to 104%, is found for different load periods [14]. As a consequence, increasing the carbon price is supposed to influence the electricity price more strongly than decreasing carbon prices. As a result, the price setting mechanism might be only affected by carbon prices exceeding a certain price threshold. In Section 4.3, we control for this effect by utilizing quantile regressions in order to compute the distributional properties of the carbon effect on electricity prices.
