Do political parties react to coverage of politically salient events in traditional media and social media, or do parties set the media agenda? Surprisingly, research on the agenda-setting power of parties and the media remains scarce and inconclusive. Only few studies analyze whether and to what degree parties respond to changes in media issue coverage or whether parties can set the issue agenda in the news. However, the answer to this question is fundamental to understand parties' responsiveness and changes in the issues they focus on. We compare issue salience in the traditional media, social media, and agenda setting by political actors by applying an extensively validated supervised machine-learning classifier to about 400,000 articles published in 84 Swiss newspapers in 2018 and 2019, 350,000 tweets on Swiss politics posted in 2019, as well as all press releases by Swiss parties in this period. We use these data and methods to test whether parties communicating on a specific issue are more likely to influence media and social media coverage on this topic. Specifically, we focus on climate policy and women's rights, two issues that emerged prominently on the Swiss political agenda during our observation period, and which were widely perceived to prompt some parties to redefine their positions facing the national elections in 2019. The findings have important implications for the literature on social media, party competition, responsiveness, salience, and issue ownership.