Considering that the European Directive has imposed that at least 20% of the total energy should come from renewable energy sources (RES) by 2020 already and the specific targets for each European Union Member State, this paper attempts to assess the importance of GDP per capita in realizing these targets and also the effects of the RES share in electricity. Contrary to previous research, this paper does not consider the connection between economic growth and RES, but rather the potential connection between the share of RES in electricity and the real GDP per capita. The panel data models indicated to a positive, but very low impact of GDP per capita on the share of RES in electricity in the period of 2007–2017 in the case of the EU countries, except Luxembourg that has outlier values of GDP per capita. However, causality between the two variables was not identified. Some groups of countries were described according to these variables using cluster analysis. Future research should focus on the extension of this model by including other important variables such as RES potential available in the countries with specific geographical conditions.